TN H01-Hand Book for Design of Steel Structures

TN H01

ACECOMS Technical Notes On

Hand Book for Design of Steel Structures Naveed Anwar Buddhi S. Sharma

© Asian Center for Engineering Computations and Software

COPYRIGHT These technical tones and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership are those of ACECOMS, AIT. Reproduction of the documentation in any form, without prior written authorization from ACECOMS, AIT, explicitly prohibited. Further information and copies of this documentation may be obtained from:

ACECOMS, AIT, PO Box 4, Klong Luang Pathumthani, 12120 – Thailand. Tel: (662) 524-5539 Fax: (662) 524-6059 E-mail: [email protected] Web: www.acecoms.ait.ac.th

Material from various sources including books and websites has been acknowledged.

Hand Book for Design of Steel Structures

ii

Author Naveed Anwar Buddhi S. Sharma

© Copyright 2003 by ACECOMS, AIT, Thailand All rights reserved. No part of this compilation may be reproduced in any form, by Photostat, microfilm, xerography or any other means or incorporated into any information retrieval system, electronic or mechanical, without the permission of its copyright owner.

All inquiries should be addressed to: Asian Center for Engineering Computations and Software ACECOMS, AIT, P.O. Box 4, Klong Luang, Pathumthani, Thailand 12120.

http://www.acecoms.ait.ac.th


3

ACKNOWLEDGEMENTS First, the author wishes to express his appreciation to his wife, Farah, for her love, support and years of understanding during development of software and writing of these books. Author is also grateful to his parents for their love and support. Numerous people have guided and helped in writing of these notes. The foremost is Prof. Worsak Kanok-Nukulchai, who as a teacher, advisor and as the Director of ACECOMS and Dean of School of Civil Engineering has inspired, encouraged and guided the author for nearly 10 years in both professional as well as personal endeavors.


4

RELATED SOFTWARE Several software packages are available through the Asian Center for Engineering Computations and Software (ACECOMS), related to analysis and design of slab systems. These include:

SYSDesigner: SYSDesinger, which stands for 'Siam Yamato Steel Designer', is a software developed by ACECOMS, AIT for Siam Yamato Co. Ltd. Thailand. This software, to be used under windows platform (Win95/98 and WinNT), has been developed for the design of structural steel members for hot rolled steel specifically those produced by SYS. The software carries out it internal calculations based on working stress design method (AISC/ASD).


5

RELATED PUBLICATIONS Various publications are available through Asian Center for Engineering Computations and Software (ACECOMS), related to these technical notes, giving in-depth knowledge and understanding of the topic as a whole. These publications include: o WN A04-Integrated Approach to Steel Design o WN E01-Design of Steel Beams o WN E02-Design of Steel Columns o WN E03-Design of Strut and Ties


vi

Table of content TABLE OF CONTENT .........................................................................................................................................................I GENERAL ................................................................................................................................................................................. 1. 2.

INTRODUCTION TO STEEL STRUCTURES...................................................................................................................1-3 DESIGN PHILOSOPHIES..............................................................................................................................................1-3 2.1. Allowable Stress Design (ASD).......................................................................................................................1-3 2.2. Limit State Design (LRFD) .............................................................................................................................1-3 3. OVERVIEW OF VARIOUS SPECIFICATIONS FOR HOT-ROLLED STEEL SHAPES ........................................................1-4 4. MECHANICAL PROPERTIES .......................................................................................................................................1-6 5. CODES AND SPECIFICATIONS ....................................................................................................................................1-6 SIAM YAMATO STEEL SECTIONS.................................................................................................................................. 1. 2. 3.

INTRODUCTION..........................................................................................................................................................2-1 PRODUCT SPECIFICATIONS.......................................................................................................................................2-1 SIZES AND PROPERTIES .............................................................................................................................................2-3

DESIGN OF TENSION MEMBERS .................................................................................................................................... 1. 2. 3. 4. 5. 6.

INTRODUCTION..........................................................................................................................................................3-1 GENERAL PROCEDURE..............................................................................................................................................3-1 EFFECTIVE NET AREA...............................................................................................................................................3-2 DESIGN EXAMPLES ....................................................................................................................................................3-4 DESIGN TABLES ........................................................................................................................................................3-6 SOFTWARE IMPLEMENTATION..................................................................................................................................3-7

DESIGN OF COMPRESSION MEMBERS........................................................................................................................ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

INTRODUCTION..........................................................................................................................................................4-1 FACTORS INFLUENCING THE STRENGTH OF COMPRESSION MEMBER ......................................................................4-1 MODES OF FAILURE OF COMPRESSION MEMBER ....................................................................................................4-2 GENERAL PROCEDURE FOR DESIGN OF COMPRESSION MEMBER ...........................................................................4-4 STRESS REDUCTION FACTOR QS ..............................................................................................................................4-6 EFFECTIVE AREA FACTOR QA...................................................................................................................................4-6 EFFECTIVE LENGTH FACTOR K................................................................................................................................4-7 DESIGN EXAMPLES ...................................................................................................................................................4-8 DESIGN TABLES ......................................................................................................................................................4-15 SOFTWARE IMPLEMENTATION ...........................................................................................................................4-15

DESIGN OF BEAMS ............................................................................................................................................................... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

INTRODUCTION..........................................................................................................................................................5-1 GENERAL PROCEDURE..............................................................................................................................................5-1 LATERAL TORSIONAL BUCKLING..............................................................................................................................5-5 LOCAL BUCKLING OF BEAM ELEMENTS AND SECTION COMPACTNESS .................................................................5-5 DESIGN FOR MOMENT ..............................................................................................................................................5-7 CHECK FOR SHEAR ....................................................................................................................................................5-8 CHECK FOR CRIPPLING .............................................................................................................................................5-9 CHECK FOR SIDE SWAY WEB BUCKLING ..............................................................................................................5-10 DESIGN EXAMPLES .................................................................................................................................................5-12 DESIGN TABLES AND CHARTS ...........................................................................................................................5-21 SOFTWARE IMPLEMENTATION ...........................................................................................................................5-22

DESIGN OF COLUMNS......................................................................................................................................................... 1.

INTRODUCTION..........................................................................................................................................................6-1


1-i

2. 3. 4. 5. 6.

MOMENT AMPLIFICATION ........................................................................................................................................6-1 COLUMN INTERACTION EQUATIONS ........................................................................................................................6-3 GENERAL PROCEDURE..............................................................................................................................................6-4 DESIGN EXAMPLES ...................................................................................................................................................6-7 SOFTWARE IMPLEMENTATION................................................................................................................................6-11

INTRODUCTION TO CONNECTION DESIGN .............................................................................................................. 1. 2. 3. 4. 5. 6.

INTRODUCTION……………………………………………………………………………………………... 7-1 TRUSS CONNECTIONS………………………………………………………………………………………. 7-1 PORTAL FRAME CONNECTIONS………………………………………………………………………………. 7-3 BUILDING FRAME CONNECTIONS……………………………………………………………………………. 7-6 COLUMN BASES……………………………………………………………………………………………. 7-11 DESIGN EXAMPLES…………………………………………………………………………………………. 7-15


1-ii

Chapter

1

General 1. Introduction to Steel Structures Steel is one of the most versatile building materials. Steel structures have always had the advantages of lightness, stiffness, and strength and lend themselves to rapid construction compared to other construction materials. The significant increase in the use of steel is due to the facts that new improvements have been made in the various aspect of steel technology. The advances in steel fabrication techniques, improved understanding of structural behavior, and the upgrading in the standards of structural steel design as well as the wide dissemination of excellent material are some of these factors. This manual is intended to present, in a condensed form, the relevant information likely to be useful to the modern structural steel designer.

2. Design Philosophies Structures and structural elements must provide adequate safety, no matter what philosophy of design is used. The design must provide some reserve strength for the possibility of overload and under strength. These can arise from various sources like variation of material properties, uncertainties in the estimation of imposed loads, various assumptions and simplifications made in analysis, and imperfections in construction procedures. In general, a thorough analysis of all uncertainties that might influence the structural strength during the service life of the structure is not practical or perhaps even possible. So, the structural safety can only be based on probabilistic methods. Two philosophies of design in current use are: •

Working Stress Design

•

Limit State Design

The Working Stress Design is also known as Allowable Stress Design (ASD). Limit State Design includes the methods commonly known as "Ultimate Strength Design (USD)", "Strength Design (SD)", "Plastic Design (PD) ", "Load Factor Design (LFD)", "Limit Design (LD) " and the recently "Load and Resistance Factor Design (LRFD)". 2.1.

Allowable Stress Design (ASD) In this philosophy all loads are assumed to have the same average variability. The entire variability of the loads and the strengths is placed on the strength side of the equation. The design procedure includes the determination of allowable or working stress on a structure member by applying factor of safety on the actual stress induced by the expected design load (service load). The analysis and design are fully based on elastic analysis.


1-3

2.2.

Limit State Design (LRFD) The structural member or their component is so proportioned that its resistance when reduced by a resistance factor equals or exceeds the service load multiplied by overload factors. As this is the probability-based model, more realistic weightage are given for different type of loads and behavior depending upon the probability of occurrence and uncertainties involved in their prediction. Plastic design is a special case of limit state design.

3. Overview of Various Specifications for Hot-rolled Steel Shapes Due to their own production and construction situation in various countries, the classification of hot-rolled steel shapes in various specifications is different. In general, the higher the industrialization level, the more the classification of structural steel. This is due to a need of various types and grades of structural steel in the complicated projects of those industrialized countries. A brief discussion for some of the model standard specifications is presented in the following section. 3.1.1. ASTM ( American Society for Testing and Materials )

For the specifications of ASTM, there are 16 specifications for structural steel approved for the use in building construction, and 6 out of those are available in hot rolled steel shapes. However, for the most commonly used grades, there are only two, i.e. A36 (Carbon Steel) and A572 (High-Strength Low-Alloy Steel). For other ASTM hot-rolled grades, they have some specific properties, such as corrosion-resistant of A242 and A588, etc. All the grades of hot-rolled shape are suitable for welded fabrication. In the design specification for steel buildings of American Institute of Steel Construction (AISC, the above-mentioned grades of steel, i.e. A36 and A572, Gr. 50 with included in the design chart and table. 3.1.2. BS (British Standards)

Structural steel available in the UK consists of four main grades: 40, 43, 50 and 55, where the figures denote the approximated value of ultimate strength in kgf/mm2. Each grade in subdivided into a descending order of the values of C.E. (Carbon Equivalent, which is a measure of weldability) from A to E. The grades of 43 and 50, which have the yield strength of 275 Mpa and 355 Mpa, respectively, are frequently used in the steel buildings. 3.1.3. DIN (Deutsches Institut fur Normung)

In general, materials to be used in the hot-rolled shape include only St 37-2, St37-3 and St 52-2 steel, or briefly referred to as St 37 and St 52, which have the yield strength of 245 Mpa and 355 Mpa, respectively. 3.1.4. JIS (Japanese Industrial Standards)

In the steel buildings, grades SS and SM are commonly used for hot-rolled shapes, in which grade SS is specified for the secondary or temporary structural member with the bolt and rivet, or welded connections. Grades SM, which cover the yield strength from 245 Mpa of SM 400 to 460 Mpa of SM 570 are included in the JIS G3106- Rolled Hand Book for Design of Steel Structures

1-4

Steel for Welded Structure. JIS G3106: Rolled Steels for Welded Structure (1992). This standard specifies the hot rolled steel product used for buildings, bridges, ships, rolling stocks, petroleum storage tanks, containers and other constructions which required superiority in weldability. JIS G3136: Rolled Steels for Building Structure (1994). This standard specifies the hot-rolled steel products used for structure members for buildings. In JIS G3136, there are 5 grades of steel available, i.e.SN400A, SN400B, SN400C, SN490B and SN490B, SM490C, SM 490YA, SM490YB, SM520B, SM520C and SM570. There are some differences in chemical composition and mechanical properties between two standards, which can be seen, in the below Table 1.1. 3.1.5. TIS (Thai Industrial Standards)

From the draft of TIS, the classification of structure steel of Thailand is quit similar to that of Japan, however not all the Japanese grades are available in Thai standard. For hot-rolled shape, only grades SM which cover from SM 400 (245 Mpa yield strength) to SM 570 (460 Mpa yield strength) are used. 3.1.6. AS (Australian Standards)

There are only two grades of structural steel, i.e. 250 and 350 (which have the yield strength of 250 Mpa and 350 Mpa, respectively) commonly used in steel buildings. 3.1.7. ISO (International Standard Organization) and EN (Europaische Norm)

Both ISO and EN specifications have similar classification of steel grade, and there are three classes, i.e. Fe 360, Fe 450 and Fe 510 (whose yield strength ranges from 235, 275 and 350 Mpa, respectively). 3.2.

Material Specifications for Hot-Rolled Steel Shapes

3.2.1. Differences in Mechanical Properties

The comparisons of mechanical properties of hot-rolled steel shape in the selected eight specifications, i.e. JIS, TIS, ASTM, BS, DIN, AS, ISO and EN are shown in Table 1.1. There are totally six groups of steel according to the different level of yield strength which is a governing material property in the design of steel member. The mechanical properties mainly include the items of yield and tensile strengths, notch toughness, and elongation. Almost all of steel grades tabulated in Table 1.1 for hot-rolled shape are suitable for welding connection, except Group 1, in which only one Japanese grade, i.e. SS 400, is for general purpose, and its weldability is not as good as that as SM 400. In the design of steel structure member, the yield strength is the main material property. As shown in Table 1.1 for all of the specifications, there is a little bit difference of yield strength for various thickness of steel plate i.e. the yield strength decreases as the plate becomes thicker. The reason is the larger effect of residual stress in the thicker plate, however, in common case, the plate thickness of hot-rolled shape is not more than 40 mm. In some specifications, there are several sub-grades under each category of steel, e.g. for JIS, SM 400A, B, or C in the grade SM 400. The meaning of sub-grade for various countries is different. In Japanese specification (JIS), the sub-grades indicate the required values of absorbed energy in Charpy test at the same test temperature 0oC, which are N/A, 27 J, 47 J, for the sub-grades A, B, C, respectively. On the other hand, in British Standards (BS), the sub-grades A to F give the index of descending Charpy Hand Book for Design of Steel Structures

1-5

test temperature for the same absorbed energy, i.e. 27 J, as can be seen clearly from Table 1.1 For Australian Standards (AS), the sub-grades (L0, L15) indicate that the Charpy test temperature is 0 oC, -15 oC, respectively, for the same absorbed energy, i.e. 27 J. In ISO specification, the sub-grades B, C and D indicate various Charpy test temperatures, i.e. +20 oC, 0 oC, or –20 oC, respectively, under the same absorbed energy of 27 J. In JIS G3106 and JISG3136, it can be seen that yield strength are almost same, except two cases, i. e. SM400A ( when t=< 16 mm) is 245 Mpa. But 235 Mpa for SN400A ( when 16
Structural steels are a mixture of iron and carbon with varying amounts of other elements- primarily manganese, phosphorus, sulfur and silicon. Carbon (C) is the principle strengthening (hardening) element in steel where each addition increases the hardness, tensile strength and yield strength of the steel. On the other hand, increased amount of carbon cause a decrease in ductility, toughness and weldability. Manganese(Mn) increases the hardness and strength of steels but to a lesser degree than does carbon and it can minimize the harmful effects of sulfur. Silicon (Si) is the principal deoxidizer used in the manufacture of structural steels. Sulfur (S) and Phosphorus (P) adversely affect the surface quality, as a strong tendency to segregate and decrease ductility, toughness and weldability, therefore it is generally considered undesirable elements. Chemical properties of various grades of steels are shown in Table 1.3. As demonstrated in Table1.3, the chemical compositions for various specifications are compared in the same steel groups as classified in the comparison of mechanical properties. The content of adverse elements, such as P and S, are most strictly controlled in Japanese specifications in comparison with other specifications, i. e. the maximum content of P and S as seen in Table1.3 This means there is no limitation for the content of C, Si and Mn. It is noted that there is no similar grade to SS400 in other countries specifications. In JIS G3106, the requirements of adverse elements (P and S) for all grade are same ( 0.0345 % ), but in JIS G3136, the requirements are varied depending on the type of sub-grades, as shown in Table 1.3, especially for subgrade C, the content of Sulfur (S) should be very low i.e. 0.008%. The requirements of the content of other elements are similar, as shown in Table 1.3 3.2.3. Differences in Test Procedures

3.2.3.1.

Tensile Test Mechanical properties depend primarily upon the chemical composition, rolling processes, and heat treatment of the steels. Other factors, which may influence the mechanical properties, are the techniques of testing, such as the rate of loading the specimen, the conditions and geometry of the specimen, the cold work, and the temperature at the time of testing.


1-6

The usual test coupon is a tensile specimen and for all practical purposes the behavior in compression is assumed to be similar to that in tension. Because the tensile test is easier to conduct, most mechanical properties are taken from the tensile stress-strain diagram. The procedures of the tensile test in various countries are quite similar, and the dimensions of the coupon are almost similar among various specifications. The most obvious difference among the specifications is the selection of gauge length. As shown in Table1.1, ASTM use both 200 mm and 50 mm for gauge length to indicate the elongation. On the other hand, in European countries and Australia, i. e. BS, DIN, AS, ISO and EN prefer proportional gauge length, i.e. L o = 5 . 65 S o Where So is the sectional area of the coupon. It is noted that the later one seems to be more rational due to the change of specimen section. 3.2.3.2.

Impact Test Brittle behavior and cleavage-type fractures are the important properties of structural steel subjected to the impact load. Among various types of impact test, the Charpy notch test seems to be the one the most commonly used method. The test evaluates the notch toughness of the steel which is defined as the resistance to fracture in the presence of notch under impact loads. The test results are used qualitatively in the selection of a steel for a specific application. For the Charpy notch test in all specifications selected in this study, there is no much difference in the specimen dimensions or the test instruments. Therefore, as can be seen in Table1.1 the test result, which means the absorbed energy under specific range of temperature, is almost the same for all of the specifications.


1-7

Table 1.1 Comparison of Mechanical Property Group

Classification Standard Description

JIS G3101

(1)

TIS ASTM BS DIN AS ISO EN JIS G3106

Rolled steel for general structure

Designation

Thickness t mm

SS 400

16 < t ≤ 40

t ≤ 16 40 < t

Strength Min. Yield Strength ( Mpa ) 245 235 215

Tensile Strength ( Mpa ) 400 – 510

Notch Toughness Test Temp. Absorbed 0 C Energy ( J ) -

-

-

-

0

27

0

47

Thickness t ( mm )

Elongation Gauge Length ( mm )

Elongation % ( min.)

t ≤5 5 < t ≤ 16 16 < t ≤ 50

50 200 200

21 17 21

t ≤5 5 < t ≤ 16 16 < t ≤ 50

50 200 200

23 18 22

200 200 50

17 21 23

A Rolled steel for welded structure

SM 400

B C

t ≤ 16 16 < t ≤ 40 40 < t ≤ 75

245 135 215 215

400 – 510

75 < t ≤ 100

6 ≤ t ≤ 12

(2)

12 < t < 16 JIS G3136

Rolled steel for building structure

SN 400

A

16 16 < t ≤ 40 40 < t ≤ 100


235 235 235 235 215

400 – 510

-

-

16 ≤ t ≤ 16 16 < t ≤ 40 40 < t ≤ 100

1-8

Table 1.1 Contd. Group

Standar d

Classification Description

Designation

Thickness t mm

Strength Min. Yield Strength (Mpa)

Tensile Strength (Mpa)

Notch Toughness Test Absorbed Temp. Energy 0 C (J)

Thickness t (mm)

Elongtion Gauge Length (mm)

Elongation % (min)

50 200 200

21 17 21

6 ≤ t ≤ 12 12 < t < 16 JIS G3136

SN 400

B

40 < t ≤ 100

Rolled steel for building structure (2)

JIS G3136

16 16 < t ≤ 40

235 235 235 235 215

400 – 510

-

27

16 ≤ t ≤ 16 16 < t ≤ 40 40 < t ≤ 100

6 ≤ t ≤ 12 SN 400

C

12 < t < 16 16 16 < t ≤ 40 40 < t ≤ 100

16 ≤ t ≤ 16

235 235 215

400 – 510

-

27

16 < t ≤ 40 40 < t ≤ 100

50 200 200

21 17 21

245 235 215 215

400 – 510

0

27

t≤5 5 < t ≤ 16 16 < t ≤ 50

50 200 200

23 18 22

t ≤ 16 16 < t ≤ 40 TIS

-

SM400

40 < t ≤ 75 75 < t ≤ 100


1-9


Classification Standard Descriptio n

ASTM

Structural carbon steel-

BS 4360

Weldable structural steels

DIN 17100

Designation

Gr. 40DD

St 37-2 Ust 37-2 RSt 37-2

Gr. 250

Structural steel

L0


Thickness t (mm)


Elongation % (min)

200 50

20 21

250 min

400 – 500

-

-

-

250 245 240 225

340 – 500

-30

27

-

40 < t ≤ 63 63 < t ≤ 100 t ≤ 16 16 < t ≤ 40

20

27

16 < t ≤ 40

235 225 215 215

63 < t ≤ 80 t ≤ 12

12 < t ≤ 40 40 < t

260 250 230

Fe 360

B C

HR unalloyed structural steel


t ≤ 16 16 < t ≤ 40 40 < t ≤ 63 t ≤ 40

Fe 360

140t ≤ 63

235 225 215

235 215

40 < t ≤ 63

340 – 470

410 min.

L15

D EN 10025

16 < t ≤ 40

40 < t ≤ 63

St 37-3

A ISO 630


t ≤ 16

(2) AS 1204


A36

Steel for general structural purpose

Ordinary weldable structural steel

Thickness t mm

360 - 460

360 340

-20

27

-

-

0

27

-15

27

-

-

+20

27

0

27

-20

27

-20

27

200 o

22 25

o

26 25 24

o

22

o

25

o

26 25

5.65 S

5.65 S

63 < t ≤ 100

-

5.65 S

-

5.65 S

-

5.65 S

1-10


Classification Standard Descriptio n JIS TIS ASTM

BS 4360

Designation

High strength low alloy steel

Thickness t mm

A572 Gr. 42

-

Gr. 43DD


Thickness t (mm)


Elongation % (min)

200 50

20 24

290 min

415 min

-

-

-

16 < t ≤ 40

275 265 255 245

430 – 580

-30

27

-

40 < t ≤ 63


40 < t ≤ 63 63 < t ≤ 80

200 5.65 S

o

20 275 265 255 245

27

20 19 18

40 < t ≤ 63 63 < t ≤ 100

430 – 540

St 44-3

3 ≤ t ≤ 40 -20

27

5.65 S

o

26 25 24

40 < t ≤ 63 63 < t ≤ 100

AS 1204

-

ISO 630

Structural steel

-

A Fe 430

B C D


t ≤ 16 16 < t ≤ 40 40 < t ≤ 63

20 22

3 ≤ t ≤ 40

16 < t ≤ 40

St 44-2 DIN 17100


t ≤ 16


63 < t ≤ 100 t ≤ 16 (3)


-

-

-

-

+20

27

0

27

-20

27

-

-

-

275 265 255

360 - 460

-

5.65 S

o

25

1-11


(3)


EN 10025


JIS G3106

Rolled steel for welded structure-

Designation

Fe 430 A SM490

B C

B

(4)

JIS G3136

Rolled steel for welded structure-

Thickness t mm

275

430

40 < t ≤ 63

255

410

t ≤ 16

325

16 < t < 40

315

40 < t ≤ 75

295

325

12 < t < 16

325

16

325

16 < t ≤ 40

325

Notch Toughness Test Absorbed Temp. Energy 0 C (J) -20

27

-

-

0 0

27 47

-

Thickness t (mm)

t ≤ 40

490 - 610

0

27

t≤5 5 < t ≤ 16 16 < t ≤ 50

-


SM 490

5.65 S

Elongation % (min) 22

o

21

50

22

200

17

200

22

50

22

16 < t < 40

200

17

40 < t ≤ 100

200

22

325

16 < t ≤ 40

325 295

t≤5 TIS


140t ≤ 63

6 ≤ t ≤ 16

295

16 40 < t ≤ 100

490 - 610

295

75 < t ≤ 100 6 ≤ t ≤ 12

12 < t < 16 C


t ≤ 40

40 < t ≤ 100 6 ≤ t ≤ 12

SN490


t ≤ 16

325

16 < t ≤ 40

315

490 - 610

0

27

5 < t < 16 16 < t ≤ 50

50

22

200

17

200

22

1-12


(4)


Designation

ASTM

-

-

BS

-

-

DIN

-

-

AS

-

-

ISO

-

-

EN

-

-

JIS G 3106

Rolled steel for general structure-

SM490

YA YB

SM520

Thickness t mm

B C

t ≤ 16 16 < t ≤ 40 40 < t ≤ 75 63 < t ≤ 100




TIS

ASTM A572



SM520

A572 Gr. 50

16 < t ≤ 40

-


-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

365

490- 610

-

-

355

0

27

335

0

27

0

47

325

520 - 640

t ≤ 16

(5)

Thickness t (mm)

365 355

345 min

490 - 610

450 min

0

-

27

-

Elongation % (min) -

t≤5

50

19

5 < t < 16

200

15

16 < t ≤ 50

200

19

t≤5

50

19

5 < t < 16

200

15

16 < t ≤ 50

200

19

-

200 50

18 21

1-13



BS 4360

Designation


Gr. 50E

Thickness t mm

t ≤ 16

355

16 < t ≤ 40

345

40 < t ≤ 63

340

63 < t ≤ 100 t ≤ 16 DIN 17100


16 < t ≤ 40

St 52-3

(5)

AS 1204


Gr. 350

L0 L15 A

ISO 630

Structural steel

Fe 510

B C D



27

-


Elongatio n % (min) 18

200 5.65 S

o

20

325

t ≤ 12

360

12 < t ≤ 40

340

40 < t

20

3 ≤ t ≤ 40

345

63 < t ≤ 80

40 < t ≤ 63

-30

Thickness t (mm)

355

335

16 < t ≤ 40

430 – 580


325

40 < t ≤ 63

t ≤ 16


490 – 630

-20

27

40 < t ≤ 63

5.65 S

o

63 < t ≤ 100

-

-

0

27

330

-15

27

-

-

355 345 335

+20

27

0

27

-20

27

490 - 630

490 - 630

-

5.65 S

-

5.65 S

19 18

o

20

o

21

1-14


(5)

Classification Standard Descriptio n EN 10025


JIS G 3106

Rolled steel for general structure-

Designation

Fe 510

Thickness t mm

355

510

40 < t ≤ 63

335

490

t ≤ 16

(6)

TIS

-

40 < t ≤ 75 63 < t ≤ 100

SM570


t ≤ 40

16 < t ≤ 40 SM 570


Notch Toughness Test Absorbed Temp. Energy 0 C (J) -20

27

460 450 430

570 - 720

0

27

420

t ≤ 16

460

16 < t ≤ 40

450

40 < t ≤ 75

430

63 < t ≤ 100

420 450 min

ASTM A572


A572 Gr. 65

-


t ≤ 16

450

BS 4360

Gr. 55C

16 < t ≤ 40

430

40 < t ≤ 63

415

490 - 610

0

27

Thickness t (mm)

t ≤ 40 140t ≤ 63

Elongtion Gauge Length (mm) 5.65 S

o

Elongatio n % (min) 21 20

t≤5

50

19

5 < t < 16

50

26

16 < t ≤ 50

50

20

t≤5

50

19

5 < t < 16

50

26

16 < t ≤ 50

50

20

200 50

15 17

200

17

550 min

-

-

-

550 – 700

0

27

-

5.65 S

o

19

DIN

-

-

-

-

-

-

-

-

-

-

-

AS

-

-

-

-

-

-

-

-

-

-

-

ISO

-

-

-

-

-

-

-

-

-

-

-

EN

-

-

-

-

-

-

-

-

-

-

-


1-15

Table 1.2 Sub-grade of BS 4360: Weldable Structural Steels Chemical Composition Grade

C max

Si m ax

Mn max

P Max

40 DD 40E

43D 43DD 43E

S max


t ≤ 16

16 < t ≤ 40

40 < t ≤ 63

0.16

1.5

0.04

0.04

0.20 0.16

1.30 0. 50

1.30 1.50

260

245

240

225

5.65 S

340/500

Remarks

o

Shape section 25

-40 -50

Plates/Strip

0.05

0.05

-

-

0

Hollow shapes

0.04

0.045

-

-

-20

Hollow shapes

0.04

-

255

245

0.04

0.04

255

245

-40

255

245

-50

275

265

0.16

1.50

0.16

1.50

0.04

0.03

1.50

0.045

0.045

355

345

-

-

50D

0.04

0.04

355

345

-

50E

0.04

0.04

355

345

50EE

0.04

0.03

355

50F

0.025

0.025

390

43EE

Elongation (%) for gauge length

-30

0.03 0.21

Charpy V-notch test Temp (0c) E (J)

63 < t ≤ 100

0. 50

40EE 43C

Yield strength

430/580

-30

22

Shape section -

27

Plate / Hollow

0.20 0.20 50C

0.20 0.18

0. 50

490/640

0

21

Hollow shapes

-

-20

21

Hollow shapes

340

325

-40

20

Shape section

345

340

325

-50

20

Plate / Hollow

390

-

-

-60

20

Plates/Strip

0.16


1-16

Table 1.2 Contd. Chemical Composition Grade

C max

Si ma x

Mn max

Yield strength

P Max

S max

0.04

0.04

55EE

0.04

55F

0.025


t ≤ 16

16 < t ≤ 40

Charpy V-notch test Temp (0c) E (J)

Elongation (%) for gauge length 5.65 S

o

Remarks

40 < t ≤ 63

63 < t ≤ 100

-

-

0.03

415

400

-50

Plate / Hollow

0.025

415

-

-60

Plate / Hollow

0.6 0.22 55C

0.22 0.16

0 0.5 0 0.5

1.60 1.60

450

430

550/700

0

19

Plate / shape

1.50

0


1-17

Table 1.3 Comparison of Chemical Composition Group

Classification Standard No JIS G3101 TIS ASTM BS

(1)

DIN AS ISO EN

Designation SS400

(2) JIS G3136

ASTM

Notations: C = Carbon Si= Silicon


-

-

Max S

0.050

0.050

0.035

0.035

-

t ≤ 50 50 < t ≤ 200 t ≤ 50 50 < t ≤ 200

0.23 0.25 0.20

SM400C

t ≤ 100

SN400A

SM400B

SN400B SN400C

TIS

-

Remarks Max P

-

SM400A JIS G3106

Chemical Composition % Max Si Mn

Max C

-

2.5 C

0.35

0.60 – 1.40-

0.035

0.035

0.18

0.35

1.40 max

0.035

0.035

6 < t ≤ 100

0.24

-

-

0.050

0.050

6 < t ≤ 50 50 < t ≤ 100 16 < t ≤ 50 50 < t ≤ 100

0.20 0.22 0.20

0.35

0.60 – 1.40

0.030

0.015

0.35

0.60 – 1.40

0.020

0.008

0.22

0.22

SM400

0.20

0.35

0.60 – 1.40

0.035

0.035

A36

0.26

0.40

-

0.04

0.05

Mn= Manganese

P= Phosphorus

S= Sulfur

1-18


Classification Standard No BS 4360

Max C

Gr. 40DD

0.16

0.50

0.20

St 37-2 USt 37-2 DIN


Designation

RSt 37-2 St 37-3

Remarks Max P

Max S

1.5 max

0.040

-

-

-

0.050

0.050

0.20

-

-

0.050

0.050

0.20

-

-

0.050

0.050

0.17

-

-

0.040

0.040

0.25

0.40

-

0.040

0.040

0.20

-

-

0.060

0.050

0.20

-

-

0.050

0.050

0.17

-

-

0.045

0.045

0.17

-

-

0.040

0.040

0.20

-

-

0.045

0.045

Gr 250 (2)

AS

Gr. 250 LO Gr 250 L15 Fe 360 A Fe 360 B

ISO 630

Fe 360 C Fe 360 D

(3)

EN 10025

Fe 360

JIS

-

TIS

-

ASTM A572

A 572 Gr 42

0.21

-

1.35 max

0.04

0.05

BS 4360

Gr 43 DD

0.16

0.50

1.5 max

0.040

0.050

DIN 17100

St 44-2

0.22

-

-

0.050

0.050


1-19


Classification Standard No AS

(3)

ISO 630

EN 10025

Max C

Fe 430 A

0.24

-

Fe 430 B

0.22

-

JIS G3136

Max S

-

0.060

0.050

-

0.050

0.050

0.20

-

-

0.045

0.045

Fe 430 D

0.20

-

-

0.040

0.040

-

-

0.045

0.045

0.55

1.60 max

0.035

0.035

0.55

1.60 max

0.035

0.035

Fe 430

0.22

t ≤ 50 50 < t ≤ 200 t ≤ 50 50 < t ≤ 200

0.20 0.22 0.18

SM490C

t ≤ 100

0.18

0.55

1.60 max

0.035

0.035

SN490A

6 < t ≤ 100

0.18

0.55

-

0.030

0.015

6 < t ≤ 50 50 < t ≤ 100 16 < t ≤ 50 50 < t ≤ 100

0.20 0.18 0.20

0.55

1.60 max

0.020

0.008

0.55

1.60 max

0.035

0.035

0.55

1.6 max

0.035

0.035

SM490B

SN490B

(4) SN490C TIS

Remarks Max P

Fe 430 C

SM490A JIS G3106


Designation -

SM 490

0.18

0.20

0.18

ASTM BS DIN AS


1-20


Classification Standard No

(4)

ISO

Designation -

EN

-

Max C


Remarks Max P

Max S

SM 490 YA SM 490 YB JIS G3106

0.55

1.6 max

0.035

0.035

0.20

0.55

1.6 max

0.035

0.035

0.20

0.55

1.6 max

0.035

0.035

SM 520C SM 520

(5)

0.20

TIS

SM520

ASTM A572

A572 Gr. 50

0.23

-

1.35 max

0.04

0.05

BS 4360

Gr. 50E

0.18

0.50

1.5 max

0.040

0.040

DIN 17100

St 52-3

0.22

-

-

0.040

0.040

0.22

0.50

1.6 max

0.040

0.040

Fe 510 B

0.22

-

-

0.050

0.050

Fe 510 C

0.22

-

-

0.045

0.045

Gr. 350 AS 1204

Gr. 350 LO Gr.350 L15

ISO 630

EN 10025

Notations: C = Carbon

Fe 510 D

0.22

-

-

0.040

0.040

Fe 510

0.22

0.55

1.60

0.045

0.045

Si= Silicon


Mn= Manganese

P= Phosphorus

S= Sulfur

1-21


Classification Standard No


Max C

JIS G3106

Designation SM 570

0.18

0.55

TIS

SM 570

0.18

ASTM A572

A 572 Gr. 65

BS 4360

Gr. 55C

DIN

-

AS

-

ISO

-

EN

-

(6)

Notations: C = Carbon

Si= Silicon


Remarks Max P

Max S

1.6 max.

0.035

0.035

0.55

1.6 max.

0.035

0.035

0.26

-

1.35 max.

0.04

0.05

0.22

0.60

1.60 max.

0.040

-

Mn= Manganese

P= Phosphorus

S= Sulfur

1-22


Classification Standard No BS 4360 TIS ASTM BS

(7)

DIN AS ISO EN

Designation Gr 40 DD

(8) JIS G3136

ASTM


Max S

0.50

1.5 max

0.040

0.050

-

2.5 C

0.035

0.035

0.35

0.60 – 1.40-

0.035

0.035

-

t ≤ 50 50 < t ≤ 200 t ≤ 50 50 < t ≤ 200

0.23 0.25 0.20

SM400C

t ≤ 100

0.18

0.35

1.40 max

0.035

0.035

SN400A

6 < t ≤ 100

0.24

-

-

0.050

0.050

6 < t ≤ 50 50 < t ≤ 100 16 < t ≤ 50 50 < t ≤ 100

0.20 0.22 0.20

0.35

0.60 – 1.40

0.030

0.015

0.35

0.60 – 1.40

0.020

0.008

0.20

0.35

0.60 – 1.40

0.035

0.035

0.26

0.40

-

0.04

0.05

SM400B

SN400B SN400C

TIS

0.16

Remarks Max P

-

SM400A JIS G3106


Max C

SM400 A36

0.22

0.22

1-23

Chapter

2

Siam Yamato Steel Sections 1. Introduction Construction industry had been expanding at a remarkable rate for many years due to the high economy growth of Thailand. Such rapid growth is followed by an increase in demand of structural steel, which is one of the basic construction materials for both public and private projects. In response to the increasing demand, Siam Yamato Steel was established in 1992 as a joint venture between The Siam Cement Public Company Limited, Yamato Kogyo Co., Ltd., Mitsui & Co., Ltd., Mitsiam International, Limited, and Sumitomo Corporation. Siam Yamato Steel has been extensively used in high rise constructions, factory buildings, piling, bridges, refinery plants etc. Siam Yamato Steel (SYS) has its factory located in the Map Ta Phut Industrial Estate, Rayong Province. The world’s leading equipment and technology are employed to ensure that SYS’s quality products conform to international standards and can compete with imported structural steel. The capital investment is over 6,000 million baht, with annual production capacity of 600,000 metric tons.

2. Product Specifications The structural steel products range from sheet materials, through optimized sections and plates, to heavy forgings and castings of intricate shape. The versatility of steel for structural applications rests on the fact that it can be readily supplied at a relatively cheap price in a wide range of different product forms and with a useful range of material properties. The key to understanding the versatility of steel lies in its basic metallurgical behavior. Steel is an efficient material for structural purposes because of its good strength-to-weight ratio. Steel can be supplied with strength levels from about 240 N/mm2 up to about 2000 N/mm2 for common structural applications, although the strength requirements may limit the product form. Although steel can be made to a wide range of strengths, it generally behaves as an elastic material with a high(and relatively constant) value of the elastic modules up to the yield or proof strength. It also usually has a high capacity for accepting plastic deformation beyond the yield strength, which is valuable for drawing and forming of different products as well as for general ductility in structural applications 17 Table2.1 as shown below gives the products manufactured by Siam Yamato Steel Co. Ltd. and corresponding specifications based on tensile strength and in some cases Charpy Impact test.

Welded structure

General structure

Type of material

Table 2.1 SYS Steel and Corresponding Specifications

2.1.

Classified by tensile strength

Specifications

Tensile strength class 2 (N/mm )

Special specification

TIS

JIS

ASTM

BS 4360

DIN 17100

400

-

SS400

G3101 SS400

A36

Gr. 43A

St 33

490

-

SS490

G3101 SS490

-

Gr. 50A

St 50-2

400

-

-

G3106 SM400A

SM 400

G 3106 SM 400B,C

Gr. 43B Gr. 43C

-

Charpy impact test

A572 Gr.42 -

Charpy impact test for low temperature -

-

-

-

Gr. 43D

-

G3106 SM 490A

-

-

Charpy impact test -

SM 490

G3106 SM 490B,C

-

Gr. 43DD -

-

G3106 SM 490 YA

A572 Gr.50

Gr. 50B

-

Charpy impact test Charpy impact test for low temperature

SM 520

G3106 SM 490YB SM520 B,C, -

-

Gr. 50C Gr. 50D

St 52-3

490

490 (High yield point)

-

-

St 37-2 RSt 372 -

-

Mechanical Properties Steel derives its mechanical properties from a combination of chemical composition, heat treatment and manufacturing process. As laid down in the different specifications for manufacture of steel products, tests are carried out on samples representing each batch of steel and the results recorded on test certificate for mechanical properties which normally include the yield point, tensile strength and elongation to failure. Table 2.2 Mechanical Properties of SYS Steel Products Yield point (N/mm2) Classifications

Tensile strength 2 (N/mm )

Elongation, %

Thickness (mm) 16 or under

Over 16

JIS G3101 SS400

245

235

JIS G3101 SS490

285

JIS G3106 SM400 A,B,C JIS G3106 SM490 A,B,C

Thickness (mm) 5 or under

5 to 16

Over 16

400-510

21

17

21

275

490-610

19

15

19

245

235

400-510

23

18

22

325

315

490-610

22

17

21


2-2

JIS G3106 SM490 YA,YB

365

355

490-610

19

15

19

JIS G3106 SM520 B,C

365

355

520-640

19

15

19

JIS G3106 SM570

460

450

570-720

19

19

26

If the fracture toughness is important, the standard charpy test is also included. Table2.2 gives the detailed mechanical properties for Siam Yamato Steel products. 2.2.

Chemical Properties As the chemical composition of steel greatly affects the important structural properties of steel, it is one of the important criteria for the selection. Although steel is basically iron, the addition of small amount of other elements can remarkably affect the type of properties of steel, and sensitivity to heat treatment. A correct proportion of elements like carbon, manganese, chromium, molybdenum, nickel, copper may improve the strength, ductility, fracture toughness, weldability heat and corrosion resistance. However, elements like vanadium and aluminium can be added in small quantities to improve grain refinement. However the presence of non-metalic inclusions specially sulphur and phosphorous must be controlled carefully, the high level of which may reduce resistance to ductile fracture and possibility of cracking problems in welded joints. Other impurities which may seriously affect the quality of steel are tin, antimony, arsenic and some dissolved gases. The following Table 2.3 gives the detailed chemical composition for Siam Yamato Steel products using the following notations. C = carbon

SI = silica

Mn = Manganese

P =Phosphorus

S = Sulfur

Table 2.3 Chemical Composition of SYS Products Classifications

Chemical Compositions, % Max. C

Max. Si

Mn

Max. P

Max. S

-

-

-

0.050

0.050

JIS G3106 SM400 A

0.23

-

2.5xCmin.

0.035

0.035

JIS G3106 SM400 B

0.20

0.35

0.60-1.40

0.035

0.035

JIS G3106 SM400 C

0.18

0.35

1.40 max.

0.035

0.035

JIS G3106 SM490 A

0.20

0.55

1.60 max.

0.035

0.035

JIS G3106 SM490 B,C

0.18

0.55

1.60 max.

0.035

0.035

JIS G3106 SM490YA, YB

0.20

0.55

1.60 max.

0.035

0.035

JIS G3101 SS400, 490

JIS G3106 SM520 B, C

0.20

0.55

1.66 max.

0.035

0.035

JIS G3106 SM570

0.18

0.55

1.60 max.

0.035

0.035

3. Sizes and Properties of SYS Sections The section dimensions and their calculated properties have been expressed in appropriate units so as to avoid too small or too long digit numbers. All section related information has been reproduced, from "Siam Yamato Hot Rolled Shapes Product Specification Book", without any further verifications. A brief description of various symbols (notations) used for cross-section properties is given below. Notations related to dimension of the section can be read directly from the figure shown in their respective tables. A = The cross-section area of section, including all radii and fillets. Ixx = The second moment of Inertia of section about XX (generally major) axis. Hand Book for Design of Steel Structures

2-3

Iyy = The second moment of inertia of section about YY (generally minor) axis. rx = The radius of gyration of cross-section about x-axis, derived as rx = ry = The radius of gyration of cross-section about y-axis, derived as ry =

I xx A

I yy A

Zxx = The section modulus or elastic modulus of section defined as the moment of Inertia Ixx divided by the extreme fibre distance measured from centroidal YY axis calculated by the following simple formula.

Z xx =

I xx y

Where y = Distance to the extreme fibre from the centroidal YY axis. Zyy = The section modulus or elastic modulus of section defined as the moment of Inertia Iyy divided by the extreme fibre distance measured from centroidal XX axis as calculated as

Z yy =

I yy x

Where x = Distance to the extreme fibre from the centroidal XX axis

4. Software Implementation Steel designers frequently need to find the sections of specific requirements based on weight, width, height or other properties for design. The section properties listed on the following tables are grouped based on primary shape of the section i.e. C shapes put in one table, H shapes in another and so on, which, in most cases, is the practical way of selection. Further, the shapes have been ordered by their nominal sizes like width and height instead of weight or any other properties. To provide the designer, any easy and quick way to find a section or group of sections which satisfy certain specified criteria, SYS Designer Software provide special tool for searching, sorting and printing those sections. User can specify the range for important section properties like weight, width or height, which further be sorted by any one of the properties. Some common and practical examples to illustrate the usefulness of this module are: 1. In the design of steel beams the designer frequently need to find the lightest section satisfying a certain minimum section modulus. 2. In the deflection checks, a sorted list of sections based on moment of inertia which is the main parameter to control the deflection, will be desirable for quick and an economic selection of the section. 3. Due to some architectural or connection restriction, in some cases, designer may need to find the section not exceeding certain width or height.


2-4

Certain SYS Sections of not so common usage are not readily available in the market, which puts an additional limit on the section selection. This market/stock availability criterion has also been included in the section selection module. The following table gives the section designation used in the software. Table 2.4 SYS Section Designation Used in SYS Designer Software Sr. No

Actual Shape

Primary Designation

Complete Designation

1

H or WF or W

H

H

2

I

I

I

3

Channel

C

C

4

T Or TH

T

T

5

Equal Angle

L

EL

6

Unequal Angle

L

UL

7

Double Angles

LL

ELL

LL

ULLL

LL

ULLS

Remark

Equal Legs 8

Double Angles Unequal Legs, Longer Leg Connected

9

Double Angles Unequal Legs, Shorter Leg Connected

10

Double C Open or Like H Shape

CC

CCI

11

Double C Close or Like Box

CC

CCB


2-5


2-6

Table 2.5 Sizes and Properties of Sections for Design for Channel Shapes Sectional Dimension (mm) Section Designation t1

t2

r1

Sectional Area (cm2)

Wght kg/m

r2

Moment Of Inertia (cm4)

Radius of Gyration (cm)

Modulus of Section (cm3)

Ix

Iy

ix

iy

Zx

Zy

C 200x80x24.6

7.5

11

12

6

31.33

24.6

1950

168

7.88

2.32

195

29.1

C 200x90x30.3

8

13.5

14

7

38.65

30.3

2490

277

8.02

2.68

249

44.2

C 250x90x34.6

9

13

14

7

44.07

34.6

4180

294

9.74

2.58

334

44.5

C 250x90x40.2

11

14.5

17

8.5

51.17

40.2

4680

329

9.56

2.54

374

49.9

C 300x90x38.1

9

13

14

7

48.57

38.1

6440

309

11.5

2.52

429

45.7

C 300x90x43.8

10

15.5

19

9.5

55.74

43.8

7410

360

11.5

2.54

494

54.1

C 300x90x48.6

12

16

19

9.5

61.9

48.6

7870

379

11.3

2.48

525

56.4

C 380x100x54.5

10.5

16

18

9

69.39

54.5

14500

535

14.5

2.78

763

70.5

C 380x100x67.3

13

20

24

12

85.71

67.3

17600

655

14.3

2.76

926

87.8


Y

t1

r2

t2

r1

X

X

H

B Y

2-7

Table 2.6 Sizes and Properties of Sections for Design for I Shapes Sectional Dimension (mm)

Section Designation t1

t2

r1


Wght kg/m

r2

Moment of Inertia (cm4)



Ix

Iy

ix

iy

Zx

Zy

I 200x100x26

7

10

10

5

33.06

26

2170

138

8.11

2.05

217

27.7

I 200x150x50.4

9

16

15

7.5

64.16

50.4

4460

753

8.34

3.43

446

100

I 250x125x38.3

7.5

12.5

12

6

48.79

38.3

5180

337

10.3

2.63

414

53.9

I 250x125x55.5

10

19

21

10.5

70.73

55.5

7310

538

10.2

2.76

858

86

I 300x150x48.3

8

13

12

6

61.58

48.3

9480

588

12.4

3.09

632

78.4

I 300x150x65.5

10

18.5

19

9.5

83.47

65.5

12700

886

12.3

3.26

849

118

I 300x150x76.8

11.5

22

23

11.5

97.88

76.8

14700

1080

12.2

3.32

978

143

I 350x150x58.5

9

15

13

6.5

74.58

58.5

15200

702

14.3

3.07

870

93.5

I 350x150x87.2

12

24

25

12.5

111.1

87.2

22400

1180

14.2

3.26

1280

158

I 400x150x72

10

18

17

8.5

91.73

72

24100

864

16.2

3.07

1200

115

I 400x150x95.8

12.5

25

27

13.5

122.1

95.8

31700

1240

16.1

3.18

1580

165

I 450x175x91.7

11

20

19

9.5

116.8

91.7

39200

1510

18.3

3.6

1740

173

I 450x175x115

13

26

27

13.5

146.1

115

48800

2020

18.3

3.72

2170

231

I 600x190x133

13

25

25

12.5

169.4

133

98400

2460

24.1

3.81

3280

259

I 600x190x176

16

35

38

19

224.5

176

130000

3540

24.1

3.97

4330

373


Y

r2

t2

t1 X

X

H

r1

B Y

2-8

Table 2.7 Sizes and Properties of Sections for Design for H Shapes Sectional Dimension (mm)

Wght kg/m




Y B

t

2

Section Designation


t2

r1

Ix

Iy

ix

iy

Zx

Zy

6

8

10

21.9

17.2

383

134

4.18

2.47

76.5

26.7

H 125x125x23.8

6.5

9

10

30.31

23.8

847

293

5.29

3.11

136

47

H 150x100x21.1

6

9

11

26.84

21.1

1020

151

6.17

2.37

138

30.1

H 150x150x31.5

7

10

11

10.14

31.5

1640

563

6.39

3.75

219

75.1

H 175x175x40.2

7.5

11

12

51.21

40.2

2880

984

7.5

4.38

330

112

H 200x100x18.2

4.5

7

11

23.18

18.2

1580

114

8.26

2.21

160

23

H 200x100x21.3

5.5

8

11

27.16

21.3

1840

134

8.24

2.22

184

26.8

H 200x150x30.6

6

9

13

39.01

30.6

2690

507

8.3

3.61

227

67.6

H 200x200x49.9

8

12

13

63.53

49.9

4720

1600

8.62

5.02

472

160

H 200x200x56.2

12

12

13

71.53

56.2

4980

1700

8.35

4.88

498

167

H 200x200x65.7

10

16

13

83.69

65.7

6530

2200

8.83

5.13

628

218

H 250x125x25.7

5

8

12

32.68

25.7

3540

255

10.4

2.79

285

41.1

H 250x125x29.6

6

9

12

37.66

29.6

4050

294

10.4

2.79

324

47

H 250x175x44.1

7

11

16

56.24

44.1

6120

984

10.4

4.18

502

113

H 250x250x64.4

11

11

16

82.06

64.4

8790

2940

10.3

5.98

720

233

H 250x250x66.5

8

13

16

84.7

66.5

9930

3350

10.8

6.29

801

269

H 250x250x72.4

9

14

16

92.18

72.4

10800

3650

10.8

6.29

867

292

H 250x250x82.2

14

14

16

104.7

82.2

11500

3880

10.5

6.09

919

304

H 300x150x32.0

5.5

8

13

40.8

32

6320

442

10.4

3.29

424

59.3

H 300x150x36.7

6.5

9

13

46.78

36.7

7210

508

12.4

3.29

481

67.7

H 300x200x56.8

8

12

18

72.38

56.8

11300

1600

12.5

4.71

771

160

H 300x200x65.4

9

14

18

83.36

65.4

13300

1900

12.6

4.77

893

189

H 300x300x84.5

12

12

18

107.7

84.5

16900

5520

12.5

7.16

1150

365


t1

H

t1 H 100x100x17.2

X

X

r Y

2-9

Table 2.7 (Continued) Sizes and Properties of Sections for Design for H Shapes Sectional Dimension

Wght kg/m




ix

iy

Zx

Zy

Y B

t

2

(mm)

Section Designation


t2

r1

Ix

Iy

H 300x300x87.0

9

14

18

110.8

87

18800

6240

13

7.51

1270

417

H 300x300x94.0

10

15

18

119.8

94

20400

6750

13.1

7.51

1360

450

H 300x300x106.0

15

15

18

134.8

106

21500

7100

12.6

7.26

1440

466

H 300x300x106.0

11

17

18

134.8

106

23400

7730

13.2

7.57

1540

514

H 350x175x41.4

6

9

14

52.68

41.4

11100

792

14.5

3.88

641

91

H 350x175x49.6

7

11

14

63.14

49.6

13600

984

14.7

3.95

775

112

H 350x175x57.6

8

13

14

73.68

57.8

16100

1180

14.8

4.01

909

134 248

H 350x250x69.2

8

12

20

88.15

69.2

18500

3090

14.5

5.92

1100

H 350x250x79.7

9

14

20

101.5

79.7

21700

3650

14.6

6

1280

292

H 350x350x106.0

13

13

20

135.3

106

28200

9380

14.4

8.33

1670

534

H 350x350x115.0

10

16

20

146

115

33300

11200

15.1

8.78

1940

646

H350x350x131.0

16

16

20

166.6

131

35300

11800

14.6

8.43

2050

669

H 350x350x137.0

12

19

20

173.9

137

40300

13600

15.2

8.84

2300

776

H 350x350x156.0

19

19

20

198.4

156

42800

14400

14.7

8.53

2450

809

H 400x200x56.6

7

11

16

72.16

56.6

20000

1450

16.7

4.48

1010

145

H 400x200x66.0

8

13

16

84.12

66

23700

1740

16.8

4.54

1190

174

H 400x200x75.5

9

15

16

96.16

75.5

27500

2030

16.9

4.6

1360

202

H 400x300x94.5

9

14

22

120.1

94.5

33700

6240

16.7

7.21

1740

418

H 400x400x172

13

21

22

218.7

172

66600

22400

17.5

10.1

3330

1120

H400x400x232

18

28

22

295.4

232

92800

31000

17.7

10.02

4480

1530

H 450x200x66.2

8

12

18

84.3

66.2

28700

1580

18.5

4.33

1290

159


t1

H

T1

X

X

r Y

2-10

Table 2.7 (Continued) Sizes and Properties of Sections for Design for H Shapes Sectional Dimension (mm)

Wght kg/m




iy

Zx

Zy

Y B

t

2

Section Designation


t2

r1

Ix

Iy

ix

H 450x200x76.0

9

14

18

96.76

H 450x200x88.9

10

17

18

113.3

76

33500

1870

18.6

4.4

1490

187

88.9

40400

2310

18.9

4.51

1770

230

H 450x300x106.0

10

15

24

135

H 450x300x124.0

11

18

24

157.4

106

46800

6690

18.6

7.04

2160

448

124

56100

8110

18.9

7.18

2550

541

H 450x300x145.0

13

21

24

H 500x200x79.5

9

14

20

184.3

145

66400

9660

19

7.24

2980

639

101.3

79.5

41900

1840

20.3

4.27

1690

H 500x200x89.6

10

16

20

185

114.2

89.6

47800

2140

20.5

4.33

1910

H 500x200x103.0

11

19

214

20

131.3

103

56500

2580

20.7

4.43

2230

254

H 500x300x114.0

11

H 500x300x128.0

11

15

26

145.5

114

60400

6760

20.4

6.82

2500

451

18

26

163.5

128

71000

8110

20.8

7.04

2910

H 500x300x150.0

541

13

21

26

191.4

150

83800

9660

20.9

7.1

3390

640

H 600x200x94.6

10

15

22

120.5

94.6

68700

1980

23.9

4.05

2310

199

H 600x200x106.0

11

17

22

134.4

106

77600

2280

24

4.12

2590

228

H 600x200x120.0

12

20

22

152.5

120

90400

2720

24.3

4.22

2980

271

H 600x200x134.0

13

23

22

170.7

134

103000

3180

24.6

4.31

3380

314

H 600x300x137.0

12

17

28

174.5

137

103000

7670

24.3

6.63

3530

511

H 600x300x151.0

12

20

28

192.5

151

118000

9020

24.8

6.85

5020

601

H 600x300x175.0

14

23

28

222.4

175

137000

10600

24.9

6.9

4620

7001

H 700x300x166.0

13

20

28

211.5

166

172000

9020

28.6

6.53

4980

602

H 700x300x185.0

13

24

28

235.5

185

201000

10800

29.3

6.78

5760

722

H 800x300x191.0

14

22

28

243.4

191

254000

9930

32.3

6.39

6410

662

H 800x300x210.0

14

26

28

267.4

210

292000

11700

33

6.62

7290

782


t1

H

t1

X

X

r Y

2-11

Table 2.8 Sizes and Properties of Sections for Design for T or TH Shapes (Cut From H) Sectional Dimension

Sectional

Wght

Moment

Radius

Modulus

(mm)

Area

kg/m

of Inertia

of Gyration

of Section

(cm4)

(cm)

(cm3)

Section Designation

(cm2) t1

t2

r1

Ix

Iy

ix

iy

Zx

Zy

Center of Gravity from Top

t2

Cx=

T 50x100x8.6

6

8

10

10.95

8.6

16.1

66.9

1.21

2.47

4.03

13.4

1.0

T 62.5x125x11.9

6.5

9

10

15.16

11.9

35

147

1.52

3.11

6.91

23.5

1.19

T 75x100x10.5

6

9

11

13.42

10.5

51.7

75.3

1.96

2.37

8.84

15.1

1.55

T 75x150x15.8

7

10

11

20.07

15.8

66.4

282

1.82

3.75

10.8

37.6

1.37

T 87.5x175x20.1

7.5

11

12

25.61

20.1

115

492

2.12

4.38

15.9

56.2

1.55 2.14

T 100x100x9.1

4.5

7

11

11.59

9.1

93.8

56.8

2.84

2.21

12.1

11.5

T 100x100x10.7

5.5

8

11

13.58

10.7

114

67.0

2.9

2.22

14.8

13.4

2.29

T 100x150x15.3

6

9

13

19.51

15.3

125

254

2.53

3.61

15.8

33.8

1.79 1.73

T 100x200x24.9

8

12

13

31.77

24.9

184

801

2.41

5.02

22.3

80.1

T 100x200x28.1

12

12

13

35.77

28.1

256

851

2.67

4.88

32.4

83.4

2.09

T 100x200x32.8

10

16

13

41.85

32.8

251

1100

2.45

5.13

29.4

109

1.91

T 125x125x12.8

5

8

12

16.34

12.8

208

127

3.57

2.79

21.3

20.5

2.68

T 125x125x14.8

6

9

12

18.83

14.8

248

147

3.63

2.79

25.6

23.5

2.78

T 125x175x22.1

7

11

16

25.12

22.1

289

492

3.2

4.18

29.1

56.3

2.27

T 125x250x32.2

11

11

16

41.03

32.2

445

1470

3.29

5.98

45.3

117

2.39

T 125x250x33.2

8

13

16

42.35

33.2

364

1670

2.93

6.29

34.9

134

1.98

T 125x250x36.2

9

14

16

43.09

36.2

412

1820

2.99

6.29

39.5

146

2.08

T 125x250x41.1

14

14

16

52.34

41.1

589

1940

3.36

6.09

59.4

152

2.58

T 150x150x16.0

5.5

8

13

30.4

16

393

551

4.39

6.29

33.8

29.7

3.26

T 150x150x18.4

6.5

9

13

23.39

18.4

464

254

4.45

3.29

40

33.8

3.41

T 150x200x28.4

8

12

18

36.19

28.4

572

802

3.97

4.71

48.2

80.2

2.83


B Y

t1 X

X

Y

2-12

H

Table 2.8 (Continued) Sizes and Properties of Sections for Design for T or TH Shapes (Cut From H) Sectional Dimension (mm) Section Designation


t1

t2

r1

T 150x200x32.7

9

14

18

41.68

T 175x175x20.7

6

9

14

T 175x175x24.8

7

11

T 175x250x34.6

8

12

T 175x250x39.8

8

T 175x350x53.1 T 175x350x57.3

Wght kg/m





Ix

Ix

Ix

Iy

Zx

Zy

Cx=

32.7

662

949

3.99

4.77

55.2

94.4

2.91

26.34

20.7

679

396

5.08

3.88

50

45.5

3.71

14

31.57

24.8

815

492

5.08

3.95

59.3

56.2

3.75

20

44.08

34.6

881

1540

4.47

5.92

64.0

124

3.02

14

20

50.76

39.8

1020

1830

4.48

6.00

73.1

146

3.09

13

13

20

67.63

53.1

1420

4690

4.59

8.3

104

267

3.21

10

16

20

73

57.3

1230

5620

4.11

8.78

84.7

323

2.67

T 175x350x65.4

16

16

20

83.32

65.4

1800

5920

4.65

8.43

131

335

3.40

T 175x350x68.2

12

19

20

86.94

68.2

1520

6790

4.18

8/.84

104

388

2.86

T 175x350x77.9

19

19

20

99.19

77.9

2200

7220

4.71

8.53

158

4.4

3.59

T 175x350x79.3

14

22

20

101

79.3

1820

8000

4.25

8.9

124

455

3.05

T 200x200x28.3

7

11

16

36.08

28.3

1190

723

4.76

4.48

76.4

72.7

4.17

T 200x200x33.0

8

13

16

42.06

33

1400

868

5.76

4.54

88.6

86.8

4.23

T 200x300x47.1

9

14

22

60.05

47.1

1530

3120

5.04

7.21

95.5

209

3.33

T 200x300x53.4

10

16

22

67.98

53.4

1730

3600

5.05

7.28

108

240

3.41 5.90

T 250x200x39.7

9

14

20

50.64

39.7

2840

922

7.49

4.27

150

92.6

T 250x200x44.8

10

16

20

57.12

44.8

3210

1070

7.5

4.33

169

107

5.96

T 250x200x51.5

11

19

20

65.65

51.5

3670

1290

7.48

4.43

190

128

5.95

T 250x300x57.1

11

15

26

72.76

57.1

3420

3380

6.85

6.82

178

225

4.92

T 250x300x64.2

11

18

26

81.76

64.2

3620

4060

6.66

7.07

184

70

4.66

T 300x200x47.3

10

15

22

60.23

47.3

5190

989

9.29

4.05

236

99.4

7.79


B Y

t2

t1 X

X

Y

2-13

H

Table 2.8 (Continued) Sizes and Properties of Sections for Design for T or TH Shapes (Cut From H) Sectional Dimension (mm) Section Designation


Wght kg/m





t1

t2

r1

T 300x200x52.8

11

17

22

67.21

T 300x200x59.8

12

20

22

76.24

T 300x200x67.0

13

23

22

85.33

67

7340

1590

9.27

4.31

322

157

7.79

T 300x300x68.5

12

17

28

87.24

68.5

6360

3830

8.54

6.63

280

256

6.39

T 300x300x75.6

12

20

28

96.24

75.6

6710

4510

8.35

6.85

288

301

6.08

T 300x300x87.3

14

23

28

111.2

87.3

7920

5290

8.44

6.9

339

350

6.33


Ix

Ix

Ix

Iy

Zx

Zy

Cx=

52.8

5810

1140

9.3

4.12

262

114

7.84

59.8

6570

1360

9.28

4.22

292

135

7.79

B Y

t2

t1 X

X

Y

2-14

H

Table 2.9 Sizes and Properties of Sections for Design for Equal Angles EL Sectional Dimension

Sectional

(mm)

Area

Wght kg/m

Moment

Radius

Modulus

of Inertia

of Gyration

of Section

2

4

(cm )

Section Designation t1

t2

r1

r2

EL 25x25x1.12

3

3

4

2

1.427

EL 30x30x1.36

3

3

4

2

EL 40x40x1.83

3

3

4.5

EL 40x40x2.95

5

5

4.5

EL 45x45x2.74

4

4

EL 45x45x3.38

4

4

EL 50x50x3.06

4

EL 50x50x3.77

5

EL 50x50x4.43

(cm )

Center of Gravity

(cm)

(cm )

(From bot and Left)

Ix

Iy

ix

iy

Zx

Zy

Cx

Cy

1.12

0.797

0.797

0.747

0.747

0.448

0.448

0.719

0.719

1.727

1.36

1.42

1.42

0.908

0.908

0.661

0.661

0.844

0.844

2

2.336

1.83

3.53

3.53

1.23

1.23

1.21

1.21

1.09

1.09

3

3.755

2.95

5.42

5.42

1.2

1.2

1.91

1.91

1.17

1.17

6.5

3

3.492

2.74

6.5

6.5

1.36

1.36

2

2

1.24

1.24

6.5

3

4.302

3.38

7.91

7.91

1.36

1.36

2.46

2.46

1.28

1.28

4

6.5

3

3.892

3.06

9.06

9.06

1.53

1.53

2.49

2.49

1.37

1.37

5

6.5

3

4.802

3.77

11.1

11.1

1.52

1.52

3.08

3.08

1.41

1.41

6

6

6.5

4.5

5.644

4.43

12.6

12.6

1.5

1.5

3.55

3.55

1.44

1.44

EL 60x60x3.68

4

4

6.5

3

4.692

3.68

16

16

1.85

1.85

3.66

3.66

1.61

1.61

EL 60x60x4.55

5

5

6.5

3

5.802

4.55

19.6

19.6

1.84

1.84

4.52

4.52

1.66

1.66

EL 65x65x5.0

5

5

8.5

3

6.367

5

25.3

25.3

1.99

1.99

5.35

5.35

1.77

1.77

EL 65x65x5.91

6

6

8.5

4

7.527

5.91

29.4

29.4

1.98

1.98

6.26

6.26

1.81

1.81

EL 65x65x7.66

8

8

8.5

6

9.761

7.66

36.8

36.8

1.94

1.94

7.96

7.96

1.88

1.88

EL 70x70x6.38

6

6

8.5

4

8.127

6.38

37.1

37.1

2.14

2.14

7.33

7.33

1.93

1.93

EL 75x75x6.85

6

6

8.5

4

8.727

6.85

46.1

46.1

2.3

2.3

8.47

8.47

2.06

2.06

EL 75x75x9.96

9

9

8.5

6

12.69

9.96

64.4

64.4

2.25

2.25

12.1

12.1

2.17

2.17

EL 75x75x13.0

12

12

8.5

6

16.56

13

81.9

81.9

2.22

2.22

15.7

15.7

2.29

2.29

EL 80x80x7.32

6

6

8.5

4

9.327

7.32

56.4

56.4

1.46

1.46

9.7

9.7

2.18

2.18

EL 90x908.28

6

6

10

5

10.55

8.28

80.7

80.7

2.77

2.77

12.6

12.6

2.42

2.42

EL 90x90x9.59

7

7

10

5

12.22

9.59

93

93

1.76

1.76

14.2

14.2

2.46

2.46


r2

(cm)

3)

H

Cy t1 t2

r1

B

2-15

Cx

Table 2.9 Sizes and Properties of Sections for Design for Equal Angles L Sectional Dimension (mm)

Sectional Wght Area kg/m (cm2)



Modulus of Section (cm3))

Section Designation

Center of Gravity

r2

(cm) (From bot and Left)

t1

t2

r1

r2

Ix

Iy

ix

iy

Zx

Zy

Cx

Cy

EL 90x90x13.3

10

10

10

7

17

13.3

125

125

1.71

1.71

19.5

19.5

2.57

2.57

EL 90x90x17.0

13

10

10

7

21.71

17

156

156

2.68

2.68

24.8

24.8

2.69

2.69

EL100x100x10.7

7

10

10

5

13.62

10.7

129

129

3.08

3.08

17.7

17.7

2.71

2.71

EL 100x100x17.9

10

10

10

7

19

17.9

175

175

3.04

3.04

24.4

24.4

2.82

2.82

EL 100x100x19.1

13

10

10

7

24.31

19.1

220

220

3

3

31.1

31.1

2.94

2.94

EL 120x120x14.7

8

12

12

5

18.74

14.7

258

258

3.71

3.71

29.5

29.5

3.24

3.24

EL 130x130x17.9

9

12

12

6

22.74

17.9

366

366

4.01

4.01

38.7

38.7

3.53

3.53

EL 130x130x23.4

12

12

12

8.5

29.76

23.4

467

467

3.96

3.96

49.9

49.9

3.64

3.64

EL 130x130x28.8

15

12

12

8.5

36.75

28.8

568

568

3.93

3.93

61.5

61.5

3.76

3.76

EL 150x150x27.3

12

14

12

7

34.77

27.3

740

740

4.61

4.61

68.1

68.1

4.14

4.14

EL 150x150x33.6

15

14

14

10

42.74

33.6

888

888

4.56

4.56

82.6

82.6

4.24

4.24

EL 150x150x41.9

19

14

14

10

53.38

41.9

1090

1090

4.52

4.52

103

103

4.40

4.40

EL 175x175x31.8

12

15

14

11

40.52

31.8

1170

1170

5.38

5.38

91.8

91.8

4.73

4.73

EL 175x175x39.4

15

15

15

11

50.21

39.4

1440

1440

5.35

5.35

114

114

4.85

4.85

EL 200x200x45.3

15

17

15

12

57.75

45.3

2180

2180

6.14

6.14

150

150

5.46

5.46

EL 200x200x59.7

20

17

17

12

76

59.7

2820

2820

6.09

6.09

197

197

5.67

5.67

EL 200x200x73.6

25

17

17

12

93.75

73.6

3420

3420

6.04

6.04

242

242

5.86

5.86

EL 250x250x93.7

25

24

25

12

119.4

93.7

6950

6950

7.63

7.63

388

388

7.10

7.10

EL 250x250x128.0

35

24

35

18

162.6

128

9110

9110

7.49

7.49

519

519

7.45

7.45


H

Cy t1 t2

r1

B

2-16

Cx

Table 2.10 Sizes and Properties of Sections for Design for Unequal Angles UL Sectional Area (cm2)

Sectional Dimension (mm)

Section Designation

Wght kg/m



Modulus Of Section (cm3))

Center of Gravity

(From bot and Left)

t1

t2

r1

r2

UL 90x75x11.0

9

9

8.5

6

14.04

UL 100x75x9.32

7

7

10

5

11.87

UL 100x75x13.0

10

10

10

7

UL 125x75x10.7

7

7

10

5

Ix

Iy

ix

iy

Zx

Zy

Cx

Cy

11

109

68.1

2.78

2.2

17.4

12.4

2.75

2.00

9.32

118

56.9

3.15

2.19

17

10

3.06

1.83

16.5

13

159

76.1

3.11

2.15

23.3

13.7

3.17

1.94

13.62

10.7

219

60.4

4.01

2.11

26.1

10.3

4.10

1.64

UL 125x75x14.9

10

10

10

7

19

14.9

299

80.8

3.96

2.06

36.1

14.1

4.22

1.75

UL 125x75x19.1

13

13

10

7

24.31

19.1

376

101

3.93

2.04

46.1

17.9

4.35

1.87

UL 125x90x16.1

10

10

10

7

20.5

16.1

318

138

3.94

2.59

37.2

20.3

3.95

2.22

UL 125x90x20.6

13

13

10

7

26.26

20.6

401

173

3.91

2.57

47.5

25.9

4.07

2.34

UL 150x90x16.4

9

9

12

6

20.94

16.4

485

133

4.81

2.52

48.2

19

4.95

1.99

UL 150x90x21.5

12

12

12

8.5

27.36

21.5

619

167

7.76

2.47

62.3

24.3

5.07

2.10

UL 150x100x17.1

9

9

12

6

21.84

17.1

502

181

4.79

2.88

49.1

23.5

4.76

2.30

UL 150x100x22.4

12

12

12

8.5

28.56

22.4

612

223

4.74

2.83

63.4

30.1

4.88

2.41

UL 150x100x27.7

15

15

12

8.5

35.25

27.7

782

276

4.71

2.8

78.2

37

5.00

2.53


r2

(cm)

H

Cy t1 t2

r1

B

2-17

Cx

Table 2.11 Properties of Sections Limited by Width-Thickness Ratio Section Designation

Stem b/t

For Qa= 1 Fy = 2400 Ksc

Fy = 3900 Ksc

Factor Qs

Cc '

Factor Qs

Cc ' --

T 50x100x8.6

6.25

--

--

--

T 62.5x125x11.9

6.94

--

--

--

--

T 74x100x10.5

8.22

--

--

--

---

T 75x150x15.8

7.50

--

--

--

T 87.5x175x20.1

7.95

--

--

--

--

T 99x99x9.1

14.14

--

--

--

--

T 100x100x10.7

12.50

--

--

--

--

T 97x150x15.3

10.78

--

--

--

--

T 100x200x24.9

8.33

--

--

--

--

T 100x204x28.1

8.33

--

--

--

--

T 104x202x32.8

6.50

--

--

--

--

T 124x124x12.8

15.50

--

--

--

--

T 125x125x14.8

13.89

--

--

--

--

T 122x175x22.1

11.09

--

--

--

--

T 122x252x32.2

11.09

--

--

--

--

T 124x249x33.2

9.54

--

--

--

--

T 125x250x36.2

8.93

--

--

--

--

T 125x255x41.1

8.93

--

--

--

--

T 149x149x16

18.63

--

--

0.917

106.17

T 150x150x18.4

16.67

--

--

--

--

T 147x200x28.4

12.25

--

--

--

--

T 149x201x32.7

10.64

--

--

--

--

T 173x176x20.7

19.22

--

--

0.885

108.06

T 175x175x24.8

15.91

--

--

--

--

T 168x249x34.6

14.00

--

--

--

--

T 170x250x39.8

12.14

--

--

--

--

T 169x351x53.1

13.00

--

--

--

--

T 172x348x57.3

10.75

--

--

--

--

T 172x354x65.4

10.75

--

--

--

--

T 175x350x68.2

9.21

--

--

--

--

T 175x357x77.9

9.21

--

--

--

--

T 178x352x79.3

8.09

--

--

--

--

T 198x199x28.3

18.00

--

--

0.950

104.30

T 200x200x33

15.38

--

--

--

--

T193x299x47.1

13.79

--

--

--

--

T 195x300x53.4

12.19

--

--

--

--

T 248x199x39.7

17.71

--

--

0.966

103.48

T 250x200x44.8

15.63

--

--

--

--

T 253x201x51.5

13.32

--

--

--

--


2-18

Table 2.11 Properties of Sections Limited by Width-Thickness Ratio Stem b/t Section Designation

For Qa= 1 Fy = 2400 Ksc

Fy = 3900 Ksc

Factor Qs

Cc '

Factor Qs

Cc ' --

T 241x300x57.1

16.07

--

--

--

T 244x300x64.2

13.56

--

--

--

--

T 298x199x47.3

19.87

--

--

0.851

110.22

T 300x200x52.8

17.65

--

--

0.969

103.29

T 303x201x59.8

15.15

--

--

--

--

T 306x202x67

13.30

--

--

--

--

T 291x300x68.5

17.12

--

--

0.997

101.82

T 294x300x75.6

14.70

--

--

--

--

T 297x302x87.3

12.91

--

--

--

--


2-19

Chapter

3

Design of Tension Member 1. Introduction This chapter describes the general concepts for the design of steel tension members. Procedures implemented in the development of SYS Designer software and design tables for tension members are also presented. Design of an axial tension member involves considerably simple analysis and design procedures compared to any other types of members. Two important considerations in the design of tension members are the net effective area of cross section and permissible tensile stresses. Whenever a tension member is to be fastened by means of bolts or rivets, holes must be provided at the connection. As a result, the member cross-sectional area at the connection is reduced and the strength of the member may also be reduced depending on the size and location of holes. Thus in most cases, the designer need to design the member size and end connections together as they influence each other. Permissible tensile stress and detailed methods to determine net effective area can be referred to the relevant design codes.

2. General Procedure A tension member can fail by reaching one of the limit states: yielding or fracture. To prevent yielding and accompanying excessive elongation, the stress on the gross area must be limited to yield stress Fy. To prevent fracture, the stress on the net area must not exceed the tensile strength Fu. With these two basic criteria, the tensile strength of a steel member is determined by using the following simple general procedures. Permissible Stresses: (AISC/ASD)

Ft = 0.6 Fy Ft = 0.5 Fu

on gross area

(3-1)

on effective area

(3-2)

Tensile Strength of a Member: The tensile strength, corresponding to the above two values for permissible stresses of, a member based on AISC/ASD is given by the smaller of the following two values for Pt.

Pt = 0.6 × Fy × A g

(3-3)

Pt = 0.5 × Fu × Ae

(3-4)

Where

Fy = Specified Yield Strength Fu = Specified Ultimate Strength Hand Book for Design of Steel Structures

3-1

Ae = Net effective area Ag = Gross area The above formulae can be used for any consistent set of units. For example, for Metric system of units, if Fy and Fu are taken in Ksc and areas on cm2, the tensile strength will be in Kg. The procedures for calculations of Ae are explained in the following sections. Design Steps: 1)

Compute Ag1 required based on yield criteria (Fy) from Eqn Error! Not a valid link.

2)

Compute Ae required based on fracture criteria (Fu) from Eqn Error! Not a valid

3)

Select appropriate reduction factor based on connection type and configuration.(usually 0.75 -1.0)

link.

Ae U

4)

Compute Ag2 based on Ae from step 3. Ag 2 =

5)

Select section to satisfy higher of Ag1 and Ag2.

6)

Check for other end connection requirements.

3. Effective Net Area As mentioned in the previous section, detailed methods to find net effective area in design calculations depends upon the code requirements. In AISC specifications, calculation of the net effective area is based on actual net area multiplied by an appropriate reduction factor, which account for efficiency of the connection. This reduction factor includes various factors affecting the strength of the joint and the important phenomenon known as shear lag. Shear lag occurs due to the partial connection of the cross section resulting into an unequal stress distribution in different cross section elements. One very common example, where this phenomenon is quite serious, is the connection of only one leg of an angle section to gusset plate. 3.1.1. Effective Area:

For bolted and riveted connections

Ae = UAn

(3-5)

For Welded Connections

Ae = UAg

(3-6)

Where, U = reduction coefficient/factor An = net area of cross section. The area after deduction of area for holes from gross area = Ag - Aholes Ag = gross area of cross section


3-2

3.1.2. Reduction Factors

The general equation for the calculation of reduction factors is given as below. Figure Error! Not a valid link.shows the definition of the parameters used for the calculations of U. −

U = 1−

x L −

x = Dis tan ce Between Centroid of the connected Area and the shear plane L = Length of the connection

L

X

X

X

X

X

Fig. 3.1. Parameters for the Calculation of Reduction Factor U

3.1.2.1. For Bolted and Riveted Connections The reduction factor for bolted and riveted connections depends mainly on four parameters namely, the cross section shape of the member, depth to width ratio, number of fasteners per line and the portion of cross section actually connected. AISC specifies the following simple rules for the approximate calculations of reduction factors for some common shapes. Error! Not a valid link. shows reduction factors for some typical bolted connections. 1) For W, M, S or H shapes with flange widths not less than two-thirds the depth

and structural tees cut from them, connected by the flanges and for bolted and riveted connections with at least three fasteners per line in the direction of the stress; U = 0.9 2) For W, M, S or H Shapes not meeting the conditions specified above, for

structural tees cut form them, and all other shapes including built-up sections and for bolted and riveted connections with at least three fasteners per line in the directions of stress; U = 1 Hand Book for Design of Steel Structures

3-3

3) For all members with bolted or riveted connections with only two fasteners per

line in the directions of stress; U = 0.75 4) If all the elements of a member cross section are connected; U = 1


3-4

WT B f / d>2/3 Bar or Plate

Ae=An

WF B f / d>2/3

Ae=0.9A n

Single or Double Angle

Ae =0.85 A n

WF B f / d>2/3

Ae =0.75 A n

Ae=0.90A n

WF B f / d<2/3

Ae=0.85A n

Single or Double Angle

Ae =0.75 A n

WF B f / d<2/3

Ae=0.75A n

Fig. 3.2. Net Effective Area for Bolted or Riveted Connections

3.1.2.2. For Welded Connections For welded connections with both transverse and longitudinal welds, the reduction factor U is calculated by the general formula given above. For two special cases of connections with only longitudinal or only transverse welds, AISC specify the two rules as given below and illustrated in Fig Error! Not a valid link.. 1. For any W, M, S, H or structural tees, connected by transverse welds alone 2. Ae = area of connected element


3-1

3. For plates and bars connected by longitudinal welds at their ends as in the following figure three values of U depending upon the relative length of length l of the weld and their spacing w U=1.0 for l >= 2w U=0.87 for 1.5 =< l < 2w U=1.0 for w =< l < 1.5w

w

w

l

Only Transverse Weld (a)

l

Only Logitudinal Weld (b)

Fig. 3.3. Reduction Factors: Special Cases for Welded Connections

4. Design Examples Design of tension member needs more considerations on the design of connections than the in calculations for the tension strength of the member itself. Welded connections are much simpler in design. The important considerations in the welded joint are the arrangement of weld so as to coincide the resisting force with center of gravity of the member and the form of welding. If the tension member is connected by a large number of rivets or bolts, the design becomes more complicated, requiring more calculations for determination of critical section for fracture on the cross section of the member and the other connecting elements like gusset plates etc. In such case the design strength will be the minimum of the member strength calculated based on the most critical failure path on the member or on the connecting element. If the connection is to be designed for eccentric load, additional calculations for the connection are required. An example is given here to demonstrate the general procedure for the design of tension members. However the detailed calculations for design of connections has not been included. They will be discussed briefly in the Chapter 7 ” Introduction to Design of Connections”


3-2

SYS

Subject: Design of Member

Siam Yamato Steel Co. Ltd.

Bolt-Connected

Design Code:

Thailand

Tension

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

Example:3 1 Sheet No:1 / 2 Reference Chapter: 3

Problem:

Design the lightest T-section whose net effective area after deduction for holes will be approximately 70% of the gross area. Maximum tensile load = 29 Ton which does not include the wind load. Use SYS steel grade with properties: Fy = 2400 Ksc (34 ksi), Fu = 4000 Ksc (56.8 ksi)

T-Section

29 Tons

Ae=0.90A n

Fig. 3.4. Bolt Connected T-section Tension Member for Design Example Error! Not a valid link. Solution:

Tensile strength = Ag × 0.6 Fy

….(1)

= Ae × 0.5 Fu

….(2)

from (1) from (2)

A g1 =

Tensile Force 29,000 = = 20.13 cm 2 0.6Fy 0.6 × 2400

Ae =

Tensile Force 29,000 = = 14.50 cm 2 0.5Fu 0.5 × 4000

Ag 2 =

Ae 14.50 = = 20.71 cm 2 0.7 0.7

So higher of above two gross area Ag1 and Ag2 is the minimum required gross area. Ag= 20.71 cm2 The SYS T sections close to this requirement are T 75x150x15.8 Kg/m

Ag = 20.07 cm2

T 150x150x16.0 Kg/m

Ag = 20.40 cm2

T 150x150x18.4 Kg/m

Ag = 23.39 cm2

So, use T 150x150x18.4 Kg/m

Ag=23.39 cm2

Actual capacity based on gross area = 23.39 × 0.6 × 2400 = 33,681 Kg Hand Book for Design of Steel Structures

3-3

SYS Siam Yamato Steel Co. Ltd.

Subject: Design Member

of

Design Code:

Thailand

AISC/ASD (1991)

Bolt-Connected

Tension

Designed by: BSS Checked by: NA

Example:3 1 Sheet No:2 / 2 Reference Chapter: 3

Actual capacity based on net effective area = 23.39 × 0.7 × 0.5 × 4000 = 32,746 Kg So safe capacity, the minimum of the above two actual capacities = 32.75 Ton > 29 Ton

(Section OK)

Use T 150x150x18.4 Kg/m


3-4


Subject: Design of Weld-Connected Tension Member

Example:3 2

Design Code:

Sheet No:1 / 2

Thailand

AISC/ASD (1991)


Reference Chapter: 3

Problem:

Compute the tension capacity of single angle section L 150x150x27.3 Kg/m connected by welds at the ends as the figure below. The length of the member = 10 m Use SYS steel grade with properties: Fy = 2400 Ksc (34 ksi), Fu = 4000 Ksc (56.8 ksi) x

L150x150x27.3 kg/m

T

c.g.

20 cm

Fig. 3.5.Bolt Connected T-section Tension Member for Design Example Error! Not a valid link. Solution:

Computation of Design Strength: Reduction factor U = 1 −

x ≤ 0. 9 L

Where x = distance from centroid of the connected area (cross section) to the shear plane L = length of the connection in the direction of the applied force. For L 150x150x37.3 Kg/m x = 4.14 cm from the outer face of the legs.

U = 1−

4.14 = 0.793 ≈ 0.8 20

Tensile strength = Ag × 0.6 Fy = 34.77 × 0.6 × 2400 = 50 Tons = Ae × 0.5 Fu = 0.8 × 34.77 × 0.5 × 4000 = 55.6 Tons

….(1) ….(2)

The minimum of the above two values gives T = 50 Tons Check for Slenderness Ratio: Radius of gyration rx = ry = r = 4.16 cm Slenderness ratio = 10,00 / 4.16 = 240.38 < 300 OK So the design tensile strength T = 50 Tons.


3-5

5. Design Tables In many design situations, the designer wants to find some section or sections that can approximately carry some tensile load without doing any calculation. The following tables will provide a quick and easy reference for the preliminary selection of the sections, which can be checked in detail later when the end connection requirements are finalized. The tensile strengths have been calculated for two different values of yield strengths Fy =2400 ksc and Fy = 4000 ksc. The tensile strengths are calculated based only on the following formula.

Pt = 0.6 × Fy × A g However the designer must verify the strength using the formula based on the fracture criteria as given below and take the minimum one as the final design strength.

Pt = 0.5 × Fu × Ae

3.1 Tension Capacity (Ton) Based on Ag

H 250x250

64.4

12.309

H 250x250

66.5

12.705

19.20204 19.8198

H 250x250

72.4

13.827

21.57012 24.4998

Section

Wght ( Kg / m)

Fy (2400 Ksc)

Fy (4000 Ksc)

H 250x250

82.2

15.705

C 200x80

24.6

4.70

7.33

H 300x150

32

6.12

9.5472

C 200x90

30.3

5.80

9.04

H 300x150

36.7

7.017

10.94652

C 250x90

34.6

6.61

10.31

H 300x200

56.8

10.857

16.93692

C 250x90

40.2

7.68

11.97

H 300x200

65.4

12.504

19.50624

C 300x90

38.1

7.29

11.37

H 300x300

84.5

16.155

25.2018

C 300x90

43.8

8.36

13.04

H 300x300

87

16.62

25.9272

C 300x90

48.6

9.29

14.48

H 300x300

94

17.97

28.0332

C 380x100

54.5

10.41

16.24

H 300x300

106

20.22

31.5432

C 380x100

67.3

12.86

20.06

H 300x300

106

20.22

31.5432

H 100x100

17.2

3.285

5.12

H 350x175

41.4

7.902

12.32712

H 125x125

23.8

4.5465

7.09

H 350x175

49.6

9.471

14.77476

H 150x100

21.1

4.026

6.28

H 350x175

57.8

11.052

17.24112

H 150x150

31.5

1.521

2.37

H 350x250

69.2

13.2225

20.6271

11.98

H 350x250

79.7

15.225

23.751

106

20.295

31.6602

H 175x175

40.2

7.6815

H 200x100

18.2

3.477

5.42

H 350x350

H 200x100

21.3

4.074

6.35

H 350x350

115

21.9

34.164

131

24.99

38.9844

137

26.085

40.6926

H 200x150

30.6

5.8515

9.12

H 350x350

H 200x200

49.9

9.5295

14.86602

H 350x350

H 200x200

56.2

10.7295

16.73802

H 350x350

156

29.76

46.4256

H 200x200

65.7

12.5535

19.58346

H 400x200

56.6

10.824

16.88544

H 250x125

25.7

4.902

7.64712

H 400x200

66

12.618

19.68408

H 250x125

29.6

5.649

8.81244

H 400x200

75.5

14.424

22.50144

H 250x175

44.1

8.436

13.16016

H 400x300

94.5

18.015

28.1034

H 400x300

107

20.4

31.824


3-6

H 400x400

140

26.775

41.769

T 250x200

44.8

8.568

13.36608

H 400x400

147

28.02

43.7112

T 250x200

51.5

9.8475

15.3621

H 400x400

168

32.16

50.1696

T 250x300

57.1

10.914

17.02584

H 400x400

172

32.805

51.1758

T 250x300

64.2

12.264

19.13184

H 400x400

232

44.31

69.1236

T 300x200

47.3

9.0345

14.09382

H 450x200

66.2

12.645

19.7262

T 300x200

52.8

10.0815

15.72714

H 450x200

76

14.514

22.64184

T 300x200

59.8

11.436

17.84016

H 450x200

88.9

16.995

26.5122

T 300x200

67

12.7995

19.96722

H 450x300

106

20.25

31.59

T 300x300

68.5

13.086

20.41416

H 450x300

124

23.61

36.8316

T 300x300

75.6

14.436

22.52016

H 450x300

145

27.645

43.1262

T 300x300

87.3

16.68

26.0208

H 500x200

79.5

15.195

23.7042

H 500x200

89.6

17.13

26.7228

H 500x200

103

19.695

30.7242

H 500x300

114

21.825

34.047

H 500x300

128

24.525

38.259

H 500x300

150

28.71

44.7876

H 600x200

94.6

18.075

28.197

H 600x200

106

20.16

31.4496

H 600x200

120

22.875

35.685

H 600x200

134

25.605

39.9438

T 125x250

33.2

6.3525

9.9099

T 125x250

36.2

6.4635

10.08306

T 125x250

41.1

7.851

12.24756

T 150x150

16

4.56

7.1136

T 150x150

18.4

3.5085

5.47326

T 150x200

28.4

5.4285

8.46846

T 150x200

32.7

6.252

9.75312

T 175x175

20.7

3.951

6.16356

T 175x175

24.8

4.7355

7.38738

T 175x250

34.6

6.612

10.31472

T 175x250

39.8

7.614

11.87784

T 175x350

53.1

10.1445

15.82542

T 175x350

57.3

10.95

17.082

T 175x350

65.4

12.498

19.49688

T 175x350

68.2

13.041

20.34396

T 175x350

77.9

14.8785

23.21046

T 175x350

79.3

15.15

23.634

T 200x200

28.3

5.412

8.44272

T 200x200

33

6.309

9.84204

T 200x300

47.1

9.0075

14.0517

T 200x300

53.4

10.197

15.90732

T 250x200

39.7

7.596

11.84976


3-7

6. Software Implementation One of the modules included in the SYS Designer software is the “Axial Member Designer” which carries out the design and verification of axial tension and compression members. The program performs internal calculation based on the specification requirements of AISC/ASD described in Chapter 2 and 3 of this manual. As the design procedure for a tension member is quite simple, the procedure adopted in the SYS Designer’s Software can be described below as steps instead of flow diagram. 1)

Compute the net effective area based on the user specified net effective area reduction factor U and the gross area Ag. The user must be aware of that the reduction factor is applied to the gross section area instead of the net area to obtain the net effective area. For example a section has a Ag= 25 cm2 ,area reduced by two 20 mm bolts = 3 cm2 and code specified reduction factor due to shear lag effect U =0.75 , the net effective area will be equal to (25-3)*0.75 = 16.5 cm2 So the use must enter a value of reduction factor = 16.5/25 = 0.66 in this case. For compressive load this reduction factor is not used for any calculation. 1) Compute the capacity of a section based on gross area and yield

strength Fy 2) Compute the capacity of a section based on the effective net area and

ultimate tensile strength Fu 3) Compute the design strength from the minimum of the above two

capacities. 4) Compare the design load with the tensile strength of the section. If the

section strength is more than the required, the section will be selected as the one that satisfies the design load, otherwise section will not be selected. More detailed information for the various input parameters and their significance in the design can be obtained from the software Users Manual. Material and cross-sectional properties are a part of input data. The gross area for any Siam Yamato Standard Steel section is obtained directly from the section database. For the section selected from database, a number of load cases can be defined. The user can select a number of available SYS sections based on one or more selection criteria e.g. by specifying type, weight and /or depth range, and ask the program to check whether the section or sections can fulfill the required strength. Thus the program can be used for two purposes that a structural steel designer require in their routine work: The first is the selection of a list of available sections in SYS products catalogue full filling the user specified section selection criteria as well as the required design strength. The second use is the code verification (check) of a particular selected SYS section against one or more input load cases. For each case, a detailed design calculation report is generated which may be used directly as designers’ calculation sheet for the design approval.


3-8

Chapter

4

Design of Compression Member 4.1. Introduction Design of structural members subjected only to axial compressive force shall be discussed in this section. Structural members subjected to both axial compressive load as well as bending moment shall be discussed in the chapter 6 “Design of Columns”. Axial compressive member means that structural member which is loaded with a load applied through the centroid of the member cross section for which the compressive stress on the section can be assumed uniform. This chapter will describe the fundamental concepts about axial compression members from a structural steel designer’s point of view. Main topic for discussions will be on what are the factors that affect the compressive strength of a member, how a compression member fails, how to compute the effective length and allowable load etc. Some design examples and aids to assist the designer will be given at the end of the chapter.

4.2. Factors Influencing the Strength of Compression Member Strength and behavior of a compression member is influenced by a number of material, member geometry and cross section properties. The interaction between the response and characteristics of the material, the cross section, the method of fabrication, the imperfections etc., in some cases, make the seemingly simple behavior member a complex one. Important parameters influencing the strength of a column are listed below. Unlike the tension member the holes in a compression member has little effect on the buckling strength of the member because as the strut compresses the axial load is transmitted by bearing on the shank of the bolt. 1) Grade of Steel

• •

Stress-strain relations Yield stress

2) Manufacturing method

• • • • •

Hot rolled shape Welded built-up shape Using flame-cut plates Using universal mill plates Cold-straightened shape • Rotorizing (continuous straightening) • Gag (point) straightening 3) Size of shape (cross section area of steel) 4) Cross section geometry (W, H, C,WT etc ) 5) Bending axis

6) Initial out-of-straightness

• Maximum value • Distribution along column length 7) End support conditions • • •

Without sway, pinned or otherwise With sway, pinned or otherwise Restrained ends, with or without sway

8) Actual length of the member

4.3. Modes of Failure of Compression member Euler was the first to recognize that columns could fail through bending or instability rather than yielding. He also showed that the column will remain straight until some critical load is reached, at which time the member may remain straight or assume a half sine wave deflection shape. Before designing any kind of structural member, it is significantly important for the designer to understand the possible mode of failure of the member and the modes which will govern under particular situation and how to provide adequate safety against the most critical one. A steel compression member can fail due to one or a combination of the following failure modes depending upon various factors listed in the previous article: A brief description of each mode of failure will be presented in the subsequent section. • • • • •

Excessive compressive stress Overall flexural buckling of member Local buckling of cross section elements Torsional buckling Flexural-torsional buckling

4.3.1. Excessive compressive stress When the element width-thickness ratio falls within certain critical limit to prevent the local buckling and the member is short and stocky (small slenderness ratio), the Euler’s buckling stress is higher than the yield stress of the material. In such cases the member fails due to excessive compressive stress on the cross section of the members, leading to direct yielding of the material. 4.3.2. Overall flexural buckling of member As slenderness ratio increases the member stability becomes more significant than the direct compressive stresses on the cross sections, so this type of failure occurs only for slender columns. The failure is associated with the deflection due to bending or flexure about the axis corresponding to the smallest radius of gyration – that is the one corresponding the greatest slenderness ratio. This failure is shown in Fig. 4.1. (a). The critical load for such buckling in elastic range is given by the following formula. Euler’s Formula:


4-2

Pcr =

π 2 EI

(4-1)

( KL) 2

Where

L= Actual unsupported length of the member K = Effective length factor E = Modulus of elasticity I = Moment of inertia of the section about the axis of bending (buckling)

4.3.3. Local buckling of cross section elements If the ratio of width to thickness of cross section elements exceed certain critical limit, the corresponding element will buckle locally at a stress lower than at which overall buckling or yielding of member occurs. This type of failure is governed by theory of local buckling of plate elements. The following equation (4-2) gives the critical buckling load for local buckling of cross section plate elements. Local buckling of plate element:

Pcr =

Kπ 2 E  b 12(1 − µ )    t

2

(Units: for any consistent set of units)

2

(4-2)

Where

Pcr = Critical buckling load K = Effective length factor E = Modulus of elasticity

µ = Poisson’s ratio t = Thickness of plate b = Width of plate 4.3.4. Torsional Buckling This is the failure due to twisting which occurs only with symmetrical cross sections with very slender cross- sectional elements. Standard hot rolled shapes are generally not susceptible to torsional buckling but built-up sections with thin plate elements should be investigated for this type of failure. The Fig.. 4.1.(b) shows the torsional buckling type of failure. 4.3.5. Flexural-Torsional buckling In this failure the twisting of the member about the member longitudinal axis is accompanied by flexural buckling. For concentric loads this failure mode can occur only with unsymmetrical cross sections, both those with one-axis of symmetry, such as structural tees, double-angle shapes and equal-leg single angles, and those with no axis of symmetry, such as unequal-leg single angles. In the design calculations all failure cases applicable for a given section should be investigated and designed according to the specific requirements.


4-3

P

P

(a) Flexural Buckling

(b) Torsional Buckling

P

(c) Flexural-Torsional Buckling

Fig. 4.1. Common Buckling Modes of Failure of a Compression Member

4.4. General Procedure for Design of Compression Member 4.4.1. General Concepts The most general procedure to cover all type of cross section shapes for the design of seemingly simple compression member involves considerations for two factors Qa and Qs in addition to the method used for commonly used shapes. Design equation for the allowable stress in a compression member can be expressed in its most general form, as:

Fa = Qa × Qs × Fa

'

(4-3)

Where

′ Fa = Permissible stress as determined by flexural buckling criteria (based on basic equations without Qa ad Qs ) given by the equations (4-4) to (4-6) .

Qa = Effective area correction factor to take into account the non-uniform post buckling stress distribution on various stiffened elements (mostly webs) of the compressed section (for unstiffened elements Qa =1.0 )


4-4

Qs = Stress reduction factor to take into account the local buckling effect of unstiffened elements (e.g projecting flanges) of the cross section based on width-thickness ratio (for stiffened elements Qs =1.0 ) Fa’ is calculated by the following formulae based on the overall cross-section properties and effective length of the member. In the following three formulas, the first formula (4-4) gives the critical buckling slenderness ratio, the second formula (4-5) gives the basic permissible stress for relatively short and medium length columns while the last equation (4-6) give that value for long columns. It is important to note here that the capacity of long columns (case 2) is independent Fy and depends solely on the E, effective length and the cross section properties.

Cc = π

2E Fy

(4-4)

For SYS (standard grade) C c = π

Case 1:

KL ≤ Cc r

Fa ' =

Case 2:

KL ≥ Cc r

Fa ' =

2E 2 × 2.1 × 10 6 =π = 131.42 Fy 2400

 1  KL / r  2    Fy 1 −   2  C c   5 3 KL / r 1  KL / r   + −  3 8 Cc 8  C c 

3

12π 2 E 23( KL / r ) 2

(4-5)

(4-6)

[ Units: Use any consistent set of units for Fy, L and r. For Metric System: Fa and Fy in Ksc, L and r in cm ] For standard hot rolled shapes that are commonly used as axial compression members, the above capacity reduction factors are generally equal to one in most of the cases. However for some shapes such as T, channels and angles, whose capacity may be limited by element width to thickness ratios, these factors need to be considered to conform to the code requirements. A brief description of the various factors used in the general form of the axial member design equation (4-3) is presented in the following sections. 4.4.2. Design Steps: 1) Assume a trial section by judgement and experience or by using design aids for

the compression member given at the end of this chapter. 2) Assume Qa =1.0 for first trial 3) Compute Qs based on the specification formula for the trial section shape. 4) Compute the critical slenderness ratio Cc. 5) Assume or compute the Kx and Ky by using alignment chart or equations. 6) Select correct formula from the two for Fa based on whether Cc is greater than Cact

or not.


4-5

7) Revise the value for Qa by using new value for Fa. If the new Qa computed is within

an acceptable accuracy (tolerance) compared to previous value (that calculated from the previous step) accept Fa (Go to next step ) otherwise revise the Fa (Go to step 4). Repeat the procedure until the desired accuracy is obtained.

8) Compute the capacity based on gross area and the Fa computed from step 7. 9) If the section capacity is more than or equal to the required capacity accept the

section otherwise try new section and repeat the whole calculation until suitable section is found. The design steps explained above has been presented in more concise form as flow diagram below. This flow diagram also forms the basis of internal calculations in SYS Designer software. However the limitations of this procedure is that it does not carry any checks for possible modes of failures by any torsion which is important for section with one axis of symmetry or no axis of symmetry.


4-6

Basic Data Load Data P Material Data E, Fy Member Data K, L Trial Cross Section Assume: Qa=1 Compute: Qs

2E

Compute: Cc =

C

Compute:

Yes

C

act

act

Q Q F a s y

(KL/r)x

=

(KL/r)y

> C

max

No

c

Compute Fa Formula ( 1 ) Below

Compute Fa Formula ( 2 ) Below

Revise: Qa New

Qa New ~ Qa

Compute: Capacity = Fa Ag

No

No

Qa= Qa New

Capacity > Load

Y e s End

Fig. 4.2. Flow Diagram for the Design of Axial Compression Member (AISC/ASD) Hand Book for Design of Steel Structures

4-7

Formula (1)

Fa ' =

Formula (2)

Fa ' =

 1  KL / r  2    Fy 1 −   2  C c   5 3 KL / r 1  KL / r   + −  3 8 Cc 8  C c 

3

12π 2 E 23( KL / r ) 2

4.5. Stress Reduction Factor Qs Commonly used hot-rolled shapes are so proportioned that their elements are thick enough to preclude local buckling yield stress. Two different approaches have been adopted to take into account the elements with local buckling. The first approach is limiting the slenderness ratio b/t of element, totally avoiding the element buckling before member flexural buckling. The second approach is to calculate the effective width of elements stressed enough to buckle, and design taking into account the post buckling strength of the plates which can be considerably larger than their corresponding buckling strength. As the stress reduction factor Qs applies only to the unstiffened elements of a section, it is important to understand the stiffened and unstiffened elements in a shape. Plates supported on both unloaded edges are called stiffened elements while those supported on only one loaded edge are called unstiffened elements. The following figure shows the stiffened and unstiffened elements of H and box shapes.

Unstiffened Element

Stiffened Element Qs= 1

All (4) Elements Stiffened Qs = 1

Fig. 4.3. Stiffened and Unstiffened Elements

The AISC/ASD specified formulas in US units to determine the factor Qs for different shapes are as follows. Permissible critical stress (reduced Fy or usable Fy) FL of the weakest unstiffened element is then calculated by FL = Qs Fy. Notations and Units Fy = Specified yield strength of steel in ksi b = width of the element in inch Hand Book for Design of Steel Structures

4-8

t = thickness of the element in inch 9) For single angles

76 b 155  b  1.340 − 0.00447 Fy t for F < t < F  y y   Qs =   b 155 15,500   for ≥ 2   Fy (b/t) t Fy  

(4-7)

For SYS Grade Fy = 2400 ksc or 34 ksi

b b   1.340 − 0.026 t for 12.9 < t < 26.3 Qs =   b   446.7 for ≥ 26 . 3 2 t   (b/t) 10) For angles or plates projecting form columns or other compression members

and for projecting elements of compression flanges of beam and girders

95 b 195  b  1.415 − 0.00437 Fy t for F < t < F  y y   Qs =   b 195 20,000   for ≥ 2   Fy (b/t) t Fy  

(4-8)


b b   1.415 − .0257 t for 16.1 < t < 33.1 Qs =   b   576.4 for ≥ 33 . 1 2 t   (b/t) 11) For stems of tees

127 b 176  b  1.908 − 0.00715 Fy t for F < t < F  y y   Qs =   b 176   20,000 for ≥   Fy (b/t) 2 t F y  

(4-9)


b b   1.908 − 0.0421 t for 21.6 < t < 29.9 Qs =   b   576.4 for ≥ 29 . 9   (b/t) 2 t


4-9

4.6. Effective Area Factor Qa When column is short enough not to fail by flexural buckling, the effective width of the stiffened elements in the section may be less than the actual width due to the nonuniform stress distribution at various elements of the sections (Karman effect). However the width of the unstiffened elements remain fully effective. So the compressive strength P of a member containing both stiffened and unstiffened (e.g. Channel, H shapes) elements is taken to be the product of the effective area of the cross section which is the sum of the reduced effective area of the stiffened elements and actual unreduced areas of the unstiffened elements and the critical stress FL of the weakest unstiffened element (4-11). Method to compute the critical stress FL has been explained in the previous section. General definition: Qa = Effective area / Gross area

(4-10)

Example: Effective area factor for a channel section In this case of channel section, the top and bottom flanges are fully effective and do not need any reduction but the web depth should be reduced by some amount as shown in the figure.

Qa =

b1

t1

b2e 2

2b1t1 + b2 e t 2 2b1t1 + b2 t 2

b2

t2

b 2e 2

So if Qs is the reduction factor flanges then

FL = Qs .Fy So applying all the effect together the final capacity P becomes as P = FL (2b1t1 + b2 e t 2 )

(4-11)

Fig. 4.4. Effective Area Factor For C

The critical stress FL of the weakest unstiffened element is computed as Qs Fy. Specification formulas to compute the effective width of uniformly compressed stiffened elements of various shapes are given in AISC/ASD specifications which are reproduced here for easy reference. Notations and Units Fy = Specified yield strength of steel in ksi b = width of the element in inch t = thickness of the element in inch For flanges of square and rectangular box sections of uniform thickness

be =

326t  64.9  ≤b 1−  f  (b / t ) f 


(4-12)

4-10

For other uniformly compressed stiffened elements

be =

326t  57.2  1− ≤b  f  (b / t ) f 

(4-13)

For axially loaded compression members f is obtained by dividing the load P by the actual cross-sectional area, rather than the effective area while for flexural members it is computed for the effective cross sections.

4.7. Effective Length Factor K K may be defined as a factor by which the actual length of a compression member is multiplied in order to determine its effective length. K is a reflection of the length of curvature between the point of inflections. K is dependent upon the restraint at the ends of the unsupported (unbraced ) length and the ability of the column to resist lateral movement. Another important criteria for determining K is the side sway condition. Figure . 4.1.illustrates some typical cases of braced and unbraced frames.

P

P 2

P

M

A

P

P

P 2

M=0 K=1

K L

Braced Frame

A

Braced by shearwall

t Section A-A

Unbraced Frame Fig. 4.5. Braced (Non-sway) and Unbraced (Sway) Frames

Side sway prevented (braced) frame is the one that receives other means of lateral support independent of its own stiffness such as special sway bracing, shear wall parallel to the plane of displacement or attachment to a laterally stable structure. For such cases K may be taken at less than or equal to unity. Hand Book for Design of Steel Structures

4-11

For unbraced frames where side sway is not prevented a rational method is employed to determine K. A clear and simplified explanations as to what is meant by a rational method is not available in references. Therefore the engineer is left with his own good structural judgment to determine K for a compression member in an unbraced frames. Considering the column as an individual segment (isolated member or standing alone or truss member) unrelated to the overall structural system, and for an approximate value of K the standard alignment charts and tables provided in below an in appendix can be used. To determine the critical slenderness ratio of a compression member, it is necessary to investigate the effective length with respect to both, XX and YY axis using their respective values of Kx and Ky. The largest slenderness ratio will be used for the design. Model

Example

Factor

1.0

0.85

0.7

2.0

1.0

Fig. 4.6. Typical K Factors for Columns in Various Structures

ACI 318-95 Approach: The following simplified equations for computing the effective length factors for braced and unbraced members are suggested in the ACI 318-95 commentary (Article 10.12) For braced compression members, an upper bound to the effective length factor may be taken as the smaller of the following two expressions:

K = 0.7 + 0.05(G A + GB ) ≤ 1.0 K = 0.85 + 0.05 G min ≤ 1.0 Hand Book for Design of Steel Structures

(4-14)

4-12

where GA and GB are stiffness ratio values at the two ends (top an bottom) of the column and Gmin is the smaller of the two values.

G=

∑( EI / L) Columns ∑( EI / L) Beams

[ Note : K α G

(4-15)

K Increase as G Increases]

For unbraced compression members restrained at both ends, the effective length factor may be taken as For Gm<2

K=

20 − Gm 1 + Gm 20

(4-16)

For Gm ≥ 2

K = 0.9 (1 +Gm )

(4-17)

Gm is the mean of the relative stiffness ratios at two ends. For unbraced compression members hinged at one end, the effective length factor may be taken as:

K = 2.0 + 0.3G

(4-18)

Where G is the relative stiffness at the restrained end.

4.8. Design Examples The examples presented in this section will illustrate design procedures for the design of some typical compression members. The first example will explain the simple procedure where the calculation steps for K factor are not required. In the subsequent examples, more emphasis has been given on the methods to calculate K factor for various cases. Two common tasks, a structure steel designer has to perform are: Verification The determination of the strength of a member for a given geometric and crosssection properties and comparing (verifying) with actual design loads. Design: The design (or selection) of an appropriate cross section for given load and end conditions. In the first procedure, that is the strength determination, the calculation has to be performed only one time. However, design of a compression member fulfilling both functional and cost requirements, may need a number of trial calculations. The designer has to consider various possibilities and select the most appropriate one. The last example is meant to explain the iterative and economic aspects of the design process. The example also describes the various alternatives for the same geometric and load values. If may be noted that a lighter steel section may sometimes provide higher compressive strength than a higher weight section under the same design conditions. Hand Book for Design of Steel Structures

4-13

As described in the preceding sections, the design of any type of compression member needs the determination of the effective length factor K. For this purpose, there may be two cases to choose at first, that is, whether the member to be designed is an isolated element(standing alone e.g. an electrical pole) or a part of a framed system (structure). If the compression member is an isolated one, the effective length can be readily obtained by referring to standard diagrams provided in the previous sections or in appendix. The typical K value may range from 0.5 (both end fix) to 2.0 (for one end fix, another free) depending upon the end conditions. On the other hand, if the member is a compression element forming part of a frame, the determination of the effective length factor requires more calculation steps. For framed members, irrespective of the sway conditions, the first three steps in the calculation for K will be common as explained in Example 4.2 below. The only difference, after first three steps, in the procedure to calculate K for sway and no sway is the selection of the different alignment chart or equations. For the illustration purpose, the frame of “Design Example 4.2” has been analyzed for both braced and un-braced conditions. The frame dimensions, cross-section and the support conditions have been selected to cover various end conditions commonly encountered in practical design. However in all the design example the calculations for two factors Qs and Qa are not included.


4-14


Subject: Design of Axial Compression Member

Example:4.1

Design Code:

Sheet No:1 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Problem:

Design an outdoor stadium electrical pole of height 6 m which carries a lamp and attachment weight of 6 tons at the top and the bottom is rigidly fixed with some other huge structure. Neglect the effect of lateral (wind) loads. Select a hollow circular section of approximate diameter 20 -25 cm and wall thickness of 10 –12 mm. Use SYS steel grade: Fy = 2400 Ksc (34 ksi)

E = 2.1E6 Ksc (2900 ksi)

6 m high 6 tons on top

Fig. 4.7.Electric Lamp Pole for Design Example Error! Not a valid link. Solution:

The design of an isolated compression member does not need any calculations for K factor. The value can be readily read from the standard values based on top and bottom end conditions .For example if one end fixed and other free K = 2 etc.

Cc = π

2E 2 × 2.1 × 10 6 =π = 131.42 2400 Fy

Case 1:

KL ≤ Cc r

Fa =

Case 2:

KL ≥ Cc r

Fa =

 1  KL / r  2    Fy 1 −   2  C c   5 3 KL / r 1  KL / r   + −  3 8 Cc 8  C c  12π 2 E 23( KL / r ) 2

From equation Error! 3

Not a valid link.

From equation (4-6)

Take thickness = 10 mm The following table gives the detailed calculations for Fa and Pc for various trial diameters. Hand Book for Design of Steel Structures

4-15



Example:4.1

Design Code:

Sheet No:2 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Dia.

Area

Ixx

r

Cm

Cm2

Cm4

cm

20

59.69

3645

6.72

357

22

65.97

2700

7.43

323

25

75.38

5438

8.5

282

KL/r


Checked by: NA

Wt

Fa Ksc

Capacity = Fa Ag

Wt./Cap.

Kg/m 46.85

80.74

4,819

9.72

51.78

98.70

6,511

7.95

59.17

129.17

9,737

6.08

-3 X10

Some important remarks: •

For circular section Qa = 1 and Qs = 1 as it does not contain any well defined stiffened and unstiffened elements.

•

Member being an isolated member, no calculations for K factor are required.

•

The weight to capacity ratio is decreasing with increasing diameter as illustrated in the above table.

•

The required capacity is satisfied by the minimum diameter of 22 cm.

•

The slenderness ratio is more than 200, which is generally the limiting value for compression members.

Now it is up to the designer whether to provide 22 cm x 1 cm with capacity just enough for the requirement by accepting a very slender member or go for 25 cm x 1 cm with an additional capacity and weight which indirectly means the additional cost.


4-16



Example:4.2

Design Code:

Sheet No:1 / 3

Thailand

Designed by: BSS

AISC/ASD (1991)


Checked by: NA

Problem:

Compute axial compressive strength of a SYS H 300×150×36.7 section with the following data:

E = 2.1 × 10 6 Ksc (29000 ksi) Fy = 2400 Ksc (34.0 ksi).

L=4 m H150X150

L=3 C

H200X100 L=3

L=3 B

3.0

A

H200X100

H300X150

5.0

H300X150

H200X100 L=3 m

H200X100 L=3

2.0

H200X100

H300X150

L=4 m H150X150

The column is a part of a multi-story structure and is located on the exterior face. The framing conditions for the member in major axis and minor axis are as shown below. The frame is braced against side sway by shear walls.

10

In Major Axis

In Minor Axis

Plane

Plane Braced Frame

Fig. 4.8. Frame for Design Example Error! Not a valid link. Solution: 1. Trial section properties Section

Ix (cm4)

Ix (in4)

Ax (cm2)

Ax(in2)

H 150x150

1640

39.40

51.21

7.94

H 200x100

1840

44.21

27.16

4.21

H 300x150

7210

17.30

46.78

7.25

As in this case, the bracing conditions for major and minor axis are different, we need to consider both the axis separately. Moreover, two segments for minor axis buckling are also not identical with respect to member actual length and end conditions. So critical slenderness ratio shall be selected considering all the three cases and choosing the maximum. Hand Book for Design of Steel Structures

4-17


Subject: Design of Compression Member

Example:4.2

Design Code:

Sheet No:2 / 3

Thailand

AISC/ASD (1991)



2. For segment (A)

Top end

I

 7210  3  1640    +  5 4  4  c = = 2.4 GA = 1840 I ∑  L  3 b

∑  L 

(Note: The stiffness of the member with far end hinged, will be reduced by 25% i.e. multiplied by ¾ ) Bottom end GB = 10 (Approximate value for hinged base) Using alignment chart for braced frame (From Appendix), KA = 0.92 (Note: values of K obtained using ACI (1995) code equations may differ slightly with this one.) 3. For segment (B)

Top end

I

 7210  3  7210    +  3 4  2  c = 4.4 = GA = 1840 I 2 ×   ∑ L  3 b

∑  L 

Bottom end

G B = 10 (Hinged Base) From the alignment chart for braced frame(From Appendix), K B = 0.94 4. For segment (C)

Top end

I

 1640   7210   +  4   2  c = 4.4 GA = = 1840 I 2 ×   ∑ L  3 b

∑  L 

Bottom end

I

 7210  3  7210     + 3 4  2  c = = 4.4 GB = 1840 I 2 ×   ∑ L  3 b

∑  L 

From the alignment chart for braced case, Kc = 0.92 Hand Book for Design of Steel Structures

4-18


Subject: Design of Compression Member

Example:4.2

Design Code:

Sheet No:3 / 3

Thailand

AISC/ASD (1991)



5. Critical KL/r

The next step is to compute the most critical slenderness ratio KL / r for the three segments.

K A L A 0.92 × 5 × 100 = = 37.0 12.4 rx

K B L B 0.94 × 3 × 100 = = 85.71 3.29 ry K C LC 0.92 × 2 × 100 = = 55.92 3.29 ry So, maximum ( KL / r ) act = ( KL / r ) max = 85.71 6. Compression capacity

Cc = π

2E 2 × 2.1 × 10 6 =π = 131.42 so, C c > KL / r Fy 2400

2  1  KL / r  2    85.7     Fy 1 −  Fy 1 − 0.5 ×     2  Cc    131.42    = Fa = 3 3 5 3  85.7  1  85.7  5 3 KL / r 1  KL / r  +   −   + −  3 8  131.42  8  131.42  3 8 Cc 8  Cc 

= 0.41 Fy Fa = 0.41 x Fy = 0.41 x 2400 = 984 ksc. Compressive strength Pc = Fa × A = 984 × 46.78 = 46.03 ton (101.26 kips) The design safe compressive load on the SYS H 300x150x36.7 Kg/m = 46.03 Ton (101.26 kips)

(Note: Calculations for Qs and Qa are not included in the design as they are not essential for most standard hot rolled sections.)


4-19



Example:4.3

Design Code:

Sheet No:1 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Problem:

Design (select) the lightest SYS H Section to carry safely, an axial compressive load of 40 Ton (66.0 kips) with the following data.

L x = 6m. (19.68 ft.)

K x = 1.0.

L y = 3m. (9.84 ft.)

K y = 0.65.

E = 2.1E6 Ksc (29000 ksi)

Fy = 2400 Ksc (34 ksi)

Solution:

Design of a compression member is a trail and error procedure. For a given member end conditions, two important parameters related to section which affect the capacity are the radius of gyrations and the gross cross section area. In this example the effective lengths of the member are given directly but if required the designer can refer to the previous examples for the procedure to compute K. First Trial Section, SYS H 300x150x36.7 (24.7 lb/ft) Section properties from SYS steel section catalogue or chapter 2 of this manual: Ax = 46.78 cm2 (7.25 in2) rx = 12.4 cm (4.88 in) ry = 3.29 cm (1.3 in) K x Lx rx

K y Ly ry

1 × 6 × 100

=

=

12.4

= 48.38

0.65 × 3 × 100 = 59.27 3.29

(Any consistent unit can be used here to compute KL/r.) So critical KL / r = 59.27 From the previous example, for Fy=2400 ksc, Cc =131.42 As KL / r < C c

Fa =

2  1  KL/r    Fy 1−   2  Cc  





3 3  KL/r  1  KL/r  −   +  3 8  Cc  8  Cc  5

=

2  59.27   1− 0.5×    × Fy   131.42  

3 3  59.27  1  59.27  +  −   3 8  131.42 8  131.42 5

= 0.493 x Fy = 1183.20 ksc (16.79 ksi) Axial Capacity Pc = Fa × Ag = 1183.20 x 46.78 = 56.38 Ton (124.03 kips) As 56.03 > 40, we have try to smaller section. Proceeding in the similar way, the following table can be obtained. Hand Book for Design of Steel Structures

4-20

SYS

Subject: Design Member


Axial

Design Code:

Thailand

Section Name

of

Designed by: BSS

AISC/ASD (1991)

Axial Compressive Capacity

Compression

Example:4.3 Sheet No:2 / 2

Checked by: NA


Weight Capacity

Weight

Remark

Ton

Kips

kg/m

lb/ft

(Normalized)

H 250x125x29.6

42.84

94.16

29.6

19.9

0.690

H 200x150x30.6

43.76

96.27

30.6

20.6

0.699

H 150x150x31.5

37.57

82.65

31.5

21.2

0.838

Max.

H 300x150x36.7

56.38

124.03

36.7

24.7

0.650

Min.

H 175x175x40.2

54.7

120.34

40.2

27.0

0.734

The table is presented to illustrate the fact that in some cases, a much lighter section can carry more axial compressive load than a heavier section If other section criteria are not governing, the designer should select the lightest section satisfying the load capacity. We should choose the section with the smallest weight to capacity ratio to make the design economic. So use: SYS H250 x 125 x 29.6 kg/m Actual Capacity = 42.84 Ton (94.248 kips) > 40 Ton (88 kips)


4-21

4.9. Design Tables The design of a typical steel compression member using specification equations is a trial-and -error procedure. The effective length factor “K” for a compression member in a frame depends upon the bending stiffness of the member relative to the stiffness of other members that connect to the ends of the member. Another important cross section parameter for design is the radius of gyration “r” of the cross-section. So unless the size of the member is known, the slenderness ratio kL/r and other stress calculation can not be carried out. That necessitates a preliminary selection (assumption) of the size of the member to be designed, which depends upon the experience and the judgement of the designer. However, “The tables for the design of compression members" given in this section may furnish a tool to assist the designer to make a preliminary selection that shall need minimum revision later for detailed design. In certain design situation like members of a truss, where the effective length factor k can be assumed in advance, even the final selection of member size may be based on the values in these tables. Another important application of these design tables provided here, can be to provide the designer, a set of sections of comparable compressive strength so the detailed design checks can be limited to only those shapes. This may save the designer time, especially when calculations are carried out by hand. Standard hot-rolled sections are generally so proportioned that their bending strength in major axis is significantly higher than in minor axis. As the compression capacity calculations are based on first critical buckling mode, generally, the strength is governed by minor axis buckling strength. However, the compressive strength can be increased considerably by providing lateral bracing at some intermediate points so as to reduce the effective length for minor axis buckling. By keeping this practical design requirement in mind, the design tables for compression member includes two common cases: Equal effective length on both major and minor axis and minor axis effective length half of major axis effective length i.e. the member is braced laterally at midpoint. It should be noted that the member lengths shown at he top of the tables are the effective lengths KxLx and KyLy, in their respective axes. Although some of the shapes are not used commonly as compression member, they have also been included in design tables for the purpose of completeness. It is very important to note here that all the listed capacities are calculated based on flexural or bend buckling mode of the member. No reduction or checks for other modes of failure are included in the capacities shown in the following tables though they are important for unsymmetrical shapes like T or L etc. For such shapes the capacity values can be used as preliminary selection. In other words the following compression capacities are calculated based only on formulae Eqs nos 4-4 to 4-6. Moreover the effect of slender stiffened and unstiffened cross sectional elements (Qa and Qs) are also not included as they are very few sections that require these factors. [Note: The availability of the sections can be checked from Chapter 2 – Table for ‘Properties of SYS Steel Sections’ ].


4-22

Table 4.1: Compression Capacity (Ton) For C Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax cm2

C 50x25

3.86

4.92

C 75x40

6.92

8.818

C 100x50

9.36

C 125x65

ry

KLx=1

KLx=2

cm

cm

Kly=1

Kly=2

1.85

0.71

2.55

0.64

0.28

1.14

0.16

0.64

0.10

0.41

0.07

0.28

0.05

0.21

0.04

0.16

0.03

0.13

2.92

1.17

8.89

3.11

1.38

5.79

0.78

3.11

0.50

1.99

0.35

1.38

0.25

1.01

0.19

0.78

0.15

0.61

11.92

3.97

1.48

13.47

6.72

2.99

10.59

1.68

6.72

1.08

4.30

0.75

2.99

0.55

2.19

0.42

1.68

0.33

1.33

13.4

17.11

4.98

1.9

20.88

14.66

7.07

18.05

3.98

14.66

2.54

10.18

1.77

7.07

1.30

5.19

0.99

3.98

0.79

3.14

C 150x75

18.6

23.71

6.03

2.22

29.92

23.11

13.37

26.80

7.52

23.11

4.81

18.86

3.34

13.37

2.46

9.82

1.88

7.52

1.49

5.94

C 150x75

24

30.59

5.86

2.19

38.50

29.54

16.79

34.40

9.44

29.54

6.04

23.93

4.20

16.79

3.08

12.33

2.36

9.44

1.87

7.46

C 180x75

21.4

27.2

7.12

2.19

34.24

26.27

14.93

30.59

8.40

26.27

5.37

21.28

3.73

14.93

2.74

10.97

2.10

8.40

1.66

6.63

C 200x80

24.6

31.33

7.88

2.32

39.85

31.43

20.24

35.99

10.85

31.43

6.95

26.20

4.82

20.24

3.54

14.18

2.71

10.85

2.14

8.58

C 200x90

30.3

38.65

8.02

2.68

50.29

41.90

30.97

46.43

17.87

41.90

11.44

36.75

7.94

30.97

5.83

24.50

4.47

17.87

3.53

14.12

C 250x90

34.6

44.07

9.74

2.58

57.03

46.92

33.67

52.38

18.88

46.92

12.08

40.68

8.39

33.67

6.17

24.66

4.72

18.88

3.73

14.92

C 250x90

40.2

51.17

9.56

2.54

66.06

54.05

38.27

60.54

21.25

54.05

13.60

46.63

9.44

38.27

6.94

27.75

5.31

21.25

4.20

16.79

C 300x90

38.1

48.57

11.5

2.52

62.63

51.09

35.93

57.32

19.85

51.09

12.71

43.96

8.82

35.93

6.48

25.93

4.96

19.85

3.92

15.69

C 300x90

43.8

55.74

11.5

2.54

71.96

58.87

41.69

65.94

23.15

58.87

14.81

50.80

10.29

41.69

7.56

30.23

5.79

23.15

4.57

18.29

C 300x90

48.6

61.9

11.3

2.48

79.62

64.56

44.73

72.70

24.50

64.56

15.68

55.25

10.89

44.73

8.00

32.00

6.13

24.50

4.84

19.36

C 380x100

54.5

69.39

14.5

2.78

90.73

76.47

57.94

84.16

34.52

76.47

22.09

67.73

15.34

57.94

11.27

47.03

8.63

34.52

6.82

27.27

8.30

33.20

C 380x100

67.3

85.71

rx

14.3

2.76

111.96

94.16

KLx=3

KLx=4

KLy=3 KLy=1.5 KLy=4 KLy=2

71.01

103.76

42.02

94.16

KLx=5

KLx=6


26.89

83.24

18.68

71.01

KLx=7

KLx=8

KLx=9

KLy=7 KLy=3.5 KLy=8 KLy=4 KLy=9 KLy=4.5

13.72

57.37

10.51

42.02

[Note: The availability of the sections can be checked from Chapter 2 – Tables for ‘Properties of SYS Steel Sections’].


4-23

Table 4.2: Compression Capacity (Ton) For I Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

I 100x75

12.9

16.43

4.14

1.7

19.46

12.36

5.43

16.24

3.06

12.36

1.96

7.82

1.36

5.43

1.00

3.99

0.76

3.06

0.60

2.41

I 125x75

16.1

20.45

5.13

1.68

24.14

15.13

6.60

20.06

3.71

15.13

2.38

9.51

1.65

6.60

1.21

4.85

0.93

3.71

0.73

2.94

I 150x75

17.1

21.83

6.12

1.62

25.47

15.28

6.56

20.87

3.69

15.28

2.36

9.44

1.64

6.56

1.20

4.82

0.92

3.69

0.73

2.91

I 150x125

36.2

46.15

6.18

2.89

60.64

51.68

40.08

56.51

24.81

51.68

15.88

46.20

11.03

40.08

8.10

33.29

6.20

24.81

4.90

19.60

I 180x100

23.6

30.06

7.45

2.14

37.66

28.54

15.75

33.49

8.86

28.54

5.67

22.82

3.94

15.75

2.89

11.57

2.22

8.86

1.75

7.00

I 200x100

26

33.06

8.11

2.05

41.06

30.35

15.90

36.17

8.94

30.35

5.72

23.60

3.97

15.90

2.92

11.68

2.24

8.94

1.77

7.07

I 200x150

50.4

64.16

8.34

3.43

85.90

76.19

63.79

81.41

48.83

76.19

31.09

70.31

21.59

63.79

15.86

56.63

12.15

48.83

9.60

40.31

I 250x125

38.3

48.79

10.3

2.63

63.31

52.43

38.21

58.31

21.72

52.43

13.90

45.73

9.65

38.21

7.09

28.37

5.43

21.72

4.29

17.16

I 250x125

55.5

70.73

10.2

2.76

92.39

77.70

58.60

85.63

34.68

77.70

22.19

68.69

15.41

58.60

11.32

47.35

8.67

34.68

6.85

27.40

I 300x150

48.3

61.58

12.4

3.09

81.56

70.72

56.76

76.55

39.70

70.72

24.22

64.11

16.82

56.76

12.36

48.64

9.46

39.70

7.48

29.90

I 300x150

65.5

83.47

12.3

3.26

111.19

97.59

80.16

104.90

59.01

97.59

36.54

89.34

25.38

80.16

18.64

70.07

14.27

59.01

11.28

45.11

I 300x150

76.8

97.88

12.2

3.32

130.63 115.10

95.22

123.45

71.15 115.10 44.44

105.68

30.86

95.22

22.67

83.73

17.36

71.15

13.72

54.87

I 350x150

58.5

74.58

14.3

3.07

98.70

68.37

92.58

47.49

28.95

77.37

20.11

68.37

14.77

58.44

11.31

47.49

8.94

35.75

I 350x150

87.2

111.1

14.2

3.26

147.99 129.90 106.70

139.63

78.55 129.90 48.64

118.91

33.78 106.70

24.81

93.27

19.00

78.55

15.01

60.05

I 400x150

72

91.73

16.2

3.07

121.40 105.10

84.10

113.88

58.41 105.10 35.61

95.16

24.73

84.10

18.17

71.88

13.91

58.41

10.99

43.97

I 400x150

95.8

122.1

16.1

3.18

162.22 141.61 115.12

152.70

82.89 141.61 50.86

129.07

35.32 115.12

25.95

99.76

19.87

82.89

15.70

62.79

I 450x175

91.7

116.8

18.3

3.6

157.08 140.59 119.60

149.44

94.40 140.59 62.35

130.63

43.30 119.60

31.81

107.53

24.36

94.40

19.25

80.13

I 450x175

115

146.1

18.3

3.72

197.04 177.36 152.38

187.92 122.45 177.36 83.28

165.49

57.84 152.38

42.49

138.03

32.53 122.45 25.70

105.57

I 600x190

133

169.4

24.1

3.81

228.92 206.87 178.92

218.69 145.51 206.87 106.36 193.59

70.34 178.92

51.68

162.89

39.57 145.51 31.26

126.70

I 600x190

176

224.5

24.1

3.97

304.38 276.82 241.98

291.58 200.47 276.82 152.08 260.26 101.22 241.98

74.36

222.05

56.93 200.47 44.99

177.18

85.45

KLy=3 KLy=1.5 KLy=4 KLy=2 KLy=5 KLy=2.5 KLy=6 KLy=3

KLx=7

85.45


[Note: The availability of the sections can be checked from Chapter 2 – Table s for ‘Properties of SYS Steel Sections’].


4-24

Table 4.3: Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

**H 100x50

9.3

11.85

3.98

1.12

11.62

3.83

1.70

6.80

0.96

3.83

0.61

2.45

0.43

1.70


0.31

1.25

0.24

0.96

0.19

0.76

H 100x100

17.2

21.9

4.18

2.47

28.15

22.79

15.73

24.16

8.60

20.42

5.50

16.09

3.82

10.95

2.81

8.04

2.15

6.16

1.70

4.86

**H 125x60

13.2

16.84

4.95

1.32

18.13

7.55

3.36

13.25

1.89

7.55

1.21

4.83

0.84

3.36

0.62

2.47

0.47

1.89

0.37

1.49

H 125x125

23.8

30.31

5.29

3.11

40.17

34.89

28.08

36.28

19.78

32.66

12.08

28.54

8.39

23.90

6.16

17.83

4.72

13.65

3.73

10.78 7.67

H 148x100

21.1

26.84

6.17

2.37

34.27

27.28

18.02

31.06

9.70

27.28

6.21

22.95

4.31

18.02

3.17

12.67

2.43

9.70

1.92

**H 150x75

14

17.85

6.11

1.66

20.99

12.98

5.63

17.36

3.17

12.98

2.03

8.10

1.41

5.63

1.03

4.14

0.79

3.17

0.63

2.50

H 150x150

31.5

40.14

6.39

3.75

54.17

48.83

42.04

50.25

33.93

46.63

23.25

42.53

16.15

37.98

11.86

32.97

9.08

27.47

7.18

20.84

**H 175x90

18.1

23.04

7.26

2.06

28.64

21.24

11.19

25.26

6.29

21.24

4.03

16.57

2.80

11.19

2.05

8.22

1.57

6.29

1.24

4.97

H 175x175

40.2

51.21

7.5

4.38

69.92

64.46

57.59

65.95

49.45

62.29

40.06

58.18

28.10

53.64

20.65

48.68

15.81

43.28

12.49

37.45

H 194x150

30.6

39.01

8.3

3.61

52.47

46.99

40.01

49.93

31.63

46.99

20.94

43.68

14.54

40.01

10.68

36.00

8.18

31.63

6.46

26.89

H 198x99

18.2

23.18

8.26

2.21

29.23

22.53

12.95

26.16

7.29

22.53

4.66

18.34

3.24

12.95

2.38

9.52

1.82

7.29

1.44

5.76

H 200x100

21.3

27.16

8.24

2.22

34.27

26.48

15.32

30.70

8.62

26.48

5.51

21.61

3.83

15.32

2.81

11.25

2.15

8.62

1.70

6.81

H 200x200

49.9

63.53

8.62

5.02

87.47

81.87

74.89

83.42

66.69

79.71

57.31

75.56

46.72

70.98

33.65

66.01

25.76

60.64

20.35

54.87

H 200x204

56.2

71.53

8.35

4.88

98.33

91.76

83.58

93.54

73.94

89.17

62.90

84.27

50.41

78.87

35.80

72.99

27.41

66.64

21.66

59.80

H 208x202

65.7

83.69

8.83

5.13

115.37 108.20

99.30

110.22

88.83 105.50 76.89

100.21

63.44

94.40

46.29

88.08

35.44

81.27

28.00

73.95

H 244x175

44.1

56.24

10.4

4.18

76.54

62.04

73.56

52.44

41.31

66.28

28.11

62.04

20.65

57.43

15.81

52.44

12.49

47.08

H 244x252

64.4

82.06

10.3

5.98

113.96 108.27 101.28

109.87

93.12 106.15 83.87

102.01

73.55

97.47

62.13

92.56

47.22

87.28

37.31

81.63

H 248x124

25.7

32.68

10.4

2.79

42.75

27.39

39.67

16.37

10.48

31.98

7.28

27.39

5.35

22.29

4.09

16.37

3.23

12.94

H 248x249

66.5

84.7

10.8

6.28

117.87 112.38 105.65

113.91

97.81 110.31 88.94

106.32

79.08 101.95

68.20

97.22

56.24

92.15

42.47

86.73

H 250x125

29.6

37.66

10.4

2.79

49.27

45.72

18.87

36.85

8.39

6.16

25.68

4.72

18.87

3.73

14.91

70.13

36.07

41.57

31.56

70.13

36.07

41.57

12.08

31.56

[Note: The availability of the sections can be checked from Chapter 2 – Table s for ‘Properties of SYS Steel Sections’ **- Currently not available].


4-25

Table 4.3 (Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

Kly=1

H 250x250

72.4

92.18

10.8

6.29

128.29 122.32 115.02

123.97 106.51 120.06 96.88

115.71

86.17 110.95

74.36

105.81

61.38 100.28 46.37

94.39

H 250x255

82.2

104.7

10.5

6.09

145.52 138.44 129.75

140.44 119.61 135.82 108.13 130.68

95.33 125.05

81.20

118.96

65.61 112.41 49.37

105.42

H 294x200

56.8

72.38

12.5

4.70

99.28

96.01

47.91

83.53

33.63

78.56

25.75

20.34

67.48

H 294x302

84.5

107.7

12.5

7.16

150.62 144.76 137.66

146.57 129.44 142.85 120.17 138.75 109.92 134.26

98.69

129.43

86.47 124.26 73.19

118.76

92.28


KLx=7

83.53

73.21

92.28

61.37

88.11


73.21

H 298x149

32

408

3.9

1.04

379.25 113.79

50.58

202.30

28.45 113.79 18.21

72.83

12.64

50.58

9.29

37.16

7.11

28.45

5.62

22.48

H 298x201

65.4

83.36

12.6

4.77

114.44 106.56

96.71

110.76

85.09 106.56 71.78

101.86

56.67

96.71

39.93

91.11

30.57

85.09

24.16

78.65

H 298x299

87

110.8

13.0

7.50

155.20 149.54 142.70

151.20 134.80 147.58 125.92 143.58 116.09 139.22 105.36

134.53

93.71 129.50 81.09

124.17

H 300x150

36.7

46.78

12.4

3.30

62.38

39.71

8.17

6.46

25.83

H 300x300

94

119.8

13.0

7.51

167.81 161.69 154.30

163.50 145.76 159.60 136.15 155.28 125.54 150.58 113.94

145.52 101.35 140.10 87.71

134.35

H 300x305

106

134.8

12.6

7.26

188.61 181.41 172.69

183.56 162.60 178.96 151.23 173.87 138.66 168.33 124.91

162.35 109.95 155.96 93.70

149.16

H 304x301

106

134.8

13.2

7.57

188.88 182.07 173.86

184.09 164.37 179.76 153.70 174.97 141.91 169.75 129.04

164.13 115.07 158.13 99.94

151.74

H 336x249

69.2

88.15

14.5

5.92

122.37 116.17 108.55

119.46

104.25

39.29

94.75

H 338x351

106

135.3

14.4

8.33

190.12 184.09 176.87

185.84 168.57 182.00 159.26 177.77 149.00 173.18 137.83

168.24 125.76 162.97 112.77

157.38

H 340x250

79.7

101.5

14.6

6.00

140.98 133.97 125.35

137.69 115.30 133.97 103.90 129.85

120.50

H 344x348

115

146

15.1

8.76

205.44 199.35 192.09

H 344x354

131

166.6

14.6

8.42

H 346x174

41.4

52.68

14.5

3.88

H 350x175

49.6

63.14

14.7

H 350x350

137

173.9

15.2

H 350x357

156

198.4

14.7

54.88

45.27

58.91

33.63

54.88

20.93

99.65 116.17 89.56

50.33

112.53

14.53

45.27

78.30 108.55

91.20 125.35

10.68

65.84

77.14

49.72

33.63

99.65

58.73 115.30 46.41

109.76

201.05 183.76 197.15 174.43 192.87 164.17 188.22 153.01

183.23 140.97 177.90 128.04

172.25

234.17 226.85 218.10

228.94 208.03 224.26 196.74 219.12 184.31 213.53 170.78

207.52 156.16 201.11 140.44

194.30

71.29

64.60

56.14

68.19

46.03

64.60

34.21

60.58

22.66

56.14

16.65

51.29

12.74

46.03

10.07

40.35

3.95

85.57

77.76

67.87

81.94

56.10

77.76

42.36

73.06

28.15

67.87

20.68

62.22

15.83

56.10

12.51

49.48

8.84

244.76 237.60 229.06

239.58 219.27 234.98 208.32 229.93 196.27 224.46 183.17

218.58 169.04 212.31 153.88

205.66

8.52

278.97 270.39 260.13

272.78 248.35 267.28 235.15 261.23 220.62 254.66 204.80

247.59 187.72 240.05 169.36

232.06

[Note: The availability of the sections can be checked from Chapter 2 – Tables for ‘Properties of SYS Steel Sections’ **- Currently not available].


4-26

Table 4.3(Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



H 354x176

57.8

73.68

14.8

4.00

99.96

91.02

79.72

H 386x299

94.3

120.1

16.8

7.21

168.00 161.53 153.69

H 388x402

140

178.5

16.6

9.56

H 390x300

107

136

16.9

7.28

H 394x398

147

186.8

17.3

10.06

263.74 257.22 249.54

H 394x405

168

214.4

16.7

9.65

302.42 294.53 285.20

H 396x199

56.6

72.16

16.6

4.48

98.68

91.22

95.80

66.26

91.02

24.80

73.26

18.99

15.00

58.72

164.95 144.60 161.53 134.38 157.77 123.06 153.69 110.67

149.29

97.19 144.60 82.55

139.63

251.72 245.07 237.20

246.99 228.20 242.78 218.16 238.17 207.13 233.19 195.17

227.84 182.29 222.15 168.51

216.13

190.31 183.08 174.32

186.90 164.19 183.08 152.78 178.88 140.16 174.32 126.35

169.42 111.33 164.19 95.04

158.64

259.03 240.78 254.87 231.03 250.34 220.33 245.44 208.73

240.20 196.27 234.62 182.95

228.71

296.78 274.54 291.78 262.65 286.30 249.60 280.38 235.44

274.03 220.20 267.28 203.90

260.12

81.87

95.21

70.80

58.06

86.77

41.48

81.87

30.47

76.54

23.33

70.80

18.43

64.65

95.95

111.17

83.33 106.62 68.82

101.54

49.77

95.95

36.57

89.88

28.00

83.33

91.22

50.59

85.64

33.75

79.72

66.26

H 400x200

66

84.12

16.8

4.55

115.14 106.62

22.12

76.32

H 400x400

172

218.7

17.5

10.12

308.82 301.25 292.33

303.36 282.17 298.54 270.84 293.28 258.43 287.61 244.98

281.52 230.52 275.05 215.08

268.21

H 400x408

197

250.7

16.8

9.74

353.70 344.59 333.82

347.14 321.53 341.35 307.82 335.01 292.77 328.15 276.45

320.80 258.89 312.98 240.12

304.70

H 404x201

75.5

96.16

16.9

4.59

131.71 122.11 110.09

127.23

103.25

H 414x405

232

295.4

17.7

10.24

417.24 407.17 395.32

410.03 381.83 403.66 366.80 396.71 350.33 389.21 332.48

**H 428x407

283

360.7

18.2

10.45

509.70 497.71 483.63

H 434x299

106

135

18.6

7.04

188.69 181.18 172.06

H 440x300

124

157.4

18.9

7.18

H 446x199

66.2

84.3

18.5

H 446x302

145

184.3

19.0

H 450x200

76

96.76

18.6

4.40

H 456x201

88.9

113.3

18.9

4.52

**H 458x417

415

528.6

18.8

10.70

25.81

87.99

381.17 313.31 372.63 292.84

363.59

501.21 467.61 493.68 449.78 485.47 430.25 476.61 409.10

467.14 386.40 457.06 362.15

446.41

185.15 161.50 181.18 149.59 176.81 136.40 172.06 121.95

166.95 106.20 161.50 89.07

155.71

220.15 211.62 201.28

216.12 189.30 211.62 175.81 206.66 160.89 201.28 144.55

195.49 126.76 189.30 107.44

182.74

4.33

115.02 105.86

110.76

7.24

257.85 247.97 236.01

94.36

95.89 122.11 79.56

80.73 105.86 64.98

116.38

100.39

60.97 110.09

45.20

94.36

42.66

33.21

87.80

32.66

25.42

95.89

20.09

73.12

253.19 222.16 247.97 206.57 242.24 189.32 236.01 170.44

229.31 149.90 222.16 127.60

80.73

214.58

132.15 121.87 108.96

127.37

93.68 121.87 76.04

115.73

53.49 108.96

39.30

101.61

30.09

23.77

85.16

155.01 143.42 128.89

149.61 111.71 143.42 91.93

136.50

66.08 128.89

48.55

120.62

37.17 111.71 29.37

102.15

747.32 730.27 710.27

735.59 687.55 725.05 662.29 713.58 634.63 701.21 604.70

688.00 572.57 673.95 538.29

659.12

93.68

[Note: The availability of the sections can be checked from Chapter 2 – Table for ‘Properties of SYS Steel Sections’ **- Currently not available].


4-27

Table 4.3 (Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation[Note: * = Not Available] Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

H 482x300

114

145.5

20.4

6.82

203.13 194.68 184.39

199.15 172.46 194.68 158.99 189.75 144.06 184.39 127.67

178.62 109.77 172.46 85.94

165.91

H 488x300

128

163.5

20.8

7.04

228.53 219.44 208.41

224.24 195.62 219.44 181.20 214.15 165.25 208.41 147.76

202.22 128.70 195.62 107.96

188.61

H 494x302

150

191.4

20.9

7.10

267.61 257.09 244.33

262.65 229.55 257.09 212.89 250.98 194.46 244.33 174.26

237.18 152.26 229.55 128.34

221.45

H 496x199

79.5

101.3

20.3

4.26

138.06 126.82 112.67

132.83

104.60

23.39

86.52

**H 498x432

605

770.1

19.7

11.07

1089.5 1065.7 1037.9 1073.57 1006.6 1059.0 971.33 1043.37 933.00 1026.4 891.55 1008.36 847.10 989.17 799.70

968.91

H 500x200

89.6

114.2

20.5

4.33

155.81 143.41 127.82

150.04 109.35 143.41 88.01

135.99

61.22 127.82

44.98

118.94

34.43 109.35 27.21

99.05

H 506x201

103

131.3

20.7

4.43

179.42 165.64 148.33

173.00 127.85 165.64 104.24 157.40

73.80 148.33

54.22

138.48

41.51 127.85 32.80

116.45

H 582x300

137

174.5

24.3

6.63

243.37 232.85 220.01

238.41 205.10 232.85 188.26 226.70 169.58 220.01 149.04

212.81 126.56 205.10 97.51

196.92

H 588x300

151

192.5

24.8

6.85

268.79 257.67 244.15

263.55 228.45 257.67 210.74 251.19 191.12 244.15 169.58

236.56 146.07 228.45 114.68

219.84

H 594x302

175

222.4

24.8

6.90

310.64 297.94 282.50

304.65 264.59 297.94 244.39 290.54 222.01 282.50 197.46

273.84 170.68 264.59 141.47

254.77

H 596x199

94.6

120.5

23.9

4.05

163.63 149.27 131.15

156.96 109.57 149.27 84.49

140.65

56.64 131.15

41.61

120.78

31.86 109.57 25.17

97.49

H 600x200

106

134.4

24.0

4.12

182.72 167.07 147.32

175.45 123.85 167.07 96.60

157.67

65.22 147.32

47.92

136.04

36.69 123.85 28.99

110.72

H 606x201

120

152.5

24.3

4.22

207.71 190.56 168.97

199.73 143.35 190.56 113.68 180.29

77.81 168.97

57.17

156.66

43.77 143.35 34.58

129.04

H 612x202

134

170.7

24.6

4.32

232.85 214.24 190.84

224.19 163.10 214.24 131.05 203.10

90.97 190.84

66.83

177.50

51.17 163.10 40.43

147.63

H 692x300

166

211.5

28.5

6.53

294.80 281.78 265.89

288.67 247.41 281.78 226.54 274.18 203.36 265.89 177.86

256.96 149.91 247.41 114.68

237.27

H 700x300

185

235.5

29.2

6.77

328.70 314.90 298.10

322.20 278.59 314.90 256.58 306.86 232.17 298.10 205.37

288.67 176.09 278.59 137.31

267.89

H 792x300

191

243.4

32.3

6.39

338.97 323.53 304.66

331.71 282.69 323.53 257.85 314.50 230.24 304.66 199.82

294.04 166.43 282.69 126.25

270.62 301.49

95.89 126.82 76.47

120.08

52.63 112.67


38.67

29.61

95.89

H 800x300

210

267.4

33.0

6.61

372.90 356.73 337.00

365.28 314.07 356.73 288.18 347.28 259.45 337.00 227.86

325.92 193.28 314.07 148.75

**H 890x299

213

270.9

35.7

6.17

376.72 358.70 336.61

368.25 310.85 358.70 281.70 348.13 249.23 336.61 213.40

324.17 173.92 310.85 130.95

296.69

**H 900x300

243

309.8

36.4

6.38

431.41 411.72 387.65

422.15 359.62 411.72 327.93 400.20 292.70 387.65 253.90

374.11 211.29 359.62 160.19

344.22

**H 912x302

286

364

37.0

6.57

507.47 485.24 458.11

497.01 426.57 485.24 390.95 472.25 351.40 458.11 307.90

442.87 260.26 426.57 199.61

409.26


4-28

Table 4.4(Continued): Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

T 50x100

8.6

10.95

1.21

2.47

11.27

4.13

1.83

1.83

1.03

1.03

0.66

0.66

0.46

0.46


0.34

0.34

0.26

0.26

0.20

0.20

T 62.5x125

11.9

15.16

1.52

3.11

17.31

9.02

4.01

4.01

2.25

2.25

1.44

1.44

1.00

1.00

0.74

0.74

0.56

0.56

0.45

0.45

T 75x100

10.5

13.42

1.96

2.37

16.50

11.85

5.90

5.90

3.32

3.32

2.12

2.12

1.47

1.47

1.08

1.08

0.83

0.83

0.66

0.66

T 75x150

15.8

20.07

1.82

3.75

24.23

16.43

7.61

7.61

4.28

4.28

2.74

2.74

1.90

1.90

1.40

1.40

1.07

1.07

0.85

0.85

T 87.5x175

20.1

25.61

2.12

4.38

32.03

24.15

13.17

13.17

7.41

7.41

4.74

4.74

3.29

3.29

2.42

2.42

1.85

1.85

1.46

1.46

T 99x99

9.1

11.59

2.84

2.21

14.61

11.26

6.48

9.89

3.64

6.02

2.33

3.85

1.62

2.67

1.19

1.96

0.91

1.50

0.72

1.19

T 100x100

10.7

13.58

2.9

2.22

17.14

13.24

7.66

11.83

4.31

7.35

2.76

4.70

1.91

3.27

1.41

2.40

1.08

1.84

0.85

1.45

T 97x150

15.3

19.51

2.53

3.61

25.17

20.56

14.51

14.51

8.04

8.04

5.14

5.14

3.57

3.57

2.62

2.62

2.01

2.01

1.59

1.59

T 100x200

24.9

31.77

2.41

5.02

40.67

32.61

21.95

21.95

11.88

11.88

7.60

7.60

5.28

5.28

3.88

3.88

2.97

2.97

2.35

2.35

T 100x204

28.1

35.77

2.67

4.88

46.52

38.71

28.53

28.53

16.41

16.41

10.50

10.50

7.29

7.29

5.36

5.36

4.10

4.10

3.24

3.24

T 104x202

32.8

41.85

2.45

5.13

53.72

43.36

29.68

29.68

16.17

16.17

10.35

10.35

7.19

7.19

5.28

5.28

4.04

4.04

3.19

3.19

T 124x124

12.8

16.34

3.57

2.79

21.38

18.04

13.70

16.65

8.19

13.08

5.24

8.58

3.64

5.96

2.67

4.38

2.05

3.35

1.62

2.65

T 125x125

14.8

18.83

3.63

2.79

24.63

20.78

15.78

19.37

9.43

15.36

6.04

10.22

4.19

7.10

3.08

5.21

2.36

3.99

1.86

3.15

T 122x175

22.1

28.12

3.2

4.18

37.39

32.68

26.64

26.64

19.29

19.29

11.86

11.86

8.24

8.24

6.05

6.05

4.63

4.63

3.66

3.66

T 122x252

32.2

41.03

3.29

5.98

54.71

48.11

39.66

39.66

29.42

29.42

18.29

18.29

12.70

12.70

9.33

9.33

7.15

7.15

5.65

5.65

T 124x249

33.2

42.35

2.93

6.29

55.74

47.69

37.26

37.26

23.40

23.40

14.98

14.98

10.40

10.40

7.64

7.64

5.85

5.85

4.62

4.62

T 125x250

36.2

46.09

2.99

6.29

60.81

52.30

41.31

41.31

26.52

26.52

16.97

16.97

11.79

11.79

8.66

8.66

6.63

6.63

5.24

5.24

T 125x255

41.1

52.34

3.36

6.09

69.93

61.77

51.34

51.34

38.71

38.71

24.34

24.34

16.90

16.90

12.42

12.42

9.51

9.51

7.51

7.51

T 149x149

16

20.4

4.39

3.29

27.20

23.92

19.72

22.96

14.63

19.73

9.10

16.00

6.32

11.25

4.64

8.26

3.55

6.33

2.81

5.00

T 150x150

18.4

23.39

4.45

3.29

31.19

27.43

22.61

26.46

16.77

22.84

10.43

18.66

7.24

13.25

5.32

9.73

4.07

7.45

3.22

5.89



4-29

Table 4.4(Continued): Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



T 147x200

28.4

36.19

3.97

4.71

49.07

44.62

39.01

39.01

32.32

32.32

24.51

24.51

16.32

16.32

11.99

11.99

9.18

9.18

7.25

7.25

T 149x201

32.7

41.68

3.99

4.77

56.53

51.45

45.03

45.03

37.38

37.38

28.48

28.48

18.98

18.98

13.95

13.95

10.68

10.68

8.44

8.44

T147x302

42.3

53.83

3.99

7.16

73.01

66.45

58.16

58.16

48.28

48.28

36.78

36.78

24.51

24.51

18.01

18.01

13.79

13.79

10.90

10.90

T 149x299

43.5

55.40

3.59

7.51

74.49

66.63

56.64

56.64

44.63

44.63

29.41

29.41

20.42

20.42

15.01

15.01

11.49

11.49

9.08

9.08

T 150x300

47.0

59.89

3.65

7.51

80.64

72.35

61.81

61.81

49.17

49.17

32.87

32.87

22.82

22.82

16.77

16.77

12.84

12.84

10.14

10.14

T 150x305

52.9

67.39

4.05

7.26

91.51

83.47

73.31

73.31

61.23

61.23

47.18

47.18

31.62

31.62

23.23

23.23

17.79

17.79

14.05

14.05

52.9

67.41

3.66

7.57

90.79

81.49

69.68

69.68

55.51

55.51

37.20

37.20

25.83

25.83

18.98

18.98

14.53

14.53

11.48

11.48

T 152x301 T 173x174

20.7

26.34

5.08

3.88

35.65

32.31

28.08

31.16

23.03

27.82

17.13

24.00

11.34

19.70

8.33

14.29

6.38

10.94

5.04

8.64

T 175x175

24.8

31.57

5.08

3.95

42.79

38.88

33.95

37.35

28.06

33.34

21.20

28.77

14.09

23.61

10.35

17.12

7.93

13.11

6.26

10.36

T 168x249

34.6

44.08

4.47

5.92

60.27

55.69

49.96

49.96

43.17

43.17

35.35

35.35

25.19

25.19

18.51

18.51

14.17

14.17

11.20

11.20

T 170x250

39.8

50.76

4.48

6

69.41

64.16

57.58

57.58

49.79

49.79

40.81

40.81

29.14

29.14

21.41

21.41

16.39

16.39

12.95

12.95

T 169x351

53.1

67.63

4.59

8.33

92.63

85.86

77.40

77.40

67.39

67.39

55.89

55.89

42.79

42.79

29.95

29.95

22.93

22.93

18.11

18.11

T 172x348

57.3

73

4.11

8.78

99.23

90.70

79.94

79.94

67.15

67.15

52.30

52.30

35.27

35.27

25.92

25.92

19.84

19.84

15.68

15.68

T 172x354

65.4

83.32

4.65

8.43

114.21 106.03

95.79

95.79

83.71

83.71

69.83

69.83

54.05

54.05

37.86

37.86

28.99

28.99

22.90

22.90

T 175x350

68.2

86.94

4.18

8.84

118.33 108.41

95.91

95.91

81.07

81.07

63.87

63.87

43.45

43.45

31.93

31.93

24.44

24.44

19.31

19.31

T 175x357

77.9

99.19

4.71

8.53

136.07 126.50 114.55

114.55 100.44 100.44 84.25

84.25

65.87

65.87

46.25

46.25

35.41

35.41

27.98

27.98

T 178x352

79.3

101

4.25

8.9

137.62 126.37 112.20

112.20

95.40

95.40

75.95

75.95

52.19

52.19

38.34

38.34

29.35

29.35

23.19

23.19

T 198x199

28.3

36.08

5.76

4.48

49.34

45.61

40.92

44.14

35.39

40.35

29.01

36.04

20.71

31.23

15.22

25.89

11.65

19.26

9.21

15.22

T 200x200

33

42.06

5.76

4.54

57.57

53.29

47.94

51.46

41.62

47.04

34.34

42.02

24.80

36.41

18.22

30.18

13.95

22.45

11.02

17.74

T 193x299

47.1

60.05

5.04

7.21

82.70

77.43

70.87

70.87

63.16

63.16

54.36

54.36

44.42

44.42

32.06

32.06

24.54

24.54

19.39

19.39



4-30

Table 4.4(Continued): Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



53.4

67.98

5.05

7.28

93.63

87.68

80.28

80.28

71.58

71.58

61.64

61.64

50.42

50.42

36.44

36.44

27.90

27.90

22.04

22.04

T 194x400

70.0

89.23

5.27

9.54

123.18 115.82 106.69

106.69

95.98

95.98

83.76

83.76

70.04

70.04

52.08

52.08

39.88

39.88

31.51

31.51

T 197x398

73.3

93.41

4.68

10.10

128.09 119.00 107.63

107.63

94.22

94.22

78.82

78.82

61.32

61.32

43.00

43.00

32.92

32.92

26.01

26.01

T 197x405

84.1

107.20

5.34

9.65

148.09 139.40 128.64

128.64 116.02 116.02 101.65 101.65

85.51

85.51

67.46

67.46

49.19

49.19

38.86

38.86

T 200x400

85.8

109.30

4.76

10.10

150.03 139.64 126.67

126.67 111.38 111.38 93.83

73.93

73.93

52.05

52.05

39.85

39.85

31.49

31.49

T 200x408

98.4

125.30

5.40

9.75

172.77 162.80 150.46

150.46 135.99 135.99 119.51 119.51 101.03 101.03

80.38

80.38

58.65

58.65

46.34

46.34

T 207x405

116.0 147.70

4.95

10.20

203.20 189.91 173.36

173.36 153.88 153.88 131.59 131.59 106.40 106.40

76.06

76.06

58.23

58.23

46.01

46.01

T 223x199

33.1

42.15

6.67

4.33

57.51

52.93

47.18

53.20

40.37

49.63

32.50

45.60

22.61

41.13

16.61

36.22

12.72

30.84

10.05

23.84

T 225x200

38.0

48.38

6.68

4.40

66.08

60.95

54.50

61.09

46.87

57.00

38.06

52.38

26.79

47.26

19.68

41.63

15.07

35.48

11.91

27.45

53.0

67.52

5.89

7.04

93.71

88.93

83.05

83.05

76.18

76.18

68.39

68.39

59.69

59.69

50.06

50.06

37.69

37.69

29.78

29.78

T 195x300

T 217x299

93.83

T 220x300

61.8

78.69

5.84

7.68

109.17 103.53

96.59

96.59

88.49

88.49

79.29

79.29

69.02

69.02

57.64

57.64

43.18

43.18

34.12

34.12

T 248x199

39.7

50.64

7.49

4.27

69.03

56.37

65.20

48.00

61.58

38.33

57.51

26.41

53.01

19.40

48.09

14.86

42.74

11.74

36.96

T 250x200

44.8

57.12

7.5

4.33

77.93

71.73

63.94

73.56

54.70

69.48

44.04

64.90

30.64

59.83

22.51

54.29

17.23

48.28

13.62

41.77

T 253x201

51.5

65.65

7.48

4.43

89.71

82.81

74.15

84.51

63.90

79.81

52.08

74.51

36.86

68.67

27.08

62.28

20.73

55.34

16.38

47.82

T 241x300

57.1

72.76

6.85

6.82

101.58

97.36

92.22

92.29

86.25

86.37

79.52

79.68

72.06

72.27

63.88

64.14

54.94

55.26

43.03

45.58

63.42

T 244x300

64.2

81.76

6.66

7.07

114.05 109.15 103.17

103.17

96.23

96.23

88.40

88.40

79.70

79.70

70.15

70.15

59.70

59.70

46.11

46.11

T 298x199

47.3

60.23

9.29

4.05

81.78

74.60

65.52

78.44

54.73

74.60

42.17

70.28

28.26

65.52

20.76

60.34

15.90

54.73

12.56

48.68

T 300x200

52.8

67.21

9.3

4.12

91.38

83.55

73.68

87.74

61.95

83.55

48.33

78.86

32.63

73.68

23.98

68.04

18.36

61.95

14.50

55.38

T 303x201

59.8

76.24

9.28

4.22

103.83

95.25

84.45

99.84

71.62

95.25

56.77

90.11

38.84

84.45

28.53

78.28

21.85

71.62

17.26

64.46



4-31

Table 4.4 (Continued): Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

KLx=3

cm

cm

cm

Kly=1

T 306x202

67.0

85.33

9.27

4.31

116.39 107.06

T 291x300

68.5

87.24

8.54

6.63

121.67 116.41 109.99

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9



95.34

112.05

81.45 107.06 65.39

101.48

45.34

95.34

33.31

88.66

25.51

81.45

20.15

73.70

114.42 102.54 109.26 94.12

103.47

84.78

97.11

74.51

90.18

63.28

82.69

48.75

74.65

89.66

T 294x300

75.6

96.24

8.35

6.85

134.39 128.83 122.08

125.86 114.24 119.97 105.39 113.38

95.59 106.12

84.84

98.21

73.10

60.28

80.46

T 297x302

87.3

111.2

8.44

6.9

155.32 148.96 141.24

145.63 132.27 138.93 122.17 131.43 110.97 123.17

98.68

114.18

85.28 104.47 70.66

94.02

T 346x300

83

105.7

10.3

6.53

147.33 140.82 132.88

141.53 123.65 136.74 113.21 131.40 101.62 125.55

88.88

119.22

74.91 112.42 57.30

105.15

T 350x300

92.4

117.7

10.1

6.78

164.29 157.40 149.02

157.30 139.29 151.81 128.30 145.70 116.13 139.00 102.76

131.74

88.15 123.93 68.79

115.59

T 396x300

95.6

121.7

12.1

6.38

169.48 161.75 152.29

165.20 141.29 160.80 128.85 155.92 115.02 150.60

99.79

144.85

83.06 138.70 62.98

132.15

T 400x300

105

133.7

11.9

6.62

186.46 178.38 168.52

181.26 157.07 176.31 144.15 170.82 129.80 164.83 114.02

158.36

96.76 151.43 74.49

144.05



4-32

Table 4.5: Compression Capacity (Ton) For EL Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

cm

cm

cm

Kly=1

Kly=2

1.427

0.747

0.747

0.82

0.21

0.09

0.09

0.05

0.05

0.73

0.73

1.24

0.31

0.14

0.14

0.08

0.908

0.908

1.41

0.37

0.16

0.16

0.09

0.88

0.88

2.19

0.55

0.25

0.25

2.336

1.23

1.23

2.43

0.91

0.40

3.08

1.21

1.21

3.17

1.16

0.52

1.2

1.2

3.85

1.39

1.19

1.19

4.57

1.63

1.36

1.36

3.81

1.66

4.302

1.36

1.36

4.70

2.96

1.52

1.52

3.38

3.892

1.53

1.53

4.45

EL 25x25

1.12

EL 25x25

1.77

2.26

EL 30x30

1.36

1.727

EL 30x30

2.18

2.78

EL 40x40

1.83

EL 40x40

2.42

EL 40x40

2.95

3.755

EL 40x40

3.52

4.48

EL 45x45

2.74

3.492

EL 45x45

3.38

EL 50x50

2.33

EL 50x50

3.06

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9


0.03

0.03

0.02

0.02

0.02

0.02

0.01

0.01

0.01

0.01

0.08

0.05

0.05

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

0.09

0.06

0.06

0.04

0.04

0.03

0.03

0.02

0.02

0.02

0.02

0.14

0.14

0.09

0.09

0.06

0.06

0.05

0.05

0.03

0.03

0.03

0.03

0.40

0.23

0.23

0.15

0.15

0.10

0.10

0.07

0.07

0.06

0.06

0.04

0.04

0.52

0.29

0.29

0.19

0.19

0.13

0.13

0.09

0.09

0.07

0.07

0.06

0.06

0.62

0.62

0.35

0.35

0.22

0.22

0.15

0.15

0.11

0.11

0.09

0.09

0.07

0.07

0.73

0.73

0.41

0.41

0.26

0.26

0.18

0.18

0.13

0.13

0.10

0.10

0.08

0.08

0.74

0.74

0.42

0.42

0.27

0.27

0.18

0.18

0.14

0.14

0.10

0.10

0.08

0.08

2.05

0.91

0.91

0.51

0.51

0.33

0.33

0.23

0.23

0.17

0.17

0.13

0.13

0.10

0.10

1.76

0.78

0.78

0.44

0.44

0.28

0.28

0.20

0.20

0.14

0.14

0.11

0.11

0.09

0.09

2.46

1.04

1.04

0.59

0.59

0.38

0.38

0.26

0.26

0.19

0.19

0.15

0.15

0.12

0.12

EL 50x50

3.77

4.802

1.52

1.52

5.48

2.86

1.27

1.27

0.71

0.71

0.46

0.46

0.32

0.32

0.23

0.23

0.18

0.18

0.14

0.14

EL 50x50

4.43

5.644

1.5

1.5

6.41

3.27

1.45

1.45

0.82

0.82

0.52

0.52

0.36

0.36

0.27

0.27

0.20

0.20

0.16

0.16

EL 60x60

3.68

4.692

1.85

1.85

5.69

3.91

1.84

1.84

1.03

1.03

0.66

0.66

0.46

0.46

0.34

0.34

0.26

0.26

0.20

0.20

EL 60x60

4.55

5.802

1.84

1.84

7.02

4.81

2.25

2.25

1.26

1.26

0.81

0.81

0.56

0.56

0.41

0.41

0.32

0.32

0.25

0.25

EL 65x65

5

6.367

1.99

1.99

7.86

5.70

2.89

2.89

1.62

1.62

1.04

1.04

0.72

0.72

0.53

0.53

0.41

0.41

0.32

0.32

EL 65x65

5.91

7.527

1.98

1.98

9.28

6.71

3.38

3.38

1.90

1.90

1.22

1.22

0.84

0.84

0.62

0.62

0.47

0.47

0.38

0.38

EL 65x65

7.66

9.761

1.94

1.94

11.97

8.53

4.20

4.20

2.36

2.36

1.51

1.51

1.05

1.05

0.77

0.77

0.59

0.59

0.47

0.47

EL 70x70

6.38

8.127

2.14

2.14

10.18

7.72

4.26

4.26

2.40

2.40

1.53

1.53

1.06

1.06

0.78

0.78

0.60

0.60

0.47

0.47


4-33

Table 4.5(Continued): Compression Capacity (Ton) For EL Sections For L=1 m To 9 m (Qs = 1and Qa = 1)-Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

EL 75x75

6.85

8.727

2.3

2.3

11.08

8.71

5.55

5.55

2.97

2.97

1.90

1.90

1.32

1.32


0.97

0.97

0.74

0.74

0.59

0.59

EL 75x75

9.96

12.69

2.25

2.25

16.05

12.48

7.35

7.35

4.13

4.13

2.65

2.65

1.84

1.84

1.35

1.35

1.03

1.03

0.82

0.82

EL 75x75

13

16.56

2.22

2.22

20.90

16.14

9.34

9.34

5.25

5.25

3.36

3.36

2.33

2.33

1.72

1.72

1.31

1.31

1.04

1.04

EL 80x80

7.32

9.327

2.46

2.46

11.98

9.68

6.66

6.66

3.63

3.63

2.33

2.33

1.61

1.61

1.19

1.19

0.91

0.91

0.72

0.72

EL 90x90

8.28

10.55

2.77

2.77

13.79

11.61

8.77

8.77

5.21

5.21

3.33

3.33

2.32

2.32

1.70

1.70

1.30

1.30

1.03

1.03

EL 90x90

9.59

12.22

2.76

2.76

15.96

13.43

10.12

10.12

5.99

5.99

3.83

3.83

2.66

2.66

1.96

1.96

1.50

1.50

1.18

1.18

EL 90x90

13.3

17

2.71

2.71

22.15

18.53

13.80

13.80

8.04

8.04

5.14

5.14

3.57

3.57

2.62

2.62

2.01

2.01

1.59

1.59

EL 90x90

15.9

20.3

2.7

2.7

26.44

22.08

16.41

16.41

9.52

9.52

6.10

6.10

4.23

4.23

3.11

3.11

2.38

2.38

1.88

1.88

EL 90x90

17

21.71

2.68

2.68

28.25

23.54

17.39

17.39

10.04

10.04

6.42

6.42

4.46

4.46

3.28

3.28

2.51

2.51

1.98

1.98

EL 100x100

10.7

13.62

3.08

3.08

18.03

15.62

12.52

12.52

8.73

8.73

5.32

5.32

3.70

3.70

2.72

2.72

2.08

2.08

1.64

1.64

EL 100x100

14.9

19

3.04

3.04

25.12

21.69

17.28

17.28

11.30

11.30

7.23

7.23

5.02

5.02

3.69

3.69

2.83

2.83

2.23

2.23

EL 100x100

17.8

22.7

3.02

3.02

29.99

25.85

20.52

20.52

13.33

13.33

8.53

8.53

5.92

5.92

4.35

4.35

3.33

3.33

2.63

2.63

EL 100x100

19.1

24.31

3

3

32.09

27.62

21.85

21.85

14.08

14.08

9.01

9.01

6.26

6.26

4.60

4.60

3.52

3.52

2.78

2.78

EL 120x120

14.7

18.76

3.71

3.71

25.30

22.76

19.54

19.54

15.68

15.68

10.64

10.64

7.39

7.39

5.43

5.43

4.15

4.15

3.28

3.28

EL 130x130

17.9

22.74

4.01

4.01

30.85

28.10

24.63

24.63

20.49

20.49

15.67

15.67

10.46

10.46

7.68

7.68

5.88

5.88

4.65

4.65

EL 130x130

23.4

29.76

3.96

3.96

40.34

36.67

32.04

32.04

26.51

26.51

20.07

20.07

13.35

13.35

9.81

9.81

7.51

7.51

5.93

5.93

EL 130x130

28.8

36.75

3.93

3.93

49.79

45.21

39.42

39.42

32.52

32.52

24.46

24.46

16.24

16.24

11.93

11.93

9.13

9.13

7.22

7.22

EL 150x150

27.3

34.77

4.61

4.61

47.63

44.18

39.85

39.85

34.74

34.74

28.87

28.87

22.19

22.19

15.53

15.53

11.89

11.89

9.39

9.39

EL 150x150

33.6

42.74

4.56

4.56

58.51

54.20

48.80

48.80

42.41

42.41

35.07

35.07

25.42

25.42

18.68

18.68

14.30

14.30

11.30

11.30

EL 150x150

41.9

53.38

4.52

4.52

73.04

67.58

60.75

60.75

52.67

52.67

43.36

43.36

31.20

31.20

22.92

22.92

17.55

17.55

13.87

13.87



4-34

Table 4.5(Continued): Compression Capacity (Ton) For EL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



EL 175x175

31.8

40.52

5.38

5.38

56.00

52.75

48.72

48.72

44.01

44.01

38.64

38.64

32.61

32.61

25.87

25.87

18.87

18.87

14.91

14.91

EL 175x175

39.4

50.21

5.35

5.35

69.37

65.31

60.28

60.28

54.39

54.39

47.68

47.68

40.14

40.14

31.71

31.71

23.12

23.12

18.27

18.27

EL 200x200

45.3

57.75

6.14

6.14

80.29

76.43

71.69

71.69

66.17

66.17

59.91

59.91

52.95

52.95

45.25

45.25

36.77

36.77

27.68

27.68

EL 200x200

59.7

76

6.09

6.09

105.63 100.49

94.18

94.18

86.82

86.82

78.49

78.49

69.20

69.20

58.94

58.94

47.62

47.62

35.84

35.84

96.37

84.76

84.76

71.93

71.93

55.03

55.03

EL 200x200

73.6

93.75

6.04

6.04

130.26 123.84 115.97

115.97 106.78 106.78 96.37

43.48

43.48

EL 250x250

93.7

119.4

7.63

7.63

167.34 161.37 154.17

154.17 145.86 145.86 136.51 136.51 126.19 126.19 114.92

114.92 102.69 102.69 89.47

89.47

EL 250x250

128.0

162.6

7.49

7.49

227.75 219.42 209.36

209.36 197.73 197.73 184.65 184.65 170.19 170.19 154.40

154.40 137.24 137.24 118.66

118.66



4-35

Table 4.6(Continued): Compression Capacity (Ton) For UL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

cm

cm

cm

Kly=1

Kly=2

UL 90x75

11

14.04

2.78

2.2

17.69

13.60

UL 100x75

9.32

11.87

3.15

2.19

14.94

11.46

6.51

11.11

UL 100x75

13

16.5

3.11

2.15

20.69

15.72

8.73

15.29

UL 125x75

10.7

13.62

4.01

2.11

17.02

12.80

6.94

14.75

UL 125x75

14.9

19.00

3.96

2.06

23.62

17.51

9.23

UL 125x75

19.1

24.31

3.93

2.04

30.16

22.23

11.58

UL 125x90

16.1

20.5

3.94

2.59

26.54

21.87

15.74

UL 125x90

20.6

26.26

3.91

2.57

33.96

27.90

19.96

UL 150x90

16.4

20.94

4.81

2.52

27.00

22.03

15.49

KLx=4

KLx=5

KLx=6


7.78

11.72

4.37

KLx=7

KLx=8

KLx=9


6.98

2.80

4.47

1.94

3.10

1.43

2.28

1.09

1.75

0.86

1.38

3.66

7.93

2.35

4.85

1.63

3.37

1.20

2.48

0.92

1.90

0.72

1.50

4.91

10.77

3.14

6.57

2.18

4.57

1.60

3.35

1.23

2.57

0.97

2.03

3.90

12.27

2.50

9.38

1.73

6.26

1.27

4.60

0.98

3.52

0.77

2.78

20.45

5.19

16.93

3.32

12.81

2.31

8.52

1.69

6.26

1.30

4.79

1.03

3.79

26.08

6.51

21.51

4.17

16.18

2.89

10.74

2.13

7.89

1.63

6.04

1.29

4.77

22.02

8.85

18.18

5.66

13.70

3.93

9.10

2.89

6.69

2.21

5.12

1.75

4.05

28.10

11.16

23.13

7.14

17.32

4.96

11.48

3.65

8.44

2.79

6.46

2.21

5.10

24.35

8.56

21.47

5.48

18.16

3.80

14.42

2.79

10.18

2.14

7.80

1.69

6.16 7.88

UL 150x90

21.5

27.36

4.76

2.47

35.17

28.47

19.65

31.71

10.74

27.88

6.88

23.49

4.77

18.51

3.51

13.03

2.69

9.97

2.12

UL 150x100

17.1

21.84

4.79

2.88

28.69

24.43

18.90

25.36

11.66

22.34

7.46

18.87

5.18

14.93

3.81

10.53

2.91

8.06

2.30

6.37

UL 150x100

22.4

28.56

4.74

2.83

37.43

31.71

24.29

33.05

14.72

29.03

9.42

24.42

6.54

19.18

4.81

13.49

3.68

10.33

2.91

8.16

UL 150x100

27.7

35.25

4.71

2.8

46.13

38.97

29.66

40.71

17.79

35.69

11.38

29.94

7.91

23.41

5.81

16.43

4.45

12.58

3.51

9.94



4-36

Table 4.7: Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) –Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

2.854

0.75

1.15

1.64

0.41

0.18

0.18

0.10

0.10

0.07

0.07

0.05

0.05

0.03

0.03

0.03

0.03

0.02

0.02

0.73

1.28

2.47

0.62

0.27

0.27

0.15

0.15

0.10

0.10

0.07

0.07

0.05

0.05

0.04

0.04

0.03

0.03

0.91

1.35

2.82

0.73

0.32

0.32

0.18

0.18

0.12

0.12

0.08

0.08

0.06

0.06

0.05

0.05

0.04

0.04

0.88

1.46

4.38

1.11

0.49

0.49

0.28

0.28

0.18

0.18

0.12

0.12

0.09

0.09

0.07

0.07

0.05

0.05

4.672

1.23

1.75

4.85

1.82

0.81

0.81

0.45

0.45

0.29

0.29

0.20

0.20

0.15

0.15

0.11

0.11

0.09

0.09

6.16

1.20

1.79

6.32

2.30

1.02

1.02

0.58

0.58

0.37

0.37

0.26

0.26

0.19

0.19

0.14

0.14

0.11

0.11

7.70

2.79

1.24

1.24

0.70

0.70

0.45

0.45

0.31

0.31

0.23

0.23

0.17

0.17

0.14

0.14

9.12

3.25

1.44

1.44

0.81

0.81

0.52

0.52

0.36

0.36

0.27

0.27

0.20

0.20

0.16

0.16

7.63

3.35

1.49

1.49

0.84

0.84

0.54

0.54

0.37

0.37

0.27

0.27

0.21

0.21

0.17

0.17

2.04

9.38

4.07

1.81

1.81

1.02

1.02

0.65

0.65

0.45

0.45

0.33

0.33

0.25

0.25

0.20

0.20

2.11

6.76

3.71

1.57

1.57

0.88

0.88

0.57

0.57

0.39

0.39

0.29

0.29

0.22

0.22

0.17

0.17

2.19

8.90

4.90

2.07

2.07

1.17

1.17

0.75

0.75

0.52

0.52

0.38

0.38

0.29

0.29

0.23

0.23

ELL 25x25

2.24

ELL 25x25

3.54

4.52

ELL 30x30

2.72

3.454

ELL 30x30

4.36

5.56

ELL 40x40

3.66

ELL 40x40

4.84

ELL 40x40

5.9

7.51

1.20

1.86

ELL 40x40

7.04

8.96

1.19

1.91

ELL 45x45

5.48

6.984

1.36

1.98

ELL 45x45

6.76

8.604

1.36

ELL 50x50

4.66

5.92

1.52

ELL 50x50

6.12

7.784

1.53


KLx=7


ELL 50x50

7.54

9.604

1.52

2.25

10.97

5.72

2.54

2.54

1.43

1.43

0.91

0.91

0.64

0.64

0.47

0.47

0.36

0.36

0.28

0.28

ELL 50x50

8.86

11.288

1.49

2.29

12.81

6.49

2.88

2.88

1.62

1.62

1.04

1.04

0.72

0.72

0.53

0.53

0.41

0.41

0.32

0.32

ELL 60x60

7.36

9.384

1.85

2.59

11.37

7.80

3.66

3.66

2.06

2.06

1.32

1.32

0.92

0.92

0.67

0.67

0.51

0.51

0.41

0.41

ELL 60x60

9.1

11.604

1.84

2.65

14.04

9.60

4.49

4.49

2.52

2.52

1.61

1.61

1.12

1.12

0.82

0.82

0.63

0.63

0.50

0.50

ELL 65x65

10

12.734

1.99

2.84

15.72

11.41

5.79

5.79

3.26

3.26

2.08

2.08

1.45

1.45

1.06

1.06

0.81

0.81

0.64

0.64

ELL 65x65

11.82

15.054

1.98

2.89

18.54

13.39

6.73

6.73

3.78

3.78

2.42

2.42

1.68

1.68

1.24

1.24

0.95

0.95

0.75

0.75

ELL 65x65

15.32

19.522

1.94

2.99

23.95

17.08

8.42

8.42

4.74

4.74

3.03

3.03

2.11

2.11

1.55

1.55

1.18

1.18

0.94

0.94

ELL 70x70

12.76

16.254

2.14

3.09

20.36

15.42

8.49

8.49

4.78

4.78

3.06

3.06

2.12

2.12

1.56

1.56

1.19

1.19

0.94

0.94


4-37

Table 4.7(Continued): Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) –Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

cm

cm

cm

Kly=1

Kly=2


17.454

2.30

3.29

22.17

17.41

11.08

11.08

32.11

24.99

14.74

14.74

8.29

8.29

5.31

41.81

32.33

18.74

18.74

10.54

10.54

6.75

ELL 75x75

13.7

5.93

5.93

3.80

3.80

ELL 75x75

19.92

25.38

2.25

3.46

ELL 75x75

26

33.12

2.22

3.65

ELL 80x80

14.64

18.654

2.46

3.49

23.96

19.37

13.31

13.31

7.26

7.26

4.65

ELL 90x90

16.56

21.1

2.77

3.88

27.57

23.20

17.52

17.52

10.39

10.39

6.65

ELL 90x90

19.18

24.44

2.76

3.94

31.92

26.84

20.24

20.24

11.97

11.97

7.66

7.66

KLx=7

KLx=8

KLx=9


2.64

2.64

1.94

5.31

3.68

3.68

2.71

6.75

4.69

4.69

3.44

4.65

3.23

3.23

2.37

6.65

4.62

4.62

3.39

5.32

5.32

1.94

1.48

1.48

1.17

1.17

2.71

2.07

2.07

1.64

1.64

3.44

2.64

2.64

2.08

2.08

2.37

1.82

1.82

1.43

1.43

3.39

2.60

2.60

2.05

2.05

3.91

3.91

2.99

2.99

2.36

2.36

ELL 90x90

26.6

34

2.71

4.10

44.31

37.06

27.62

27.62

16.09

16.09

10.30

10.30

7.15

7.15

5.25

5.25

4.02

4.02

3.18

3.18

ELL 90x90

31.8

40.6

2.70

4.23

52.88

44.17

32.82

32.82

19.05

19.05

12.19

12.19

8.47

8.47

6.22

6.22

4.76

4.76

3.76

3.76

ELL 90x90

34

43.42

2.68

4.28

56.49

47.08

34.80

34.80

20.08

20.08

12.85

12.85

8.93

8.93

6.56

6.56

5.02

5.02

3.97

3.97

ELL 100x100

21.4

27.24

3.08

4.34

36.06

31.24

25.02

25.02

17.43

17.43

10.63

10.63

7.38

7.38

5.42

5.42

4.15

4.15

3.28

3.28

ELL 100x100

29.8

38

3.03

4.50

50.23

43.36

34.50

34.50

22.53

22.53

14.42

14.42

10.01

10.01

7.36

7.36

5.63

5.63

4.45

4.45

ELL 100x100

35.6

45.4

3.02

4.62

59.97

51.71

41.05

41.05

26.65

26.65

17.05

17.05

11.84

11.84

8.70

8.70

6.66

6.66

5.26

5.26

ELL 100x100

38.2

48.62

3.01

4.68

64.20

55.30

43.81

43.81

28.32

28.32

18.12

18.12

12.59

12.59

9.25

9.25

7.08

7.08

5.59

5.59

ELL 120x120

29.4

37.52

3.71

5.20

50.59

45.51

39.07

39.07

31.34

31.34

21.26

21.26

14.76

14.76

10.84

10.84

8.30

8.30

6.56

6.56

ELL 130x130

35.8

45.48

4.01

5.65

61.71

56.21

49.26

49.26

40.99

40.99

31.36

31.36

20.94

20.94

15.38

15.38

11.78

11.78

9.31

9.31

ELL 130x130

46.8

59.52

3.96

5.80

80.68

73.36

64.09

64.09

53.04

53.04

40.17

40.17

26.72

26.72

19.63

19.63

15.03

15.03

11.87

11.87

ELL 130x130

57.6

73.5

3.93

5.98

99.58

90.43

78.85

78.85

65.05

65.05

48.95

48.95

32.50

32.50

23.87

23.87

18.28

18.28

14.44

14.44

ELL 150x150

54.6

69.54

4.61

6.61

95.27

88.37

79.73

79.73

69.52

69.52

57.79

57.79

44.44

44.44

31.10

31.10

23.81

23.81

18.82

18.82

ELL 150x150

67.2

85.48

4.56

6.76

117.02 108.39

97.58

97.58

84.80

84.80

70.10

70.10

50.80

50.80

37.33

37.33

28.58

28.58

22.58

22.58

ELL 150x150

83.8

106.76

4.52

7.00

146.07 135.16 121.48

121.48 105.31 105.31 86.70

86.70

62.36

62.36

45.82

45.82

35.08

35.08

27.72

27.72


4-38

Table 4.7(Continued): Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

cm

cm

cm

Kly=1

ELL 175x175

63.6

81.04

5.37

7.57

111.98 105.48

ELL 175x175

78.8 100.42

5.36

7.75

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9



97.42

97.42

87.97

87.97

77.20

77.20

65.12

65.12

51.62

51.62

37.65

37.65

29.75

29.75

138.74 130.64 120.60

120.60 108.83 108.83 95.43

95.43

80.37

80.37

63.55

63.55

46.34

46.34

36.62

36.62

ELL 200x200

90.6

115.5

6.14

8.74

160.59 152.87 143.40

143.40 132.36 132.36 119.87 119.87 105.95 105.95

90.58

90.58

73.64

73.64

55.43

55.43

ELL 200x200

119.4

152

6.09

9.03

211.27 200.99 188.37

188.37 173.66 173.66 156.99 156.99 138.43 138.43 117.92

117.92

95.29

95.29

71.71

71.71

ELL 200x200

147.2 187.5

6.04

9.33

260.51 247.68 231.93

231.93 213.55 213.55 192.73 192.73 169.52 169.52 143.86

143.86 110.06 110.06 86.96

86.96

ELL 250x250

187.4 238.8

7.63

11.31

334.68 322.74 308.34

308.34 291.71 291.71 273.02 273.02 252.38 252.38 229.83

229.83 205.37 205.37 178.91

178.91

7.49

11.86

455.49 438.81 418.67

418.67 395.39 395.39 369.21 369.21 340.27 340.27 308.65

308.65 274.30 274.30 237.10

237.10

ELL 250x250

256

325.2



4-39

Table 4.8: Compression Capacity (Ton) For ULL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

ULLL 90x75 ULLL 100x75

22

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

cm

cm

cm

Kly=1

Kly=2


28.08

2.79

3.29

36.73

30.98

23.50

18.64 23.74

23.50

14.03

14.03

8.98

KLx=7

KLx=8

KLx=9


8.98

6.24

6.24

4.58

4.58

3.51

3.51

2.77

2.77 3.00

3.15

3.09

31.44

27.26

21.88

22.24

15.30

15.88

9.34

9.72

6.48

6.75

4.76

4.96

3.65

3.80

2.88

ULLL 100x75

26

33

3.10

3.25

43.73

37.96

30.53

30.53

21.46

21.46

13.10

13.10

9.10

9.10

6.68

6.68

5.12

5.12

4.04

4.04

ULLL 125x75

21.4

27.24

4.01

2.90

35.81

30.54

23.72

29.50

14.72

24.54

9.42

18.77

6.54

12.53

4.81

9.21

3.68

7.05

2.91

5.57

ULLL 125x75

29.8

38

3.97

3.05

50.26

43.45

34.67

40.94

23.92

33.91

14.58

25.71

10.13

17.11

7.44

12.57

5.70

9.62

4.50

7.60

ULLL 125x75

38.2

48.62

3.93

3.24

64.73

56.74

46.50

52.17

34.06

43.05

21.04

32.40

14.61

21.51

10.73

15.80

8.22

12.10

6.49

9.56

ULLL 125x90

32.2

41

3.94

3.76

55.34

49.90

43.00

44.03

34.74

36.35

23.86

27.39

16.57

18.19

12.18

13.37

9.32

10.23

7.37

8.09

ULLL 125x90

41.2

52.52

3.91

3.94

71.12

64.53

56.18

56.18

46.23

46.23

34.60

34.60

22.94

22.94

16.86

16.86

12.90

12.90

10.20

10.20

ULLL 150x90

32.8

41.88

4.81

3.51

56.19

50.05

42.23

48.71

32.81

42.95

21.23

36.34

14.74

28.86

10.83

20.39

8.29

15.61

6.55

12.33 15.74

ULLL 150x90

43

54.72

4.76

3.66

73.70

66.15

56.56

63.40

45.06

55.74

30.19

46.94

20.97

36.97

15.40

26.02

11.79

19.92

9.32

ULLL 150x100

34.2

43.68

4.79

3.98

59.23

53.89

47.14

50.74

39.10

44.70

29.73

37.77

19.80

29.91

14.55

21.10

11.14

16.16

8.80

12.76

ULLL 150x100

44.8

57.12

4.74

4.13

77.67

71.04

62.68

66.11

52.74

58.07

41.20

48.84

27.85

38.37

20.46

26.99

15.66

20.66

12.38

16.32

ULLL 150x100

55.4

70.5

4.71

4.31

96.16

88.46

78.78

81.41

67.31

71.39

54.05

59.88

37.49

46.81

27.54

32.87

21.09

25.17

16.66

19.88



4-41

Table 4.9: Compression Capacity (Ton) For ULLS Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

cm

cm

cm

Kly=1

Kly=2


ULLS 75x90

22

28.08

2.20

4.24

35.38

27.22

15.58

ULLS 75x100

18.6

23.74

2.19

4.64

29.88

22.92

13.02

13.02

7.32

7.32

4.69

ULLS 75x100

26

33

2.15

4.81

41.38

31.42

17.42

17.42

9.80

9.80

6.27

ULLS 75x125

21.4

27.24

2.11

5.99

34.02

25.55

13.82

13.82

7.78

7.78

4.98

ULLS 75x125

29.8

38

2.06

6.17

47.25

35.06

18.49

18.49

10.40

10.40

ULLS 75x125

38.2

48.62

2.04

6.36

60.30

44.42

23.11

23.11

13.00

13.00

15.58

8.77

8.77

5.61

5.61

KLx=7

KLx=8

KLx=9


3.90

3.90

2.86

4.69

3.26

3.26

2.39

6.27

4.35

4.35

3.20

4.98

3.46

3.46

2.54

6.66

6.66

4.62

4.62

8.32

8.32

5.78

5.78

2.86

2.19

2.19

1.73

1.73

2.39

1.83

1.83

1.45

1.45

3.20

2.45

2.45

1.94

1.94

2.54

1.94

1.94

1.54

1.54

3.40

3.40

2.60

2.60

2.05

2.05

4.25

4.25

3.25

3.25

2.57

2.57

ULLS 90x125

32.2

41

2.59

5.94

53.10

43.77

31.55

31.55

17.76

17.76

11.37

11.37

7.90

7.90

5.80

5.80

4.44

4.44

3.51

3.51

ULLS 90x125

41.2

52.52

2.57

6.13

67.91

55.77

39.85

39.85

22.27

22.27

14.25

14.25

9.90

9.90

7.27

7.27

5.57

5.57

4.40

4.40

ULLS 90x150

32.8

41.88

2.52

7.23

54.00

44.05

30.98

30.98

17.12

17.12

10.96

10.96

7.61

7.61

5.59

5.59

4.28

4.28

3.38

3.38

ULLS 90x150

43.0

54.72

2.47

7.40

70.34

56.95

39.31

39.31

21.50

21.50

13.76

13.76

9.55

9.55

7.02

7.02

5.37

5.37

4.25

4.25

ULLS 100x150

34.2

43.68

2.88

7.08

57.37

48.84

37.79

37.79

23.30

23.30

14.91

14.91

10.36

10.36

7.61

7.61

5.82

5.82

4.60

4.60

ULLS 100x150

44.8

57.12

2.83

7.25

74.84

63.38

48.51

48.51

29.35

29.35

18.78

18.78

13.04

13.04

9.58

9.58

7.34

7.34

5.80

5.80

ULLS 100x150

55.4

70.5

2.80

7.43

92.26

77.91

59.27

59.27

35.53

35.53

22.74

22.74

15.79

15.79

11.60

11.60

8.88

8.88

7.02

7.02



4-42

Table 4.10: Compression Capacity (Ton) For CCI Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

CCI 50x25

7.72

rx

ry

KLx=1

KLx=2

cm

cm

cm

Kly=1

Kly=2

9.84

1.85

1.28

10.42

4.13

KLx=3

KLx=4

KLx=5

KLx=6


1.83

3.84

1.03

2.16

0.66

1.38

0.46

0.96

KLx=7

KLx=8

KLx=9


0.34

0.71

0.26

0.54

0.20

0.43 1.91

CCI 75x40

13.84 17.636

2.92

1.93

21.60

15.34

7.52

15.48

4.23

9.69

2.71

6.20

1.88

4.31

1.38

3.17

1.06

2.42

0.84

CCI 100x50

18.72 23.84

3.97

2.32

30.33

23.92

15.41

25.70

8.26

21.29

5.29

16.16

3.67

10.76

2.70

7.90

2.07

6.05

1.63

4.78

CCI 125x65

26.8

4.98

2.91

45.00

38.41

29.89

40.24

18.62

35.76

11.91

30.64

8.27

24.86

6.08

17.82

4.65

13.64

3.68

10.78

CCI 150x75

37.2

47.42

6.03

3.42

63.48

56.28

47.09

58.63

36.00

53.96

22.89

48.68

15.90

42.79

11.68

36.27

8.94

27.71

7.07

21.89

CCI 150x75

48

61.18

5.86

3.52

82.12

73.22

61.87

75.16

48.21

68.88

31.31

61.77

21.74

53.82

15.97

45.02

12.23

33.79

9.66

26.70

CCI 180x75

42.8

54.4

7.12

3.31

72.58

63.92

52.83

68.58

39.40

63.92

24.57

58.66

17.07

52.83

12.54

46.42

9.60

39.40

7.58

30.34

CCI 200x80

49.2

62.66

7.89

3.47

83.98

74.66

62.76

79.67

48.42

74.66

31.09

69.02

21.59

62.76

15.86

55.91

12.14

48.42

9.60

40.27

CCI 200x90

60.6

77.3

8.03

4.13

105.11

96.13

84.80

100.55

71.34

95.55

55.71

89.93

37.65

83.74

27.66

76.99

21.18

69.69

16.73

61.81

CCI 250x90

69.2

88.14

9.74

3.85

119.20 107.88

93.54

113.95

76.42 107.88 56.37

101.07

37.30

93.54

27.40

85.33

20.98

76.42

16.58

66.78

CCI 250x90

80.4 102.34

9.56

3.89

138.53 125.60 109.23

132.53

89.69 125.60 66.86

117.82

44.30 109.23

32.55

99.85

24.92

89.69

19.69

78.71

CCI 300x90

76.2

97.14

11.51

3.67

130.87 117.54 100.61

124.69

80.31 117.54 53.98

109.50

37.49 100.61

27.54

90.88

21.09

80.31

16.66

68.84

CCI 300x90

87.6 111.48

11.53

3.81

150.65 136.15 117.76

143.92

95.78 136.15 70.03

127.41

46.32 117.76

34.03

107.22

26.05

95.78

20.59

83.41

CCI 300x90

97.2

123.8

11.28

3.80

167.25 151.06 130.53

159.74 105.98 151.06 73.52

141.30

51.06 130.53

37.51

118.75

28.72 105.98 22.69

92.15

109

138.78

14.46

4.04

188.41 171.80 150.81

180.69 125.84 171.80 96.79

161.82

64.81 150.81

47.61

138.82

36.45 125.84 28.80

111.85

134.6 171.42

14.33

4.22

233.47 214.18 189.90

224.50 161.07 214.18 127.70 202.62

87.37 189.90

64.19

176.04

49.15 161.07 38.83

144.97

CCI 380x100 CCI 380x100

34.22



4-43

Table 4.11: Compression Capacity (Ton) For CCB Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Designation Effective KL (m) Section Name

Wght Kg/m

Ax 2

CCB 50x25

7.72

rx

ry

KLx=1

KLx=2

cm

cm

cm

Kly=1

Kly=2

9.84

19.91

1.83

11.90

8.12

KLx=3

KLx=4

KLx=5

KLx=6


3.79

10.18

2.13

8.12

1.36

5.45

0.95

3.79

KLx=7

KLx=8

KLx=9


0.70

2.78

0.53

2.13

0.42

1.68

CCB 75x40

13.84 17.636

14.87

2.96

23.25

19.95

15.68

21.72

9.97

19.95

6.38

17.93

4.43

15.68

3.26

13.19

2.49

9.97

1.97

7.88

CCB 100x50

18.72 23.84

12.79

3.76

32.18

29.02

25.01

30.72

20.22

29.02

13.90

27.12

9.65

25.01

7.09

22.71

5.43

20.22

4.29

17.51

CCB 125x65

26.8

10.68

4.98

47.09

44.04

40.23

45.67

35.76

44.04

30.64

42.22

24.85

40.23

17.82

38.08

13.64

35.76

10.78

33.28

CCB 150x75

37.2

47.42

9.07

5.67

65.70

62.17

57.81

62.65

52.70

60.07

46.91

57.19

40.43

54.03

33.23

50.59

24.56

46.88

19.40

42.91

CCB 150x75

48

61.18

7.98

5.63

84.74

80.13

74.45

79.52

67.80

75.53

60.25

71.06

51.80

66.12

42.40

60.73

31.25

54.90

24.69

48.61

CCB 180x75

42.8

54.4

8.47

5.80

75.45

71.52

66.67

71.27

61.01

68.01

54.59

64.36

47.41

60.34

39.46

55.96

29.46

51.23

23.28

46.15

CCB 200x80

49.2

62.66

7.89

6.24

87.18

83.07

78.04

81.31

72.18

77.15

65.55

72.48

58.18

67.33

50.04

61.72

41.08

55.63

30.98

49.06

CCB 200x90

60.6

77.3

8.03

6.81

107.91 103.42

97.94

100.55

91.59

95.55

84.42

89.93

76.48

83.74

67.75

76.99

58.23

69.69

45.56

61.81

CCB 250x90

69.2

88.14

9.74

7.09

123.22 118.36 112.47

117.36 105.64 113.03 97.94

108.21

89.42 102.92

80.09

97.17

69.92

91.00

58.86

84.39

CCB 250x90

80.4 102.34

9.56

7.07

143.07 137.40 130.54

136.01 122.58 130.85 113.61 125.10 103.68 118.79

92.80

111.94

80.94 104.56 68.05

96.67

CCB 300x90

76.2

97.14

11.51

7.23

135.90 130.69 124.38

131.35 117.07 127.58 108.84 123.41

89.78

113.91

78.94 108.62 67.17

102.99

CCB 300x90

87.6 111.48

11.53

7.13

155.89 149.79 142.39

150.76 133.82 146.44 124.17 141.66 113.49 136.43 101.79

130.78

89.05 124.72 75.20

118.27

CCB 300x90

97.2

123.8

11.28

7.16

173.14 166.41 158.25

167.11 148.80 162.17 138.15 156.68 126.37 150.68 113.47

144.20

99.43 137.24 84.16

129.83

CCB 380x100

109

138.78

14.46

8.08

194.84 188.41 180.69

190.63 171.80 186.70 161.83 182.37 150.83 177.67 138.84

172.61 125.86 167.22 111.87

161.49

CCB 380x100 134.6 171.42

14.46

7.96

240.55 232.45 222.70

235.47 211.47 230.61 198.85 225.26 184.94 219.46 169.77

213.21 153.34 206.54 135.61

199.47

34.22

99.74 118.84



4-44

Table 4.12: Compression Capacity (Ton) For C Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax cm2

C 50x25

3.86

4.92

C 75x40

6.92

8.818

C 100x50

9.36

C 125x65

ry

KLx=1

KLx=2

cm

cm

Kly=1

Kly=2

1.85

0.71

2.55

0.64

0.28

1.14

0.16

0.64

0.10

0.41

0.07

0.28

0.05

0.21

0.04

0.16

0.03

0.13

2.92

1.17

8.89

3.11

1.38

5.79

0.78

3.11

0.50

1.99

0.35

1.38

0.25

1.01

0.19

0.78

0.15

0.61

11.92

3.97

1.48

13.47

6.72

2.99

10.59

1.68

6.72

1.08

4.30

0.75

2.99

0.55

2.19

0.42

1.68

0.33

1.33

13.4

17.11

4.98

1.9

20.88

14.66

7.07

18.05

3.98

14.66

2.54

10.18

1.77

7.07

1.30

5.19

0.99

3.98

0.79

3.14

C 150x75

18.6

23.71

6.03

2.22

29.92

23.11

13.37

26.80

7.52

23.11

4.81

18.86

3.34

13.37

2.46

9.82

1.88

7.52

1.49

5.94

C 180x75

21.4

27.2

7.12

2.19

34.24

26.27

14.93

30.59

8.40

26.27

5.37

21.28

3.73

14.93

2.74

10.97

2.10

8.40

1.66

6.63

C 150x75

24

30.59

5.86

2.19

38.50

29.54

16.79

34.40

9.44

29.54

6.04

23.93

4.20

16.79

3.08

12.33

2.36

9.44

1.87

7.46

C 200x80

24.6

31.33

7.88

2.32

39.85

31.43

20.24

35.99

10.85

31.43

6.95

26.20

4.82

20.24

3.54

14.18

2.71

10.85

2.14

8.58

C 200x90

30.3

38.65

8.02

2.68

50.29

41.90

30.97

46.43

17.87

41.90

11.44

36.75

7.94

30.97

5.83

24.50

4.47

17.87

3.53

14.12

C 250x90

34.6

44.07

9.74

2.58

57.03

46.92

33.67

52.38

18.88

46.92

12.08

40.68

8.39

33.67

6.17

24.66

4.72

18.88

3.73

14.92

C 300x90

38.1

48.57

11.5

2.52

62.63

51.09

35.93

57.32

19.85

51.09

12.71

43.96

8.82

35.93

6.48

25.93

4.96

19.85

3.92

15.69

C 250x90

40.2

51.17

9.56

2.54

66.06

54.05

38.27

60.54

21.25

54.05

13.60

46.63

9.44

38.27

6.94

27.75

5.31

21.25

4.20

16.79

C 300x90

43.8

55.74

11.5

2.54

71.96

58.87

41.69

65.94

23.15

58.87

14.81

50.80

10.29

41.69

7.56

30.23

5.79

23.15

4.57

18.29

C 300x90

48.6

61.9

11.3

2.48

79.62

64.56

44.73

72.70

24.50

64.56

15.68

55.25

10.89

44.73

8.00

32.00

6.13

24.50

4.84

19.36

C 380x100

54.5

69.39

14.5

2.78

90.73

76.47

57.94

84.16

34.52

76.47

22.09

67.73

15.34

57.94

11.27

47.03

8.63

34.52

6.82

27.27

8.30

33.20

C 380x100

67.3

85.71

rx

14.3

2.76

111.96

94.16

KLx=3

KLx=4


71.01

103.76

42.02

94.16

KLx=5

KLx=6


26.89

83.24

18.68

71.01

KLx=7

KLx=8

KLx=9


13.72

57.37

10.51

42.02



4-45

Table 4.13: Compression Capacity (Ton) For I Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax

rx

ry

KLx=1

KLx=2

cm2

cm

cm

Kly=1

Kly=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9


I 100x75

12.9

16.43

4.14

1.7

19.46

12.36

5.43

16.24

3.06

12.36

1.96

7.82

1.36

5.43

1.00

3.99

0.76

3.06

0.60

2.41

I 125x75

16.1

20.45

5.13

1.68

24.14

15.13

6.60

20.06

3.71

15.13

2.38

9.51

1.65

6.60

1.21

4.85

0.93

3.71

0.73

2.94

I 150x75

17.1

21.83

6.12

1.62

25.47

15.28

6.56

20.87

3.69

15.28

2.36

9.44

1.64

6.56

1.20

4.82

0.92

3.69

0.73

2.91

I 180x100

23.6

30.06

7.45

2.14

37.66

28.54

15.75

33.49

8.86

28.54

5.67

22.82

3.94

15.75

2.89

11.57

2.22

8.86

1.75

7.00

I 200x100

26

33.06

8.11

2.05

41.06

30.35

15.90

36.17

8.94

30.35

5.72

23.60

3.97

15.90

2.92

11.68

2.24

8.94

1.77

7.07

I 150x125

36.2

46.15

6.18

2.89

60.64

51.68

40.08

56.51

24.81

51.68

15.88

46.20

11.03

40.08

8.10

33.29

6.20

24.81

4.90

19.60

I 250x125

38.3

48.79

10.3

2.63

63.31

52.43

38.21

58.31

21.72

52.43

13.90

45.73

9.65

38.21

7.09

28.37

5.43

21.72

4.29

17.16

I 300x150

48.3

61.58

12.4

3.09

81.56

70.72

56.76

76.55

39.70

70.72

24.22

64.11

16.82

56.76

12.36

48.64

9.46

39.70

7.48

29.90

I 200x150

50.4

64.16

8.34

3.43

85.90

76.19

63.79

81.41

48.83

76.19

31.09

70.31

21.59

63.79

15.86

56.63

12.15

48.83

9.60

40.31

I 250x125

55.5

70.73

10.2

2.76

92.39

77.70

58.60

85.63

34.68

77.70

22.19

68.69

15.41

58.60

11.32

47.35

8.67

34.68

6.85

27.40

I 350x150

58.5

74.58

14.3

3.07

98.70

85.45

68.37

92.58

47.49

85.45

28.95

77.37

20.11

68.37

14.77

58.44

11.31

47.49

8.94

35.75

I 300x150

65.5

83.47

12.3

3.26

111.19

97.59

80.16

104.90

59.01

97.59

36.54

89.34

25.38

80.16

18.64

70.07

14.27

59.01

11.28

45.11

I 400x150

72

91.73

16.2

3.07

121.40 105.10

84.10

113.88

58.41 105.10 35.61

95.16

24.73

84.10

18.17

71.88

13.91

58.41

10.99

43.97

I 300x150

76.8

97.88

12.2

3.32

130.63 115.10

95.22

123.45

71.15 115.10 44.44

105.68

30.86

95.22

22.67

83.73

17.36

71.15

13.72

54.87

I 350x150

87.2

111.1

14.2

3.26

147.99 129.90 106.70

139.63

78.55 129.90 48.64

118.91

33.78 106.70

24.81

93.27

19.00

78.55

15.01

60.05

I 450x175

91.7

116.8

18.3

3.6

157.08 140.59 119.60

149.44

94.40 140.59 62.35

130.63

43.30 119.60

31.81

107.53

24.36

94.40

19.25

80.13

I 400x150

95.8

122.1

16.1

3.18

162.22 141.61 115.12

152.70

82.89 141.61 50.86

129.07

35.32 115.12

25.95

99.76

19.87

82.89

15.70

62.79

I 450x175

115

146.1

18.3

3.72

197.04 177.36 152.38

187.92 122.45 177.36 83.28

165.49

57.84 152.38

42.49

138.03

32.53 122.45 25.70

105.57

I 600x190

133

169.4

24.1

3.81

228.92 206.87 178.92

218.69 145.51 206.87 106.36 193.59

70.34 178.92

51.68

162.89

39.57 145.51 31.26

126.70

I 600x190

176

224.5

24.1

3.97

304.38 276.82 241.98

291.58 200.47 276.82 152.08 260.26 101.22 241.98

74.36

222.05

56.93 200.47 44.99

177.18


4-46

Table 4.14: Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

H 100x50

9.3

11.85

3.98

1.12

11.62

3.83

1.70

6.80

0.96

3.83

0.61

2.45

0.43

1.70


0.31

1.25

0.24

0.96

0.19

0.76

H 125x60

13.2

16.84

4.95

1.32

18.13

7.55

3.36

13.25

1.89

7.55

1.21

4.83

0.84

3.36

0.62

2.47

0.47

1.89

0.37

1.49

H 150x75

14

17.85

6.11

1.66

20.99

12.98

5.63

17.36

3.17

12.98

2.03

8.10

1.41

5.63

1.03

4.14

0.79

3.17

0.63

2.50

H 100x100

17.2

21.9

4.18

2.47

28.15

22.79

15.73

24.16

8.60

20.42

5.50

16.09

3.82

10.95

2.81

8.04

2.15

6.16

1.70

4.86

H 175x90

18.1

23.04

7.26

2.06

28.64

21.24

11.19

25.26

6.29

21.24

4.03

16.57

2.80

11.19

2.05

8.22

1.57

6.29

1.24

4.97

H 198x99

18.2

23.18

8.26

2.21

29.23

22.53

12.95

26.16

7.29

22.53

4.66

18.34

3.24

12.95

2.38

9.52

1.82

7.29

1.44

5.76

H 148x100

21.1

26.84

6.17

2.37

34.27

27.28

18.02

31.06

9.70

27.28

6.21

22.95

4.31

18.02

3.17

12.67

2.43

9.70

1.92

7.67

H 200x100

21.3

27.16

8.24

2.22

34.27

26.48

15.32

30.70

8.62

26.48

5.51

21.61

3.83

15.32

2.81

11.25

2.15

8.62

1.70

6.81

H 125x125

23.8

30.31

5.29

3.11

40.17

34.89

28.08

36.28

19.78

32.66

12.08

28.54

8.39

23.90

6.16

17.83

4.72

13.65

3.73

10.78

H 248x124

25.7

32.68

10.4

2.79

42.75

36.07

27.39

39.67

16.37

36.07

10.48

31.98

7.28

27.39

5.35

22.29

4.09

16.37

3.23

12.94

H 250x125

29.6

37.66

10.4

2.79

49.27

41.57

31.56

45.72

18.87

41.57

12.08

36.85

8.39

31.56

6.16

25.68

4.72

18.87

3.73

14.91

H 194x150

30.6

39.01

8.3

3.61

52.47

46.99

40.01

49.93

31.63

46.99

20.94

43.68

14.54

40.01

10.68

36.00

8.18

31.63

6.46

26.89

H 150x150

31.5

40.14

6.39

3.75

54.17

48.83

42.04

50.25

33.93

46.63

23.25

42.53

16.15

37.98

11.86

32.97

9.08

27.47

7.18

20.84

H 298x149

32

408

3.9

1.04

379.25 113.79

50.58

202.30

28.45 113.79 18.21

72.83

12.64

50.58

9.29

37.16

7.11

28.45

5.62

22.48

H 300x150

36.7

46.78

12.4

3.30

62.38

45.27

58.91

33.63

54.88

20.93

50.33

14.53

45.27

10.68

39.71

8.17

33.63

6.46

25.83

H 175x175

40.2

51.21

7.5

4.38

69.92

64.46

57.59

65.95

49.45

62.29

40.06

58.18

28.10

53.64

20.65

48.68

15.81

43.28

12.49

37.45

H 346x174

41.4

52.68

14.5

3.88

71.29

64.60

56.14

68.19

46.03

64.60

34.21

60.58

22.66

56.14

16.65

51.29

12.74

46.03

10.07

40.35

H 244x175

44.1

56.24

10.4

4.18

76.54

70.13

62.04

73.56

52.44

70.13

41.31

66.28

28.11

62.04

20.65

57.43

15.81

52.44

12.49

47.08

H 350x175

49.6

63.14

14.7

3.95

85.57

77.76

67.87

81.94

56.10

77.76

42.36

73.06

28.15

67.87

20.68

62.22

15.83

56.10

12.51

49.48

H 200x200

49.9

63.53

8.62

5.02

87.47

81.87

74.89

83.42

66.69

79.71

57.31

75.56

46.72

70.98

33.65

66.01

25.76

60.64

20.35

54.87

54.88



4-47

Table 4.14(Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1) –Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



H 200x204

56.2

71.53

8.35

4.88

98.33

91.76

83.58

93.54

73.94

89.17

62.90

84.27

50.41

78.87

35.80

72.99

27.41

66.64

21.66

59.80

H 396x199

56.6

72.16

16.6

4.48

98.68

91.22

81.87

95.21

70.80

91.22

58.06

86.77

41.48

81.87

30.47

76.54

23.33

70.80

18.43

64.65

H 294x200

56.8

72.38

12.5

4.70

99.28

92.28

83.53

96.01

73.21

92.28

61.37

88.11

47.91

83.53

33.63

78.56

25.75

73.21

20.34

67.48

H 354x176

57.8

73.68

14.8

4.00

99.96

91.02

79.72

95.80

66.26

91.02

50.59

85.64

33.75

79.72

24.80

73.26

18.99

66.26

15.00

58.72

H 244x252

64.4

82.06

10.3

5.98

113.96 108.27 101.28

109.87

93.12 106.15 83.87

102.01

73.55

97.47

62.13

92.56

47.22

87.28

37.31

81.63

H 298x201

65.4

83.36

12.6

4.77

114.44 106.56

96.71

110.76

85.09 106.56 71.78

101.86

56.67

96.71

39.93

91.11

30.57

85.09

24.16

78.65

H 208x202

65.7

83.69

8.83

5.13

115.37 108.20

99.30

110.22

88.83 105.50 76.89

100.21

63.44

94.40

46.29

88.08

35.44

81.27

28.00

73.95

H 400x200

66

84.12

16.8

4.55

115.14 106.62

95.95

111.17

83.33 106.62 68.82

101.54

49.77

95.95

36.57

89.88

28.00

83.33

22.12

76.32

H 446x199

66.2

84.3

18.5

4.33

115.02 105.86

94.36

110.76

80.73 105.86 64.98

100.39

45.20

94.36

33.21

87.80

25.42

80.73

20.09

73.12

H 248x249

66.5

84.7

10.8

6.28

117.87 112.38 105.65

113.91

97.81 110.31 88.94

106.32

79.08 101.95

68.20

97.22

56.24

92.15

42.47

86.73

H 336x249

69.2

88.15

14.5

5.92

122.37 116.17 108.55

119.46

99.65 116.17 89.56

112.53

78.30 108.55

65.84

104.25

49.72

99.65

39.29

94.75

H 250x250

72.4

92.18

10.8

6.29

128.29 122.32 115.02

123.97 106.51 120.06 96.88

115.71

86.17 110.95

74.36

105.81

61.38 100.28 46.37

94.39

H 404x201

75.5

96.16

16.9

4.59

131.71 122.11 110.09

127.23

95.89 122.11 79.56

116.38

60.97 110.09

42.66

103.25

32.66

95.89

25.81

87.99

H 450x200

76

96.76

18.6

4.40

132.15 121.87 108.96

127.37

93.68 121.87 76.04

115.73

53.49 108.96

39.30

101.61

30.09

93.68

23.77

85.16

H 496x199

79.5

101.3

20.3

4.26

138.06 126.82 112.67

132.83

95.89 126.82 76.47

120.08

52.63 112.67

38.67

104.60

29.61

95.89

23.39

86.52

H 340x250

79.7

101.5

14.6

6.00

140.98 133.97 125.35

137.69 115.30 133.97 103.90 129.85

91.20 125.35

77.14

120.50

58.73 115.30 46.41

109.76

H 250x255

82.2

104.7

10.5

6.09

145.52 138.44 129.75

140.44 119.61 135.82 108.13 130.68

95.33 125.05

81.20

118.96

65.61 112.41 49.37

105.42

H 294x302

84.5

107.7

12.5

7.16

150.62 144.76 137.66

146.57 129.44 142.85 120.17 138.75 109.92 134.26

98.69

129.43

86.47 124.26 73.19

118.76

H 298x299

87

110.8

13.0

7.50

155.20 149.54 142.70

151.20 134.80 147.58 125.92 143.58 116.09 139.22 105.36

134.53

93.71 129.50 81.09

124.17

H 456x201

88.9

113.3

18.9

4.52

155.01 143.42 128.89

149.61 111.71 143.42 91.93

120.62

37.17 111.71 29.37

102.15


136.50

66.08 128.89

48.55

4-48

Table 4.14(Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1) –Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

H 500x200

89.6

114.2

20.5

4.33

155.81 143.41 127.82

150.04 109.35 143.41 88.01

34.43 109.35 27.21

99.05

H 300x300

94

119.8

13.0

7.51

167.81 161.69 154.30

163.50 145.76 159.60 136.15 155.28 125.54 150.58 113.94

145.52 101.35 140.10 87.71

134.35

H 386x299

94.3

120.1

16.8

7.21

168.00 161.53 153.69

164.95 144.60 161.53 134.38 157.77 123.06 153.69 110.67

149.29

97.19 144.60 82.55

139.63

H 596x199

94.6

120.5

23.9

4.05

163.63 149.27 131.15

156.96 109.57 149.27 84.49

140.65

56.64 131.15

41.61

120.78

31.86 109.57 25.17

97.49

H 506x201

103

131.3

20.7

4.43

179.42 165.64 148.33

173.00 127.85 165.64 104.24 157.40

73.80 148.33

54.22

138.48

41.51 127.85 32.80

116.45

H 300x305

106

134.8

12.6

7.26

188.61 181.41 172.69

183.56 162.60 178.96 151.23 173.87 138.66 168.33 124.91

162.35 109.95 155.96 93.70

149.16

H 304x301

106

134.8

13.2

7.57

188.88 182.07 173.86

184.09 164.37 179.76 153.70 174.97 141.91 169.75 129.04

164.13 115.07 158.13 99.94

151.74

H 338x351

106

135.3

14.4

8.33

190.12 184.09 176.87

185.84 168.57 182.00 159.26 177.77 149.00 173.18 137.83

168.24 125.76 162.97 112.77

157.38

H 434x299

106

135

18.6

7.04

188.69 181.18 172.06

185.15 161.50 181.18 149.59 176.81 136.40 172.06 121.95

166.95 106.20 161.50 89.07

155.71

H 600x200

106

134.4

24.0

4.12

182.72 167.07 147.32

175.45 123.85 167.07 96.60

136.04

110.72

135.99

157.67

61.22 127.82

65.22 147.32


44.98

47.92

118.94

36.69 123.85 28.99

H 390x300

107

136

16.9

7.28

190.31 183.08 174.32

186.90 164.19 183.08 152.78 178.88 140.16 174.32 126.35

169.42 111.33 164.19 95.04

158.64

H 482x300

114

145.5

20.4

6.82

203.13 194.68 184.39

199.15 172.46 194.68 158.99 189.75 144.06 184.39 127.67

178.62 109.77 172.46 85.94

165.91 172.25

H 344x348

115

146

15.1

8.76

205.44 199.35 192.09

201.05 183.76 197.15 174.43 192.87 164.17 188.22 153.01

183.23 140.97 177.90 128.04

H 606x201

120

152.5

24.3

4.22

207.71 190.56 168.97

199.73 143.35 190.56 113.68 180.29

156.66

H 440x300

124

157.4

18.9

7.18

220.15 211.62 201.28

H 488x300

128

163.5

20.8

7.04

H 344x354

131

166.6

14.6

8.42

H 612x202

134

170.7

24.6

H 350x350

137

173.9

15.2

H 582x300

137

174.5

H 388x402

140

178.5

43.77 143.35 34.58

129.04

216.12 189.30 211.62 175.81 206.66 160.89 201.28 144.55

195.49 126.76 189.30 107.44

182.74

228.53 219.44 208.41

224.24 195.62 219.44 181.20 214.15 165.25 208.41 147.76

202.22 128.70 195.62 107.96

188.61

234.17 226.85 218.10

228.94 208.03 224.26 196.74 219.12 184.31 213.53 170.78

207.52 156.16 201.11 140.44

194.30

4.32

232.85 214.24 190.84

224.19 163.10 214.24 131.05 203.10

51.17 163.10 40.43

147.63

8.84

244.76 237.60 229.06

239.58 219.27 234.98 208.32 229.93 196.27 224.46 183.17

218.58 169.04 212.31 153.88

205.66

24.3

6.63

243.37 232.85 220.01

238.41 205.10 232.85 188.26 226.70 169.58 220.01 149.04

212.81 126.56 205.10 97.51

196.92

16.6

9.56

251.72 245.07 237.20

246.99 228.20 242.78 218.16 238.17 207.13 233.19 195.17

227.84 182.29 222.15 168.51

216.13


77.81 168.97

90.97 190.84

57.17

66.83

177.50

4-49

Table 4.14(Continued): Compression Capacity (Ton) For H Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight [Note: * = Not Available] Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2 Kly=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

Cm

cm

cm

Kly=1

H 388x402

140

178.5

16.6

9.56

251.72 245.07 237.20

246.99 228.20 242.78 218.16 238.17 207.13 233.19 195.17


227.84 182.29 222.15 168.51

216.13

H 446x302

145

184.3

19.0

7.24

257.85 247.97 236.01

253.19 222.16 247.97 206.57 242.24 189.32 236.01 170.44

229.31 149.90 222.16 127.60

214.58

H 394x398

147

186.8

17.3

10.06

263.74 257.22 249.54

259.03 240.78 254.87 231.03 250.34 220.33 245.44 208.73

240.20 196.27 234.62 182.95

228.71

H 494x302

150

191.4

20.9

7.10

267.61 257.09 244.33

262.65 229.55 257.09 212.89 250.98 194.46 244.33 174.26

237.18 152.26 229.55 128.34

221.45

H 588x300

151

192.5

24.8

6.85

268.79 257.67 244.15

263.55 228.45 257.67 210.74 251.19 191.12 244.15 169.58

236.56 146.07 228.45 114.68

219.84

H 350x357

156

198.4

14.7

8.52

278.97 270.39 260.13

272.78 248.35 267.28 235.15 261.23 220.62 254.66 204.80

247.59 187.72 240.05 169.36

232.06

H 692x300

166

211.5

28.5

6.53

294.80 281.78 265.89

288.67 247.41 281.78 226.54 274.18 203.36 265.89 177.86

256.96 149.91 247.41 114.68

237.27

H 394x405

168

214.4

16.7

9.65

302.42 294.53 285.20

296.78 274.54 291.78 262.65 286.30 249.60 280.38 235.44

274.03 220.20 267.28 203.90

260.12

H 400x400

172

218.7

17.5

10.12

308.82 301.25 292.33

303.36 282.17 298.54 270.84 293.28 258.43 287.61 244.98

281.52 230.52 275.05 215.08

268.21

H 594x302

175

222.4

24.8

6.90

310.64 297.94 282.50

304.65 264.59 297.94 244.39 290.54 222.01 282.50 197.46

273.84 170.68 264.59 141.47

254.77

H 700x300

185

235.5

29.2

6.77

328.70 314.90 298.10

322.20 278.59 314.90 256.58 306.86 232.17 298.10 205.37

288.67 176.09 278.59 137.31

267.89

H 792x300

191

243.4

32.3

6.39

338.97 323.53 304.66

331.71 282.69 323.53 257.85 314.50 230.24 304.66 199.82

294.04 166.43 282.69 126.25

270.62

H 400x408

197

250.7

16.8

9.74

353.70 344.59 333.82

347.14 321.53 341.35 307.82 335.01 292.77 328.15 276.45

320.80 258.89 312.98 240.12

304.70

H 800x300

210

267.4

33.0

6.61

372.90 356.73 337.00

365.28 314.07 356.73 288.18 347.28 259.45 337.00 227.86

325.92 193.28 314.07 148.75

301.49

*H 890x299

213

270.9

35.7

6.17

376.72 358.70 336.61

368.25 310.85 358.70 281.70 348.13 249.23 336.61 213.40

324.17 173.92 310.85 130.95

296.69

H 414x405

232

295.4

17.7

10.24

417.24 407.17 395.32

410.03 381.83 403.66 366.80 396.71 350.33 389.21 332.48

381.17 313.31 372.63 292.84

363.59

*H 900x300

243

309.8

36.4

6.38

431.41 411.72 387.65

422.15 359.62 411.72 327.93 400.20 292.70 387.65 253.90

374.11 211.29 359.62 160.19

344.22

*H 428x407

283

360.7

18.2

10.45

509.70 497.71 483.63

501.21 467.61 493.68 449.78 485.47 430.25 476.61 409.10

467.14 386.40 457.06 362.15

446.41

*H 912x302

286

364

37.0

6.57

507.47 485.24 458.11

497.01 426.57 485.24 390.95 472.25 351.40 458.11 307.90

442.87 260.26 426.57 199.61

409.26

*H 458x417

415

528.6

18.8

10.70

747.32 730.27 710.27

735.59 687.55 725.05 662.29 713.58 634.63 701.21 604.70

688.00 572.57 673.95 538.29

659.12

*H 498x432

605

770.1

19.7

11.07

1089.5 1065.7 1037.9 1073.57 1006.4 1059.1 971.33 1043.37 933.00 1026.4 891.55 1008.36 847.10 989.17 799.70

968.91


4-50

Table 4.15: Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

T 50x100

8.6

10.95

1.21

2.47

11.27

4.13

1.83

1.83

1.03

1.03

0.66

0.66

0.46

0.46


0.34

0.34

0.26

0.26

0.20

0.20

T 99x99

9.1

11.59

2.84

2.21

14.61

11.26

6.48

9.89

3.64

6.02

2.33

3.85

1.62

2.67

1.19

1.96

0.91

1.50

0.72

1.19

T 74x100

10.5

13.42

1.96

2.37

16.50

11.85

5.90

5.90

3.32

3.32

2.12

2.12

1.47

1.47

1.08

1.08

0.83

0.83

0.66

0.66

T 100x100

10.7

13.58

2.9

2.22

17.14

13.24

7.66

11.83

4.31

7.35

2.76

4.70

1.91

3.27

1.41

2.40

1.08

1.84

0.85

1.45

T 62.5x125

11.9

15.16

1.52

3.11

17.31

9.02

4.01

4.01

2.25

2.25

1.44

1.44

1.00

1.00

0.74

0.74

0.56

0.56

0.45

0.45

T 124x124

12.8

16.34

3.57

2.79

21.38

18.04

13.70

16.65

8.19

13.08

5.24

8.58

3.64

5.96

2.67

4.38

2.05

3.35

1.62

2.65

T 125x125

14.8

18.83

3.63

2.79

24.63

20.78

15.78

19.37

9.43

15.36

6.04

10.22

4.19

7.10

3.08

5.21

2.36

3.99

1.86

3.15

T 97x150

15.3

19.51

2.53

3.61

25.17

20.56

14.51

14.51

8.04

8.04

5.14

5.14

3.57

3.57

2.62

2.62

2.01

2.01

1.59

1.59

T 75x150

15.8

20.07

1.82

3.75

24.23

16.43

7.61

7.61

4.28

4.28

2.74

2.74

1.90

1.90

1.40

1.40

1.07

1.07

0.85

0.85

T 149x149

16

20.4

4.39

3.29

27.20

23.92

19.72

22.96

14.63

19.73

9.10

16.00

6.32

11.25

4.64

8.26

3.55

6.33

2.81

5.00

T 150x150

18.4

23.39

4.45

3.29

31.19

27.43

22.61

26.46

16.77

22.84

10.43

18.66

7.24

13.25

5.32

9.73

4.07

7.45

3.22

5.89

T 87.5x175

20.1

25.61

2.12

4.38

32.03

24.15

13.17

13.17

7.41

7.41

4.74

4.74

3.29

3.29

2.42

2.42

1.85

1.85

1.46

1.46

T 173x174

20.7

26.34

5.08

3.88

35.65

32.31

28.08

31.16

23.03

27.82

17.13

24.00

11.34

19.70

8.33

14.29

6.38

10.94

5.04

8.64

T 122x175

22.1

28.12

3.2

4.18

37.39

32.68

26.64

26.64

19.29

19.29

11.86

11.86

8.24

8.24

6.05

6.05

4.63

4.63

3.66

3.66

T 175x175

24.8

31.57

5.08

3.95

42.79

38.88

33.95

37.35

28.06

33.34

21.20

28.77

14.09

23.61

10.35

17.12

7.93

13.11

6.26

10.36

T 100x200

24.9

31.77

2.41

5.02

40.67

32.61

21.95

21.95

11.88

11.88

7.60

7.60

5.28

5.28

3.88

3.88

2.97

2.97

2.35

2.35

T 100x204

28.1

35.77

2.67

4.88

46.52

38.71

28.53

28.53

16.41

16.41

10.50

10.50

7.29

7.29

5.36

5.36

4.10

4.10

3.24

3.24

T 198x199

28.3

36.08

5.76

4.48

49.34

45.61

40.92

44.14

35.39

40.35

29.01

36.04

20.71

31.23

15.22

25.89

11.65

19.26

9.21

15.22

T 147x200

28.4

36.19

3.97

4.71

49.07

44.62

39.01

39.01

32.32

32.32

24.51

24.51

16.32

16.32

11.99

11.99

9.18

9.18

7.25

7.25

T 122x252

32.2

41.03

3.29

5.98

54.71

48.11

39.66

39.66

29.42

29.42

18.29

18.29

12.70

12.70

9.33

9.33

7.15

7.15

5.65

5.65


4-51

Table 4.15(Continued): Compression Capacity (Ton) For T Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



T 149x201

32.7

41.68

3.99

4.77

56.53

51.45

45.03

45.03

37.38

37.38

13.95

T 104x202

32.8

41.85

2.45

5.13

53.72

43.36

29.68

29.68

16.17

16.17

10.35

10.35

7.19

7.19

5.28

5.28

4.04

4.04

3.19

3.19

T 200x200

33.0

42.06

5.76

4.54

57.57

53.29

47.94

51.46

41.62

47.04

34.34

42.02

24.80

36.41

18.22

30.18

13.95

22.45

11.02

17.74 23.84

28.48

28.48

18.98

18.98

13.95

10.68

10.68

8.44

8.44

T 223x199

33.1

42.15

6.67

4.33

57.51

52.93

47.18

53.20

40.37

49.63

32.50

45.60

22.61

41.13

16.61

36.22

12.72

30.84

10.05

T 124x249

33.2

42.35

2.93

6.29

55.74

47.69

37.26

37.26

23.40

23.40

14.98

14.98

10.40

10.40

7.64

7.64

5.85

5.85

4.62

4.62

T 168x249

34.6

44.08

4.47

5.92

60.27

55.69

49.96

49.96

43.17

43.17

35.35

35.35

25.19

25.19

18.51

18.51

14.17

14.17

11.20

11.20

T 125x250

36.2

46.09

2.99

6.29

60.81

52.30

41.31

41.31

26.52

26.52

16.97

16.97

11.79

11.79

8.66

8.66

6.63

6.63

5.24

5.24

T 225x200

38.0

48.38

6.68

4.40

66.08

60.95

54.50

61.09

46.87

57.00

38.06

52.38

26.79

47.26

19.68

41.63

15.07

35.48

11.91

27.45

T 248x199

39.7

50.64

7.49

4.27

69.03

63.42

56.37

65.20

48.00

61.58

38.33

57.51

26.41

53.01

19.40

48.09

14.86

42.74

11.74

36.96

T 170x250

39.8

50.76

4.48

6

69.41

64.16

57.58

57.58

49.79

49.79

40.81

40.81

29.14

29.14

21.41

21.41

16.39

16.39

12.95

12.95

T 125x255

41.1

52.34

3.36

6.09

679.93

61.77

51.34

51.34

38.71

38.71

24.34

24.34

16.90

16.90

12.42

12.42

9.51

9.51

7.51

7.51

T147x302

42.3

53.83

3.99

7.16

73.01

66.45

58.16

58.16

48.28

48.28

36.78

36.78

24.51

24.51

18.01

18.01

13.79

13.79

10.90

10.90

T 149x299

43.5

55.40

3.59

7.51

74.49

66.63

56.64

56.64

44.63

44.63

29.41

29.41

20.42

20.42

15.01

15.01

11.49

11.49

9.08

9.08

T 250x200

44.8

57.12

7.5

4.33

77.93

71.73

63.94

73.56

54.70

69.48

44.04

64.90

30.64

59.83

22.51

54.29

17.23

48.28

13.62

41.77

T 150x300

47.0

59.89

3.65

7.51

80.64

72.35

61.81

61.81

49.17

49.17

32.87

32.87

22.82

22.82

16.77

16.77

12.84

12.84

10.14

10.14

T 193x299

47.1

60.05

5.04

7.21

82.70

77.43

70.87

70.87

63.16

63.16

54.36

54.36

44.42

44.42

32.06

32.06

24.54

24.54

19.39

19.39

T 298x199

47.3

60.23

9.29

4.05

81.78

74.60

65.52

78.44

54.73

74.60

42.17

70.28

28.26

65.52

20.76

60.34

15.90

54.73

12.56

48.68

T 253x201

51.5

65.65

7.48

4.43

89.71

82.81

74.15

84.51

63.90

79.81

52.08

74.51

36.86

68.67

27.08

62.28

20.73

55.34

16.38

47.82

T 300x200

52.8

67.21

9.3

4.12

91.38

83.55

73.68

87.74

61.95

83.55

48.33

78.86

32.63

73.68

23.98

68.04

18.36

61.95

14.50

55.38



4-52


Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



T 150x305

52.9

67.39

4.05

7.26

91.51

83.47

73.31

73.31

61.23

61.23

47.18

47.18

31.62

31.62

23.23

23.23

17.79

17.79

14.05

14.05

T 152x301

52.9

67.41

3.66

7.57

90.79

81.49

69.68

69.68

55.51

55.51

37.20

37.20

25.83

25.83

18.98

18.98

14.53

14.53

11.48

11.48

T 217x299

53.0

67.52

5.89

7.04

93.71

88.93

83.05

83.05

76.18

76.18

68.39

68.39

59.69

59.69

50.06

50.06

37.69

37.69

29.78

29.78

T 169x351

53.1

67.63

4.59

8.33

92.63

85.86

77.40

77.40

67.39

67.39

55.89

55.89

42.79

42.79

29.95

29.95

22.93

22.93

18.11

18.11

T 195x300

53.4

67.98

5.05

7.28

93.63

87.68

80.28

80.28

71.58

71.58

61.64

61.64

50.42

50.42

36.44

36.44

27.90

27.90

22.04

22.04

T 241x300

57.1

72.76

6.85

6.82

101.58

97.36

92.22

92.29

86.25

86.37

79.52

79.68

72.06

72.27

63.88

64.14

54.94

55.26

43.03

45.58

T 172x348

57.3

73

4.11

8.78

99.23

90.70

79.94

79.94

67.15

67.15

52.30

52.30

35.27

35.27

25.92

25.92

19.84

19.84

15.68

15.68

T 303x201

59.8

76.24

9.28

4.22

103.83

95.25

84.45

99.84

71.62

95.25

56.77

90.11

38.84

84.45

28.53

78.28

21.85

71.62

17.26

64.46

T 220x300

61.8

78.69

5.84

7.68

109.17 103.53

96.59

96.59

88.49

88.49

79.29

79.29

69.02

69.02

57.64

57.64

43.18

43.18

34.12

34.12

T 244x300

64.2

81.76

6.66

7.07

114.05 109.15 103.17

103.17

96.23

96.23

88.40

88.40

79.70

79.70

70.15

70.15

59.70

59.70

46.11

46.11

T 172x354

65.4

83.32

4.65

8.43

114.21 106.03

95.79

95.79

83.71

83.71

69.83

69.83

54.05

54.05

37.86

37.86

28.99

28.99

22.90

22.90

T 306x202

67.0

85.33

9.27

4.31

116.39 107.06

95.34

112.05

81.45 107.06 65.39

101.48

45.34

95.34

33.31

88.66

25.51

81.45

20.15

73.70

T 175x350

68.2

86.94

4.18

8.84

118.33 108.41

95.91

95.91

81.07

63.87

63.87

43.45

43.45

31.93

31.93

24.44

24.44

19.31

19.31

T 291x300

68.5

87.24

8.54

6.63

121.67 116.41 109.99

114.42 102.54 109.26 94.12

103.47

84.78

97.11

74.51

90.18

63.28

82.69

48.75

74.65

5.27

9.54

123.18 115.82 106.69

106.69

95.98

95.98

83.76

83.76

70.04

70.04

52.08

52.08

39.88

39.88

31.51

31.51

94.22

94.22

78.82

78.82

61.32

81.07

70.0

89.23

T 197x398

73.3

93.41

4.68

10.10

128.09 119.00 107.63

107.63

61.32

43.00

43.00

32.92

32.92

26.01

26.01

T 294x300

75.6

96.24

8.35

6.85

134.39 128.83 122.08

125.86 114.24 119.97 105.39 113.38

95.59 106.12

84.84

98.21

73.10

89.66

60.28

80.46

T 175x357

77.9

99.19

4.71

8.53

136.07 126.50 114.55

114.55 100.44 100.44 84.25

84.25

65.87

65.87

46.25

46.25

35.41

35.41

27.98

27.98

T 178x352

79.3

101

4.25

8.9

137.62 126.37 112.20

112.20

75.95

52.19

52.19

38.34

38.34

29.35

29.35

23.19

23.19

T 194x400

95.40

95.40

75.95



4-53


Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

Kly=1

Kly=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

T 346x300

83

105.7

10.3

6.53

147.33 140.82 132.88

141.53 123.65 136.74 113.21 131.40 101.62 125.55

88.88

119.22

74.91 112.42 57.30

105.15

T 197x405

84.1

107.20

5.34

9.65

148.09 139.40 128.64

128.64 116.02 116.02 101.65 101.65

85.51

85.51

67.46

67.46

49.19

49.19

38.86

38.86

T 200x400

85.8

109.30

4.76

10.10

150.03 139.64 126.67

126.67 111.38 111.38 93.83

73.93

73.93

52.05

52.05

39.85

39.85

31.49

31.49

T 297x302

87.3

111.2

8.44

6.9

155.32 148.96 141.24

145.63 132.27 138.93 122.17 131.43 110.97 123.17

98.68

114.18

85.28 104.47 70.66

94.02

T 350x300

92.4

117.7

10.1

6.78

164.29 157.40 149.02

157.30 139.29 151.81 128.30 145.70 116.13 139.00 102.76

131.74

88.15 123.93 68.79

115.59

T 396x300

95.6

121.7

12.1

6.38

169.48 161.75 152.29

165.20 141.29 160.80 128.85 155.92 115.02 150.60

99.79

144.85

83.06 138.70 62.98

132.15

98.4

125.30

5.40

9.75

172.77 162.80 150.46

150.46 135.99 135.99 119.51 119.51 101.03 101.03

80.38

80.38

58.65

46.34

46.34

T 400x300

105

133.7

11.9

6.62

186.46 178.38 168.52

181.26 157.07 176.31 144.15 170.82 129.80 164.83 114.02

158.36

96.76 151.43 74.49

144.05

T 207x405

116.0 147.70

4.95

10.20

203.20 189.91 173.36

173.36 153.88 153.88 131.59 131.59 106.40 106.40

76.06

58.23

46.01

T 200x408


KLx=7

93.83


76.06

58.65

58.23

46.01

Note: The availability of the sections can be checked from Chapter 2 – Table for ‘Properties of SYS Steel Sections’ **- Currently not available].


4-54

Table 4.16: Compression Capacity (Ton) For EL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

cm

cm

cm

Kly=1

Kly=2

1.12

1.427

0.747

0.747

0.82

0.21

EL 30x30

1.36

1.727

0.908

0.908

1.41

0.37

0.16

0.16

EL 25x25

1.77

2.26

0.73

0.73

1.24

0.31

0.14

0.14

EL 40x40

1.83

2.336

1.23

1.23

2.43

0.91

0.40

0.40

EL 30x30

2.18

2.78

0.88

0.88

2.19

0.55

0.25

EL 50x50

2.33

2.96

1.52

1.52

3.38

1.76

0.78

EL 40x40

2.42

3.08

1.21

1.21

3.17

1.16

EL 45x45

2.74

3.492

1.36

1.36

3.81

1.66

EL 40x40

2.95

3.755

1.2

1.2

3.85

EL 50x50

3.06

3.892

1.53

1.53

EL 45x45

3.38

4.302

1.36

1.36

EL 40x40

3.52

4.48

1.19

EL 60x60

3.68

4.692

EL 50x50

3.77

4.802

EL 50x50

4.43

5.644

EL 60x60

4.55

5.802

EL 65x65

5.00

6.367

EL 25x25

KLx=4

KLx=5

KLx=6


0.09

0.09

0.05

0.05

0.03

0.03

0.02

0.02

0.09

0.09

0.06

0.06

0.04

0.04

0.08

0.08

0.05

0.05

0.03

0.03

0.23

0.23

0.15

0.15

0.10

0.10

0.25

0.14

0.14

0.09

0.09

0.06

0.78

0.44

0.44

0.28

0.28

0.20

0.52

0.52

0.29

0.29

0.19

0.19

0.74

0.74

0.42

0.42

0.27

0.27

1.39

0.62

0.62

0.35

0.35

0.22

4.45

2.46

1.04

1.04

0.59

0.59

4.70

2.05

0.91

0.91

0.51

0.51

1.19

4.57

1.63

0.73

0.73

0.41

1.85

1.85

5.69

3.91

1.84

1.84

1.52

1.52

5.48

2.86

1.27

1.27

1.5

1.5

6.41

3.27

1.45

1.45

0.82

0.82

0.52

1.84

1.84

7.02

4.81

2.25

2.25

1.26

1.26

0.81

1.99

1.99

7.86

5.70

2.89

2.89

1.62

1.62

1.04

KLx=7

KLx=8

KLx=9


0.02

0.02

0.01

0.01

0.01

0.01

0.03

0.03

0.02

0.02

0.02

0.02

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.07

0.06

0.06

0.04

0.04

0.06

0.05

0.05

0.03

0.03

0.03

0.03

0.20

0.14

0.14

0.11

0.11

0.09

0.09

0.13

0.13

0.09

0.09

0.07

0.07

0.06

0.06

0.18

0.18

0.14

0.14

0.10

0.10

0.08

0.08

0.22

0.15

0.15

0.11

0.11

0.09

0.09

0.07

0.07

0.38

0.38

0.26

0.26

0.19

0.19

0.15

0.15

0.12

0.12

0.33

0.33

0.23

0.23

0.17

0.17

0.13

0.13

0.10

0.10

0.41

0.26

0.26

0.18

0.18

0.13

0.13

0.10

0.10

0.08

0.08

1.03

1.03

0.66

0.66

0.46

0.46

0.34

0.34

0.26

0.26

0.20

0.20

0.71

0.71

0.46

0.46

0.32

0.32

0.23

0.23

0.18

0.18

0.14

0.14

0.52

0.36

0.36

0.27

0.27

0.20

0.20

0.16

0.16

0.81

0.56

0.56

0.41

0.41

0.32

0.32

0.25

0.25

1.04

0.72

0.72

0.53

0.53

0.41

0.41

0.32

0.32

EL 65x65

5.91

7.527

1.98

1.98

9.28

6.71

3.38

3.38

1.90

1.90

1.22

1.22

0.84

0.84

0.62

0.62

0.47

0.47

0.38

0.38

EL 70x70

6.38

8.127

2.14

2.14

10.18

7.72

4.26

4.26

2.40

2.40

1.53

1.53

1.06

1.06

0.78

0.78

0.60

0.60

0.47

0.47

EL 75x75

6.85

8.727

2.3

2.3

11.08

8.71

5.55

5.55

2.97

2.97

1.90

1.90

1.32

1.32

0.97

0.97

0.74

0.74

0.59

0.59


4-55

Table 4.16(Continued): Compression Capacity (Ton) For EL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

EL 80x80

7.32

9.327

2.46

2.46

11.98

9.68

6.66

6.66

3.63

3.63

2.33

2.33

1.61

1.61


1.19

1.19

0.91

0.91

0.72

0.72

EL 65x65

7.66

9.761

1.94

1.94

11.97

8.53

4.20

4.20

2.36

2.36

1.51

1.51

1.05

1.05

0.77

0.77

0.59

0.59

0.47

0.47

EL 90x90

8.28

10.55

2.77

2.77

13.79

11.61

8.77

8.77

5.21

5.21

3.33

3.33

2.32

2.32

1.70

1.70

1.30

1.30

1.03

1.03

EL 90x90

9.59

12.22

2.76

2.76

15.96

13.43

10.12

10.12

5.99

5.99

3.83

3.83

2.66

2.66

1.96

1.96

1.50

1.50

1.18

1.18

EL 75x75

9.96

12.69

2.25

2.25

16.05

12.48

7.35

7.35

4.13

4.13

2.65

2.65

1.84

1.84

1.35

1.35

1.03

1.03

0.82

0.82

EL 100x100

10.7

13.62

3.08

3.08

18.03

15.62

12.52

12.52

8.73

8.73

5.32

5.32

3.70

3.70

2.72

2.72

2.08

2.08

1.64

1.64

EL 75x75

13

16.56

2.22

2.22

20.90

16.14

9.34

9.34

5.25

5.25

3.36

3.36

2.33

2.33

1.72

1.72

1.31

1.31

1.04

1.04

EL 90x90

13.3

17

2.71

2.71

22.15

18.53

13.80

13.80

8.04

8.04

5.14

5.14

3.57

3.57

2.62

2.62

2.01

2.01

1.59

1.59

EL 120x120

14.7

18.76

3.71

3.71

25.30

22.76

19.54

19.54

15.68

15.68

10.64

10.64

7.39

7.39

5.43

5.43

4.15

4.15

3.28

3.28

EL 100x100

14.9

19

3.04

3.04

25.12

21.69

17.28

17.28

11.30

11.30

7.23

7.23

5.02

5.02

3.69

3.69

2.83

2.83

2.23

2.23

EL 90x90

15.9

20.3

2.7

2.7

26.44

22.08

16.41

16.41

9.52

9.52

6.10

6.10

4.23

4.23

3.11

3.11

2.38

2.38

1.88

1.88

EL 90x90

17.0

21.71

2.68

2.68

28.25

23.54

17.39

17.39

10.04

10.04

6.42

6.42

4.46

4.46

3.28

3.28

2.51

2.51

1.98

1.98

EL 100x100

17.8

22.7

3.02

3.02

29.99

25.85

20.52

20.52

13.33

13.33

8.53

8.53

5.92

5.92

4.35

4.35

3.33

3.33

2.63

2.63

EL 130x130

17.9

22.74

4.01

4.01

30.85

28.10

24.63

24.63

20.49

20.49

15.67

15.67

10.46

10.46

7.68

7.68

5.88

5.88

4.65

4.65

EL 100x100

19.1

24.31

3

3

32.09

27.62

21.85

21.85

14.08

14.08

9.01

9.01

6.26

6.26

4.60

4.60

3.52

3.52

2.78

2.78

EL 130x130

23.40

29.76

3.96

3.96

40.34

36.67

32.04

32.04

26.51

26.51

20.07

20.07

13.35

13.35

9.81

9.81

7.51

7.51

5.93

5.93

EL 150x150

27.3

34.77

4.61

4.61

47.63

44.18

39.85

39.85

34.74

34.74

28.87

28.87

22.19

22.19

15.53

15.53

11.89

11.89

9.39

9.39

EL 130x130

28.8

36.75

3.93

3.93

49.79

45.21

39.42

39.42

32.52

32.52

24.46

24.46

16.24

16.24

11.93

11.93

9.13

9.13

7.22

7.22

EL 175x175

31.8

40.52

5.38

5.38

56.00

52.75

48.72

48.72

44.01

44.01

38.64

38.64

32.61

32.61

25.87

25.87

18.87

18.87

14.91

14.91

EL 150x150

33.6

42.74

4.56

4.56

58.51

54.20

48.80

48.80

42.41

42.41

35.07

35.07

25.42

25.42

18.68

18.68

14.30

14.30

11.30

11.30



4-56

Table 4.16(Continued): Compression Capacity (Ton) For L Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2



EL 175x175

39.4

50.21

5.35

5.35

69.37

65.31

60.28

60.28

54.39

54.39

47.68

47.68

40.14

40.14

31.71

31.71

23.12

23.12

18.27

18.27

EL 150x150

41.9

53.38

4.52

4.52

73.04

67.58

60.75

60.75

52.67

52.67

43.36

43.36

31.20

31.20

22.92

22.92

17.55

17.55

13.87

13.87

EL 200x200

45.3

57.75

6.14

6.14

80.29

76.43

71.69

71.69

66.17

66.17

59.91

59.91

52.95

52.95

45.25

45.25

36.77

36.77

27.68

27.68

EL 200x200

59.7

76

6.09

6.09

105.63 100.49

94.18

94.18

86.82

86.82

78.49

78.49

69.20

69.20

58.94

58.94

47.62

47.62

35.84

35.84

96.37

84.76

84.76

71.93

71.93

55.03

55.03

EL 200x200

73.6

93.75

6.04

6.04

130.26 123.84 115.97

115.97 106.78 106.78 96.37

43.48

43.48

EL 250x250

93.7

119.4

7.63

7.63

167.34 161.37 154.17

154.17 145.86 145.86 136.51 136.51 126.19 126.19 114.92

114.92 102.69 102.69 89.47

89.47

EL 250x250

128.0

162.6

7.49

7.49

227.75 219.42 209.36

209.36 197.73 197.73 184.65 184.65 170.19 170.19 154.40

154.40 137.24 137.24 118.66

118.66



4-57

Table 4.17: Compression Capacity (Ton) For UL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) –Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

cm

cm

cm

Kly=1

Kly=2

11.87

3.15

2.19

14.94

11.46

13.62

4.01

2.11

17.02

12.80

6.94

14.04

2.78

2.2

17.69

13.60

7.78

3.11

2.15

20.69

15.72

8.73

15.29

KLx=4

KLx=5

KLx=6


UL 100x75

9.32

6.51

UL 125x75

10.7

UL 90x75

11

UL 100x75

13

16.5

UL 125x75

14.9

19.00

3.96

2.06

23.62

17.51

9.23

UL 125x90

16.1

20.5

3.94

2.59

26.54

21.87

15.74

11.11

3.66

7.93

2.35

4.85

1.63

14.75

3.90

12.27

2.50

9.38

1.73

11.72

4.37

6.98

2.80

4.47

1.94

4.91

10.77

3.14

6.57

2.18

20.45

5.19

16.93

3.32

12.81

22.02

8.85

18.18

5.66

13.70

3.37

KLx=7

KLx=8

KLx=9


1.20

2.48

0.92

1.90

0.72

1.50

6.26

1.27

4.60

0.98

3.52

0.77

2.78

3.10

1.43

2.28

1.09

1.75

0.86

1.38

4.57

1.60

3.35

1.23

2.57

0.97

2.03

2.31

8.52

1.69

6.26

1.30

4.79

1.03

3.79

3.93

9.10

2.89

6.69

2.21

5.12

1.75

4.05

UL 150x90

16.4

20.94

4.81

2.52

27.00

22.03

15.49

24.35

8.56

21.47

5.48

18.16

3.80

14.42

2.79

10.18

2.14

7.80

1.69

6.16

UL 150x100

17.1

21.84

4.79

2.88

28.69

24.43

18.90

25.36

11.66

22.34

7.46

18.87

5.18

14.93

3.81

10.53

2.91

8.06

2.30

6.37

UL 125x75

19.1

24.31

3.93

2.04

30.16

22.23

11.58

26.08

6.51

21.51

4.17

16.18

2.89

10.74

2.13

7.89

1.63

6.04

1.29

4.77

UL 125x90

20.6

26.26

3.91

2.57

33.96

27.90

19.96

28.10

11.16

23.13

7.14

17.32

4.96

11.48

3.65

8.44

2.79

6.46

2.21

5.10

UL 150x90

21.5

27.36

4.76

2.47

35.17

28.47

19.65

31.71

10.74

27.88

6.88

23.49

4.77

18.51

3.51

13.03

2.69

9.97

2.12

7.88

UL 150x100

22.4

28.56

4.74

2.83

37.43

31.71

24.29

33.05

14.72

29.03

9.42

24.42

6.54

19.18

4.81

13.49

3.68

10.33

2.91

8.16

UL 150x100

27.7

35.25

4.71

2.8

46.13

38.97

29.66

40.71

17.79

35.69

11.38

29.94

7.91

23.41

5.81

16.43

4.45

12.58

3.51

9.94



4-58

Table 4.18: Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

ELL 25x25

2.24

2.854

0.75

1.15

1.64

0.41

0.18

0.18

0.10

0.10

0.07

0.07

0.05

0.05

0.03

0.03

0.03

0.03

0.02

0.02

ELL 25x25

2.72

3.454

0.73

1.28

1.89

0.47

0.21

0.21

0.12

0.12

0.08

0.08

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

ELL 30x30

3.54

4.52

0.91

1.35

3.68

0.96

0.43

0.43

0.24

0.24

0.15

0.15

0.11

0.11

0.08

0.08

0.06

0.06

0.05

0.05

ELL 30x30

3.66

4.672

0.88

1.46

3.68

0.93

0.42

0.42

0.23

0.23

0.15

0.15

0.10

0.10

0.08

0.08

0.06

0.06

0.05

0.05

ELL 40x40

4.36

5.56

1.23

1.75

5.77

2.16

0.96

0.96

0.54

0.54

0.35

0.35

0.24

0.24

0.18

0.18

0.14

0.14

0.11

0.11

ELL 40x40

4.66

5.92

1.20

1.79

6.08

2.21

0.98

0.98

0.55

0.55

0.35

0.35

0.25

0.25

0.18

0.18

0.14

0.14

0.11

0.11

ELL 40x40

4.84

6.16

1.20

1.86

6.31

2.29

1.02

1.02

0.57

0.57

0.37

0.37

0.25

0.25

0.19

0.19

0.14

0.14

0.11

0.11

ELL 40x40

5.48

6.984

1.19

1.91

7.11

2.53

1.13

1.13

0.63

0.63

0.41

0.41

0.28

0.28

0.21

0.21

0.16

0.16

0.13

0.13

ELL 45x45

5.9

7.51

1.36

1.98

8.21

3.60

1.60

1.60

0.90

0.90

0.58

0.58

0.40

0.40

0.29

0.29

0.22

0.22

0.18

0.18

ELL 45x45

6.12

7.784

1.36

2.04

8.49

3.68

1.64

1.64

0.92

0.92

0.59

0.59

0.41

0.41

0.30

0.30

0.23

0.23

0.18

0.18

ELL 50x50

6.76

8.604

1.52

2.11

9.83

5.39

2.28

2.28

1.28

1.28

0.82

0.82

0.57

0.57

0.42

0.42

0.32

0.32

0.25

0.25

ELL 50x50

7.04

8.96

1.53

2.19

10.24

5.64

2.39

2.39

1.34

1.34

0.86

0.86

0.60

0.60

0.44

0.44

0.34

0.34

0.27

0.27

ELL 50x50

7.36

9.384

1.52

2.25

10.71

5.58

2.48

2.48

1.40

1.40

0.89

0.89

0.62

0.62

0.46

0.46

0.35

0.35

0.28

0.28

ELL 50x50

7.54

9.604

1.49

2.29

10.90

5.52

2.45

2.45

1.38

1.38

0.88

0.88

0.61

0.61

0.45

0.45

0.34

0.34

0.27

0.27

ELL 60x60

8.86

11.288

1.85

2.59

13.68

9.39

4.40

4.40

2.48

2.48

1.59

1.59

1.10

1.10

0.81

0.81

0.62

0.62

0.49

0.49

ELL 60x60

9.1

11.604

1.84

2.65

14.04

9.60

4.49

4.49

2.52

2.52

1.61

1.61

1.12

1.12

0.82

0.82

0.63

0.63

0.50

0.50

ELL 65x65

10

12.734

1.99

2.84

15.72

11.41

5.79

5.79

3.26

3.26

2.08

2.08

1.45

1.45

1.06

1.06

0.81

0.81

0.64

0.64

ELL 65x65

11.82

15.054

1.98

2.89

18.54

13.39

6.73

6.73

3.78

3.78

2.42

2.42

1.68

1.68

1.24

1.24

0.95

0.95

0.75

0.75

ELL 65x65

12.76

16.254

1.94

2.99

19.94

14.22

7.01

7.01

3.94

3.94

2.52

2.52

1.75

1.75

1.29

1.29

0.99

0.99

0.78

0.78

ELL 70x70

13.7

17.454

2.14

3.09

21.86

16.55

9.12

9.12

5.13

5.13

3.28

3.28

2.28

2.28

1.67

1.67

1.28

1.28

1.01

1.01



KLx=7


4-59

Table 4.18(Continued): Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2


ELL 75x75

14.64

18.654

2.30

3.29

23.69

18.61

11.84

11.84

6.34

6.34

4.06

4.06

2.82

2.82


2.07

2.07

1.59

1.59

1.25

1.25

ELL 75x75

15.32

19.522

2.25

3.46

24.70

19.22

11.34

11.34

6.38

6.38

4.08

4.08

2.83

2.83

2.08

2.08

1.59

1.59

1.26

1.26

ELL 75x75

16.56

21.1

2.22

3.65

26.63

20.59

11.94

11.94

6.72

6.72

4.30

4.30

2.99

2.99

2.19

2.19

1.68

1.68

1.33

1.33

ELL 80x80

19.18

24.44

2.46

3.49

31.39

25.37

17.43

17.43

9.51

9.51

6.09

6.09

4.23

4.23

3.11

3.11

2.38

2.38

1.88

1.88

ELL 90x90

19.92

25.38

2.77

3.88

33.16

27.91

21.07

21.07

12.50

12.50

8.00

8.00

5.55

5.55

4.08

4.08

3.12

3.12

2.47

2.47

ELL 90x90

21.4

27.24

2.76

3.94

35.58

29.92

22.56

22.56

13.34

13.34

8.54

8.54

5.93

5.93

4.36

4.36

3.34

3.34

2.64

2.64

ELL 90x90

26

33.12

2.71

4.10

43.16

36.10

26.90

26.90

15.67

15.67

10.03

10.03

6.97

6.97

5.12

5.12

3.92

3.92

3.10

3.10

ELL 90x90

26.6

34

2.70

4.23

44.28

36.99

27.48

27.48

15.95

15.95

10.21

10.21

7.09

7.09

5.21

5.21

3.99

3.99

3.15

3.15

ELL 90x90

29.4

37.52

2.68

4.28

48.82

40.68

30.07

30.07

17.35

17.35

11.11

11.11

7.71

7.71

5.67

5.67

4.34

4.34

3.43

3.43

ELL 100x100

29.8

38

3.08

4.34

50.31

43.58

34.91

34.91

24.31

24.31

14.83

14.83

10.30

10.30

7.56

7.56

5.79

5.79

4.58

4.58

ELL 100x100

31.8

40.6

3.03

4.50

53.66

46.33

36.86

36.86

24.07

24.07

15.40

15.40

10.70

10.70

7.86

7.86

6.02

6.02

4.75

4.75

ELL 100x100

34

43.42

3.02

4.62

57.36

49.45

39.26

39.26

25.48

25.48

16.31

16.31

11.33

11.33

8.32

8.32

6.37

6.37

5.03

5.03

ELL 100x100

35.6

45.4

3.01

4.68

59.95

51.63

40.91

40.91

26.44

26.44

16.92

16.92

11.75

11.75

8.63

8.63

6.61

6.61

5.22

5.22

ELL 120x120

35.8

45.48

3.71

5.20

61.32

55.17

47.35

47.35

37.99

37.99

25.76

25.76

17.89

17.89

13.15

13.15

10.06

10.06

7.95

7.95

ELL 130x130

38.2

48.62

4.01

5.65

65.97

60.09

52.66

52.66

43.82

43.82

33.52

33.52

22.39

22.39

16.45

16.45

12.59

12.59

9.95

9.95

ELL 130x130

46.8

59.52

3.96

5.80

80.68

73.36

64.09

64.09

53.04

53.04

40.17

40.17

26.72

26.72

19.63

19.63

15.03

15.03

11.87

11.87

ELL 130x130

54.6

69.54

3.93

5.98

94.21

85.56

74.61

74.61

61.55

61.55

46.31

46.31

30.75

30.75

22.59

22.59

17.29

17.29

13.66

13.66

ELL 150x150

57.6

73.5

4.61

6.61

100.70

93.40

84.27

84.27

73.48

73.48

61.08

61.08

46.97

46.97

32.88

32.88

25.17

25.17

19.89

19.89

ELL 150x150

63.6

81.04

4.56

6.76

110.94 102.76

92.51

92.51

80.40

80.40

66.46

66.46

48.17

48.17

35.39

35.39

27.09

27.09

21.41

21.41

ELL 150x150

67.2

85.48

4.52

7.00

116.96 108.22

97.27

97.27

84.32

84.32

69.42

69.42

49.93

49.93

36.68

36.68

28.09

28.09

22.19

22.19



4-60

Table 4.18(Continued): Compression Capacity (Ton) For ELL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

cm

rx

ry

KLx=1

KLx=2

Kly=1

Kly=2

KLx=3

KLx=4

KLx=5

KLx=6


KLx=7

KLx=8

KLx=9

cm

cm

ELL 175x175

78.8 100.42

5.37

7.57

138.76 130.70 120.71

120.71 109.00 109.00 95.67

95.67

80.70

80.70


63.97

63.97

46.66

46.66

36.86

36.86

ELL 175x175

83.8 106.76

5.36

7.75

147.50 138.89 128.22

128.22 115.70 115.70 101.45 101.45

85.45

85.45

67.56

67.56

49.27

49.27

38.93

38.93

ELL 200x200

90.6

115.5

6.14

8.74

160.59 152.87 143.40

143.40 132.36 132.36 119.87 119.87 105.95 105.95

90.58

90.58

73.64

73.64

55.43

55.43

ELL 200x200

119.4

152

6.09

9.03

211.27 200.99 188.37

188.37 173.66 173.66 156.99 156.99 138.43 138.43 117.92

117.92

95.29

95.29

71.71

71.71

ELL 200x200

147.2 187.5

6.04

9.33

260.51 247.68 231.93

231.93 213.55 213.55 192.73 192.73 169.52 169.52 143.86

143.86 110.06 110.06 86.96

86.96

ELL 250x250

187.4 238.8

7.63

11.31

334.68 322.74 308.34

308.34 291.71 291.71 273.02 273.02 252.38 252.38 229.83

229.83 205.37 205.37 178.91

178.91

7.49

11.86

455.49 438.81 418.67

418.67 395.39 395.39 369.21 369.21 340.27 340.27 308.65

308.65 274.30 274.30 237.10

237.10

ELL 250x250

256

325.2



4-61

Table 4.18: Compression Capacity (Ton) For ULLL Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

cm

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9

cm

cm

Kly=1

Kly=2


ULLL 90x75

18.64 23.74

2.79

3.29

31.05

26.19

19.87

19.87

11.86

11.86

7.59

7.59

5.27

5.27


3.87

3.87

2.97

2.97

2.34

2.34

ULLL 100x75

21.4

27.24

3.15

3.09

36.08

31.28

25.11

25.51

17.56

18.22

10.71

11.15

7.44

7.75

5.46

5.69

4.18

4.36

3.31

3.44

ULLL 100x75

22

28.08

3.10

3.25

37.21

32.30

25.98

25.98

18.26

18.26

11.15

11.15

7.74

7.74

5.69

5.69

4.35

4.35

3.44

3.44

ULLL 125x75

26

33

4.01

2.90

43.38

36.99

28.73

35.74

17.83

29.73

11.41

22.73

7.92

15.18

5.82

11.15

4.46

8.54

3.52

6.75

ULLL 125x75

29.8

38

3.97

3.05

50.26

43.45

34.67

40.94

23.92

33.91

14.58

25.71

10.13

17.11

7.44

12.57

5.70

9.62

4.50

7.60

ULLL 125x75

32.2

41

3.93

3.24

54.58

47.85

39.21

43.99

28.72

36.30

17.74

27.32

12.32

18.14

9.05

13.33

6.93

10.20

5.48

8.06

ULLL 125x90

32.8

41.88

3.94

3.76

56.53

50.98

43.92

44.97

35.49

37.13

24.38

27.98

16.93

18.58

12.44

13.65

9.52

10.45

7.52

8.26

ULLL 125x90

34.2

43.68

3.91

3.94

59.15

53.66

46.72

46.72

38.44

38.44

28.78

28.78

19.08

19.08

14.02

14.02

10.73

10.73

8.48

8.48

ULLL 150x90

38.2

48.62

4.81

3.51

65.23

58.11

49.02

56.55

38.09

49.86

24.64

42.19

17.11

33.50

12.57

23.67

9.63

18.12

7.61

14.32

ULLL 150x90

41.2

52.52

4.76

3.66

70.73

63.49

54.29

60.85

43.25

53.49

28.98

45.06

20.12

35.48

14.78

24.97

11.32

19.12

8.94

15.11

ULLL 150x100

43

54.72

4.79

3.98

74.21

67.52

59.06

63.57

48.98

55.99

37.25

47.31

24.81

37.47

18.23

26.43

13.96

20.24

11.03

15.99

ULLL 150x100

44.8

57.12

4.74

4.13

77.67

71.04

62.68

66.11

52.74

58.07

41.20

48.84

27.85

38.37

20.46

26.99

15.66

20.66

12.38

16.32

ULLL 150x100

55.4

70.5

4.71

4.31

96.16

88.46

78.78

81.41

67.31

71.39

54.05

59.88

37.49

46.81

27.54

32.87

21.09

25.17

16.66

19.88



4-62

Table 4.19: Compression Capacity (Ton) For ULLS Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

cm

rx

ry

KLx=1

KLx=2

cm

cm

Kly=1

Kly=2


2.20

4.24

29.91

23.02

13.18

ULLS 75x90

18.64 23.74

ULLS 75x100

21.4

27.24

2.19

4.64

34.28

26.30

ULLS 75x100

22

28.08

2.15

4.81

35.21

26.73

ULLS 75x125

26

33

2.11

5.99

41.21

30.95

ULLS 75x125

29.8

38

2.06

6.17

47.25

ULLS 75x125

32.2

41

2.04

6.36

50.85

ULLS 90x125

32.8

41.88

2.59

5.94

ULLS 90x125

34.2

43.68

2.57

6.13

ULLS 90x150

38.2

48.62

2.52

7.23

KLx=3

KLx=4

KLx=5

KLx=6

KLx=7

KLx=8

KLx=9


13.18

7.41

7.41

4.74

4.74

3.29

3.29

2.42

2.42

1.85

1.85

1.46

1.46

14.94

14.94

8.40

8.40

5.38

5.38

3.74

3.74

2.74

2.74

2.10

2.10

1.66

1.66

14.82

14.82

8.34

8.34

5.33

5.33

3.70

3.70

2.72

2.72

2.08

2.08

1.65

1.65

16.75

16.75

9.42

9.42

6.03

6.03

4.19

4.19

3.08

3.08

2.35

2.35

1.86

1.86

35.06

18.49

18.49

10.40

10.40

6.66

6.66

4.62

4.62

3.40

3.40

2.60

2.60

2.05

2.05

37.46

19.49

19.49

10.96

10.96

7.02

7.02

4.87

4.87

3.58

3.58

2.74

2.74

2.17

2.17

54.24

44.71

32.23

32.23

18.15

18.15

11.61

11.61

8.06

8.06

5.93

5.93

4.54

4.54

3.58

3.58

56.48

46.38

33.14

33.14

18.52

18.52

11.85

11.85

8.23

8.23

6.05

6.05

4.63

4.63

3.66

3.66

62.69

51.14

35.97

35.97

19.88

19.88

12.72

12.72

8.83

8.83

6.49

6.49

4.97

4.97

3.93

3.93 4.08

ULLS 90x150

41.2

52.52

2.47

7.40

67.51

54.66

37.73

37.73

20.63

20.63

13.21

13.21

9.17

9.17

6.74

6.74

5.16

5.16

4.08

ULLS 100x150

43

54.72

2.88

7.08

71.87

61.19

47.35

47.35

29.19

29.19

18.68

18.68

12.97

12.97

9.53

9.53

7.30

7.30

5.77

5.77

ULLS 100x150

44.8

57.12

2.83

7.25

74.84

63.38

48.51

48.51

29.35

29.35

18.78

18.78

13.04

13.04

9.58

9.58

7.34

7.34

5.80

5.80

ULLS 100x150

55.4

70.5

2.80

7.43

92.26

77.91

59.27

59.27

35.53

35.53

22.74

22.74

15.79

15.79

11.60

11.60

8.88

8.88

7.02

7.02



4-63

Table 4.20: Compression Capacity (Ton) For CCI Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

cm

cm

cm

Kly=1

Kly=2

9.84

1.85

1.28

10.42

4.13

13.84 17.636

2.92

1.93

21.60

18.72 23.84

3.97

2.32

30.33

CCI 125x65

26.8

34.22

4.98

2.91

CCI 150x75

37.2

47.42

6.03

CCI 150x75

42.8

54.4

5.86

CCI 180x75

48

61.18

CCI 200x80

49.2

62.66

CCI 200x90

60.6

77.3

CCI 50x25

7.72

CCI 75x40 CCI 100x50

KLx=3

KLx=4

KLx=5

KLx=6


2.16

0.66

1.38

0.46

0.96

KLx=7

KLx=8

KLx=9


1.83

3.84

1.03

0.34

0.71

0.26

0.54

0.20

0.43

15.34

7.52

15.48

4.23

9.69

2.71

6.20

1.88

4.31

1.38

23.92

15.41

25.70

8.26

21.29

5.29

16.16

3.67

10.76

2.70

3.17

1.06

2.42

0.84

1.91

7.90

2.07

6.05

1.63

45.00

38.41

29.89

40.24

18.62

35.76

11.91

30.64

8.27

24.86

6.08

17.82

4.78

4.65

13.64

3.68

10.78

3.42

63.48

56.28

47.09

58.63

36.00

53.96

22.89

48.68

15.90

42.79

11.68

36.27

8.94

27.71

7.07

21.89

3.52

73.02

65.10

55.01

66.83

42.87

61.25

27.84

54.92

19.33

47.86

14.20

40.03

10.87

30.05

8.59

23.74

7.12

3.31

81.63

71.89

59.41

77.12

44.31

71.89

27.64

65.97

19.19

59.41

14.10

52.20

10.80

44.31

8.53

34.12

7.89

3.47

83.98

74.66

62.76

79.67

48.42

74.66

31.09

69.02

21.59

62.76

15.86

55.91

12.14

48.42

9.60

40.27

8.03

4.13

105.11

96.13

84.80

100.55

71.34

95.55

55.71

89.93

37.65

83.74

27.66

76.99

21.18

69.69

16.73

61.81

CCI 250x90

69.2

88.14

9.74

3.85

119.20 107.88

93.54

113.95

76.42 107.88 56.37

101.07

37.30

93.54

27.40

85.33

20.98

76.42

16.58

66.78

CCI 250x90

76.2

97.14

9.56

3.89

131.49 119.22 103.68

125.79

85.13 119.22 63.47

111.83

42.05 103.68

30.89

94.78

23.65

85.13

18.69

74.71

CCI 300x90

80.4 102.34

11.51

3.67

137.87 123.84 105.99

131.37

84.61 123.84 56.87

115.36

39.49 105.99

29.02

95.75

22.22

84.61

17.55

72.53

CCI 300x90

87.6 111.48

11.53

3.81

150.65 136.15 117.76

143.92

95.78 136.15 70.03

127.41

46.32 117.76

34.03

107.22

26.05

95.78

20.59

83.41

CCI 300x90

97.2

123.8

11.28

3.80

167.25 151.06 130.53

159.74 105.98 151.06 73.52

141.30

51.06 130.53

37.51

118.75

28.72 105.98 22.69

92.15

CCI 380x100

109

138.78

14.46

4.04

188.41 171.80 150.81

180.69 125.84 171.80 96.79

161.82

64.81 150.81

47.61

138.82

36.45 125.84 28.80

111.85

CCI 380x100 134.6 171.42

14.33

4.22

233.47 214.18 189.90

224.50 161.07 214.18 127.70 202.62

87.37 189.90

64.19

176.04

49.15 161.07 38.83

144.97



4-64

Table 4.21: Compression Capacity (Ton) For CCB Sections For L=1 m To 9 m (Qs = 1and Qa = 1) -Sorted by Section Weight Effective KL (m) Section Name

Wght Kg/m

Ax 2

rx

ry

KLx=1

KLx=2

KLx=3

KLx=4

KLx=5

KLx=6

KLx=8

KLx=9

cm

cm

cm

Kly=1

Kly=2

9.84

19.91

1.83

11.90

8.12

3.79

10.18

13.84 17.636

14.87

2.96

23.25

19.95

15.68

21.72

9.97

19.95

6.38

17.93

18.72 23.84

12.79

3.76

32.18

29.02

25.01

30.72

20.22

29.02

13.90

27.12

26.8

34.22

10.68

4.98

47.09

44.04

40.23

45.67

35.76

44.04

30.64

42.22

CCB 150x75

37.2

47.42

9.07

5.67

65.70

62.17

57.81

62.65

52.70

60.07

46.91

CCB 150x75

42.8

54.4

7.98

5.63

75.35

71.25

66.20

70.71

60.29

67.16

53.57

CCB 180x75

48

61.18

8.47

5.80

84.85

80.43

74.98

80.15

68.62

76.49

CCB 200x80

49.2

62.66

7.89

6.24

87.18

83.07

78.04

81.31

72.18

77.15

CCB 200x90

60.6

77.3

8.03

6.81

107.91 103.42

97.94

100.55

91.59

95.55

CCB 250x90

69.2

88.14

9.74

7.09

CCB 250x90

76.2

97.14

9.56

7.07

CCB 300x90

80.4 102.34

11.51

7.23

CCB 300x90

87.6 111.48

11.53

7.13

155.89 149.79 142.39

150.76 133.82 146.44 124.17 141.66 113.49 136.43 101.79

CCB 300x90

97.2

123.8

11.28

7.16

173.14 166.41 158.25

167.11 148.80 162.17 138.15 156.68 126.37 150.68 113.47

CCB 380x100 109

138.78

14.46

8.08

194.84 188.41 180.69

190.63 171.80 186.70 161.83 182.37 150.83 177.67 138.84

172.61 125.86 167.22 111.87

161.49

CCB 380x100 134.6 171.42

14.46

7.96

240.55 232.45 222.70

235.47 211.47 230.61 198.85 225.26 184.94 219.46 169.77

213.21 153.34 206.54 135.61

199.47

CCB 50x25

7.72

CCB 75x40 CCB 100x50 CCB 125x65


KLx=7

2.13

8.12

1.36

5.45

0.95


3.79

0.70

2.78

4.43

15.68

3.26

13.19

9.65

25.01

7.09

22.71

24.85

40.23

17.82

38.08

57.19

40.43

54.03

33.23

63.18

46.06

58.79

37.70

61.39

72.38

53.32

67.86

65.55

72.48

58.18

67.33

84.42

89.93

76.48

83.74

123.22 118.36 112.47

117.36 105.64 113.03 97.94

108.21

89.42 102.92

135.80 130.42 123.90

129.10 116.35 124.20 107.83 118.74

98.41 112.75

143.18 137.69 131.04

138.38 123.34 134.41 114.67 130.01 105.08 125.20

94.58

0.53

2.13

0.42

1.68

2.49

9.97

1.97

7.88

5.43

20.22

4.29

17.51

13.64

35.76

10.78

33.28

50.59

24.56

46.88

19.40

42.91

54.00

27.78

48.82

21.95

43.22

44.37

62.93

33.13

57.62

26.18

51.90

50.04

61.72

41.08

55.63

30.98

49.06

67.75

76.99

58.23

69.69

45.56

61.81

80.09

97.17

69.92

91.00

58.86

84.39

88.08

106.25

76.83

99.25

64.59

91.76

120.00

83.16 114.43 70.76

108.50

130.78

89.05 124.72 75.20

118.27

144.20

99.43 137.24 84.16

129.83



4-65

4.10. Software Implementation The axial member design module of the SYSDesigner (SYS Steel Designer’s Software) has been developed based on the theory described in chapter 3 and 4 of this manual. The flow diagram for the design of axial compression member on which this module has been based is shown in the “General Procedure “ section of this chapter. However the factors Qa and Qs are not incorporated into the program thought they are shown in the flow diagram because these factors are applicable for very few hot rolled sections and the effect is also not so significant. Moreover the program will check only the bend buckling or flexural buckling mode of failure of member which may be important for some shapes such as T or L. The program computes the axial compression capacity of a member based on the user specified geometric and restraint conditions. User can specify different bracing and end conditions, independently for two principal axes of the section. In general Lx and Kx are related to buckling about the major axis i.e. the moment of inertia of the section is higher than the other axis (which may be an exception for shapes such as T or L). However they can very easily be checked in the detailed design report generated by the program. The module also includes the graphical built-in effective length factor K calculator which is linked very conveniently to the SYS section database. This can be used for almost all practically possible end restraint conditions, ranging from a simple isolated member to any general member in a frame, based on ACI318-95 code recommended method. The concept of ‘Design Segments’ and ‘Unified Code Ratio-R’ used in the program have been described in the ‘Technical Background ‘ chapter of the ‘SYSDesigner’s Software Users Manual’. Some major screen captures of the program related to design of compression member are shown below.




4-68


4-69


4-70


4-71

Chapter

5

Design of Beams 1. Introduction Structural members that support transverse loads and are therefore subjected to flexure (bending) are called beams. Beams are more specifically described by various names depending upon their purpose or location in a structural system. The term used in this chapter include all the structural members whose design is primarily governed by uniaxial bending such as floor beam, girder, girt, header, joist, lintel, purlin, rafter, spandrel, beam stringer, trimmer etc. The most common shapes that are used as beam are H, I and Channels. The basic concept of bending behavior of beams can be studied by considering a originally straight beam subjected to transverse load causing a moment M. Assuming that the plane cross section normal to the length of the unbent beam are still plane after the beam is bent and referring to the Fig 5.1, the bending moment M can be expressed as:

M = f

b

S

x

(5-1) y

x

M

L

Fig. 5.1. Elastic Analysis of Beam

Where

fb = Extreme fiber stress Sx =

IX y max

= Section modulus

This is the basic equation used in the design of beam member by elastic methods.

2. General Procedure A beam can fail by any one of the following modes due to the flexural effects: 1) Development of full plastic moment 2) Lateral torsional buckling, either elastically or inelastically 3) Flange local buckling, either elastically or inelastically 4) Web local buckling , either elastically or inelasticlally

So the general procedure for the design of beam needs the consideration for all the above possible mode of failure. The first failure mode is associated with excessive stresses on the section so as to the form enough plastic hinges before failure while the rest three are related to stability of the beam. Lateral instability of a member can be controlled by providing enough lateral bracing to preclude the lateral displacement accompanied with twist while the cross section element stability can be achieved by limiting the ratio b/t of each element under compression or taking into account their post buckling strength. The general design procedure must take into account the following important criteria. 1) Axis of bending ( Major or Minor ) 2) Spacing of lateral bracing ( longest unbraced length ) 3) Compactness of the section ( compact ,noncompact or slender) 4) Shape of the section ( symmetrical or asymmetrical) 5) Moment variation along the unbraced segment 6) Shear, deflection and effects due to concentrated loads like web yielding,

crippling, side sway buckling etc The flow diagram shown in this chapter, represent schematically the general design procedure for moment and also forms the basis for the development of the beam design module of SYS Steel Designers Software.


5-2

Flow Diagram For the Design of Beam Basic Info

Trial Unbraced Length

4

Trial Cross Section

Bending about Major Axis

Yes

Box-type Section

Yes

No No 76b

Lb < 2500

No

Yes

b Fy

Yes b t

f

≤

190 F y

3 b 2t

Lb ≤

2

No

1

f

Doubly sym. I & H, solid round, square & rectag. shape

f

≤

52.5 F y

Yes

MR=0.75 F Y Sminor

Fy and

No

No

20,000 Lb ≤ d   A Fy  f

L b

No f

r t

No

≤

102000C b F y

Yes

5 b

Yes

Yes MR=0.66 F y Smajor

No

2t

f

≤

95 F y

f

  b f   MR=  0.79 − .002 Fy Fy Smajor 2t   f  

No

MR=0.60 F y Smajor

Shape with slender elements ( special design )

MR > M max Yes End

Fig. 5.2.(a) Flow Diagram for Design of Beam Based on AISC/ASD (1991)


5-3

2

b t

≤

238 F y

f

MR=0.60 F y S

4

No

Special Design

MR > M max

Yes End

5

Yes

L b r t

≤

No

L b

510000C b F y

r t

2

2 − F  Lb  3 y  rT  3 Fb = 1530x10 Cb 12x103 Lbd / Af

Comp. flange solid ,appx. rect. and

≤

510000C b F y

170x103Cb 2

 Lb    Fb =  rT  12x103 Lbd / Af

max

2

2 − F  Lb  3 y  rT  Fb = 1530x103Cb

Fb =

170x103Cb 2

 Lb   r  T

max

Yes

Yes MR=F b Smajor

4

No

MR > M max

Yes End

Fig. 5.2(b) Flow Diagram for Design of Beam Based on AISC/ASD (1991)


5-4

3. Lateral Torsional Buckling The most economical beam shapes are the ones whose moment of inertia about the major principal axis is considerably larger than that about the minor principle axis. As a result , they are relatively weak in resistance to torsion and to bending about the minor axis. So, if they are not supported laterally by some bracing or floor construction, they may become unstable under load. This phenomenon of sidewise bending associated to torsion is called lateral-torsional buckling. There are various ways to provide lateral support to a member like complete or compression flange embedment into floor slab, support from a laterally stable component or by specifically providing a bracing member. It has been observed from laboratory test that the bracing member provides reliable lateral support if designed for 2 percent of the compressive force in the flange of the beam it braces.

u

u

Fig. 5.3. Lateral Torsional Buckling of Beam

Most of the specification formula for flexural design are the simplified form of the general equations to compute critical end moments from lateral-torsional buckling analysis of an perfectly straight, simply supported unbraced segment of a beam subjected to equal end moments. The following equation is the generalized form of the equation which can be used for any combination of end restraint and moments. Mcr =Const.( Saint-Venant torsional stiffness + warping stiffness )0.5 2

2

 π

M cr = C b 

2

 (KL )

2

EI y GJ +

π

4

(KL )

4



EI y EC W 

(5-2)

(5-3)



Where

M cr = Critical end moment at which a perfect beam just begins to bend out of plane. Cb = Coefficient to take into account the variability of moment along the unbraced length. K = Effective length factor whose value depends upon the restraint condition at the ends. AISC/ASD uses the following equation obtained from numerical analysis for Cb Hand Book for Design of Steel Structures

5-5

 M1 M  2

 M  + 0.3  1  M   2

C b = 1.75 − 1.05 

   

2

(5-4)

≤ 2.3

where M1 is smaller of the two end moments M1 and M2 and the ratio M1/M2 is positive for reverse curvature and negative for single curvature bending. The following figure shows the variation of Cb for various end moment ratios. Cb For Beams 2.50 2.00 Cb

1.50 1.00 0.50 0.00 -1

-0.5

0

0.5

1

1.5

M1/M2 Ratio

Fig. 5.4. Variation of Cb (AISC/ASD) with Different End Moment Ratios

However Limit State Design(AISC/LRFD) uses the more refined expression for Cb which takes into account the nonlinear variation of the moment along the unbraced segment. The nonlinearity is accounted for by using the moment at every quarter points of the unbraced segment.

4. Local Buckling of Beam Elements and Section Compactness The maximum moment which a beam can support depends not only on the over all lateral buckling of the beam but also on the integrity of the cross-sectional elements. The cross-sectional integrity will be lost either by buckling of the compression flange called flange local buckling, or by buckling of the compression part of the web, called web local buckling. The strength of a section for local buckling depends upon the width-to-thickness ratio and end stiffness condition. However, commonly used hot-rolled beam shapes are usually large enough and have plate elements thick enough to preclude local buckling at stresses less than the yield stress. The following equation derived for the buckling strength of a simply supported rectangular plate subjected to in-plane uniform compression forms the basis for the classification of shapes into some standard types with respect to local buckling. The same equation can be used for various end support and loading conditions by using an appropriate value of K

Fcr =

Kπ 2 E

( t)

12(1 − µ 2 ) b

2

(5-5)

Where Hand Book for Design of Steel Structures

5-6

K = A constant which depends upon how the edges are supported, upon the ratio of plate length to plate width and upon the nature of the loading.

µ = Poisson’s ratio b = Length of loaded edge of plate (except that it is the smaller lateral dimension when the plate is subjected only to shearing force ) t = Plate thickness

Simple

Fixed

K=4 Fixed

Simple

K = 5.4

Simple

Simple

Simple

Fixed K=7

Fixed

Simple

Simple

Simple

Simple

Simple

Simple

Values of K to be used in the above equation for common cases are shown below. In the figures below “simple” indicates the simply supported edge and “fixed” means that for fixed edge.

Free K = 1.33

Fig. 5.5. Constant K for Plate Buckling

In specifications, depending upon the slenderness ratio of cross section elements, a section may be termed as compact, non compact or slender elements as defined in the following paragraph. Compactness of the section is one of the important parameters to be considered in the design of beams. Compact Section

Section which can develop a fully plastic moment Mp (= plastic section modulus Z x Fy) before local buckling of any of its compression elements. Thus for compact shapes the design strength for moment is governed by either the lateral torsional buckling or yielding depending upon the unbraced length of the compression flange. Most of the hot rolled shapes fall in this category. Design Aids Table 5.1 gives the details for compactness classification of all SYS shapes commonly used as beams. NonCompact Section

Section that can develop a moment equal to or greater than My (= elastic section modulus S x Fy)but less than Mp , before local buckling of any of its cross section element occurs. Slender Section

Shapes with elements slenderer than those designated by noncompact are categorized as slender section or shape with slender elements.


5-7

5. Design for Moment As described in “General Procedure” section of this chapter, the factors that govern the design for flexure are : 5) Axis of bending 6) Spacing of lateral bracing 7) Section compactness 8) Section shape (symmetry ) 9) Moment variation along the unbraced segment 10) Maximum moment

It is not always necessary to consider all the criteria to design a beam. A typical design involves the design of a symmetric I or channel compact section bending about major axis with adequate bracing. Some common design cases shall be explained in the following paragraphs for stepwise calculations based on AISC/ASD specifications. Case 1: Bending About Minor Axis

Design Steps: 1) No need to check for the lateral bracing if loaded through shear center 2) Check the compactness of section. Allowable stress may vary from 0.75Fy

to 0.6Fy for shapes commonly used as beams. Refer to relevant code or Appendix for the appropriate specification formulas. 3) Applicable shapes for normal design procedure are symmetrical I shapes,

round and square bars, and solid rectangular bars bent about minor axis. Permissible stresses for minor axis bending is usually higher than the corresponding major axis bending. The reason for this is the stronger lateral resistance and higher shape factor of cross section for minor axis. Case 2: Bending About Major Axis

Design Steps: 1)

Compute the critical laterally unsupported length Lc.

2) If the actual laterally unsupported length or unbraced length Lb is less than the

critical length Lc, it is not necessary to consider the lateral stability of the member. But it is necessary to examine the compactness of the section. Depending upon the compactness of the section the permissible stress vary from 0.66 Fy to 0.6 Fy according to AISC/ASD. The typical moment strength curves for commonly used shapes are shown in Fig.5.5. It is very clear from the figure that the moment strength reduces considerably as the unbraced length increases.

3) If the actual unbraced length Lb is more than the critical unbraced length, the

design is governed by the design equations simplified from the lateral torsional buckling.

To further illustrate the design procedure explained above, design examples have been presented later in this chapter. Hand Book for Design of Steel Structures

5-8

Typical Moment Strength Curves

Moment (Kg-m)

35000.00 30000.00

H 300x305x106 Kg/m

25000.00

H 304x301x106 Kg/m

20000.00

H 346x174x41.4 Kg/m

15000.00

H 350x175x49.6 Kg/m

10000.00

H 354x176x57.8 Kg/m

5000.00

H 336x249x69.2 Kg/m

0.00 0

5

10

15

Unbraced Length (m) Fig. 5.6. Moment Strength Curves for H Shapes

6. Check for Shear Steel beams are rarely designed for shearing stress but it is usually calculated as a check after the beam has been designed for flexure. However it may govern the design of beams which support heavy concentrated loads near the reaction points and of very short span beams with heavy uniform load. In such cases the web of the beam may buckle at shearing stresses less than the shearing yield strength of the steel. The phenomenon of shear buckling of web on the basis of which the permissible shear stresses are specified, shall be discussed in the following paragraphs.

h

a

Fig. 5.7. Shear in Beam

Let us consider a flat plate acted upon by shear stresses distributed uniformly along the four boundaries as shown in Fig. . 5.1. . In this case, the shear stresses are equivalent to principal stresses of the same magnitude, one tension and another compression acting at 45 degree to the shear stresses as shown in the figure for an interior element of the beam web. The critical shear stress Fv ,cr at which buckling of a perfect plate begins is given by the following equation


5-9

Fv ,cr =

kπ 2 E

( t)

12(1 − µ 2 ) h

(5-6)

2

This equation is similar to the equation already described in the section “Local buckling of plate elements and section compactness” in this chapter. The factor k depends upon the type of support on the edges. Two most common cases are 1)

All four edges simply supported

k = 4+

5.34

k = 5.34 + 2)

( h ) < 1.0

(5-7)

( )

(5-8)

for a

(a / h )2

4.0 for a ≥ 1.0 h (a / h )2

All four edges clamped

k = 5. 6 +

8.98

(a / h )2

k = 8.98 +

( h ) < 1. 0

for a

( )

5.6 for a ≥ 1.0 h (a / h )2

(5-9)

(5-10)

Most of the formulae in the specifications for permissible shear stresses are based on the above equations though they may appear in different and, normally, in simplified forms in the codes. As an example the AISC/ASD uses the following form of equations for shear strength calculation.

( t ) ≤ 380F

Fv = 0.4 Fy for h

(5-11)

y

Fv =

( )

Cv Fv 380 ≤ 0.4 Fy for h > t 2.89 Fy

(5-12)

Where Cv is the ratio of the critical shear stress to the yield stress in shear.

Cv =

Cv =

45,000k if Cv < 0.8 2 Fy h t

( )

190

(h t )

k if Cv > 0.8 Fy

(5-13)

(5-14)

It is important to note that the stress Fv is defined as the average stress on the area equal to the overall depth d of the beam times the web thickness (area of the web).

7. Check for Web Yielding and Crippling When a beam carries a heavy concentrated load on the top flange or reaction from the support is large, significant direct compressive stresses in the vertical direction of the web are produced. The concentrated compressive stresses are dispersed gradually Hand Book for Design of Steel Structures

5-10

into larger area from the maximum at the point of application to zero at the opposite flange (bottom flange). When the load is transmitted through the thin web plate, the web plate is crippled at the section nearest to the load and of thickness t w . In hot rolled sections, this will be at the toe of the fillet, a distance k, as shown in figure below , from the outside face of the flange. Specifications generally assume the divergence 1 angle of 2 2 horizontal to 1 vertical. So the area nearest to the fillet bearing the load will be (2.5k + N )t w near the support (one side divergence) and (5k + N )t w at any intermediate locations(both sides divergence). Locally high Bearing Stresses at the Junction

tw

k

N

Fig. 5.8. Concentrated Load in Beam

AISC/ASD uses the following equations to calculate the resistance capacity of a beam for web yielding and crippling: [Units: US system R in Kips; Fy and Fyw in ksi; tw, tf, N and d in inches] For support reaction (or load within d/2 distance from end):

R = 0.66 FY t w ( N + 2.5k )

(5-15)

1. 5  F t   N  t  2 yw f R = 34t w 1 + 3  w       d  t f   t w  

(5-16)

Web yielding:

R = 0.66 FY t w ( N + 5k )

(5-17)

Web crippling:

1. 5    N  t w   Fywt f  R = 67.5t w 1 + 3    d  t f   t w  

(5-18)

Web yielding: Web crippling:

For interior loads:

2

Where R = capacity (resistance) to concentrated load or reaction N = bearing length (length over which the load in acting)

t w = web thickness k =distance from extreme fiber to toe of fillet (available in section properties tables) Fy = Yield strength of the steel Fyw = Yield strength of the web for hybrid beams (Different grades of steels for web and flange. For SYS hot rolled sections Fy = Fyw)


5-11

8. Check for Side Sway Web Buckling Side sway web buckling is an overall buckling failure of a beam web. An exact solution of this problem requires a stability analysis of the entire web with different load systems on two opposite edges(top and bottom). However for approximate analysis it is assumed that the critical vertical compression stress for the web of a beam supporting a uniformly distributed load is twice the critical stress for a plate uniformly compressed on two opposite edges for which analytical solutions are available. Several cases of plate buckling have been described in the preceding sections ”Local buckljng of plate elements and section compactness” and “Check for shear”. The following equation gives the critical compression stress for the web of a beam for side sway web buckling.

Fv ,cr =

2π 2 E

( t)

12(1 − µ 2 ) b

2

(5-19)

Where E =Modulus of elasticity of steel

µ = Poisson’s’ ratio b = depth of the web t = thickness of the web Various forms of web buckling due to loads applied to the compression flange are shown in figures 5.9 and 5.10. Web buckling due to concentrated loads is more complex to determine than that for uniform loads. Let us consider a beam of rectangular cross section of unit thickness and depth ‘d’ supporting a concentrated load ‘P’. Figure 5.10 shows the variation of the stresses along the depth of the section. It will be noted that at all the three levels, the stress is compressive over a length (along the span) approximately equal to the depth ‘d’. The stress at the mid depth varies from zero at each end of the length d to 0.91P/d at the center. The average stress on the area is about 0.5P/d. In the average stress, the decrease in the compression with depth is the same as that for a uniformly distributed load. The web stability analysis of this case is very complex without many approximations.

Fig. 5.9. Various Forms of Beam Side Sway Web Buckling Due To Loads On Top


5-12

P

d

2.46 P d P 0.91 d 0.29 P d

d/2

d/2

Fig. 5.10.Stress Distribution Under The Concentrated Load on Rectangular Section of Unit Thickness (Similar for Beam Webs)

In AISC/ASD specification the following formulas have been specified for the side sway web buckling. Loaded flange restrained against rotation and (d c / t w ) /(l / b f ) < 2.3

6800t w R= h

2

3     1 + 0.4 d c / t w    l /b    f    

(5-20)

if (d c / t w ) /(l / b f ) > 2.3 No limit Loaded flange not restrained against rotation and (d c / t w ) /(l / b f ) < 1.7 3 2 6800t w   d c / t w   R= 0.4 h   l / b f    

(5-21)

if (d c / t w ) /(l / b f ) > 1.7 : No limit where R = Resistance of the beam to side sway web buckling

d c = web depth clear of fillets or corner radius (= h) t w = web thickness l = largest unbraced length along the either flange (max of Lb,ten and Lb,comp) at the point of load

b f = flange width If the applied load or reaction is more than the capacity of the section for web yielding web crippling, web stiffeners must be provided. The stiffeners must be proportioned such that the applied load is carried directly as column. The weld connecting the web stiffeners (transverse or vertical) must be sized to transmit the force in the stiffener to the web. However, for cases when the strength provided by the beam is not enough for side sway web buckling, local lateral bracing shall be provided at both the flanges at the point of application of the concentrated load. Hand Book for Design of Steel Structures

5-13

9. Design Examples Design calculations for a steel beam may vary from that involving very few steps to few pages. The simplest calculation is for the simply supported beams of only one segment with enough lateral bracing at compression flange and compact I or C sections. On the other hand, the design of a beam with long multiple segments with variation of moment along the segments and trial sections which needs to check for compactness, requires calculations significantly more than the former case. Common design cases in practice are the design or verification of H shapes for small to medium spans (typically 2 - 6m) as floor or other beams and Channels as purlins. The examples presented in this section have been selected to illustrate design cases ranging from very simple ones to quite complicated ones. They are intended to cover the following three major aspects of steel beam design. 1) Computing the capacity of a beam section for bending about any one or

both principal axis. 2) Selecting appropriate SYS beam sections for given loading and support

condition. 3) Various checks for shear and concentrated load on beams.

The problems have been solved in two different unit systems wherever logical to help the users to understand the solution. The ‘Beam Design’ module of the SYS designer’s software can also be used as a tool to carry out the calculations similar to the one presented in the following examples.


5-14

SYS

Example:

Subject: Design of Beam


Design Code:

Thailand

AISC/ASD (1991)


51

Sheet No:1 / 2 Reference Chapter: 5

Problem:

Find the moment capacity for 1) major axis bending 2) minor axis bending

of SYS H200x150x 30.6 kg/m whose compression flange is supported against lateral bracing by the floor slab or by close spacing of lateral ties. Fy = 2400 ksc (34.0 ksi) Solution:

Section properties for SYS H200x150 x 30.6 kg/m (20.6 lb/ft) bf = 15 cm = 5.91 in d = 19.4 cm = 7.64 in tf = 9 mm = 0.354 in tw = 6 mm = 0.236 in Sx = 227 cm3 = 16.9 in4 Sy = 67.6 cm3 = 4.13 in4 The allowable bending stress for H shaped members of steels with Fy ≤ 65 ksi (4580 ksc), supported against lateral buckling and bent about the major or minor axis are computed as follow. 1. Major Axis Bending

•

Fb = 0.66 Fy for compact section

•

Fb = 0.6 Fy < Fb < 0.66 Fy for non compact section

Check the compactness: b f = 5.91 = 8.347 2t 2 × 0.354 f

65 65 = = 11.14 Fy 34 As

bf 2t f

<

65 Fy

Section is compact

The section compactness can also be read directly from the design aid table provided at the end of this chapter. Mx = 0.66 x 34 x 16.9 = 379.23 kips-in = 31.60 kips-ft


5-15

SYS

Example:



Design Code:

Thailand

AISC/ASD (1991)


51


2. Minor Axis Bending

•

Fb = 0.75 Fy for compact section

•

0.5 Fy ≤ Fb < 0.75 Fy for non compact section

As the shape is compact My = 0.75 x 34 x 4.13 = 105.315 in-kips = 8.77 ft-kips

[Note: Lateral bracing is not required for members bent about the minor axis if the load is applied through the shear center of the section.]


5-16

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

52


Problem:

Design (select) the lightest SYS H section for the following floor beam carrying heavy UDL of 10 ton. The top flange of the beam shall be partly embedded into the slab. Neglect the shear check. UDL = 10 t/m

5m

Fig. 5.11.Simply Supported Floor Beam for Design Example

Solution:

M max =

10000 x5 2 = 31250 kg-m 8

V

max

=

10000 x 5 = 25000 kg 2

1. Preliminary Section Selection

For the first trial assuming Fb = 0.6 Fy = 0.6 x 2400 = 1440 Ksc

S xx , req =

31250 x 100 = 2170 cm 3 1440

SYS H sections with Sxx very close to this requirements are: Sxx (cm3)

Weight (Kg/m)

H 344x348x115 kg/m

1940

115

H 434x299x106 kg/m

2160

106

H 506x201x103 kg/m

2230

103

H 350x350x137 kg/m

2300

137

H 596x199x94.6 kg/m

2310

94.6

Section

[Note: Quick and an easy way to find the sections of certain type or types, sorted in some order (by A or Sxx or Weight), is to use ‘Section properties’ in the SYS Designers software SYS Designer. It provides complete tools for the selection, viewing and printing of shapes which can be selected by various criteria e.g. max. and min. weight, width, depth etc. and further they can be sorted by any property. The above table was prepared by searching the database by H shape and sorted by Sxx .] 2. Detailed Checks:


5-17

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

52


It is given in the problem that the compression flange of the beam is fully restrained (braced) from lateral buckling. So in this case it is not necessary to check for the lateral torsional buckling requirements. Only check necessary to determine the moment capacity is the section compactness. Depending upon the compactness the permissible stress Fb may vary from 0.66 Fy to 0.6 Fy . However it is always safe if Fb = 0.6 Fy is used without checking for compactness. Compactness Checks Section

bf

65

95

Fy

Fy

2t f H 596x199x94.6 kg/m

6.63

H 506x201x103 kg/m

5.29

H 434x299x106 kg/m

9.96

H 344x348x115 kg/m

10.87

H 350x350x137 kg/m

9.21

11.1

16.2

Fb ksc

Kg-m

Type

All shapes compact

Moment Capacity

0.66Fy

Weight / Capacity X

10-2

3659

2.58

3532

2.91

=

3421

3.09

1584

3072

3.74

3643

3.76

[Note: The compactness of any section can be read directly from design aids tables provided at the end of this chapter.] Important Points: 1. All the sections that are considered in this example are compact for flange local buckling. 2. The moment capacity of the section does not vary in the same proportion of the weight. That means much lighter section, sometimes, may give higher moment capacity than heavier section. This fact is point is important for economical design of the beams. 3. Efficient way to design for such fully braced beams is to sort the section first by Sxx and the by weight and pick the lightest section giving the required Sxx. 4. The design procedure for fully braced beam is very simple and needs only few checks. So use H 596x199x94.6 kg/m giving, Mr =3659 Kg-m > 3125 Kg-m.


5-18

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

53


Problem:

Determine the moment capacity of SYS H 300x150x36.7 kg/m (24.7 lb/ft) of Fy = 2400 ksc (34 ksi) steel with compression flange braced at intervals of 3.0 m (9.84 ft). Assume Cb = 1.0 [Case: maximum moment occurs at some point between the braced points or the most conservative capacity for any other cases] Solution: 1. Trial Section

Section properties for SYS H300x150x36.7 Section parameter Fy

Metric Unit

U.S. Unit

2400 ksc

34 ksi

Bf

15 cm

5.91 inch

D

30 cm

11.81 inch

tf

9.0mm

0.354 inch

tw

6.5 mm

0.256 inch

Sx

481 cm3

29.35 inch3

2

Af

13.9 cm

2.154 inch2

Ix

7210 cm4

173.22 inch4

4

Iy

12.2 inch4

508 cm

2. Checks For Lateral Bracing

Critical lateral bracing Lc is given by the smaller of the following two formulae

Lc =

76 b f

Lc =

Fy

For US units Lc1 =

Lc2 =

76 x5.9 34

20,000 F y xd / A f

= 76.89 in = 6.40 ft

20,000 =107.28in = 8.94 ft. 34 x 11.81 / 2.154

So critical unbraced length

Lc = 8.94 ft

Actual unbraced length

Lb = 9.84 ft. (3m)

So, Lb > Lc Therefore, the lateral bracing condition will govern the design. The procedure to design for the case when the lateral bracing is the governing condition is given below.


5-19

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

53


For H shapes and when Lb > Lc then permissible Fb must be computed using two formulas - one based on

Ld Lb and the other based on b criteria and the larger be rT Af

taken for design. 3. Permissible Stress Fb Based on Lb/rT Ratio

rT ≈

Iy /2 Af

12.2 / 2 =1.6828 in 2.154

=

Lb 9.8 ×12 = = 70.168 in rT 1.6828 So this value of Lb/rT shall be checked against the following specified limits based on Cb and Fy.

102,000 Cb 102,000 x 1 = = 54.77 in Fy 34

510,000 C b 510,000 x 1 = =122.47 in Fy 34 So the case is

102,000 C b L ≤ b ≤ Fy rT 54.77 ≤ For the value of

70.168

510,000 C b Fy ≤122.47

Lb calculate above, Fb is computed as: rT

2  L   Fy  b  2  rT  Fb1 =  − 3 1530 ×10 3 × C b   

   2 34 (70.168)2   F =  y  3 − 1530 ×10 3 ×1 Fy = 0.55 × Fy     

Fb1 = 0.55 x 34 = 18.7 Ksi So Fb based on

lb criteria: Fb1 = 18.7 Ksi rT

4. Permissible Stress Fb Based on Lb d/Af Ratio


5-20

SYS

Example:5 3



Design Code:

Thailand

AISC/ASD (1991)



Lb d 9.84 × 12 × 11.81 = = 647.41 2.154 Af 20,000Cb = 588.23 Fy The case is:

Fb based on

Fb2 =

Lb d 20,000 Cb > Af Fy

Lb d criteria is given by Af 12,000C b 12,000 x 1 = = 18.53 ksi Lbd 647.41 Af

5. Final Permissible Stress Fb and Moment Capacity

Fb1 = 19.61 ksi Fb2 = 18.53 ksi

So higher of the two values should be used for design. Fb = 19.61 ksi (1380 ksc) Moment capacity = Fb x Sx = 19.61 x 29.35 = 575.55 in-kips = 48 ft-kips (6.64 ton-m) Safe design moment capacity = 48 ft-kips (6.64 ton-m)


5-21

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

54


Problem:

Select the lightest SYS H section for a beam (or beam segment) subjected to the bending moment due to two point loads as shown in the diagram below. The compression flange is braced at 4.0 m (13.12 ft) interval. (Unit conversion: 1 kip-inch = 11.5 kg-m) Fy = 2400 ksc = 34 ksi M1 = 1300 kips-in. (14.95 ton-m) M2 = 1480 kips-in (17.02 ton-m) M1=14.95 ton-m ( 1300 kips-in )

1.0 m

M2=16.95 ton-m ( 1470 kips-in )

4.0 m

1.0 m

Fig. 5.12.:Moment Diagram for Design Example Solution: 1. Preliminary Section Selection

Assume the self weight of the beam = 66 Kg/m (44.25 lb/ft) Max. moment due to self weight = =

1 ω l2 8 1 × 44.25 ×19.68 2 8

= 2.14 in-kips (too small compared to the applied moment) Assuming Fb = 0.6 Fy = 0.6 x 34.0 = 20.4 ksi (1440 ksc) Sx required =

M max Fb

=

1470 20.4

= 72.05 in 3

From the Siam Yamato Steel Table’s select H 400x200x66 Kg/m (44.4 lb/ft), with Sx =72.6 in3(1190 cm3) 2. Check for Bracing Criteria

Critical spacing of lateral bracing for the selected H 400x200x66 section is calculated as:


5-22

SYS

Design Code:

Thailand

Lc 1 =

Lc 2 =

Example:



Designed by: BSS

AISC/ASD (1991)

76 b f Fy

=

76 × 7.87 34

Checked by: NA

54


= 102.57 in = 8.54 ft (2.60 m)

20,000 20,000 = = 173.71 in = 14.47 ft (4.4 m) Fy × d/Af 34 ×15.75 /(7.87 × 0.591)

So critical is the smaller of the above two critical length values: Lc = 8.54 ft (2.6 m) This shows that the design condition is Lb > Lc where Lb = 10.16 ft 3. Design for Lb>Lc

The largest lateral bracing spacing Lc for which the allowable stress 0.6 Fy may be used is given by the larger of the following two lengths for Lc. L c 1 = rT

Lc 2 =

102,000 C b Fy

20,000C b F y d/A f

Before be able to use these two equations we need to compute Cb and rT 4. Computation for Cb and rT

rT ≈

I y /2 Af

=

10.62/2

(7.87 × 0.512 )  M1 M  2

C b = 1.75 −1.05 

= 1.1479 in

 M  + 0.3  1   M2

2  ≤ 2.3 (Where M1< M2 ) 

[Units: Any consistent units for moments can be used] 2 Cb = 1 . 75 − 1 .05  1300  + 0 . 3  1300  = 1 .058 ≤ 2 . 3 1470 1470    

5. Permissible Stress Fb and Final Capacity

So substituting rT and Cb into above equations for Lc Lc 1 = 1.1479

102,000 × 1.058


34

= 56.33 in = 4.69 ft. (1.42 m)

5-23

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Lc 2 =

20,000 × 1.058 34 ×15.75 / 7.87 × 0.512

Checked by: NA

54


= 159.22 in = 13.26 ft (4.04 m)

Adopting higher of Lc1 and Lc2 final

Lc = 13.26 ft (4.04 m)

Actual unbraced length

Lb = 10.16 ft (3.09 m)

So the final design case is: Lb
Fb = 0.6 Fy = 0.6 x 34.0 = 20.4 Ksi Or

Fb = 0.6 Fy = 0.6 x 2400 = 1440 ksc Moment Capacity = Fb x Sx

= 20.4 x 72.6 = 1481 in-kips > (1470 + 2.14 due to self wt.) Hence use H 400 x 200 x 66 kg/m


5-24

SYS

Example:

Subject: Beam Checks


Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

55


Problem:

Check the capacity of the beam shown in the figure below for •

shear

•

web crippling

•

side sway web buckling 7.8 in

H 350 x 175 x 49.6 kg/m

20'

Fig. 5.13.:Concentrated Load on Beam Example Problem Solution:

Section properties for H350x175x49.6 (33 lb/ft)

bf = 17.5 cm = 6.89 in d = 35 cm = 13.78 in tw = 7 mm = 0.276 in tf = 11 mm = 0.433 in r = 14 mm = 0.551 in 1. Shear Capacity:

h = d-2tf – 2 radius = 13.78 – 2 x 0.433 – 2 x 0.551 = 11.812 in

h 11.812 = = 42.8 t w 0.276 380 380 = = 65.169 34 Fy So,

h 380 ≤ tw Fy

Fv = 0.4 Fy = 0.4 x 34 = 13.6 ksi Shear Capacity V = d x tw x Fv Hand Book for Design of Steel Structures

5-25

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

54 5


= 13.78 x 0.276 x 13.6 = 51 kips (24.54 ton) 2. Local Web Yielding

Length of bearing N = 7.8 in Thickness of web tw = 0.276 in Distance from extreme fiber to toe of fillet k = tf + r = 0.433 + 0.551 = 0.984 in For the concentrated load which is not near by the support Web yielding capacity = 0.66 Fy x tw (N + 5k)

R = 0.66 x 34 x 0.276 (7.8 + 5 * 0.984) R = 77.66 kips ( 35.30 ton) 3. Web Crippling

R = 67.5t

2 w

  N  t 1 + 3    w  d  t f 

  

1.5

  

F yw × t f tw

where: d = length between the vertical stiffeners Assume d = 80 in. R = 67.5 (0.276



)2 1 + 3  7.8

  0.276     80   0.433 

1.5

 = 5.14 [1 + 0.1488 ] x 7.303

 × 

34x 0.433 0.276

= 43.12 kips (16.9 ton) 4. Side sway web buckling

Assume the largest unbraced length along either flange l = 180 in and loaded flange not restrained against rotation.

d c h 11.812 = = = 42.8 t w t w 0.276 180 l = = 26.124 b f 6.89

d c /t w 42.8 = = 1.63 l /b f 26.124

For loaded flange not restrained and d c /t w < 1.7 l /b f


5-26

SYS

Example:



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA

54


The resistance to side sway web buckling is given by 

R =

6800 t w 3  0.4  h



 d c /t w   l /b f

3     

6800 x 0.276 3  0.4 × 1.63 3    11.812 = 20.96 kips (9.53 ton) =

5. Design (Checks) Summary Final Capacities

For shear = 51 kips (24.54 ton) Web yielding = 77.66 kips (35.30 ton) Web crippling = 43.12 kips (16.9 ton) Side sway web buckling = 2096 kips (9.53 ton)


5-27

10. Design Aids It has been mentioned earlier in this chapter that the design of a beam primarily needs calculations for the determination of the critical unbraced lengths Lc and Lu and checking the section compactness. In some cases if the compression flange of the compact section beam has a continuous lateral support, the moment strength can be obtained without any calculations to check the adequacy of the lateral bracing. So the following three types of SYS beam design aids shall be provided to assist the structural steel designer in his regular design works. Table 5.1 Allowable Stress Design Selection (For Shapes Used as Beam)

These tables are useful to check the critical unbraced length limits and to find the moment capacity when the lateral torsional buckling checks are not required or the unbraced length is less than that given by Lc. The table also gives the compactness of the sections for Fy = 2400 ksc (the most common standard grade of Siam Yamato steel) based on Fy’ criteria as explained below. Notations: Lc = Maximum unbraced length of the compression flange at which the allowable bending stress may be taken as 0.66 Fy for compact shapes and between 0.6 Fy and 0.66 Fy for noncompact shapes. Lu = Maximum unbraced length of the compression flange at which the allowable bending stress may be taken as 0.6 Fy. Lb = Unbraced length of the compression flange. Mr = Moment capacity of the section when Lb< Lu. Fy’ = The theoretical maximum yield stress based on the width-thickness ratio of onehalf the unstiffened compression flange, beyond which a particular shape is not “compact” based on flange local buckling criteria and is given by the following formula.

  65 = b f  2t f

    

2

Fy’’ = The theoretical maximum yield stress based on the depth-thickness ratio of web, beyond which a particular shape is not “compact” based on web local buckling criteria and is given by the following formula. It is only applicable for the cases of pure bending i.e. fa = 0 (no axial load)

  412  = d   t w 

2

Fy’’’ = The theoretical maximum yield stress based on the depth-thickness ratio of web, beyond which a particular shape is not “compact” for any condition of combined bending and axial stresses based on web local buckling criteria and is given by the following formula. Hand Book for Design of Steel Structures

5-28

  257  = d   t w 

2

Table 5.2 Properties of Sections for Beam Design

These tables are meat to assist the designer in saving time and effort for the calculation of important parameters when the beam design is carried out by hand calculation. Some intermediate calculations can be avoided by directly reading the values from these tables. Although some of the parameters for compactness checks are repeated from the previous tables, they are presented in slightly different form to provide more easy and practical way of beam design. As the notations used are quite obvious and standard ones, no explanation are provided here. Table 5.3 Allowable Moment Capacity (Arranged According to Section Designations)

The allowable moment tables give the capacity in ton-m for various shapes that are commonly used as beam. Only parameter required to pick the correct value of the moment capacity for a given shape is the unbraced length of the compression flange. To cover most practical cases, the capacity have been computed for the unbraced length of 1 m to 10 m which may be too large for small sections. The sections in these tables have been arranged in the increasing order of the width and depth in the similar way in the SYS product catalogues. Table 5.4 Allowable Moment Capacity (Arranged According to Section Weight)

Minimum weight criteria is one of the most important consideration in the design of steel structures. These tables provide an easy way to find a particular section or sections that has the minimum weight for a given moment strength requirement. These are the tables produced by rearranging the Tables 5.4 in the increasing order of weight instead of designation as in Tables 5.4. To pick a section that can carry certain required moment for a known unbraced length, the designer should move down along the column for that unbraced length, until he gets the moment capacity equal to more than that required. The section corresponding to this first occurrence will be the lightest section (most economical section) for the requirement.


5-29

Table 5.1 Allowable Stress Design Selection (For Shapes Used as Beam) Section Designation

Sx cm3

Fy’ Ksc

Fy’’ Ksc

Fy’’’ Ksc

Compactness for Fy=2400 ksc

Lc m

Lu m

Mr (=0.6FySx) ton-m

C 200x90x30.3 Kg/m

195.00

5639

Comp

1.04

2.59

2808.0

C 200x90x30.3 Kg/m

249.00

6710

Comp

1.17

3.57

3585.6

C 250x90x34.6 Kg/m

334.00

6222

Comp

1.17

2.75

4809.6

C 250x90x40.2 Kg/m

374.00

7741

Comp

1.17

3.07

5385.6

C 300x90x38.1 Kg/m

429.00

6222

Comp

1.17

2.29

6177.6

C 300x90x43.8 Kg/m

494.00

8846

Comp

1.17

2.74

7113.6

C 300x90x48.6 Kg/m

525.00

9426

Comp

1.17

2.82

7560.0

C 380x100x54.5 Kg/m

763.00

7635

Comp

1.30

2.48

10987.2

C 380x100x67.3 Kg/m

926.00

11929

Comp

1.30

3.10

13334.4

H 100x100x17.2 Kg/m

76.50

4295

Comp

1.30

3.53

1101.6

H 125x125x23.8 Kg/m

136.00

3226

Comp

1.63

3.82

1958.4

H 148x100x21.1 Kg/m

138.00

4295

Comp

1.30

2.39

1987.2

H 150x150x31.5 Kg/m

219.00

2598

Comp

1.96

4.12

3153.6

H 175x175x40.2 Kg/m

330.00

2191

NonComp

2.28

4.41

4752.0

H 198x99x18.2 Kg/m

160.00

2465

Comp

1.29

1.96

2304.0

H 200x100x21.3 Kg/m

184.00

3609

Comp

1.30

1.91

2649.6

H 194x150x30.6 Kg/m

227.00

1909

NonComp

1.96

2.91

3268.8

H 200x200x49.9 Kg/m

472.00

1909

NonComp

2.61

4.71

6796.8

H 200x204x56.2 Kg/m

498.00

4128

Comp

2.66

7.20

7171.2

H 208x202x65.7 Kg/m

628.00

2924

Comp

2.63

5.71

9043.2

H 248x124x25.7 Kg/m

285.00

1940

NonComp

1.47

2.48

4104.0

H 250x125x29.6 Kg/m

324.00

2749

Comp

1.63

2.43

4665.6

H 244x175x44.1 Kg/m

502.00

1909

NonComp

2.28

3.47

7228.8

H 244x252x64.4 Kg/m

720.00

2273

NonComp

3.29

6.68

10368.0

H 248x249x66.5 Kg/m

801.00

1231

NonComp

3.25

5.02

11534.4

H 250x250x72.4 Kg/m

867.00

1546

NonComp

3.26

5.30

12484.8

H 250x255x82.2 Kg/m

919.00

3596

Comp

3.32

8.40

13233.6

H 298x149x32 Kg/m

424.00

1625

NonComp

1.62

2.85

6105.6

H 300x150x36.7 Kg/m

481.00

2240

NonComp

1.91

2.80

6926.4

H 294x200x56.8 Kg/m

771.00

1909

NonComp

2.61

3.87

11102.4

H 298x201x65.4 Kg/m

893.00

H 294x302x84.5 Kg/m

1150.00

1884

NonComp

3.94

7.25

16560.0

H 298x299x87 Kg/m

1270.00

1081

NonComp

3.90

5.90

18288.0


2392

NonComp

2.62

3.97

12859.2

5-30

Table 5.1 (Continued) Allowable Stress Design Selection (For Shapes Used as Beam) Section Designation

Sx cm3

Fy’ Ksc

Fy’’ Ksc

Fy’’’ Ksc

Compactness for Fy=2400 ksc

Lc m

Lu m

Mr (=0.6FySx) ton-m

C 200x90x30.3 Kg/m

195.00

5639

Comp

1.04

2.59

2808.0

C 200x90x30.3 Kg/m

249.00

6710

Comp

1.17

3.57

3585.6

C 250x90x34.6 Kg/m

334.00

6222

Comp

1.17

2.75

4809.6

C 250x90x40.2 Kg/m

374.00

7741

Comp

1.17

3.07

5385.6

C 300x90x38.1 Kg/m

429.00

6222

Comp

1.17

2.29

6177.6

C 300x90x43.8 Kg/m

494.00

8846

Comp

1.17

2.74

7113.6

C 300x90x48.6 Kg/m

525.00

9426

Comp

1.17

2.82

7560.0

C 380x100x54.5 Kg/m

763.00

7635

Comp

1.30

2.48

10987.2

C 380x100x67.3 Kg/m

926.00

11929

Comp

1.30

3.10

13334.4

H 100x100x17.2 Kg/m

76.50

4295

Comp

1.30

3.53

1101.6

H 125x125x23.8 Kg/m

136.00

3226

Comp

1.63

3.82

1958.4

H 148x100x21.1 Kg/m

138.00

4295

Comp

1.30

2.39

1987.2

H 150x150x31.5 Kg/m

219.00

2598

Comp

1.96

4.12

3153.6

H 175x175x40.2 Kg/m

330.00

2191

NonComp

2.28

4.41

4752.0

H 198x99x18.2 Kg/m

160.00

2465

Comp

1.29

1.96

2304.0

H 200x100x21.3 Kg/m

184.00

3609

Comp

1.30

1.91

2649.6

H 194x150x30.6 Kg/m

227.00

1909

NonComp

1.96

2.91

3268.8

H 200x200x49.9 Kg/m

472.00

1909

NonComp

2.61

4.71

6796.8

H 200x204x56.2 Kg/m

498.00

4128

Comp

2.66

7.20

7171.2

H 208x202x65.7 Kg/m

628.00

2924

Comp

2.63

5.71

9043.2

H 248x124x25.7 Kg/m

285.00

1940

NonComp

1.47

2.48

4104.0

H 250x125x29.6 Kg/m

324.00

2749

Comp

1.63

2.43

4665.6

H 244x175x44.1 Kg/m

502.00

1909

NonComp

2.28

3.47

7228.8

H 244x252x64.4 Kg/m

720.00

2273

NonComp

3.29

6.68

10368.0

H 248x249x66.5 Kg/m

801.00

1231

NonComp

3.25

5.02

11534.4

H 250x250x72.4 Kg/m

867.00

1546

NonComp

3.26

5.30

12484.8

H 250x255x82.2 Kg/m

919.00

3596

Comp

3.32

8.40

13233.6

H 298x149x32 Kg/m

424.00

1625

NonComp

1.62

2.85

6105.6

H 300x150x36.7 Kg/m

481.00

2240

NonComp

1.91

2.80

6926.4

H 294x200x56.8 Kg/m

771.00

1909

NonComp

2.61

3.87

11102.4

H 298x201x65.4 Kg/m

893.00

H 294x302x84.5 Kg/m

1150.00

1884

NonComp

3.94

7.25

16560.0

H 298x299x87 Kg/m

1270.00

1081

NonComp

3.90

5.90

18288.0


2392

NonComp

2.62

3.97

12859.2

5-31

Table 5.2 Properties of Section for Beam Design (For Shapes Used as Beam) Section Designation

Radius rT

Compact Section Criteria d / Af

Bf / 2tf

cm

Fy'

d / tw

Ksc

Fy''

Fy''’

Torsional Constant J

Ksc

Ksc

cm4

Warping Constant Cw cm6

C200x80x24.6

2.95

0.33

5.33

--

16.82

--

--

5.06

12,047.06

C200x90x30.3

3.44

0.28

5.63

--

13.63

--

--

6.49

17,601.08

C250x90x34.6

3.30

0.31

5.00

--

17.85

--

--

10.45

33,306.76

C250x90x40.2

3.21

0.25

4.09

--

15.72

--

--

19.08

40,708.27

C300x90x38.1

3.25

0.37

5.00

--

21.69

--

--

11.66

50,964.91

C300x90x43.8

3.28

0.33

4.50

--

18.06

--

--

16.00

56,627.68

C300x90x48.6

3.17

0.28

3.75

--

17.25

--

--

27.65

67,953.21

C380x100x54.5

3.60

0.36

4.76

--

22.44

--

--

22.38

136,664.29

C380x100x67.3

3.57

0.29

3.85

--

17.70

--

--

42.48

169,203.40

H100x100x17.2

2.73

0.13

6.25

--

14.00

--

--

5.12

3,333.33

H125x125x23.8

3.41

0.11

6.94

--

16.46

--

--

9.11

11,444.09

H148x100x21.1

2.68

0.16

5.56

--

21.67

--

--

8.46

8,214.00

H150x150x31.5

4.10

0.10

7.50

--

18.57

--

--

15.00

31,640.63

H175x175x40.2

4.79

0.09

7.95

--

20.40

--

--

23.29

75,226.64

H198x99x18.2

2.60

0.29

7.07

--

40.89

--

--

4.53

11,094.88

H200x100x21.3

2.61

0.25

6.25

--

33.45

--

--

6.83

13,333.33

H194x150x30.6

4.05

0.14

8.33

--

29.33

--

--

12.00

47,633.06

H200x200x49.9

5.48

0.08

8.33

--

22.00

--

--

34.56

160,000.00

H200x204x56.2

5.46

0.08

8.50

--

14.67

--

--

35.02

169,793.28

H208x202x65.7

5.54

0.06

6.31

--

17.60

--

--

83.56

237,733.03

H248x124x25.7

3.26

0.25

7.75

--

46.40

--

--

8.47

39,088.33

H250x125x29.6

3.27

0.22

6.94

--

38.67

--

--

12.15

45,776.37

H244x175x44.1

4.72

0.13

7.95

--

31.71

--

--

26.35

146,243.05

H244x252x64.4

6.76

0.09

11.45

2,269

20.18

--

--

33.19

436,679.41

H248x249x66.5

6.85

0.08

9.58

3,246

27.75

--

--

54.63

514,320.12

H250x250x72.4

6.86

0.07

8.93

3,734

24.67

--

--

68.60

569,661.46

H250x255x82.2

6.83

0.07

9.11

3,589

15.86

--

--

69.51

604,529.30

H298x149x32

3.88

0.25

9.31

3,432

51.27

--

--

10.17

97,919.70

H300x150x36.7

3.89

0.22

8.33

--

43.38

--

--

14.58

113,906.25

H294x200x56.8

5.35

0.12

8.33

--

33.75

--

--

39.97

345,744.00

H298x201x65.4

5.40

0.11

7.18

--

30.00

--

--

64.03

420,666.08


5-32

Table 5.3 Properties of Section for Beam Design (For Shapes Used as Beam) Section Designation

Radius rT

Compact Section Criteria d / Af

Bf / 2tf

cm

Fy'

d / tw

Ksc

Fy''

Fy''’

Torsional Constant J

Ksc

Ksc

cm4

Warping Constant Cw cm6

H294x302x84.5

8.09

0.08

12.58

1,880

22.50

--

--

51.72

1,190,379.65

H298x299x87

8.21

0.07

10.68

2,610

30.00

--

--

81.95

1,384,722.94

H300x300x94

8.22

0.07

10.00

2,977

27.00

--

--

101.25

1,518,750.00

H300x305x106

8.16

0.07

10.17

2,880

18.00

--

--

102.38

1,595,960.16

H304x301x106

8.25

0.06

8.85

3,798

24.55

--

--

148.37

1,785,189.54

H346x174x41.4

4.55

0.22

9.67

3,186

54.67

--

--

16.86

236,500.04

H350x175x49.6

4.59

0.18

7.95

--

46.86

--

--

31.06

300,906.58

H354x176x57.8

4.62

0.15

6.77

--

41.00

--

--

51.70

370,063.83

H336x249x69.2

6.71

0.11

10.38

2,765

39.00

--

--

48.04

871,458.28


5-33

Table 5.4 Allowable Moment Capacity (ton-m) SYS Section

Unbraced Length 5m 6m

1m

2m

3m

4m

7m

8m

9m

10m

C 200x90x30.3 Kg/m

4008.46

3644.06

3144.70

2358.52

1886.82

1572.35

1347.73

1179.26

1048.23

943.41

C 200x90x30.3 Kg/m

5118.50

4653.18

4653.18

4158.13

3326.51

2772.09

2376.08

2079.07

1848.06

1663.25

C 250x90x34.6 Kg/m

6865.78

6241.61

5729.07

4296.80

3437.44

2864.53

2455.31

2148.40

1909.69

1718.72

C 250x90x40.2 Kg/m

7688.02

6989.11

6989.11

5366.55

4293.24

3577.70

3066.60

2683.27

2385.13

2146.62

C 300x90x38.1 Kg/m

8818.62

8016.92

6132.16

4599.12

3679.30

3066.08

2628.07

2299.56

2044.05

1839.65

C 300x90x43.8 Kg/m

10154.77

9231.61

8419.21

6314.41

5051.53

4209.61

3608.23

3157.20

2806.40

2525.76

C 300x90x48.6 Kg/m

10792.01

9810.92

9236.17

6927.13

5541.70

4618.09

3958.36

3463.56

3078.72

2770.85

C 380x100x54.5 Kg/m

15684.39

14258.54

11774.77

8831.08

7064.86

5887.38

5046.33

4415.54

3924.92

3532.43

C 380x100x67.3 Kg/m

19035.06

17304.60

17304.60

13397.08

10717.66

8931.39

7655.47

6698.54

5954.26

5358.83

H 100x100x17.2 Kg/m

1572.55

1429.59

1429.59

1261.73

1009.38

841.15

720.99

630.86

560.77

504.69

H 125x125x23.8 Kg/m

2795.65

2541.50

2541.50

2429.99

1943.99

1620.00

1388.57

1215.00

1080.00

972.00

H 148x100x21.1 Kg/m

2836.76

2578.87

2182.62

1651.55

1230.30

1025.25

878.79

768.94

683.50

615.15

H 150x150x31.5 Kg/m

4501.81

4092.56

4092.56

4092.56

3371.20

2809.34

2408.00

2107.00

1872.89

1685.60

H 175x175x40.2 Kg/m

6721.31

6721.31

6166.86

6166.86

5442.74

4659.70

3887.67

3401.72

3023.75

2721.37

H 198x99x18.2 Kg/m

3288.99

2976.18

2543.64

1938.09

1275.85

886.00

650.94

498.38

439.82

395.84

H 200x100x21.3 Kg/m

3782.34

3402.59

2880.15

2148.73

1396.95

970.11

794.81

695.46

618.19

556.37

H 194x150x30.6 Kg/m

4554.74

4242.06

4211.63

3821.37

3319.61

2706.35

2033.09

1556.59

1286.58

1157.92

H 200x200x49.9 Kg/m

9470.65

9470.65

8820.48

8820.48

8303.76

7449.61

6600.67

5621.12

4613.20

4151.88

H 200x204x56.2 Kg/m

10237.00

10237.00

9306.36

9306.36

9306.36

9306.36

9306.36

8377.87

7446.99

6702.29

H 208x202x65.7 Kg/m

12909.30

12909.30

11735.73

11735.73

11735.73

11176.59

9579.93

8382.44

7451.06

6705.95


5-34

Table 5.5 Allowable Moment Capacity (ton-m) SYS Section H 248x124x25.7 Kg/m

1m

2m

3m

4m

5728.86

5325.93

5054.85

4383.75

Unbraced Length 5m 6m 3520.90

2536.60

7m

8m

9m

10m

1863.63

1426.84

1127.38

913.18

H 250x125x29.6 Kg/m

6660.21

6054.74

5698.30

4897.82

3868.63

2748.46

2019.28

1546.01

1221.54

1068.76

H 244x175x44.1 Kg/m

10072.59

10072.59

9381.11

9040.02

8261.84

7310.72

6186.68

4908.45

3878.28

3141.41

H 244x252x64.4 Kg/m

14720.15

14720.15

14720.15

13454.98

13454.98

13454.98

12848.45

11242.39

9993.24

8993.91

H 248x249x66.5 Kg/m

15181.01

15181.01

15181.01

14968.66

14968.66

14259.52

13402.85

12414.38

11294.12

10042.06

H 250x250x72.4 Kg/m

16958.92

16958.92

16958.92

16202.03

16202.03

15340.27

14379.00

13269.84

12012.79

10607.86

H 250x255x82.2 Kg/m

18891.16

18891.16

18891.16

17173.78

17173.78

17173.78

17173.78

17173.78

16032.97

14429.67

H 298x149x32 Kg/m

8346.52

7923.49

7824.99

7063.64

6084.76

4888.35

3635.84

2783.69

2199.46

1781.56

H 300x150x36.7 Kg/m

9819.22

8988.67

8837.88

7943.79

6794.26

5389.27

3984.46

3050.60

2410.35

1952.39

H 294x200x56.8 Kg/m

15470.06

15470.06

14408.04

14302.19

13342.14

12168.75

10782.02

9181.95

7415.34

6006.42

H 298x201x65.4 Kg/m

18350.45

18350.45

16687.91

16659.99

15601.28

14307.32

12778.08

11013.58

9020.76

7306.82

H 294x302x84.5 Kg/m

23039.86

23039.86

23039.86

21490.59

21490.59

21490.59

21490.59

19483.25

17318.45

15586.60

H 298x299x87 Kg/m

23586.05

23586.05

23586.05

23733.08

23733.08

23642.19

22657.11

21520.48

20232.30

18792.57

H 300x300x94 Kg/m

26053.36

26053.36

26053.36

25414.96

25414.96

25228.24

24141.08

22886.66

21464.99

19876.06

H 300x305x106 Kg/m

29600.95

29600.95

29600.95

26909.95

26909.95

26909.95

26909.95

26909.95

26828.88

24146.00

H 304x301x106 Kg/m

30238.93

30238.93

30238.93

28778.70

28778.70

28778.70

27504.45

26135.50

24584.03

22850.03

H 346x174x41.4 Kg/m

12395.97

11978.67

11978.67

11439.17

10387.04

9101.10

7581.36

5919.22

4676.91

3788.30

H 350x175x49.6 Kg/m

15550.32

15550.32

14482.79

13956.20

12754.83

11286.48

9551.15

7577.79

5987.39

4849.78

H 354x176x57.8 Kg/m

18685.60

18685.60

16986.91

16473.31

15122.72

13472.01

11521.17

9273.10

7326.89

5934.78

H 336x249x69.2 Kg/m

20847.83

20847.83

20847.83

20556.21

20387.46

19308.24

18032.80

16561.13

14893.25

13029.14


5-35


1m

2m

3m

4m

7m

8m

9m

10m

H 340x250x79.7 Kg/m

25037.38

25037.38

25037.38

23919.96

23848.54

22647.69

21228.52

19591.00

17735.15

15660.97

H 340x250x79.7 Kg/m

25037.38

25037.38

25037.38

23919.96

23848.54

22647.69

21228.52

19591.00

17735.15

15660.97

H 338x351x106 Kg/m

32901.85

32901.85

32901.85

32901.85

31208.07

31208.07

31208.07

30986.53

27543.58

24789.23

H 344x348x115 Kg/m

35473.20

35473.20

35473.20

35473.20

36253.69

36253.69

36195.36

34944.38

33526.61

31942.04

H 344x354x131 Kg/m

42140.24

42140.24

42140.24

42140.24

38309.31

38309.31

38309.31

38309.31

38309.31

37113.46

H 350x350x137 Kg/m

44408.91

44408.91

44408.91

44408.91

42981.18

42981.18

42981.18

41467.42

39796.78

37929.60

H 350x357x156 Kg/m

50362.73

50362.73

50362.73

50362.73

45784.30

45784.30

45784.30

45784.30

45784.30

45784.30

H 396x199x56.6 Kg/m

19636.69

19636.69

18874.34

18823.57

17615.36

16138.66

14393.48

12379.80

10111.48

8190.30

H 400x200x66 Kg/m

23877.26

23877.26

22238.09

22238.09

20924.11

19258.76

17290.62

15019.70

12445.98

10081.80

H 404x201x75.5 Kg/m

27946.94

27946.94

25414.96

25414.96

24046.89

22202.44

20022.63

17507.46

14656.93

11889.35

H 386x299x94.5 Kg/m

32314.75

32314.75

32314.75

32516.19

32516.19

32391.66

31042.02

29484.75

27719.85

25747.30

H 390x300x107 Kg/m

37930.62

37930.62

37930.62

37001.19

37001.19

37001.19

35527.20

33817.43

31879.69

29713.99

H 388x4002x140 Kg/m

49739.84

49739.84

49739.84

49739.84

49739.84

47092.42

47092.42

47092.42

47092.42

43062.46

H 394x398x147 Kg/m

51397.48

51397.48

51397.48

51397.48

51397.48

53259.28

53259.28

53259.28

51778.58

50043.15

H 394x405x168 Kg/m

62172.43

62172.43

62172.43

62172.43

62172.43

56623.03

56623.03

56623.03

56623.03

56623.03

H 400x400x172 Kg/m

63327.21

63327.21

63327.21

63327.21

63327.21

62229.27

62229.27

62229.27

60480.42

58448.31


H 414x405x232 Kg/m

91924.91

91924.91

91924.91

91924.91

91924.91

83719.86

83719.86

83719.86

83719.86

83719.86

H 446x199x66.2 Kg/m

25913.04

25913.04

24106.83

23908.04

22289.54

20311.37

17973.54

15276.04

12313.47

9973.91

14887.85

12059.16

H 450x200x76 Kg/m

30628.76

30628.76

27844.33

27763.23

25977.34

23794.59

21214.98

18238.50

H 456x201x88.9 Kg/m

36384.50

36384.50

33076.82

33076.82

31424.91

29080.98

26310.89

23114.62

Table 5.5 Allowable Moment Capacity (ton-m) Hand Book for Design of Steel Structures

5-36

SYS Section

1m

2m

3m

4m


7m

8m

H 434x299x106 Kg/m

41418.09

41418.09

41418.09

40364.93

40364.93

40041.58

38305.23

36301.75

H 440x300x124 Kg/m

50113.06

50113.06

50113.06

47653.04

47653.04

47653.04

45913.48

H 446x302x145 Kg/m

60750.99

60750.99

60750.99

55688.65

55688.65

55688.65

53665.59

H 496x199x79.5 Kg/m

34740.00

34740.00

31581.82

31449.42

29401.09

26897.57

H 500x200x89.6 Kg/m

39262.37

39262.37

35693.06

35693.06

33484.71

30768.04

H 506x201x103 Kg/m

45840.36

45840.36

41673.05

41673.05

39693.29

H 482x300x114 Kg/m

49130.45

49130.45

49130.45

46718.67

46718.67

H 488x300x128 Kg/m

57187.84

57187.84

57187.84

54380.53

H 494x302x150 Kg/m

69109.35

69109.35

69109.35

63350.52

9m

10m

43760.11

41319.63

38592.02

51152.11

48303.50

45119.77

23938.86

20524.96

16698.81

13526.04

27557.44

23852.89

19655.94

15921.31

36784.84

33347.59

29381.53

24886.66

20272.04

45831.03

43635.98

41103.22

38232.77

35024.61

54380.53

54380.53

52395.39

49938.01

47152.99

44040.31

63350.52

63350.52

61049.11

58189.82

54949.28

51327.52

H 596x199x94.6 Kg/m

47484.86

43168.05

43168.05

42825.08

39934.16

36400.81

32225.03

27406.82

22105.52

17905.47

H 600x200x106 Kg/m

53240.60

53240.60

48400.54

48246.13

45134.24

41330.81

36835.86

31649.37

25815.97

20910.94

H 606x201x120 Kg/m

61257.52

61257.52

55688.65

55688.65

52736.02

48714.29

43961.36

38477.19

32261.81

26179.99

H 612x202x134 Kg/m

69480.01

69480.01

63163.64

63163.64

60527.58

56279.70

51259.49

45466.94

38902.05

31886.78

H 582x300x137 Kg/m

70829.19

70829.19

70829.19

65966.76

65966.76

65044.03

62064.02

58625.53

54728.57

50373.16

H 588x300x151 Kg/m

100725.93

100725.93

100725.93

93811.09

93811.09

93811.09

90651.72

86493.72

81781.30

76514.50

H 594x302x175 Kg/m

94969.72

94969.72

94969.72

86336.10

86336.10

86336.10

83436.15

79611.81

75277.56

70433.40

H 692x300x166 Kg/m

101662.60

101662.60

101662.60

93063.59

93063.59

92679.32

88806.51

84337.90

79273.47

73613.22

H 700x300x185 Kg/m

117585.65

117585.65

117585.65

107639.81

107639.81

107639.81

105498.68

101182.00

96289.78

90822.00

H 792x300x191 Kg/m

131765.34

131765.34

131765.34

119786.67

119786.67

119592.53

114716.17

109089.61

102712.83

95585.84


5-37


1m

2m

3m

4m


H 800x300x210 Kg/m

149854.81

149854.81

149854.81

136231.64

136231.64

I 200x100x26 Kg/m

4460.70

4055.18

3976.68

2982.51

2386.01

I 200x150x50.4 Kg/m

9168.07

8334.61

8334.61

8334.61

I 250x125x38.3 Kg/m

8510.27

7736.61

7736.61

7112.68

I 250x125x55.5 Kg/m

17637.23

16033.85

16033.85

I 300x150x48.3 Kg/m

12991.53

11810.48

11810.48

I 300x150x65.5 Kg/m

17452.23

15865.66

I 300x150x76.8 Kg/m

20103.98

18276.34

I 350x150x58.5 Kg/m

17883.91

7m

8m

9m

10m

136231.64

133627.36

128196.39

122041.32

115162.10

1988.34

1704.29

1491.26

1325.56

1193.01

8334.61

8334.61

8334.61

7355.95

6538.62

5884.76

5690.14

4741.78

4064.39

3556.34

3161.19

2845.07

16033.85

16033.85

14937.31

12803.41

11202.98

9958.21

8962.39

11292.32

9033.86

7528.21

6452.75

5646.16

5018.81

4516.93

15865.66

15865.66

15865.66

14391.66

12335.71

10793.75

9594.44

8635.00

18276.34

18276.34

18276.34

18276.34

16898.43

14786.12

13143.22

11828.90

16258.10

16258.10

15373.99

12299.19

10249.32

8785.14

7686.99

6832.88

6149.59

I 350x150x87.2 Kg/m

26311.96

23919.96

23919.96

23919.96

23919.96

23919.96

20680.41

18095.36

16084.76

14476.29

I 400x150x72 Kg/m

24667.46

22424.96

22424.96

22265.77

17812.62

14843.85

12723.30

11132.89

9895.90

8906.31

I 400x150x95.8 Kg/m

32478.82

29526.20

29526.20

29526.20

29526.20

27145.00

23267.14

20358.75

18096.67

16287.00

I 450x175x91.7 Kg/m

35767.81

35767.81

32516.19

32516.19

29761.00

24800.83

21257.86

18600.62

16533.89

14880.50

I 450x175x115 Kg/m

44606.99

44606.99

40551.81

40551.81

40551.81

40208.71

34464.61

30156.53

26805.80

24125.22

I 600x190x133 Kg/m

67424.39

67424.39

61294.89

61294.89

57103.00

47585.83

40787.86

35689.37

31723.89

28551.50

I 600x190x176 Kg/m

89008.41

89008.41

80916.74

80916.74

80916.74

80916.74

75382.93

65960.06

58631.16

52768.05


5-38

11. Software Implementation The beam design module of the SYS Designers Software has been developed based on the flow diagram as described in “General Procedure“ section of this chapter. The module can carry out all necessary design, investigation and checks according to AISC/ASD (1992) specifications. In addition to flexural strength calculation about both principal axis, various standard beam checks like shear, web yielding, crippling and side sway web buckling can also be carried out Built-in SYS section database facilitates the quick selection, design and verification of the beam.


5-39

Chapter

6

Design of Columns 1. Introduction In the previous two chapters, we have discussed about the design of members subjected to only axial compression or flexure. While many structural members can be treated as either axially loaded members or beams with only flexural loading, many of them are subjected to some degree, of both bending and axial load. In many cases, the effects due to bending are so small that they can be considered as secondary effects and can be neglected, with negligible errors. P Mx Top

My Top

My Bot Mx Bot

P

•

Fig. 6.1.General Steel Column

Structural members subjected to both significant compression and flexure are called beam-columns or columns in general. The rafter and column of a gable frame and top chord member of a truss with a purlin placed between the joints are the some common examples of such columns. Design of a column requires the determination of the stresses due to the axial loads and bending, and checks the combined effect by using some interaction formulae. The basic concepts for axial load are explained in Chapter 3 and 4 and for bending in chapter 5. This chapter describes the additional concepts and considerations specific to columns. Important topics to be covered in this chapter are the magnification (amplification) of actual moment due to presence of axial Hand Book for Design of Steel Structures

6-1

force and column design using interaction formulae. Design examples and flow diagrams that form the basis of internal calculation for SYS designer are also included at the end.

2. Moment Amplification For the design of columns, the moments obtained from elastic first-order analysis are magnified to take into account the following two type of effects. •

Secondary moment due to the deflection within the length of the member ( P − δ effects ) Fig 6.1(a)

•

Secondary moment due to the effect of sway when the member is a part of a part of an unbraced frame ( P − ∆ effects ) Fig.6.2(b).

∆

δ

(a)

(b)

•

Fig. 6.2.Second Order Effects

Some specifications (e.g. AISC/LRFD) require separate first-order elastic analysis for ‘lateral translation (LT)’ and ‘No lateral Translation (NT)’ cases and using different amplification factor for moment obtained from each analysis. An analytical expression for a column subjected to an axial load P and unequal end moments M 1 and M 2 is given as follows. •

M max = MF x M 2

•

(6-1)

Where MF = moment magnification factor Mmax = maximum or magnified moment for design The analytical solution for the pin-ended column segment as shown in figure 6.3 is given by

MF =

(M1 / M 2 ) + 2(M1 / M 2 ) cos kl + 1 sin2 kl


•

(6-2)

6-2

The location of the point of maximum moment can be calculated using the following equation. M1

M2

xc

M1

M2 Mmax

•

Fig. 6.3. Single Curvature Bending

tan( kx c ) =

− (M1 / M 2 ) cos kl + 1 (M1 / M 2 ) sin kl

(6-3)

•

Where

•

P • (6-4) EI And M1/M2 is positive for double curvature bending and negative for single curvature. The MF can also be written as k=

MF = Cm . sec(Kl / 2)

(6-5)

•

Where

•

1 Cm = • (6-6) Sec (kl / 2) where the above exact solution has been simplified with the following assumptions for practical design purposes.

sec( kl / 2) =

1 1−

P Pe

(6-7)

•

And

•

Cm = 0.6 − 0.4(M1 / M 2 ) Finally the moment magnification factor takes the form as Cm P 1− Pe Where Eulers’ Load is given as

•

(6-8)

•

(7-9)

MF =

Pe =

π 2EI (kL / r )2


•

(6-10)

6-3

Equation 6-9 forms the basis for the moment magnification factors used in various forms in different specifications. Use of this moment magnifier in the column design interaction equations are discussed in the subsequent article ”Column Interaction Equations”

3. Column Interaction Equations Column interaction equations are, basically, derived considering the column as simply supported and subjected to axial load and equal external moment at two ends. To generalize the equations such that they may be applied for members with other loading and boundary conditions, and for members in general frameworks, various factors to approximate the actual behavior are introduced. Such equations are based on linear first-order elastic analysis and amplified to account for second-order effects. So the major portion of the analysis/design of columns is devoted to the assessment of the procedure for calculations of the effective length and moment amplifications factors. Although various codes to permit the use of more rational second-order inelastic analysis, such analysis are impractical for manual calculations and can only be carried out with advanced computing tools. Column interaction equations include two types of second-order effect P − δ and P − ∆ which are explained in the previous article “Moment Amplification”. For the illustration purposes, the interaction equations for AISC/ASD will be discussed in this article. •

For axial compression and bending

f For a < 0.15 Fa fby fa f + bx + ≤ 1.0 Fa Fbx Fby fa ≥ 0.15 following two equations Fa fby Cmy fa f Cmx + bx + ≤ 1.0 Fa Fbx 1 − fa Fbx Fby 1 − fa Fby

•

•

And for

fby fa f + bx + ≤ 1.0 0.6Fy Fbx Fby •

•

•

(6-12)

•

(6-13)

For axial tension and bending

fby fa fbx + + ≤ 1.0 Ft Fbx Fby

•

•

In the above column interaction equations, the term C 1− f

mx F

a

bx

(6-11)

(6-14) •

•

(6-15)

is the moment amplification factor. It can be noted in the equation 6-11 that the amplification factor is equal to one. This means for small axial load (fa/Fa<0.15) the secondary effects are less significant and can be neglected without any serious error. The factor Cm is incorporated to account for the unequal end moments and the Hand Book for Design of Steel Structures

6-4

restraint conditions as explained in the previous section. Detailed procedures for the calculations of various parameters of the above equations has been shown in the ‘General Procedure” section of this chapter for AISC/ASD specifications.

4. General Procedure General procedure for the design of a column is the combination of corresponding general procedures for the design of an axial compression and flexural members. In addition to this, column design also needs computations of factors for moment magnification. The following flow diagram describes schematically the stepwise design procedure for the design of a column. The details for sub parts can be referred to the general procedures described in last two chapters. This flow diagram, also forms the basis for the development of the column design module of the SYS Designers Software. (Flow diagrams for the design of columns are shown in the following pages)


6-5

Flow Diagram for Column Design Basic Data

Trial Cross Section

Compute: Fa

Compute: Fbx, Fby No Compute: fa,fbx, fby

No Yes

fa / Fa< 0.15

No Compute: Cmx,Cmy

f a fbx fby + + < 1.0 Fa Fbx Fby

Compute: FEX',FEY'

P A M = x Zx

fa = f bx

f by =

My

FEX ' =

f by C my f a f bx C mx + + < 1 .0 Fby 1 − f a Fa Fbx 1 − f a ' ' FEX FEY

Yes

f by fa f + bx + ≤ 1.0 0 .6 F y Fbx Fby

Zy 12π 2 E 23 ( kL / r ) 2x

Yes

12π 2 E FEY ' = 23 ( kL / r ) 2y

End

Fig. 6.4. Flow diagram for a typical column design based on AISC/ASD specifications Hand Book for Design of Steel Structures

6-6

Flow Diagram for Computation of C m Basic Date

Transverse Load on t he member

Yes

Relative End Translation

Yes

No

No

End Rotationally Restrained Yes

Yes

Relative End Translation

No

No

Cm=1

Cm = 0.6-0.4M1/ M2 M1 < M2

Cm=0.85

End

Fig. 6.5. Flow diagram for the computation of coefficient Cm based on AISC/ASD specifications

5. Design Examples The example given in this section illustrates the complete design steps for a typical steel column subjected to moment and axial force at the ends.


6-7

SYS

Example:6 1



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Sheet No:1 / 4

Checked by: NA


Problem:

Check the adequacy of the column of the gable frame shown below 10@ 4.4 = 44

44' 4.4 = 10@ .7 50x36 300x1 SYS H

SYS H300x150x36.7

20'

'

75'

•

Fig. 6.6.General Column 7.26 Kips

7.26 Kips •

P

2.64 Kips

2.64 Kips

29.60 ft- Kips

20.94 ft- Kips

V

M

Fig. 6.7.Design Actions Obtained from 2D Frame Analysis Solution: Determine of effective length factor K and Fa

At top,

∑ (EI / L )c = G = 1 / 20 = 3.9 1 / (2 x39 ) ∑ (EI / L )b

At base, G = 1 (fixed base ) Using Alignment chart for unbraced case Kx = 1.6

K x L x 1.6 x 20 x12 = = 78.68 rx 4.88 Normally, the column is braced laterally at mid height and K can be taken as 1 for that direction.

K y Ly ry

=

1× Lx / 2 = 78.68 ry


6-8

SYS

Example:6 1



Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Kl So, critical = 92.3 r Cc = π

2E 2 × 29000 =π =129.75 Fy 34

Design Condition :

Actual fa = So,

 1  KL / r  2    Fy 1 −   2  Cc   Fa = = 13.44 Ksi 3  KL   KL  5 3 r  1 r  −   +  3 8  Cc  8  C c         

Kl < Cc r

P 7.26 = =1.001 ksi A 7.25

fa 1.001 = = 0.0744 Fa 13.44

Determination of Fb

Maximum unbraced length = 10 ft. Maximum value of Lc for which Fb = 0.66 Fy is given by the smaller of

Lc1 = Lc2 =

76 bf 76 × 5.91 = = 77.03 in Fy 34 20,000 = 904.20 in d Fy × Af

smaller of the two, Lc = 77.03 = 6.41 ft. Actual unbraced length Lb = 10 ft. So Lb > Lc Computation of Cb and rT : 2

M  M  Cb =1.75 −1.05  1  + 0.3  1  ≤ 2.3 M  2  M2  2

 20.94   20.94  Cb = 1.75 −1.05   + 0.3   =1.1573 ≤ 2.3  29.60   29.60  So use Cb = 1.157


6-9

SYS

Design Code:

Thailand

AISC/ASD (1991)

Iy /2

rT ≈

Example:6 1



Af

=

12.2 / 2

(5.91× 0.354)



= 1.70

Maximum spacing of lateral brace for the allowable stress 0.6 Fy is given by the higher of the following two equation.

Lc1 = rT

Lc2 =

102,000 cb 102,000 ×1.157 = 1.7 = 100.15 in Fy 34

20,000 cb 20,000 ×1.157 = =120.43 in d 11.81 Fy × 34 × Af 2.09

So Lc = 120.43 = 10.0 ft. Again Lb >= Lc

102,000 C b = Fy

102,000 ×1.157 = 57.65 in 35.5

510,000 C b = Fy

510,000 ×1.157 = 128.92 in 35.5

L 10 ×126 = = 70.58 in rT 1. 7

102,000 C b L ≤ ≤ Fy rT

So

510,000 × C b Fy

2  L   F y    2 2 35.5 (70.58)  2  rT   × F = − Fb1 =  −   x Fy = 0.566 × Fy = 20.120 ksi  y 3 3 3  3 1530 ×10 ×1.157   1530 ×10 cb      Ld Computing Fb based on Af

L d 10 ×12 ×11.81 = = 678 Af 2.09

20,000 C b 20,000 ×1.157 = = 651.83 Fy 35.5 So,

L d 20,000 Cb > Af Fy

Fb2 =

12,000 Cb 12,000 ×1.157 = = 20.47 ksi L d / Af 678


6-10

SYS

Example:6 1



Design Code:

Thailand

AISC/ASD (1991)



So, using the higher of the Fb1 and Fb2 : Fb = 20.47 ksi Actual Fb =

Max. moment 29.60 ×12 = =12.08 ksi Sx 29.4

f b 12.08 = = 0.59 Fb 20.47 Computation of Cm

As the frame is not braced against lateral translation cm=0.85 Computation of FEX’

FEX ' =

12 π 2 E  KL  23   r 

2

=

12 x π 2 × 29000 =17.52 ksi 2 23(92.3)

Final check

The above computed values of cm. and FEX ' is used only for the cases when

fa fa > 0.15 . But in this case = 0.0725 < 0.15 so the following simplified check shall Fa Fa apply.

fa f bx f by + + ≤1.0 Fa Fbx Fby 0.0725 + 0.59 + 0 0.66 < 1.0 Hence the section H300 x 150 is OK for column of the Gable frame.


6-11

6. Software Implementation The column design module of the software has been developed based on the flow diagram shown in “General Procedure” section of this chapter. As the design of a column is more complicated than any other steel members. The SYS steel designer’s software has been developed to assist the structural steel designer, from design point of view, primarily in the following two different ways: Member Design : To find or select the most appropriate section available in SYS steel section database built in the program, for the designer specified member and loading conditions that confirm to AISC/ASD specification. Code Verification : To check an user specified member, loading and SYS section for AISC/ASD specification. For the complete information regarding the software, reader is referred to the “SYS Steel Designers Software User’s Manual”.


6-12

Chapter

7

Introduction to Connection Design 1. Introduction The design of connections can be approached from a number of directions: The type of fasteners such as bolts, rivets, welds and special devices like cable sockets; the type of structures such as buildings, bridges, transmission towers etc. and also the type of loading like static and dynamic etc.. Irrespective of the type and classification of the design of any connection are interrelated criteria of strength, stiffness, ductility, predictability, practicability and cost. It is beyond the scope of this manual to cover comprehensively the detail of the connections from all criteria. The purpose of this chapter is to introduce some of the underlying common concerns and objectives to the design of most common type of connections with practical examples. The following connections shall be covered briefly followed by some examples on some typical type of connections. • • • •

Truss Connections Portal Frame Connections Building Frame Connections Column Bases

2. Truss connections The connections used in a truss or lattice girder can be internal joint, external joint, site splice and bracing connection. Internal joints are needed to join the individual members together to form a complete truss while external joint are required to connect the truss as a whole to the structural element which supports the truss. To facilitate the transportation, very large trusses are assembled as component parts first and then site spliced to form the complete unit. Bracing connections are required to fix the diagonal members between building columns, portal frame members and adjacent trusses. The common truss connections though analyzed as pin joints do not reflect the idealization of pinned joints. The cost of connections is a major item in the total cost of steel structures. It is very expensive to make a truss with truly pinned joint that requires special plant, equipment and techniques. It has been found from experience that conventional fabrication and erection techniques can satisfy the relevant performance criteria. The following are some useful guidelines on the selection of joint type to give the most economic solution. 1)

In general shop joints should be welded and site joints bolted.

2)

If a large number of trusses are to be made, welded joints are usually more economical than bolted joints. Welded joints are aesthetically better and maintenance cost also less than with bolted joints.


2.1.

3)

Gusset plates can be eliminated for directly welded connections. The selection depends upon the type of member for example hollow sections do not need gusset plate where as double angle members generally require gusseted joints.

4)

Standard joints should be used with as much repetition of member shapes and sizes, end preparation and fabrication operation as possible. This can be achieved readily with parallel chord lattice girders.

Joint Behavior Members framing into a joint should be so arranged that either their centroidal axes or in case of bolted connections, the bolt centerlines coincide at a point. If this can not be achieved the connection must be designed to resist the moment due to eccentricity. However the concentricity requirement may need for large gusset plates. One common method to minimize the size of the gusset plate is nesting the member as shown in Fig 7.1 The moment arising from eccentricity is distributed between the members meeting at the joint and the connections in proportion to their stiffnesses. As the trued behavior of a joint is complicated, the small eccentricities and secondary stresses are ignored in conventional analysis and design.

Fig. 7.1 Truss Connections

2.2.

Design Considerations The main point in the design of fasteners and the gusset plate if provided, for a truss joint is discussed briefly as follows. 2.2.1. Bolted Joints

If the centroidal axis of the connected parts meet at a point, the bolts are designed for direct load, otherwise the eccentricity in the plane of the joint should be taken into account. The small eccentricity between the centroidal axis and the bolt gauge line is ignored. Ordinary bolts are designed for single or double shear and bearing whereas pre-loaded bolts are designed for slip resistance, and shear and bearing where appropriate. In the bracing connections that connect the diagonal to the other building frame element, is designed for tension and shear and should be arranged as far as possible, to avoid any eccentricity. 2.2.2. Gusset Plates

The thickness of the gusset plate should be equal to or slightly larger than the thickest part to be connected and its size large enough to accommodate the required fasteners. Common design practice is to check the plate as a beam section in axial Hand Book for Design of Steel Structures

7-2

load, bending and shear or alternatively to check the direct stress in the plate at the end of each member assuming an dispersance angle of 30 degree on either side of the member.

3. Portal Frame Connections The portal frames that will be discussed in this section are single-story pitched roof portal frame. Depending upon the location and performance requirements, pitched roof portal frame connections may be divided into the following three types. Eaves Connections Ridge Connections Base Connections 3.1.

Eaves Connections Eaves connections are further divided into two types:

3.2.

• Unhanuched Eaves Connections • Haunched Eaves Connections Unhaunched Eaves Connections: Commonly used type unhaunched fully rigid eaves connections and their force transfer diagrams are shown in Fig 7.2 (a), (b), ©. In the connection with cover plate, the force on the flange of the rafter is transmitted to the web of the column and the force in rafter web into the column flanges. The vertical shear in the rafter web passes through the web welds into the end plate. from this it passes through the connecting bolts into the column flange. Similarly, the tensile force in the rafter top flange passes to cover plate and then to column web. The compressive force in the bottom flange of the rafter passes into the web stiffener plate and through the connecting weld into the column web.

(a) Extended End Plate

(b) Cover Plate and Extended End Plate

(c) Force Diagram

Fig. 7.2 Unhanched Eaves Connections(a)


7-3

(d) With Diagonal End Plates

(e) Force Diagram

Fig. 7.3 Unhaunched Eaves Connections (b)

In the case of connection with diagonal end plates Fig.7.2.©, the welds are designed to transmit the flange forces and web forces into the end -plates. This element is designed to take compressive forces as struts. The end plate must also be checked for local buckling near the tension flange. The bolts are designed to transmit the bending moment at the eaves and the axial and shear forces that act perpendicular and parallel to the plane of the end plates.

(d) Flush End Plate and Extended Plate

(e) Force Diagram

Fig. 7.4 Haunched Eaves Connections


7-4

3.3.

Haunched Eaves Connections: Fig 7.3 shows some fully rigid haunched eaves connections and methods to resolve the forces in the connected parts. The vertical shear force in the rafter and haunch webs is transferred subsequently from web welds to end plate, end plate to connecting bolts and finally to column flange. The compressive force in the bottom flange of the haunch passes into the compression stiffeners on the column and through their to connecting welds into the column web. The fasteners can be divided by taking equal division of load in all or by assuming that it is taken only by the group of bolts near the haunch compression flange without any shear force in bolts near rafter tension flange. In the connection without top cover plate Fig.7.3 (a) the tensile force in the top flange of the rafter is passed through the bolt group near the rafter top flange. The concentrated load at the transfer point at column flange is distributed into column web by top stiffener plate. The shear stress on the portion of the column web between top and Some of the advantages and disadvantages of the connections are: Connection with extended end plate Fig.7.3.(a) provides better tension load transfer mechanism than others. Although the connection with top cover plate may need more fabrication cost, it is aesthetically preferable bottom stiffener plates can be controlled by adjusting the spacing between the plate, i. .e the distance hp. Alternatively diagonal web stiffener plate can be provided.

3.4.

Ridge Connections The fully rigid ridge connections can be analyzed and designed in a similar way to eaves connections. However in case of three-pin portal frame, the ridge or apex is designed as pinned connection allowing fairly free rotation. Some of the usual type of apex connections and their load transfer diagram are shown in Fig. 7.4

WF Cutting

WF Cutting or Plate

(a) Long Haunches

(b) Short Haunches

PC

M

Q

Q

F

M F

PT

(c) Force Diagram

(d) Pinned Apex Connections

Fig. 7.5 Ridge Connections


7-5

3.5.

Building Frame Connections Multi-story frame connections may conveniently be classified into the following five types. 1)

Beam-to-beam connections

2)

Beam-to-column connections

3)

Column splices

4)

Column bases

5)

Bracing Connections

Each type shall be explained briefly in the following sections. 3.5.1. Beam-to-beam connections

Fig.7.5 shows different beam-to-beam connections. The conventional design procedure for beam-to-beam connections assumes that they are simple connections and offer no resistance to rotation of the end of the beam in the vertical plane . So beam reaction is the only force be considered in the design. The connection between the flange or web of one beam to web of the main beam can be made with the use of angles, tees or welded plates as shown in Fig. 7.5 (d). and called accordingly as teeframed shear connection or single-plate shear connection. The size of these connecting elements depends upon the space available and the number of fasteners to be accommodated. Various standard design manual (e.g. AISC Manual) give connection details for standard type of framed connections.

x

x

(a)

(b)

Fig. 7.6 (a-b) Beam-to-beam Connections

(c)


(d)

7-6

Fig. 7.6 (c-d) Beam-to-beam Connections

x

x

x

(e)

x

(f)

Fig. 7.6 (e-f) Beam-to-beam Connections

(h) (g) Fig.7.6 (g-h) Beam-to-beam connections 3.5.2. Beam-to-Column Connections

Beam-to-column connections can be further classified based on: 1)

Type of fastener

• fully welded • fully bolted • shop welded / site bolted 2) Rigidity of joint • rigid joints • semi-rigid (partial ) joints • simple joints Another way of classifications based on rigidity of joint is • Erection stiff • Fully rigid Typical beam –to-column connections are shown in Fig 7.6 and Fig 7.7 .


7-7

(a) Fully Bolted Erection Stiff

(a) Fully Bolted Erection Stiff

(c) Fully Bolted Fully Rigid

Fig. 7.7 (a-c) Beam-to-column Connections

(d) Fully Bolted Erection Stiff

(e) Fully Bolted Erection Stiff ( Stiffened )

(f) Fully Welded Erection Stiff

Fig.7.7 (d-f) Beam-to-column connections

It is the beyond the scope of this manual to describe the detailed analysis and design procedures for all the connection shown in the figures. However some of the general considerations for the design of various components of the beam-to-column connections shall be pointed here. •

Fasteners for erection stiff or simple beam-to-column connections are designed for the shear force only.


7-8

(a) Fully Rigid Site Bolted Shop Welded

(b) Fully Rigid Site Bolted Shop Welded

(c) Fully Rigid Site Bolted Shop Welded

Fig. 7.8 (a-c) Beam-to-column Fully Rigid Connections

(d) Erection Stiff Site Bolted Shop Welded

(e) Erection Stiff Site Bolted Shop Welded

Fig.7.8 (d-e) Beam-to-column connections 3.5.3. Column Bases

Column bases are special type of connections. They are more complicated than other type of connections because of two different materials i.e. steel and concrete interaction. The interaction with soil poses one more complication if very accurate analysis and design is required. However, such an analysis and design is beyond the scope of this manual. Although semi-rigid connections are now being recognized, two primary type of connections namely pinned and fixed connections, being of more practical significance, shall be introduced here. 3.5.3.1. Pinned Connections Typical pinned column base connections are shown in the Fig.7.7.These connections can be considered as hinge if the axial force in column, the theoretical rotation small and when the length of the plate in the direction of shear is limited to 300 mm. The Hand Book for Design of Steel Structures

7-9

size of the end plate must be such that the bearing pressure on the concrete is within allowable limits and the thickness must be such as to allow for rotation to occur i.e. less rigid. Single base plate with shear connector provides more flexibility in vertical and horizontal alignment of the column during erection. However in the other solution with secondary base plate, as the secondary plate is already fixed to the concrete it is difficult to adjust position of the column. The anchor bolts must therefore be placed very carefully. P V

Fig. 7.9 Pinned Column Bases -Type1

3.5.3.2. Column with welded end plate and intermediate plate The rotation capacity of the column with only one welded plate may be less to assume

Fig. 7.10 Pinned Column Bases -Type2


7-10

as pinned connection for large column with heavy loading. The better solution for such cases can be to add an intermediate plate welded under the end plate to improve the rotation capacity. The axial force is transferred from column to intermediate plate to base plate and finally to the concrete. To prevent the web buckling the column web may be stiffened as shown in Fig 7.8. Fig.7.8 also shows the pinned and vertical forks connections that are practically possible to resemble an ideal hinge connection. In addition to the size of the base plate to distribute the load on concrete safely, more attention must be paid to the stress concentration at various points in the connection such as at the intersection of fork plates and column wall; and between pin and fork plates. The pin is designed only for single or double shear as the case may be. 3.5.3.3. Fixed Connections Fixed connection as the term suggests, ideally, must be as stiff as practically possible to prevent any rotation, which usually need for stiffening of the base plate and column wall and more fasteners. Some common practical type of fixed connections is described briefly in this article. Fig.7.9.and Fig 7.10 show the various different fixed column bases with I-shaped and tubular columns. Connections with bolts on only two sides of the column are commonly used for uniaxial moment with axial forces while those connections with fasteners all around the column are used for columns subjected to biaxial bending. Suitability of a particular type depends upon a number of design factors. Design assumptions and procedures for some common type moment resisting column bases are given in the examples later in this chapter.

Fig.7.1.(a) Fixed column bases


7-11

Fig.7.10 (b) Fixed column bases

• Fig.7.10 (c-d) Fixed column bases


7-12


Subject: Design of Tension Connection

Example:7

Design Code:

Sheet No:1 / 1

Thailand

AISC/ASD (1991)


1


Problem:

Design a bearing type connection to connect two channels SYS 200x80x 24.6 ( Smallest) to a single gusset plate as shown in Figure below. Assume: Design tensile load = 45.5 ton (100 kips) A325 bolts with threads not excluded from shear plane Standard holes

Fy = 2500 Ksc.(35.5 ksi) Solution:

First Trial Size of bolt: ¾ in. Allowable bolt shearing stress = 21 ksi Allowable shear per bolt in double shear = 2 x 21 x .44 =18.5 kips Allowable bolt bearing stress =1.2 Fu = 1.2 x 58 = 69.6 ksi Allowable bearing on two channels of thickness (7.5mm/25.4 = 0.295 in) = 69.6 x 2 x 0.295 x 3/4 = 30.8 kips So the minimum of the shearing and bearing will be the design capacity of the bolt = 18.5 kips Number of bolts required = 100/18.5 = 5.4 Use 6 bolts Use gusset plate length

= 6 in to accommodate 6 of bolts in two lines

Thickness of Gusset plate thickness required = t =

100 6 x 69.6 x 3/4

= 0.315

So use 5/16 inch thick gusset plate. (Note :The gusset plate must also be checked for gross area, net area and block shear)


7-13


Subject: Design of Unstiffened Beam Seat

Example:7 2

Design Code:

Sheet No:1 / 1

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Problem:

Design a unstiffened beam seat to transfer a design load of 10 ton (22 kips ) from a SYS H300x150x36.7 beam to SYS H400x200x66 column. Assume A325 bolts , Standard holes , beam & column Fy = 2500 Ksc( 35.5 ksi) Cleaarance 1/2" R / Fc t

N

k Critical Section for Bending

Fig. 7. 11 Unstiffened Beam Seat Solution: Find Required Bearing Length N

For H300x150x36.7 from properties table k = t f + r = 8+13 mm = 21 mm

t w = 6.5 mm Using : R = 0.66 FY t w ( N + 2.5k ) 10,000 = 0.66 x 2500 x 0.65 ( N + 2.5 x 2.1) Solving for N, we get N = 4.0 cm So use N = 4 cm Find Required Thickness of Bearing Seat

As channel sections are not available ,at present 1998), in Siam Yamato Steel Products Let us assume that the k distance for the beam seat angle will be = 25 mm To allow for setback and underrun in the length of the beam use total clearance of 20 mm. The reaction is assumed to act at the center of the bearing length. Largest length of the seat that can be accommodated in the SYS H400x200 = 200 mm So b = 200 mm

M = R(

N 2

+ Clearance − k)

4 M = 10,000( + 2 − 2.5) 2 = 15000 kg-cm = 150 kg-m


7-14


Subject: Design of Unstiffened Beam Seat

Example:7 2

Design Code:

Sheet No:2 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


F = 0.66 Fy =0.66 x 2500 =1650 Ksc b

6M 6 x15000 = =16.5 mm F b 1650 x 20 b

t=

Check for Web Crippling

  N  t 2 R = 34t w 1 + 3  w  d  t f  t=

  

1.5

 Fyw t f   t w

Use US units, but non dimensional terms can be in any consistent units

6M 6x15000 = = 16.5 mm Fb b 1650x20

1.5   4  6.5   35.5 x9 R = 34 x(6.5 / 25.4) 2 1 + 3    6.5  30  9   

N.G

= 19.44kips (8.837 ton) which is less than the applied reaction 10 ton so another section for beam or larger seat to increase N should be selected so that R >10 ton Assuming the threads are excluded from the shear plane the allowable shear stress Fv = 30 ksi (2113 ksc)

For ¾ inch bolt, resistance for shearing R = 30x 0.44 = 13.2 kips (6 ton) Number of bolt required n =

10 ton 6 ton

= 1.66

So use 2 no ¾ in bolts The selected angle seat should be checked for the following • • • •

Size enough to accommodate these bolts Thickness not less than t Assumed and actual value of k Bolts excluded from shear plane or not


7-15


Subject: Design of Welded Bracket

Example:7 3

Design Code:

Sheet No:1 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Problem:

Design the welded bracket connection as shown in the figure below. Assume beam reaction = 12 ton (26.4 kips) Assume: E70 weld

5

H 350x175

5

8

H 300x150

X

20

Y

Fig. 7.12 Welded Bracket Connection Solution: 1. Find Required Bearing Length N

Web Yielding Criteria: For H300x150x36.7 from properties table k = t f + r =8+13 mm=21 mm and t w =6.5 mm Using R = 0.66 FY t w ( N + 2.5k ) [concentrated load within d distance from beam end] 12,000 = 0.66 x 2500 x 0.65 ( N + 2.5 x 2.1 ) Solving for N, we get N = 5.93 cm So use N =larger of k and 5.93 cm = 5.93 cm Web Crippling Criteria:

R = 34t w

2

  N  t 1 + 3  w  d  t f 

  

1.5

 Fyw t f   t w

[Use US units for dimensional parameters and any consistent units for non dimensional parameters]

  

1.5 

 N cm  0.65 cm     30 cm  0.9 cm 

12x2.2 kips = 34x(6.5/25.4 in)2 1 + 3

  

35.5 ksi x 0.9 cm 0.65 cm

Solving for N, we get N = 11.45 cm From the above two criteria the required minimum N = 11.45 cm Providing for clearance, total bearing length of the seat = 11.45 + 1.2 =12.65 cm Hand Book for Design of Steel Structures

7-16


Subject: Design of Welded Bracket

Example:7 3

Design Code:

Sheet No:2 / 2

Thailand

AISC/ASD (1991)



Use 13 cm. Moment at the critical section = 12,000 x (13-13/5-1.2) =63600 kg-cm = 636 kg-m Try vertical leg = 20 cm and Horizontal leg = 5 cm

y=

2x20x2x5 2x20 + 2x5

= 8 cm

  8 3 + (20 − 8) 3 I x = 2 + 2x8 2  = 1749 cm 3 3  

qz =

My Ix

qz =

63600x8 = 290.9 kg/cm 1749

qz =

R 6000 = = 120 kg/cm total length 50 2

2

q = q y + q z = 120 2 + 290.9 2 = 314.67 kg/cm So use E70 fillet weld with q = 314.67 or more .


7-17


Subject: Beam-to-column T-stub Connection

Example:7 4

Design Code:

Sheet No:1 / 2

Thailand

AISC/ASD (1991)



Problem:

Design the T-stub moment connection for SYS H250x125x29.6 beam to SYS H300x150x36.7 column as shown in the figure below. Use Steel: A36 and A325 bolts Design beam shear = 18 kips (8.18 ton) and beam moment = 55 ft-kips (7.6 ton-m)

Fig. 7.13 Beam-to-column T-stub Connection Solution: 1. Computing Bolt Strengths

Strength for

For dia 7/8 in

For dia 1 in

Tension = 44 Ab

26.4

34.6

Single shear = 30 Ab

18

23.6

Bearing on beam flange

69.9 x 7/8 x 0.512

69.9 x 1 x 0.512

= 31.31

= 35.63

69.9 x 7/8 x 0.551

69.9 x 1 x 0.551

= 33.70

= 38.51

= 69.6 x 0.57 x d Bearing on column flange = 69.6 x 0.57 x d Connection Between Tee and Beam

Force on bolts = M / d = 55 x 12 / 9.84 = 67 kips No of 7/8 in bolt required = 67 / 18 = 3.72 So use 4 No -7/8 in bolts. Connection Between Tee and Column

Force on bolts P =67 / 4 = 16.75 kips / bolt No of 7/8 in bolt required = 67 / 18 = 3.72 Assume Q/P= 0.5; Q = 0.5 x 16.75 = 8.375 kips Total Tension = T = P+Q =16.75 + 8.375 = 25.125 kips Try 4No-7/8 in bolts.


7-18


Subject: Beam-to-column T-stub Connection

Example:7 4

Design Code:

Sheet No:2 / 2

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


T-stub

Try some T section with tf = 1 in , tw =0.6 in and bf = 8 in Vertical spacing of bolts g = 4.5 in Horizontal spacing of bolts = column flange width – 2 x edge distance = 5.9-2x1.5 = 2.9 in half the width of the Tee w = 6/2 = 3 in a = (8 – 4.5 ) / 2 = 1.75 in < 2 tf b = (4.5-0.6 )/2 –1/16 = 1.88 in

( ) ( )

2 2 7 100bd 2 − 18wt 2 100x1.88x 8 − 18x4.25x1 = = = 0.36 2 P 70ad 2 + 21wt 2 70x1.75x 7 + 21x4.25x12 8

Q

P = 16.75 Q =0.36 x 16.75 = 6.03 kips T= P+Q = 22.78 < 26.4 (bolt strength in tension)

OK

Bending in Flange

Moment M1 = Q a = 6.03 x 1.75 = 10.55 kips at bolt line Moment M2 = Q ( a + b )-T b = 6.03 ( 1.75 + 1.88 ) – 25.125 x 1.88 = 25.34 kips at web

S=

f=

wt 2 6

=

4.25x12 6

= 0.708 inch 3

shear force 18 = = 25.4 ksi < 27ksi S 0.708

OK

Shear

Direct shear stress = shear force / no of bolts = 18/8 = 2.25 kips/bolt Shear stress fv = 2.25 / 0.6 = 3.75 ksi

Ft = 44 2 − 2.15f v

f=

2

= 44 2 − 2.15x3.75 2 = 43.65 ksi

shear force 18 = = 25.4 ksi < 27ksi S 0.708

Total strength = 43.65 x 0.6 = 26.19 > T (25.125)


OK OK

7-19


Subject: Beam-to-column Moment Connection

Example:7 5

Design Code:

Sheet No:1 / 3

Thailand

AISC/ASD (1991)



Problem:

Design the moment resistant connection for SYS H300x150x36.7 beam to SYS H400x200x66 column as shown in the figure below. Assume • • • • •

Slip critical connection Steel yield strength = 35.5 ksi (2500 ksc) A325 bolts and E70 electrodes Design beam shear = 40 kips (18.2 ton) Beam moment = 160 ft-kips (22.12 ton-m)

Fig. 7.14 Beam-to-column Moment Connection 1. Top Flange Plate

Tension force on the flange T = Moment / Depth = 160 x 12 / 11.81 = 162.57 kips Area of plate required A s =

T =162.57 / (0.6 x 36 ) = 7.526 sq. inch. 0.6Fy

Available flange width of the column = 7.87 in Providing 1.5 inch for welding space Maximum available width = 7.87-1.5 =6.37 inch So use 1.25 x 6 in. = 7.5 sq. inch For 3/8 inch bolt q = 21 x 0.707 x 3/8 = 5.56 kips/ inch Length of the weld required = 162.57 / 5.56 = 29.23 inch Provide 6 inch along end and 12 inch on each side. Total = 6+2 x 12 = 30 > 29.23 inch

OK

Bottom Flange Plate 1

To facilitate the welding the bottom flange is chosen about 1 2 inch wider than the beam flange. Plate width = 5.91+1.25 = 7.16 So use 7.5 inch x 1 inch = 7.5 sq. inch Use

3 8

inch x 15 inch weld on each side of the plate.


7-20



Example:7 5

Design Code:

Sheet No:2 / 3

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Shear Plate Bolts strength:

single shear strength: So for Bearing = 1.2 x 58 x

1 7 x 4 8

3 8

inch bolt strength in single shear = 17 x 0.6 = 10.2 kips

=15.2 kips (Assuming plate thickness =

1 4

)

No of bolts required , n = Shear force / bolt strength = 40/10.2 = 3.92 3

Use 4 - 8 inch bolts. Length of shear plate = ( n-1 ) x spacing + 2 x edge distance 1

= 3x3+2x1 2 =12 inch Thickness of plate required t = So use

shear force Fv L

=

40 0.4 x 35.5 x 12

= 0.234 inch

1 inch x 5 inch (So assumed plate thickness OK) 4

Length required for

3 16

inch weld L =

shear force weld strength/inch

=

40 2.78

= 14.4 inch

Use 10-in weld on each side. Column-Flange Stiffener at Top Flange

Min. thickness of col. flange = 0.4 A = 0.4 x 7.5 = 1.10 > 0.512 in. Stiffeners f required. Column-flange stiffener at bottom flange

Check for web crippling:



 N  t 2 R = 67.5t w 1 + 3  w   d  t f 

1.5 

  

  

Fyw t f tw

1.5   1  0.315   35.5 x0.512 R = 67.5 x(0.315) 2 1 + 3    0.315  15.75  0.512   

= 6.69 x 1.09 x 7.596 = 55.39 < 162.57 kips

tw ≥

Af tbf + 5kc

=

Stiffeners required

7.5 1 + 5 x (0.63 + 0.512)

= 1.12 inch.> tw ( .315 )

Stiffeners required

Area of stiffener required As =7.5 – 0.315 (0.75+ 5 x 1.142) = 5.465 sq. inch Hand Book for Design of Steel Structures

7-21



Example:7 6

Design Code:

Sheet No:3 / 3

Thailand

Designed by: BSS

AISC/ASD (1991)

Checked by: NA


Area for each stiffener = 5.465 / 2 =2.7325 sq inch. So use two - 1 inch x 3 inch stiffeners both on top and bottom. Column-Web shear

fv =

V dc t w

=

162.57 (15.75 − 2x0.512 − 2x.63)x0.315

Actual shear stress = 38.32 ksi > (0.4 x35.5)

As =

Total V − Fv dc t w 162.57 − 0.4x35.5x13.46x0.315 = Ft Cosθ 0.6x35.5xCos(33.68)

= 5.77 sq. inch Area for one plate = 5.77 /2 = 2.885 sq. inch Use two - 1inch x 3 inch plates, one on each side.


7-22

SYS

Example:7 6

Subject: Column Splice


Design Code:

Thailand

Designed by: BSS

AISC/ASD (1991)

Sheet No:1 / 2

Checked by: NA


Problem:

Design a column splice between two columns of sizes SYS H150x150x31.5 and SYS H200x150x30.6 with the following data. Material properties: Steel yield strength Ultimate strength A325

bolts and electrodes

= 35.5 ksi

(2500 ksc)

= 56.8 ksi

(4000 ksc)

E70 (bolt threads not excluded from the shear plane)

Design loads: Load Case

Axial

Moment

(kips)

Shear

(ft-kips)

(kips)

DL

40 (18.18 ton)

--

--

LL

70 (31.81 ton)

--

--

WL

3 (1.36 ton)

20 (2.76 ton-m)

4 (1.82 ton)

Solution 1.

Flange Splice Plates

AISC requires considering the tension due to lateral loads acting in conjunction with 75 percent of the dead-load stress and no live load. Axial load on each flange due to 75 % of dead load = 0.5 x 0.75 x 40 = 15.0 kips Axial load on each flange due to moment =

Moment depth

=

20x 12 7.64

= 31.42 kips

Total tension = 15.0 + 31.42 = 46.42 kips Gross area of plate, Ag =

Tension 46.42 = = 2.17 sq. inch 0.6x35.5 0.6F y

Flange width available = 5.91 inch; use plate width = 5.5 inch Thickness of plate based on gross area requirement = 2.17 /5.5 = 0.39 inch Net area of plate, A n =

Tension 46.42 = = 1.63 sq. inch 0.5Fu 0.5x56.8

Assume 2 no ¾ bolts Thickness of plate based on net area requirement = 1.63 /(5.5-2x7/8) = 0.434 inch So use ½ inch x 5.5 inch plate Fasteners

Try ¾ inch bolts Strength in single shear = 21 x 0.44 = 9.24 kips Hand Book for Design of Steel Structures

7-23

SYS

Example:7 7

Subject: Column Splice


Design Code:

Thailand

AISC/ASD (1991)



Strength in bearing = 1.2 x 56.8 x 0.315 x ¾ = 16.10 kips No of bolts required = 46.42 / (4/3 x 9.24) = 3.76 Use 4 ¾ inch bolts. Weld for Shop Connection

Length of

3 16

E70 weld required = 46.42 / (0.3x70x.707x3/16) = 16.67 inch

Use 17 inch of

3 16

inch weld.

Fill plate thickness = (7.84-5.87) / 2 = 0.98 inch


Use 1 inch.

7-24

References 1. Nishino Fumio, Sato Naohiko, Hsegawa Akio, Critical Comments on the Recent Trends of Design Code Change to Load Factor Design, Proceedings of Japan-Thai Civil Engineering Conference, Bangkok, March 1985 2. Johnson,B.b., Lin,F.J., Glambos,T.V., Basic Steel Design, 3rd Ed., Prentice-Hall, 1986 3. Bresler, B., Lin, T. Y., Scalzi, J. B., Design of Steel Structures, 2nd Ed., John Wiley & Sons, 1993 4. Crawley, S. W., Dillon, R. M., Steel Buildings Analysis and Design, 4th Ed., John Wiley & Sons, 1992 5. Gaylord, Jr., E. H. Gaylord, C.N., Stallmeyer, J.E., Design of Steel Structure, 3rd Ed. McGraw-Hill, 1992 6. Dowling, P. J., Harding, J. E., Constructional Steel Design An International Guide, Elsevier Applied Science, 1992 7. Nethercot, D. A., Limit States Design of Structural Steelwork, 2nd Ed., Chapman and Hall, 1993 8. Morris, L.J., Plum, D. R., Structural Steelwork Design to BS 5950, Longman Scientific & Technical, 1988 9. Martin, L. H., Purkiss, J. A., Structural Design of Steelwork to BS 5950, Edward Arnold, 1992 10. Chanakya, A., Design of Structural Elements, E & FN SPON, 1994 11. The Steel Construction Institute, Steel Designer’s Manual, 5th Dd., Blackwell Scientific Publications, 1992 12. Hogan, T. J., Thomas, I. R., Design of Structural Connection, 4th Ed., Australian Institute of Steel Construction 13. AISC, Manual of Steel Construction, Allowable Stress Design, 9th Ed., 1989 14. AISC, Manual of Steel Construction, Load and Resistance Factor Design,2nd Ed., 1993 15. AISC, Engineering for Steel Construction, A Source Book on Connection, 1984 16. AISC, Engineering for Steel Construction, Detailing for Steel Construction, 1983 17. JIS, 1994 JIS Handbook Ferrous Materials & Metallurgy, Japanese Standards Association, 1994 18. The International Technical Information Institute, Handbook of Comparative World Steel Standards, 1990


8-1

19. AIJ, Design Standard for Steel Structures, Architectural Institute of Japan, 1973 (in Japanese) 20. Uniform Building Code, 1991 Ed. 21. ASTM Standards •

A 6/A 6M-92, Standard Specification for General Requirements for Rolled Steel Plates, Shapes, Sheet Pilling, and Bars for Structural Use

•

A 36/A 36M, Standard Specification for Structural Steel

•

A 242/A 242M - 91a, Standard Specification for High-Strength Low-Alloy Structural Steel

•

A 283/A 283M-92, Standard Specification for Low and Intermediate Tensile Strength Carbon Steel Plates

•

A 284/A 284 M-90, Standard Specification for Low and Intermediate Tensile Strength CarbonSilicon Steel Plates for Machine Parts and General Construction

•

A 328/A 328 M-90, Standard Specification for Steel Sheet Piling

•

A 529/A 529 M-92, Standard Specification for High-Strength Carbon-Manganese Steel of Structural Quality

•

A 570/A 570 M-92, Standard Specification for Steel, Sheet an Strip, Carbon, Hot-Rolled, Structural Quality

•

A 588/A 588 M-91a, Standard Specification for High-Strength Low-Alloy Structural Steel with 50 ksi [345 Mpa] Minimum Yield Point to 4 in. [100 mm] Thick

•

A 633/A 633 M-92, Standard Specification for Normalized High-Strength Low-Alloy Structural Steel

•

A 656/A 656 M-89, Standard Specification for Hot-rolled Structural Steel, High-Strength LowAlloy Plate with Improved Formability

•

A 678/A 678 M-92, Standard Specification for Quenched-and-Tempered Carbon-Steel- Hotrolled Structural Steel and High-Strength Low-Alloy Steel Plates for Structural Applications

•

A 709/A 709 M-92, Standard Specification for Structural Steel for Bridges

•

A 808/A 808 M-91, Standard Specification for High-Strength, Low Alloy Carbon, Manganese, Columbium, Vanadium Steel of Structural Quality with Improved Notch Toughness

•

A 370, Standard Test Methods and Definitions for Mechanical Testing of Steel Products

•

E23-94a, Standard Test Method for Fire Test of Building Construction and Materials


8-2

22. JIS Standards •

JIS G 0303, General Rules for Inspection of Steel

•

JIS G 0301, Rolled Steel for General Structures

•

JIS G 3106, Rolled Steel for Welded Structures

•

JIS G 3192, Dimensions, Mass and Permissible Variations of Hot rolled Steel Sections

•

JIS G 3194, Dimensions, Mass and Permissible Variations of Hot rolled Steel Plates, Sheets and Strips

•

JIS Z 2201, Test Pieces for Tensile Test for Metallic Materials

•

JIS Z 2202, Test Pieces for Impact Test for Metallic Materials

•

JIS Z 2241, Method of Tensile Test for Metallic Materials

23. BS Standards •

BS4: Part 1: 1980, Structural Steel Section Part1. Specifications for Hot-rolled Sections

•

BS 476: Fire Test on Building Materials and Structures

•

BS 4360: 1990, British Standard Specifications for Weldable Structural Steels

•

BS 5950: Part 1: 1990, British Standard Structural Use of Steelwork in Building •

Part 1: Code of Practice for Design in Simple and Continuous Construction: Hot rolled Sections

•

Part 2: Specifications for Materials, Fabrications and Erections: Hot rolled sections

•

Part 3: Design in Composite Construction

•

Part 4: Code of Practice for Fire Resistant Design

24. DIN Standards •

DIN 17100, 1980, Steels for General Structural Purposes

•

DIN 50145, 1975, Testing of Metallic Materials- Tensile Test

•

DIN 50115, 1991, Notched Bar Impact Testing of Metallic Materials


8-3

25. AS Standards •

AS 1204–1980, Structural Steels Ordinary Weldable Grades

•

AS 3679-1990, Hot-rolled Structural Steel Bars and Sections

•

AS 4100-1990, Steel Structures

26. ISO Standards •

ISO 83-1976, Steel – Charpy Impact Test (U-Notch)

•

ISO 148-1983, Steel – Charpy Impact Test (V-Notch)

•

ISO 404-1992, Steel and Steel Products – General Technical Delivery Requirements

•

ISO 630 – 1980, Structural Steels

27. EN Standards •

EN 10025–1, 1991, Hot Rolled Unalloyed Structural Steel Products – Technical Delivery Conditions

•

EN 10045-1, 1991, Charpy Impact Test on Metallic Materials

28. TIS Standards •

TIS 224 No. – 1982, Tensile Test of Steel and Iron

•

TIS 244 NO. 8- 1982, Charpy Impact Test for Steel

•

TIS 1227-1994, Hot-Rolled Structural Steel Shapes


8-4

TN H01-Hand Book for Design of Steel Structures

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