STRC07 Steel Part2 0716 R1

Structural Engineering Exam Review Course

Steel (Part 2)

Steel (Part 2)

Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.

© 2015 Professional Publications, Inc.

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Steel (Part 2)

Steel Part 2

Lesson Overview

Chapter 4: Structural Steel Design (Part 2) • Design of Tension Members

• Design of Bolted Connections

• Design of Welded Connections • Plate Girders

• Composite Beams



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Steel Part 2

Learning Objectives

You will learn how to

• design bolted and welded connections for a range of loading conditions • account for tension field action in plate girders • design composite steel members



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Steel Part 2

Prerequisite Knowledge

You should already be familiar with • load combinations • design for flexure • design for shear

• design for compression



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Steel Part 2

Referenced Codes and Standards

• International Building Code (IBC, 2012)

• Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7, 2010) • Seismic Design Manual (AISC, 2012)

• Specification for Structural Steel Buildings (AISC 360, 2010) • Steel Construction Manual (AISC, 2011)



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Steel Part 2

Mechanism Design Method

• Apply a virtual displacement to each potential plastic hinge mechanism and equate internal and external work.

Figure 4.19 Mechanism Design Method

• solve for Mp using equations (see next slide) for • beam mechanism • sway mechanism

• combined mechanism

• The largest value of Mp governs. STRC ©2015 Professional Publications, Inc.


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Steel (Part 2)

Steel Part 2

Design of Tension Members

section overview

• plates in tension

• rolled section in tension • design for fatigue



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Steel (Part 2)

Steel Part 2

Plates in Tension

For yielding of gross section, AISC 360 Sec. D2 gives

For tensile rupture, AISC 360 Sec. D2 gives

• allowable strength

• allowable strength

• design strength

• design strength



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Steel Part 2

Plates in Tension

Figure 4.20 Effective Net Area of Bolted Connection



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Steel Part 2

Effective Net Area–Bolted Connections

• effective net area, Ae, of a bolted connection

• effective hole diameter for standard size holes

• (Section numbers refer to bolted plates in Fig. 4.20.)



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Steel (Part 2)

Steel Part 2

Effective Net Area–Welded Connections

AISC 360 Sec. D3.1 gives the effective net area as follows.

• shear lag factor, U

• flat plate with longitudinal welded connection

• flat plate with transverse fillet welded connection (shown in Fig. 4.21)

Figure 4.21 Welded Connections for Plates



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Steel Part 2

Example: Plates in Tension Example 4.32



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Steel Part 2

Example: Plates in Tension Example 4.32



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Steel Part 2

Example: Plates in Tension



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Steel Part 2

Rolled Sections in Tension–Bolted Connections

• effective net area

AISC 360 Eq. D3-1

• shear lag factor • 0.60 ≤ U ≤ 0.90

nomenclature l

̅

distance between first and last fasteners in line

distance from connection plane member centroid



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Steel (Part 2)

Steel Part 2

Rolled Sections in Tension–Bolted Connections

AISC 360 Table D3.1 permits the adoption of the following values for the shear lag factor.

• U = 0.90 for T, W, M, and S shapes with bf ≥ 2d/3, connected by the flange, with not fewer than three bolts in line in the direction of stress. • U = 0.85 for T, W, M, and S shapes with bf < 2d/3, connected by the flange, with not fewer than three bolts in line in the direction of stress.

• U = 0.70 for T, W, M, and S shapes connected by the web, with not less than four bolts in line in the direction of stress. • U = 0.80 for single or double angles with not less than four bolts in line in the direction of stress. • U = 0.60 for single or double angles with two or three bolts in line in the direction of stress.



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Steel (Part 2)

Steel Part 2

Rolled Sections in Tension–Welded Connections

• force transmitted only by transverse welds • force transmitted by longitudinal welds AISC Eq. D3-1

nomenclature l

̅

distance between first and last fasteners in line

distance from connection plane member centroid



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Steel Part 2

Rolled Sections in Tension–Welded Connections Figure 4.22 Welded Connections for Rolled Sections



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Steel Part 2

Example: Rolled Sections in Tension Example 4.33



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Steel Part 2

Example: Rolled Sections in Tension



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Steel Part 2

Poll: Design for Fatigue

Is the following statement true or false?

Fatigue effects in design account for the age of steel members and connections. (A) true

(B) false



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Steel (Part 2)

Steel Part 2

Poll: Design for Fatigue


Fatigue effects in design account for the age of steel members and connections. (A) true

(B) false

Solution

Fatigue is the weakening of a material caused by repeatedly applied loads. Fatigue effects are not necessarily related to age. The answer is (B) false.



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Steel Part 2

Design for Fatigue

• Fatigue failure is caused by fluctuations of tensile stress that cause crack propagation.

• Establish applicable loading condition from AISC 360 Table A-3.1. • stress categories A, B, B´, C, D, E, and E´

• stress category F

• FTH is the maximum stress range for indefinite design life (i.e., infinite number of cycles).



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Steel Part 2

Design for Fatigue

AISC 360 Table A-3.1 Fatigue Design Parameters (partial table shown)

Reproduced from Steel Construction Manual, Fourteenth ed., 2012. American Institute of Steel Construction, Inc., Chicago, IL. STRC ©2015 Professional Publications, Inc.


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Example: Design for Fatigue Example 4.34



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Steel Part 2

Example: Design for Fatigue Example 4.34



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Example: Design for Fatigue

AISC 360 Table A-3.1 Fatigue Design Parameters (partial table shown)

The range of the load is 57 kips.



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Steel Part 2

Design of Bolted Connections

section overview • types of bolts

• bearing-type bolts in shear and tension

• slip-critical bolts in shear and tension • bolts in bearing

• bolt group eccentrically loaded in plane of the faying surface

• bolt group eccentrically loaded normal to the faying surface STRC ©2015 Professional Publications, Inc.


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Steel Part 2

Types of Bolts

common bolts

• grade A307 with a nominal tensile strength of 45 kips/in2 • used in bearing-type or snug-tight connections only

high-strength bolts

• grade A325, F182, A354 BC, and A449 with a nominal tensile strength of 90 kips/in2

• grade A490, F2280, and A354 BD with a nominal tensile strength of 113 kips/in2 • used in bearing-type, pretensioned and slip-critical connections



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Types of Bolt Connections

bearing-type (snug-tight)

• must be tightened sufficiently to bring plies into firm contact

• transfer of load depends on bearing of bolts against side of holes • no specific level of installed tension specified

• may be used when pretensioned or slip-critical connections not required

pretensioned

• Bolts must be pretensioned to a minimum of 70% of bolt’s tensile strength.

• faying surfaces may be uncoated, coated, or galvanized without regard to the slip coefficient obtained

• transfer of load depends on bearing of bolts against side of holes



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slip-critical

• required to be pretensioned to a minimum of 70% of bolt’s tensile strength • load transferred through friction

• at strength limit state, connection slips, so bolts may be in bearing



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Steel Part 2


Pretensioned connections are required when bearing-type connections are used in

Slip-critical connections are required where

• bracing members in buildings over 125 ft tall (see AISC 360 Sec. J1.10)

• bolts are used in oversize holes or slotted holes parallel to the direction of load

• supports of machinery causing impact or stress reversal

• bolts are used in conjunction with welds

• column splices in buildings over 125 ft tall

• structures carrying cranes of over 5 ton capacity

• fatigue load occurs

• slip at the faying surfaces will affect the performance of the structure



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Steel Part 2

Bearing-Type Bolts in Shear and Tension nomenclature Fnv

nominal shear strength of bolt

Φ

resistance factor

Rn Ω

nominal shear capacity safety factor



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Bearing-Type Bolts in Shear and Tension

Per AISC 360 Sec. J3.3,

• minimum permissible distance between centers of holes, smin = 2.67d

• available strength in tension (AISC 360 Sec. J3.6)

• preferred distance between centers of holes, spref = 3.0d • available strength in shear

AISC 360 Eq. J3-1 STRC ©2015 Professional Publications, Inc.


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Example: Bearing-Type Bolts in Shear and Tension The connection shown consists of 11 grade A307 ¾ in diameter bolts. Determine the design shear strength of the bolts in the connection.



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Example: Bearing-Type Bolts in Shear and Tension The connection shown consists of 11 grade A307 ¾ in diameter bolts. Determine the design shear strength of the bolts in the connection.

Solution

From AISC Manual Table 7-1, the available strength of the 11 bolts in shear is 

kips 

 Rn   Fnv Ab   8.97  11 bolts  bolt    98.7 kips

 LRFD

Rn Fnv Ab n  kips     5.97  11 bolts    bolt    65.7 kips  ASD  STRC ©2015 Professional Publications, Inc.


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Steel Part 2

Slip-Critical Bolts in Shear

• minimum pretension force, Tb, in a bolt (AISC 360 Table J3.1) 0.70Fu

• nominal slip resistance (AISC 360 Eq. J3-4)

• slip coefficient for class A surfaces μ = 0.30 • slip coefficient for class B surfaces μ = 0.50

• ratio of mean installed bolt tension to specified minimum bolt pretension Du = 1.13



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Slip-Critical Bolts in Tension nomenclature Du

bolt tension multiplier

Ta

number of bolts carrying the applied tension applied tensile force on the bolt (ASD)

Tu

applied tensile force on the bolt (LRFD)

Nb Tb

specified pretension force on the bolt



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Steel Part 2

Slip-Critical Bolts in Tension

• nominal tensile strength

• combined shear and tension

• available strength in tension unaffected

• available tensile strength

• available resistance to shear reduced by

• See AISC 360 Table J3.2 for values of nominal tensile stress, Fnt. • See AISC 360 Table 7-2 for values of ϕRn and Rn/Ω.



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Steel Part 2

Example: Slip-Critical Bolts in Shear and Tension The connection shown consists of 11 grade A490 ¾ in diameter slip-critical bolts. The bolts are in standard holes with a class A faying surface. No fillers are used. Determine the available resistance to shear of the bolts in the connection.



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Steel Part 2

Example: Slip-Critical Bolts in Shear and Tension The connection shown consists of 11 grade A490 ¾ in diameter slip-critical bolts. The bolts are in standard holes with a class A faying surface. No fillers are used. Determine the available resistance to shear of the bolts in the connection.

Solution

For bolts in standard holes and with a class A faying surface, AISC Manual Table 7-3 gives the available single shear strength of the 11 bolts in shear as  Rn  11.9 kips 11 bolts   131 kips

 LRFD

Rn   7.91 kips 11 bolts    87 kips  ASD  STRC ©2015 Professional Publications, Inc.


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Steel Part 2

Bolts in Bearing nomenclature

db

nominal bolt diameter

Rn

nominal bearing capacity

Fu

tensile strength of the critical connected part clear distance, in the direction of force, between edge of hole and edge of adjacent hole or edge of the connected part edge distance, in the direction of force, between the bolt center and the edge of the connected part

t

thickness of the connected part

Dn Lc Le

nominal hole diameter

S

bolt center-to-center spacing

symbols Φ Ω

resistance factor safety factor



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Steel Part 2

Bolts in Bearing

• Bearing strength must be checked for both bearing-type bolts and slip-critical bolts. • nominal bearing strength (AISC 360 Eq. J3-6a and Eq. J3-6b) • when deformation is a design consideration,

• when deformation is not a design consideration,

• available bearing strength

• See AISC Manual Tables 7-5 and 7-6 for values of ϕRn and Rn/Ω. STRC ©2015 Professional Publications, Inc.


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Steel (Part 2)

Steel Part 2

Example: Bolts in Bearing

The connection shown consists of 11 grade A307 ¾ in diameter bolts in standard holes. Plate thickness is 0.5 in. The edge distance is Lc = 2.5 in, s = 3 in, and Fu = 58 ksi. Determine the available bearing strength of the bolts in the A36 plates.



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The connection shown consists of 11 grade A307 ¾ in diameter bolts in standard holes. Plate thickness is 0.5 in. The edge distance is Lc = 2.5 in, s = 3 in, and Fu = 58 ksi. Determine the available bearing strength of the bolts in the A36 plates.

Solution

From AISC Manual Table 7-5, the minimum edge distance for full bearing strength is Lc = 2.25 in < 2.5 in [provided]

The edge distance does not govern.



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Steel Part 2


From AISC Manual Table 7-4, the available strength of the 11 bolts in bearing is kips      Rn   78.3 in   0.5 in 11 bolts  bolt      431 kips  LRFD

kips     Rn   52.2 in   0.5 in 11 bolts    bolt     287 kips  ASD 



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Steel Part 2

Poll: Eccentrically Loaded Connections


A bolt group loaded eccentrically has a higher capacity than one loaded through its centroid. (A) true

(B) false



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Steel Part 2

Poll: Eccentrically Loaded Connections


A bolt group loaded eccentrically has a higher capacity than one loaded through its centroid. (A) true

(B) false

Solution

The higher the eccentricity of the applied load, the lower the design strength of a bolt group. Moments, along with shear, are applied to the bolt group. The answer is (B) false.



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Steel Part 2

Bolt Group Eccentrically Loaded in Plane of Faying Surface • vertical force on bolt i due to applied load, Pr

• horizontal force on bolt i due to eccentricity, e

• vertical force on bolt i due to eccentricity, e

• resultant force on bolt i due to eccentricity, e

• horizontal force on bolt i due to eccentricity



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Steel Part 2

Bolt Group Eccentrically Loaded in Plane of Faying Surface Figure 4.23 Eccentrically Loaded Bolt Group



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Steel Part 2 Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface Example 4.38



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Steel Part 2 Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface Example 4.38



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Steel Part 2 Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface



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Steel Part 2 Bolt Group Eccentrically Loaded Normal to Faying Surface • LRFD method shown, ASD method similar

nomenclature

• tensile force in each bolt above the neutral axis due to the eccentricity

e

• shear force in each bolt due to the applied load

Pu

• plastic stress distribution

dm n

n'

moment arm between resultant tensile and compressive forces in the bolts Eccentricity

number of bolts in the connection

number of bolts above the neutral axis Required axial strength



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Steel Part 2 Bolt Group Eccentrically Loaded Normal to Faying Surface Figure 4.24 Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)



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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface Example 4.39

Assume that threads are not excluded from the shear plane. STRC ©2015 Professional Publications, Inc.


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Steel Part 2

Example: Bolt Group Eccentrically Loaded Normal to Faying Surface Example 4.39

Assume that threads are not excluded from the shear plane. STRC ©2015 Professional Publications, Inc.


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Steel Part 2

Example: Bolt Group Eccentrically Loaded Normal to Faying Surface



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Example: Bolt Group Eccentrically Loaded Normal to Faying Surfac



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Steel Part 2 Bolt Group Eccentrically Loaded Normal to Faying Surface elastic stress distribution

A trial position for the neutral axis can be selected at one-sixth of the total bracket depth, measured upward from the bottom.

• The effective width of the compression block, beff, should be taken as beff = 8tf < bf • The assumed location of the neutral axis can be evaluated by checking static equilibrium.



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Steel Part 2

Design of Welded Connections

section overview

• Weld Design Strength

• Complete-Penetration Groove Weld

• Partial-Penetration Groove Weld

• Fillet Weld Design Considerations

• Weld Group Eccentrically Loaded in Plane of Faying Surface • Weld Group Eccentrically Loaded Normal to Faying Surface



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Weld Design Strength

• strength of welded connection depends on both base metal and weld metal strength

• Weld nominal stress values, effective areas, resistance factors, and safety factors are tabulated in AISC 360 Table J2.5.

• nominal strength of base metal (AISC 360 Eq. J2-2) Rn = FnBMABM

• nominal strength of weld metal (AISC 360 Eq. J2-3) Rn = FnwAwe



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Complete-Penetration Groove Weld

• nominal strength governed by base metal

Figure 4.26 Complete-Penetration Groove Weld

• computation of strength of weld not required • thinner part joined is the effective thickness, te



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Steel Part 2

Example: Complete-Penetration Groove Weld Example 4.41



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Example: Complete-Penetration Groove Weld Example 4.41



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Example: Complete-Penetration Groove Weld



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Partial-Penetration Groove Weld

Nominal strength is governed by effective throat thickness, te

Figure 4.27 Partial-Penetration Groove Weld



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Example: Partial-Penetration Groove Weld Example 4.42



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Example: Partial-Penetration Groove Weld Example 4.42



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Example: Partial-Penetration Groove Weld



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Example: Partial-Penetration Groove Weld



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Fillet Weld

• Leg length, w, is used to designate nominal weld size.

Figure 4.28 Fillet Weld

• effective throat thickness (AISC 360 Sec. J2.2a) te = 0.707w

• Minimum permissible length of fillet weld is four times the nominal weld size.



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Fillet Weld

• Permitted minimum (AISC 360 Table J2.4) and maximum weld sizes (AISC 360 Sec. J2.2b) are shown in Table 4.2 and Table 4.3.

• When longitudinal fillet welds are used alone in a connection, the length of each fillet weld must not be less than the perpendicular distance between them, because of shear lag.

Table 4.2 Minimum Size of Fillet Welds

Table 4.3 Maximum Size of Fillet Welds



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Fillet Weld

Nominal strength of a linear weld group is Rn = FwAw where Fw = 0.60FEXX(1.0 + 0.50sin1.5θ)

Nominal strength of a concentrically loaded weld group is the greater of Rn = Rwl + Rwt or Rn = 0.85Rwl + 1.5Rwt STRC ©2015 Professional Publications, Inc.


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Fillet Weld

nomenclature ABM effective area of base metal Aw

effective area of weld metal

FEXX

weld metal classification strength

FBM Fw

Rwl Rwt

nominal strength of base metal

symbols θ angle of inclination of loading measured from weld longitudinal axis

nominal strength of weld metal

total nominal strength of longitudinally loaded fillet welds total nominal strength of transversely loaded fillet welds



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Available Strength of a 1/16 in Fillet Weld

To simplify calculations, determine available strength of a ⁄ in fillet weld per inch run of E70XX grade electrodes.

• ASD method, allowable strength

• LRFD method, design strength



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Example: Counting in Sixteenths Example 4.43



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Example: Counting in Sixteenths Example 4.43



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Example: Counting in Sixteenths



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Fillet Weld Size Governed by Base Metal Thickness • capacity of weakest shear plane governs design of welded connection • design shear strength of weld per linear inch

• design shear rupture strength per linear inch, with grade 50 base material (AISC 360 Eq. J4-4)

• largest effective weld size



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Fillet Weld Size Governed by Base Metal Thickness Table 4.4 Effective Weld Size



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Example: Effective Fillet Weld Size Example 4.44



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Example: Effective Fillet Weld Size Example 4.44



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Strength of Fillet Weld Groups

methods presented in AISC 360 Sec. J2.4 • AISC 360 Sec. J2.4(a): linear weld group with uniform leg size loaded through center of gravity

• AISC 360 Sec. J2.4(b): instantaneous center of rotation method

• AISC 360 Sec. J2.4(c): weld group with concentric loading with uniform leg size and elements oriented longitudinally or transversely to direction of applied load STRC ©2015 Professional Publications, Inc.


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Example: Weld Design Strength Example 4.45



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Example: Weld Design Strength Example 4.45



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Example: Weld Design Strength



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Steel Part 2 Weld Group Eccentrically Loaded in Plane of Faying Surface • polar moment of inertia of weld group about centroid • vertical force per linear inch of weld due to Pr

• horizontal force at i due to e

• resultant force at i

• vertical force at i due to e



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Steel Part 2 Weld Group Eccentrically Loaded in Plane of Faying Surface nomenclature l

total length of weld

i

point i

Pr e

Figure 4.29 Eccentrically Loaded Weld Group

applied load eccentricity



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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface Example 4.46



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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface Example 4.46



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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface



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Steel Part 2 Weld Group Eccentrically Loaded Normal to Faying Surface • vertical force per linear inch of weld due to pr

• moment of inertia about x-axis

• horizontal force at i due to e

• resulting force at i



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Steel Part 2 Weld Group Eccentrically Loaded Normal to Faying Surface Figure 4.30 Weld Group Eccentrically Loaded Normal to Faying Surface



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Steel Part 2

Example: Weld Group Eccentrically Loaded Normal to Faying Surface Example 4.47



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Example: Weld Group Eccentrically Loaded Normal to Faying Surface Example 4.47



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Example: Weld Group Eccentrically Loaded Normal to Faying Surface



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Plate Girders

section overview

• girder proportions • design for flexure

• design for shear without tension field action • design for shear with tension field action • design of intermediate stiffeners • design of bearing stiffeners



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Girder Proportions

typical overall girder depth

Figure 4.31 Plate Web Girder

L/12 < d < L/10

typical flange width h/5 < bf < h/3

intermediate stiffeners not required when unstiffened web requires



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Girder Proportions

requirements for web with stiffeners • For a/h > 1.5,

Figure 4.31 Plate Web Girder

AISC Eq. F13-4

• For a/h ≤ 1.5, AISC Eq. F13-3

Refer to AISC 360 Sec. F5, F13, G2, and G3. STRC ©2015 Professional Publications, Inc.


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Steel (Part 2)

Steel Part 2

Example: Girder Proportions Example 4.48



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Steel (Part 2)

Steel Part 2

Example: Girder Proportions Example 4.48



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Steel Part 2

Design for Flexure

• web slender if

• Nominal flexural strength, Mn, is less than plastic moment, Mp. • Flexural is design of girder governed by AISC 360 Sec. F5.

• flexural strength of girder governed by the following limit states • compression flange yielding

AISC Eq. F5-1

• lateral-torsional buckling

AISC Eq. F5-2

• compression flange local buckling AISC Eq. F5-7



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Steel Part 2

Example: Design for Flexure Example 4.49



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Steel (Part 2)

Steel Part 2

Example: Design for Flexure Example 4.49



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Steel Part 2

Example: Design for Flexure



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Steel Part 2




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Steel Part 2




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Steel Part 2




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Steel Part 2

Poll: Tension Field Action


Tension field action is the post-buckling development of diagonal tensile stresses in slender plate-girder web panels and compressive forces in the transverse stiffeners that border those panels. (A) true

(B) false



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Steel (Part 2)

Steel Part 2

Poll: Tension Field Action


Tension field action is the post-buckling development of diagonal tensile stresses in slender plate-girder web panels and compressive forces in the transverse stiffeners that border those panels. (A) true

(B) false

The answer is (A) true.



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Steel Part 2

Tension Field Action

• induced when elastic critical load, enhanced by stiffeners, is reached

• Stiffeners in compression and girder web in tension produce an equivalent Pratt truss.

Figure 4.32 Tension Field Action

• design using tension field action not permitted in • end-panels

• panels with large hole

• large panel aspect ratios STRC ©2015 Professional Publications, Inc.


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Steel (Part 2)

Steel Part 2

Design for Shear Without Tension Field Action • For , Vn is governed by shear yielding of web.

• For , Vn is governed by elastic buckling of web

Cv = 1.0 (AISC 360 Eq. G2-3)

• For , where Cv = right portion of equation for this case (AISC 360 Eq. G2-4), Vn is governed by inelastic buckling of web.

• AISC Manual Tables 3-16a and 3-17a provide values of φvVn/Aw and Vn/ΩbAw for a range of values of h/tw and a/h.



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Steel (Part 2)

Steel Part 2

Example: Design for Shear Without Tension Field Action Example 4.50



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Steel (Part 2)

Steel Part 2

Example: Design for Shear Without Tension Field Action Example 4.50



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Steel Part 2

Example: Design for Shear Without Tension Field Action



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Steel (Part 2)

Steel Part 2

Example: Design for Shear Without Tension Field Action



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Steel Part 2

Design for Shear With Tension Field Action

• Vn determined in accordance with AISC 360 Sec. G3.2

• AISC Manual Tables 3-16b and 3-17b provide values of φvVn/Aw and Vn/ΩbAw for a range of values of h/tw and a/h. • tension field action not permitted in end panels and when a/h > 3.0 or a/h > (260tw/h)2

(Along with other cases per AISC 360 Sec. G3.1, nominal shear strength is given by AISC 360 Sec. G2.1 as .)



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Steel (Part 2)

Steel Part 2

Example: Design for Shear With Tension Field Action Example 4.51



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Steel (Part 2)

Steel Part 2

Example: Design for Shear With Tension Field Action Example 4.51



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Steel (Part 2)

Steel Part 2

Example: Design for Shear With Tension Field Action



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Steel Part 2

Design of Intermediate Stiffeners

tension field action excluded

tension field action included

AISC Eq. G2-7

 V  Vc1  I st  I st 1   I st 2  I st 1   r   Vc 2  Vc1 

• From AISC 360 Sec. G2.2, required moment of inertia of stiffener is • maximum allowable width-tothickness ratio of a stiffener = 0.56

See AISC 360 Eq. G3-3.

• the minimum transverse stiffener moment of inertia is

• fabrication detail: stiffener stopped short of tension flange to avoid fatigue cracking (does not apply to bearing stiffeners)



AISC Eq. G3-4

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Steel (Part 2)

Steel Part 2

Example: Design of Intermediate Stiffeners Example 4.52



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Steel (Part 2)

Steel Part 2

Example: Design of Intermediate Stiffeners Example 4.52



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Steel (Part 2)

Steel Part 2

Example: Design of Intermediate Stiffeners



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Steel Part 2

Design of Bearing Stiffeners

• required when applied load exceeds web’s yielding, crippling, or sidesway buckling capacity

Figure 4.33 Bearing Stiffeners

• designed as axially loaded cruciform column, including • 25tw web strip (interior) • 12tw web strip (ends)

• effective length factor, K = 0.75 (AISC 360 Sec. J10.8)

• available bearing strength

• nominal bearing strength, Rn = 1.8FyApb AISC 360 Eq. J7-1



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Steel (Part 2)

Steel Part 2

Example: Design of Bearing Stiffeners Example 4.53



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Steel (Part 2)

Steel Part 2

Example: Design of Bearing Stiffeners Example 4.53



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Steel Part 2

Example: Design of Bearing Stiffeners



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Steel Part 2

Example: Design of Bearing Stiffeners



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Steel Part 2

Composite Beams

section overview

• section properties • shear connection

• deck ribs parallel to steel beam

• deck ribs perpendicular to steel beam • design for flexure



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Steel Part 2

Section Properties

• if sufficient shear connector ensures full composite action, depth of stress block is • if insufficient shear connectors are provided, depth of stress block is • From AISC Manual Table 3-20, lower bound on the actual moment of inertia, ILB, is used to determine deflection of composite member.



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Steel Part 2

Section Properties

For the composite beam shown in Fig. 4.35, the effective width of the concrete slab, on either side of the beam centerline, is the lesser of • •

Figure 4.35 Fully Composite Beam Section Properties

⁄ of the beam span

⁄ of the beam spacing

• the distance to the edge of the slab



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Steel Part 2

Example: Section Properties Example 4.54



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Steel Part 2

Example: Section Properties Example 4.54



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Steel (Part 2)

Steel Part 2

Example: Section Properties



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Steel Part 2

Shear Connection nomenclature Asc

cross-sectional area of a stud

Ec

modulus of elasticity of concrete

Fu w

Rg Rp

tensile strength of a stud unit weight of concrete stud group coefficient

stud position coefficient



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Steel Part 2

Shear Connection

• Shear force transferred across interface is the lesser of

• Provide n = V'/Qn connectors on either side of maximum moment.

• Rg and Rp parameters are provided in AISC 360 Sec. I8-2a.

• Shear connector placement limitations are provided in AISC 360 Sec. I8-2a and Fig. 4.34.

• AISC 360 Eq. I8-1 gives nominal strength of one stud shear connector as



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Steel Part 2

Shear Connection

Figure 4.36 Placement of Shear Connectors



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Steel Part 2

Deck Ribs Parallel to Steel Beam

• Maximum permitted diameter of stud shear connectors is 2.5 times the thickness of the base metal.

• Maximum deck to beam connection or weld spacing is 18 in. • Rg = 1.0 [when wr ≥ 1.5hr]

• Rg = 0.85 [when wr < 1.5hr] • Rp = 0.75



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Steel Part 2

Deck Ribs Parallel to Steel Beam

Figure 4.37 Deck Ribs Parallel to Steel Beam, Rg and Rp Values



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Steel Part 2

Deck Ribs Perpendicular to Steel Beam

stud group coefficient

stud position coefficient

• Rg = 0.85 [two studs welded in steel deck rib]

• Rp = 0.60 [studs welded in steel deck rib with emid-ht < 2 in]

• Rg = 1.0 [one stud welded in steel deck rib] • Rg = 0.70 [three or more studs welded in steel deck rib]

• Rp = 0.75 [studs welded in steel deck rib with emid-ht ≥ 2 in]



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Steel Part 2

Deck Ribs Perpendicular to Steel Beam Figure 4.38 Deck Ribs Perpendicular to Steel Beams, Rg Values



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Steel Part 2

Deck Ribs Perpendicular to Steel Beam Figure 4.39 Deck Ribs Perpendicular to Steel Beams, Rp Values



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Steel Part 2

Example: Shear Connection Example 4.55



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Steel Part 2

Example: Shear Connection Example 4.55



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Steel Part 2

Example: Shear Connection



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Steel Part 2

Design for Flexure

• φMn for range of Y1, Y2, and ΣQn is found in AISC Manual Table 3-19.

• From AISC 360 Sec. I3.2d, ΣQn is the least of • 0.85

• Design to support total factored loads for shored and unshored construction. • Steel beam alone must support all loads before concrete attains 75% of its strength.

• F y As • nQn



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Steel Part 2


Example 4.56

Example 4.54



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Steel Part 2


Example 4.56

Example 4.54



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Steel Part 2

Learning Objectives

You have learned how to

• design bolted and welded connections for a range of loading conditions • account for tension field action in plate girders • design composite steel members



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Steel Part 2

Lesson Overview

Chapter 4: Structural Steel Design, Part 2 • Plastic Design

• Design of Tension Members

• Design of Bolted Connections

• Design of Welded Connections • Plate Girders

• Composite Beams



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STRC07 Steel Part2 0716 R1

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