TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES 938 Aurora Boulevard Cubao, Quezon City
A Project in Partial Fulfilment for the Requirements in
CE473 (TIMBER DESIGN)
Entitled as
STRUCTURAL ANALYSIS AND DESIGN Of a Proposed Two – Storey Timber Residential House
Submitted by EMMANUEL M. LAZO
Submitted to Engr. Billy I. Rejuso
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October, 2015
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ABSTACT
This project is entitled as “A Structural Analysis and Design of a Proposed Two-Storey Timber Residential House” is presented by Emmanuel M. Lazo, as partial fulfilment for the requirements for CE 473 (Timber Design). The project was about structural analysis and design of identified parts of a two storey timber residential structure. Design specifications from NSCP were utilized in the design process. The parts analysed and designed included: joists, beams, truss, columns and connections. Design schedule and member details of the structure were also presented in the last chapter.
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TABLE OF CONTENTS CHAPTER 1. PROJECT BACKGROUND........................................................................................................3 1.1 Introduction.............................................................................................................................................3 1.2 The Project..............................................................................................................................................6 1.3 Project Objectives...................................................................................................................................6 1.4 Project Scope and Limitation..................................................................................................................7 1.5 Project Development Process................................................................................................................7 CHAPTER 2. DESIGN INPUTS........................................................................................................................9 2.1 Architectural Plans..................................................................................................................................9 2.2 Structural Plans.....................................................................................................................................13 2.3 Truss Details.........................................................................................................................................17 2.4 Structural Idealization...........................................................................................................................20 2.5 List of Loading per Area........................................................................................................................21 CHAPTER 3. STRUCTURAL ANALYSIS AND DESIGN................................................................................22 3.1 Design Process for Joists, Beams, and Girders...................................................................................22 I. SECOND FLOOR....................................................................................................................................23 I.A Design of Floor Sheathing.................................................................................................................23 I.B Design of Floor Joists........................................................................................................................24 I.C Design of Beams and Girders...........................................................................................................29 II. GROUND FLOOR...................................................................................................................................38 II.A Design of Floor Sheathing................................................................................................................38 II.B Design of Floor Joists.......................................................................................................................38 II.C Design of Beams..............................................................................................................................41 3.2 Design Process for Purlins, Truss, and Columns.................................................................................49 I. Design of Purlins..................................................................................................................................49 II. Design of Truss...................................................................................................................................54 III. Design of Columns.............................................................................................................................57 3.3 Design of Connections..........................................................................................................................66 I. Beam-Column, Beam-Beam................................................................................................................69 II. Truss-Column, Truss-Beam................................................................................................................72 CHAPTER 4. DESIGN SCHEDULES AND SUMMARY.................................................................................74 4
4.1. Joists....................................................................................................................................................74 4.2. Beam/Girder Schedule.........................................................................................................................75 4.3. Columns...............................................................................................................................................76 APPENDIX - REFERENCES..........................................................................................................................77
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CHAPTER 1. PROJECT BACKGROUND 1.1 Introduction The use of timber as a structural material is not new, in fact dating back many centuries. As time passes, developments in the various types of timber components which are available and their use in different structural forms have occurred; new advanced timber products are now available enabling structural engineers to achieve the performance and efficiency in building forms being demanded in the 21st century. There are thousands of species of tree from which timber can be obtained, each with different rates of growth, structural properties and degrees of durability. The timber supply chain has responded to nature’s variability and now provides repeatable product supply from managed forests. The industry has also created grading processes to deliver reliable technical performance (grades) for these products. The UK construction industry generally uses the word ‘timber’ to describe structural products of wood, whereas in North America the word ‘lumber’ is used. ‘Wood’ is often used to describe furniture and other non-structural items. Nevertheless, all three terms are commonly used to
Figure 1. Timber as Structural Material
describe structural products. Timber is categorised as either ‘softwood’ or ‘hardwood’. Softwood is obtained from coniferous trees and hardwood comes from broad-leaved trees. Softwood and hardwood are botanical terms and do not necessarily refer to the density or hardness of the wood. For example Balsa, which is known to be soft and used for building lightweight models, is a hardwood whereas Douglas Fir is a softwood with good durability and high strength properties. Softwood is commonly used for timber structures as it is readily available, easily worked, of relatively low cost and its fast rate of growth gives a continuous supply from regenerated forest areas. Hardwoods are typically used for exposed structures and claddings where durability and particular aesthetic characteristics, such as colour or grain pattern, are required. As a natural and renewable building material, timber has excellent ecological attributes. It acts as a carbon sink and has low embodied energy. The energy needed to convert trees into wood and hence into structural timber is significantly lower than that required by other structural materials such as steel and concrete. 6
Advantages of Timber as Construction Material Thermal Properties. Wood does not practically expand against heat. On the contrary, by the effect of heat, it dries out and gains strength. The coefficient of thermal conductivity of the wood is very low. For this reason, wood is used for making matches, handles of hardware equipment, ceilings and wall coverings. Mechanical Properties. Although wood is a light material, its strength is quite high. For instance, while the tensile strength of wood with 0.6/cm3 specific gravity is 100 N/mm2, the tensile strength of steel with 7.89/cm3 specific gravity is 500 N/mm2. Dividing tensile strength by specific gravity gives the breaking length and quality of material. Aesthetic Properties. Wood is a decorative material when considered as an aesthetic material. Each tree has its own color, design and smell the design of a tree does change according to the way it is sliced. It is possible to find different wooden materials according to color and design preference. Oxidation Properties. Although wood has oxidation characteristics in some way, it is not the kind of oxidation seen in metals. Metals get rust, wood doesn’t. For such characteristics, use of wood is preferred to avoid rust when necessary. Working Properties. It is easy to repair and maintain wood. While old woods can be renewed by special touches other materials are highly difficult and costly to maintain and to repair. Therefore they are usually disposed of. Variation. There are more than 5000 kinds of woods in the world. Their specific gravity, macroscopic and microscopic structures are different. Because of this variety, it is possible to find wood suitable for needs. For instance, for heat isolation and sound absorption woods in lightweight are used.
Disadvantages of Timber as Construction Material Shrinkage and Swelling of Wood. Wood is a hygroscopic material. This means that it will adsorb surrounding condensable vapors and loses moisture to air below the fiber saturation point. 7
Deterioration of Wood. The agents causing the deterioration and destruction of wood fall into two categories: Biotic (biological) and abiotic (non-biological). Biotic agents include decay and mold fungi, bacteria and insects. Fungi. It is necessary to give some short information about fungi agents to take measures against the wood deterioration. Oxygen is essential for the growth of fungi. In the absence of oxygen no fungi will grow. It is well known that storage of wood under water will protect them against attacks by fungi. Moisture. Generally wood will not be attacked by the common fungi at moisture contents below the fiber saturation point. The fiber saturation point (FSP) for different wood lies between 20 to 35% but 30% is accepted generally. Nutrients. Wood is an organic compound and consists of 50% carbon. That means that wood is a very suitable nutrient for fungi because fungi derive their energy from oxidation of organic compounds. Decay fungi wood rotters can use polysaccharides while stain fungi evidently require simple forms such as soluble carbohydrates, proteins and other substances present in the parenchyma cell of sapwood. Additionally, the presence of nitrogen in wood is necessary for the growth of fungi in wood. Insects. Insects are only second to decay fungi in the economic loss they cause to lumber and wood in service. Insects can be separated into four categories: Termites, powderpost beetles, carpenter ants and marine borers. Fire. Another disadvantage of wood is that it easily catches fire. Wood consists of organic compounds which are composed mainly of carbon and hydrogen. They can combine with oxygen and burns. Because of these properties, wood is classified as a combustible material.
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1.2 The Project The project is a two-storey residential house utilizing timber as the main structural material. The structure has a total lot area of the plan is 234 sq. m. with dimensions 13 m x 18 m, and the total floor area of the structure is 270 sq. m. Each storey has a height of 3 m from the natural grade line.
Figure 2. Perspective View of the Residential House
1.3 Project Objectives The main objective of this project is to analyse and design a timber structure in accordance with the principles written in NSCP 2010. Other objectives of the project are as follows: a. To design a two-storey residential house that will have an acceptable probability of performing satisfactorily during its intended life time. b. To provide all the necessary architectural plans, structural plans, and computations for the structural analysis and design of the structure. 9
1.4 Project Scope and Limitation The following were the scope covered by the design project: 1.) The project was designed in accordance to the National Structural Code of the Philippines. 2.) Analysis of structural members through conventional methods, and analysis of truss with the help of GRASP software. 3.) All architectural plans (floor plans and elevation plans) and structural plans (framing plans) were provided. The following were the limitations of the design project: 1.) Only joists, beams, columns, truss and connections were considered in the design. 2.) The cost estimate for the whole structure is not provided. 3.) The interior design of the structure was not considered. 1.5 Project Development Process The first phase of the project development process was the planning/conceptualization of the residential house that will be constructed. This stage includes the naming of the objectives, written proposals, and identification of necessary information of the client, location, etc. (these was not shown in the project). In the second stage, the architectural and structural plans were created. Next was the identification of the material properties that was used in the structure. As what was said, there are many variation of woods considering its density and other properties, that’s why knowing the wood type was necessary. The fourth phase done was the identification of the loads on the structure. These loads included the dead load, live load, and wind load. Knowing the loads and the material properties, the designer was able to proceed to the last step of the process which is the structural analysis and design of the structure.
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PLANNING/CONCEPTUALIZATION
CREATION OF ARCHITECTURAL AND STRUCTURAL PLANS
IDENTIFICATION OF MATERIAL PROPERTIES
IDENTIFICATION OF LOADS ON THE STRUCTURE
STRUCTURAL ANALYSIS AND DESIGN OF THE STRUCTURE
Figure 3. Project Development Process
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CHAPTER 2. DESIGN INPUTS 2.1 Architectural Plans
Figure 4. Ground Floor Plan
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Figure 5. Second Floor Plan
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Figure 6. Front Elevation
Figure 7. Rear Elevation
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15
Figure 8. Right Side Elevation
Figure 9. Left Side Elevation
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2.2 Structural
Plans
Figure 10. Ground Floor Framing Plan
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Figure 11. Second Floor Framing Plan
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19
For Framing Plans, S means Joist Group In a beam name FA-B1, F means Frame/Grid, and B Figure 12. Roof Beam Plan Beam
Beam Column Joist means
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Figure 13. Framing System
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2.3 Truss Details
Figure 14. Roof Truss
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Figure 15. Truss Details
Figure 16. Purlin Details
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Figure 17. Truss Division
Figure 18. Truss Tributary Areas 24
2.4 Structural Idealization
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In this structure, the main wood used was Yakal, which is from the Group I (High Strength), with 80% Stress Grade. For some minimal parts (walls), Bayok was used, which is from Group IV (Moderately Low Strength) with 50% Stress Grade. STUDS
COLUMNS JOISTS
PANELS GIRDER
BEAM
WALLS
Figure 19. Structural Idealization
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2.5 List of Loading per Area
Ground Floor Area S-1 S-2 S-3 S-4 S-5 S-6 S-7
Dimension Short Side (m) Long Side (m) 4 5 4 5 5 5 4 5 4 5 5 5 3 4 Total Ground Floor Area
Area (m2) 20 20 25 20 20 25 12 142
Minimum Design Load Occupancy Live Load (kPa) Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9
Second Floor Area S-1 S-2 S-3 S-4 S-5 S-6 S-7
Dimension Long Side 4 5 4 5 5 5 4 5 1.5 4 5 5 3 4 Total Second Floor Area Total Floor Area Short Side
Area 20 20 25 20 6 25 12 128 270
Minimum Design Load Occupancy Live Load (kPa) Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Basic Floor Area 1.9 Exterior Balcony 2.9*
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CHAPTER 3. STRUCTURAL ANALYSIS AND DESIGN 3.1 Design Process for Joists, Beams, and Girders
Figure 20. Design Process for Joist, Beam and Girder
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I. SECOND FLOOR I.A Design of Floor Sheathing
Procedure 1. Assume the spacing of the joists that will carry the load from the panels. 2. Choose the panel span thickness and width (Table 6.10 NSCP) according to the panel span rating (joist spacing). 3. Calculate the quantity of the panels that can be placed within the beam.
Slab S-1 S-2 S-3 S-4 S-5 S-6 S-7 Quantity=
length (s) 4 4 5 4 1.5 5 3
length(l) 5 5 5 5 4 5 4
Sheathing Dimensions (m) spacing(s) panel(t) 0.4 0.016 0.4 0.016 0.4 0.016 0.4 0.016 0.4 0.016 0.4 0.016 0.4 0.016
panel(w) 0.6 0.6 0.6 0.6 0.6 0.6 0.6
Quantity 14 14 17 14 5 17 10
length(s) x2 panel(w)
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I.B Design of Floor Joists Procedure Part 1. Solving for Total Weight to be carried by Joists a. b. c. d. e. f.
Get the Total Weight due to Floor Sheathing Calculate the Area of Openings of Walls within the Floor Joists Choose the Stud Dimensions from NSCP Table 6.23. Get the Total Weight due to Wall Studs within the Floor Joists considering Area of Openings Get the Total Weight due to Walls within the Floor Joists considering Area of Openings Sum up all the Weights.
Part 2. Design the Dimensions of the Floor Joists a. b. c. d.
Assume the width (b) of the floor joist. Get the maximum shear and maximum moment due to the total weight. Solve for the depth (d) using the allowable bending stress, shearing stress, and deflection. Get the maximum d among the three.
Part 3 a. Solve for stress adjustments. b. Solve for the new Weight of the building (include the self-weight of the joist already). c. Investigate whether the dimensions will be safe due to the allowable bending stress, shearing stress, and deflection.
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ϒ (kN/m3) 6.867 6.867 6.867 6.867 6.867 6.867 6.867
S-1 S-2 S-3 S-4 S-5 S-6 S-7
W DL=
Weight due to panels E Mpa WDL kPa WLL kPa 9780 0.7691 1.9 9780 0.7691 1.9 9780 0.9339 1.9 9780 0.7691 1.9 9780 0.7691 1.9 9780 0.9339 1.9 9780 0.5494 1.9
W (kN/m) 1.0676 1.0676 1.1336 1.0676 1.0676 1.1336 0.9797
ϒ ( panel(t))(quantity ) 2 W spacing (¿¿ DL+W ¿ )¿ ) W =¿ Weight due to Wall Studs
S-1 S-2 S-3 S-4 S-5 S-6 S-7
L (wall) m
h (m)
s (m)
b (m)
d (m)
ϒ (kN/m3)
0 5 6 8 0 9 3
2.8 2.8 2.8 2.8 2.8 2.8 2.8
0.6 0.6 0.6 0.6 0.6 0.6 0.6
0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.1 0.1 0.1 0.1 0.1 0.1 0.1
6.867 6.867 6.867 6.867 6.867 6.867 6.867
quantity (pcs) 0 9 10 14 0 15 5
W (kN) 0 0.2163105 0.192276 0.336483 0 0.288414 0.16023
quantity =L/s
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W=
ϒ (bdh)( quantity) length( s)
*There are no area of openings. *Some have zero weights because those floor areas do not contain interior walls. *Values of b, d, and s came from NSCP Table 6.23.
Weight due to Walls (Bayok was used) ϒ (kN/m3) h (m) t (m) ρ (kg/m3) 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164 2.8 0.02 0.44 4.3164
S-1 S-2 S-3 S-4 S-5 S-6 S-7
W (kN/m) 0.2417184 0.2417184 0.2417184 0.2417184 0.2417184 0.2417184 0.2417184
W =ϒ th
*The value of t is assumed (.01 x 2 as it is side by side)
S-1 S-2 S-3 S-4 S-5 S-6 S-7
WT (kN/m) 1.3094 1.5257 1.5676 1.6458 1.1116 1.6637 1.7817
V (kN) 2.6187 3.0513 3.9189 3.2917 0.8337 4.1592 2.6725
M (kNm) 2.6187 3.0513 4.8986 3.2917 0.3126 5.1991 2.0044
b (mm) 100 100 100 100 100 100 100 32
V=
W T length( s) 2 length( s) ¿ ¿ ¿2 WT¿ M =¿
*The breadth (b) is assumed.
S-1 S-2 S-3 S-4 S-5 S-6 S-7
Bending Fb (Mpa) d (mm) 24.5 80.0824 24.5 86.4446 24.5 109.5291 24.5 89.7846 24.5 27.6701 24.5 112.8378 24.5 70.0624
Shearing Fv (Mpa) d (mm) 2.49 19.6990 2.49 21.2640 2.49 21.5539 2.49 22.0856 2.49 18.1504 2.49 22.2050 2.49 22.9790
Fb =
6M b d2
F v=
3V 2 bd
Deflection δ(a) (mm) d (mm) 11.1111 157.8083 11.1111 157.8083 13.8889 201.2396 11.1111 157.8083 4.1667 55.2719 13.8889 201.2396 8.3333 128.9185
d' (mm) 170 170 220 170 70 220 140
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3
384 E(
bd ) 12
¿ 5W L4 δ= ¿
*Solve the depth (d) for the following equations and get the maximum (d’)
S-1 S-2 S-3 S-4 S-5 S-6 S-7
le (m) 4 4 5 4 4 5 3 l e =l u
Adjustment due to Slenderness Cs Ck 8.24621 16.20344053 8.24621 16.20344053 10.4881 16.20344053 8.24621 16.20344053 8.24621 16.20344053 10.4881 16.20344053 6.245 16.20344053
F'b (Mpa) 23.952185 23.952185 23.066488 23.952185 23.952185 23.066488 24.319804
Single span beam uniformly distributed
C s=
√
le d b2
C k =0.811 √ E/ F b *If Cs < 10, '
Fb =F b *If 10 < Cs < Ck
Cs Ck 1 1− ¿ 3 ¿ ¿ ' Fb =F b ¿ *If Ck < Cs < 50 34
F b' =
Wnew 1.4261 1.6424 1.7186 1.7626 1.1597 1.8148 1.8778
Bending M 2.8522 3.2848 5.3707 3.5252 0.3262 5.6712 2.1126
fb 5.9215 6.8197 6.6579 7.3187 3.9937 7.0304 6.4670
Remarks Ok Ok Ok Ok Ok Ok Ok
0.438 E C s2
Shearing V 2.8522 3.2848 4.2966 3.5252 0.8697 4.5369 2.8167
fv 0.2517 0.2898 0.2929 0.3110 0.1864 0.3093 0.3018
Remarks Ok Ok Ok Ok Ok Ok Ok
Deflection δ 11.8720 13.6727 16.1167 14.6732 2.7345 17.0183 8.8560
Remarks ok ok ok ok ok ok ok
W new =W T +ϒ bd ' *If fb < Fb’, the dimensions is safe against bending, else, change dimension. *If fv < Fv, the dimensions is safe against shearing, else, change dimension. *If δ < δa, the dimensions is safe against shearing, else, change dimension. I.C Design of Beams and Girders Procedure Part 1. Solving for Total Weight to be carried by Joists a. b. c. d. e. f.
Get the Total Weight due to Floor Sheathing Calculate the Area of Openings of Walls within the Floor Joists Choose the Stud Dimensions from NSCP Table 6.23. Get the Total Weight due to Wall Studs within the Floor Joists considering Area of Openings Get the Total Weight due to Walls within the Floor Joists considering Area of Openings Sum up all the Weights.
Part 2. Design the Dimensions of the Floor Joists a. b. c. d.
Assume the width (b) of the floor joist. Get the maximum shear and maximum moment due to the total weight. Solve for the depth (d) using the allowable bending stress, shearing stress, and deflection. Get the maximum d among the three.
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Part 3 a. Solve for stress adjustments. b. Solve for the new Weight of the building (include the self-weight of the joist already). c. Investigate whether the dimensions will be safe due to the allowable bending stress, shearing stress, and deflection.
Beam/ Girder F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
Length (m) 5 5 5 5 5 5 5 5 4 4 4
FA-B1 FA-B2 FA-B3 FB-B1 FB-B2
4 4 5 4 4
Joist (left) 0 10 10 10 0 10 10 10 0 8 8
Weight due to Joists and Floor Sheathing Joist (right) W(l-joist) W(r-joist) Resultant (kN) 10 0 2.852198 28.52198 10 2.852198 2.852198 57.04396 10 2.852198 4.296583 71.48781 0 4.296583 0 42.96583 10 0 2.852198 28.52198 10 2.852198 0 28.52198 10 0 4.296583 42.96583 0 4.296583 0 42.96583 8 0 0.86974455 6.9579564 8 0.86974455 2.8167456 29.4919212 0 2.8167456 0 22.5339648
W (kN/m) 5.704396 11.408792 14.297562 8.593166 5.704396 5.704396 8.593166 8.593166 1.7394891 7.3729803 5.6334912
NO JOIST
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FB-B3 FD-B1 FD-B3
5 4 5
*Those with asterisks are girders. Resultant=∑ W∗quantity W =Resultant∗Length
F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
FA-B1 FA-B2 FA-B3 FB-B1
A(wall) m2 14
14 14
14 11.2 6
11.2 11.2 14
Opening A(opening) m2 Area (m2) 0 14 No Walls No Walls 1.5 12.5 0 14 No Walls No Walls 1.5 12.5 0 11.2 No Walls 0 6
3 2.25 0.75
8.2 8.95 13.25
% 100
89.2857143 100
89.2857143 100 100
73.2142857 79.9107143 94.6428571
No Walls 37
FB-B2 FB-B3 FD-B1 FD-B3
11.2
0
11.2
100
9.2 12
82.1428571 85.7142857
No Walls 11.2 14
2 2
A= A ( wall )− A(opening)
A ∗100 ( A( wall ))
=
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F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
W ( i )=
Weight due to Studs quantity ϒ (kn/m3) d (m) (pcs) 0.1 6.867 9 No Walls No Walls 0.1 6.867 9 0.1 6.867 9 No Walls No Walls 0.1 6.867 9 0.1 6.867 7 No Walls 0.1 6.867 7
h (m) 2.8
s (m) 0.6
b (m) 0.05
2.8 2.8
0.6 0.6
0.05 0.05
2.8 2.8
0.6 0.6
0.05 0.05
1.5
0.6
0.05
2.8 2.8 2.8
0.6 0.6 0.6
0.05 0.05 0.05
0.1 0.1 0.1
2.8
0.6
0.05
0.1
2.8 2.8
0.6 0.6
0.05 0.05
0.1 0.1
6.867 6.867 6.867 No Walls 6.867 No Walls 6.867 6.867
W(i) kN 0.865242
W (kN/m) 0.1730484
0.772538 0.865242
0.1545075 0.1730484
0.772538 0.672966
0.1545075 0.1682415
0.360518
0.0901294
7 7 9
0.492707 0.537772 0.81889
0.1231768 0.134443 0.163778
7
0.672966
0.1682415
7 9
0.552794 0.741636
0.1381984 0.1483272
ϒ bdh(quantity )( ) 100 W =W (i ) / L
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F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
W ( i )=
Weight due to Exterior Walls (Wood:Bayok) ϒ (kN/m3) ρ (kg/m3) W(i) kN/m 0.44 4.3164 0.2417184 No Walls No Walls 0.44 4.3164 0.2417184 0.44 4.3164 0.2417184 No Walls No Walls 0.44 4.3164 0.2417184 0.44 4.3164 0.2417184 No Walls 0.44 4.3164 0.129492
h (m) 2.8
t (m) 0.02
2.8 2.8
0.02 0.02
2.8 2.8
0.02 0.02
1.5
0.02
2.8 2.8 2.8
0.6 0.6 0.6
0.05 0.05 0.05
2.8
0.6
0.05
2.8 2.8
0.6 0.6
0.05 0.05
0.1 0.1 0.1 No Walls 0.1 No Walls 0.1 0.1
W (kN/m) 0.2417184
0.21582 0.2417184
0.21582 0.2417184 0.129492
0.168 0.168 0.168
0.123 0.13425 0.159
0.168
0.168
0.168 0.168
0.138 0.144
ϒ ht ( ) 100 W =W (i ) / L
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F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
WT (kN/m) 6.1191628 11.408792 14.297562 8.9634935 6.1191628 5.704396 8.593166 8.9634935 2.149449 7.3729803 5.853112575
V (kN) 15.297907 28.52198 35.743905 22.4087338 15.297907 17.5970878 24.8190128 22.4087338 4.298898 14.7459606 11.7062252
M (kNm) 19.1223838 35.652475 44.6798813 28.0109172 19.1223838 15.522958 24.52361 28.0109172 4.298898 14.7459606 11.7062252
b (mm) 200 200 200 200 200 200 200 200 200 200 200
E(MPa) 9780 9780 9780 9780 9780 9780 9780 9780 9780 9780 9780
FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
0.246176813 0.268692984 0.32277795 0 0.3362415 0 0.276198375 0.2923272
0.49235363 0.53738597 0.80694488 0 0.672483 0 0.55239675 0.730818
0.49235363 0.53738597 1.00868109 0 0.672483 0 0.55239675 0.9135225
200 200 200 200 200 200 200 200
9780 9780 9780 9780 9780 9780 9780 9780
For beams, W T =W ( joist∧floor sheathing ) +W (walls∧studs) V and M are solved same as joists.
For Girders 41
W T =W ( joist∧floor sheathing ) +W (walls∧studs)
The Shear and Moment Diagrams of the girders are obtained. V max is equal to the highest value between V1 and V2 M max is the highest moment.
F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2* F2-B2* F1-B2 FC-B1 FD-B2 FE-B1
Bending Fb (Mpa) d (mm) 24.5 153.020142 24.5 208.940403 24.5 233.901814 24.5 185.200114 24.5 153.020142 24.5 137.868429 24.5 173.288517 24.5 185.200114 24.5 72.5531304 24.5 134.373652 24.5 119.725324
Shearing Fv (Mpa) d (mm) 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675 2.49 18.675
δ(a) (mm) 13.88889 13.88889 13.88889 13.88889 13.88889 13.88889 13.88889 13.88889 11.11111 11.11111 11.11111
Deflection d (mm) 280.189528 344.853351 371.799293 318.209884 280.189528 273.710286 313.765819 318.209884 158.156459 238.520425 220.8548
d' (mm) 300 360 390 330 300 290 330 330 170 250 240
42
FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
le (m) 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 7.68 7.68 7.68
7.68 7.68 9.6 7.68 7.68 9.6 7.68 9.6
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
24.5536553 25.6519714 35.1442699 0 28.6957936 0 26.0077716 33.4454628
2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49
Adjustment due to Slenderness Cs Ck F'b (Mpa) 8.4853 16.2034 24.5 9.2952 16.2034 24.5 9.6747 16.2034 24.5 8.8994 16.2034 24.5 8.4853 16.2034 24.5 8.3427 16.2034 24.5 8.8994 16.2034 24.5 8.8994 16.2034 24.5 5.7131 16.2034 24.5 6.9282 16.2034 24.5 6.7882 16.2034 24.5
4.1569 4.1569 5.3666 6.6453 4.3818 7.4297 4.1569 5.3666
16.2034 16.2034 16.2034 16.2034 16.2034 16.2034 16.2034 16.2034
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
18.675 18.675 18.675 18.675 18.675 18.675 18.675 18.675
11.11111 11.11111 13.88889 11.11111 11.11111 13.88889 11.11111 13.88889
76.8057259 79.0793928 105.080593 0 85.2174082 0 79.8089487 101.666445
Adjustment due to Size Factor Cf F'b (Mpa) 1.0000 24.5000 0.9799 24.0087 0.9713 23.7961 0.9895 24.2419 1.0000 24.5000 1.0000 24.5000 0.9895 24.2419 0.9895 24.2419 1.0000 24.5000 1.0000 24.5000 1.0000 24.5000
1.1431 1.1431 1.1072 1.0300 1.1298 1.0300 1.1431 1.1072
28.0068 28.0068 27.1257 25.2341 27.6809 25.2341 28.0068 27.1257
90 90 120 100 100 100 90 120
F'b (Mpa) 24.5 24.0086736 23.796096 24.2419135 24.5 24.5 24.2419135 24.2419135 24.5 24.5 24.5
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
Adjustment due to slenderness factor 1 300 9 ¿ d' F b' =¿
43
Bending
Shearing
Wnew (kN/m)
M (kNm)
fb (Mpa)
Remarks
6.5312
20.4099
6.8033
Ok
11.9032
37.1976
8.6105
Ok
14.8332
46.3537
9.1427
Ok
9.4167
29.4272
8.1067
Ok
6.5312
20.4099
6.8033
ok
6.1027
22.8127
8.1377
ok
9.0464
28.2700
7.7879
ok
9.4167 2.3829
31.9573 4.7659
8.8037 4.9473
ok ok
7.7163
15.4327
7.4077
ok
6.1827
12.3655
6.4403
0.3698 0.3923 0.4876 0.3159 0.4736 0.3159 0.3998 0.4571
0.7396 0.7846 1.5237 0.6318 0.9472 0.9871 0.7996 1.4285
2.7391 2.9059 3.1744 0.3583 2.8415 0.5598 2.9615 2.9761
Deflection
fv (Mpa)
Remarks
δ (mm)
Remarks
0.4082
ok
12.0770
ok
0.6200
ok
12.7376
ok
0.7131
ok
12.4845
ok
0.5350
ok
13.0824
ok
0.4082
ok
12.0770
ok
0.4808
ok
12.4927
ok
0.5898
ok
12.5680
ok
0.5350 0.2103
ok ok
13.0824 9.9187
ok ok
0.4630
ok
10.0991
ok
ok
V (kN) 16.328 0 29.758 0 37.083 0 23.541 8 16.328 0 18.592 8 25.952 1 23.541 8 4.7659 15.432 7 12.365 5
0.3864
ok
9.1461
ok
ok ok ok ok ok ok ok ok
0.7396 0.7846 1.2190 0.6318 0.9472 0.7897 0.7996 1.1428
0.0616 0.0654 0.0762 0.0206 0.0710 0.0258 0.0666 0.0714
ok ok ok ok ok ok ok ok
10.3731 11.0048 14.0877 0.5309 9.6847 1.2962 11.2153 13.2078
ok ok ok ok ok ok ok ok
44
II. GROUND FLOOR
II.A Design of Floor Sheathing
Slab S-1 S-2 S-3 S-4 S-5 S-6 S-7
length (s)
length(l)
4 4 5 4 4 5 3
5 5 5 5 4 5 4
Sheathing Dimensions (m) spacing(s) panel(t) 0.4 0.4 0.4 0.4 0.4 0.4 0.4
0.016 0.016 0.016 0.016 0.016 0.016 0.016
panel(w)
Quantity
0.6 0.6 0.6 0.6 0.6 0.6 0.6
14 14 17 14 14 17 10
II.B Design of Floor Joists
45
ϒ (kN/m3) S-1 S-2 S-3 S-4 S-5 S-6 S-7
6.867 6.867 6.867 6.867 6.867 6.867 6.867
Weight due to panels E Mpa WDL kPa WLL kPa 9780 9780 9780 9780 9780 9780 9780
0.7691 0.7691 0.9339 0.7691 0.7691 0.9339 0.5494
W (kN/m)
1.9 1.9 1.9 1.9 1.9 1.9 1.9
1.0676 1.0676 1.1336 1.0676 1.0676 1.1336 0.9797
Weight due to Wall Studs
S-1 S-2 S-3 S-4 S-5 S-6 S-7
L (wall) m
h (m)
s (m)
b (m)
d (m)
ϒ (kN/m3)
quantity (pcs)
W (kN)
4 0 5 5.5 0 5 0
3.2 3.2 3.2 3.2 3.2 3.2 3.2
0.6 0.6 0.6 0.6 0.6 0.6 0.6
0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.1 0.1 0.1 0.1 0.1 0.1 0.1
6.867 6.867 6.867 6.867 6.867 6.867 6.867
7 0 9 10 0 9 0
0.7691 0 0.19777 0.27468 0 0.19777 0
46
Weight due to Walls (Bayok was used) ϒ (kN/m3) h (m) t (m) ρ (kg/m3) S-1 S-2 S-3 S-4 S-5 S-6 S-7
S-1 S-2 S-3 S-4 S-5 S-6 S-7
3.2 0.02 3.2 0.02 3.2 0.02 WT (kN/m) 3.2 2.1130 0.02 3.2 1.3439 0.02 3.2 1.6076 0.02 3.2 1.6186 0.02 1.3439 1.6076 1.2560
2.6878 4.0190 1.8840
Bending Fb (Mpa) d (mm) S-1 S-2 S-3 S-4 S-5 S-6 S-7
0.44 0.44 0.44 V (kN) 4.2260 0.44 2.6878 0.44 4.0190 0.44 3.2371 0.44
24.5 24.5 24.5 24.5 24.5 24.5 24.5
2.49 2.49 2.49 2.49 2.49 2.49 2.49
Wnew
Bending M
fb
Remarks
2.2297 1.4606 1.7587 1.7353 1.4606 1.7587 1.3453
4.4595 2.9213 5.4958 3.4706 2.9213 5.4958 1.5134
9.2584 6.0649 6.8130 7.2054 6.0649 6.8130 5.3731
ok ok ok ok ok ok ok
S-1 S-2 S-3 S-4 S-5 S-6 S-7
7.68 7.68 9.6 7.68 7.68 9.6 5.76
le (m)
2.6878 5.0237 1.4130
Shearing Fv (Mpa) d (mm)
101.7318 81.1315 110.9186 89.0376 81.1315 110.9186 58.8251
Cs
Shearing V
4.3164 4.3164 4.3164 M (kNm) 4.22604.3164 2.68784.3164 5.02374.3164 3.23714.3164
25.0244 19.9571 21.8274 21.9018 19.9571 21.8274 19.2934
fv
0.27625 0.27625 0.27625 b (mm) 1000.27625 1000.27625 1000.27625 1000.27625 100 100 100
Deflection δ(a) (mm) d (mm) 11.1111 11.1111 13.8889 11.1111 11.1111 13.8889 8.3333
Remarks
4.4595 0.3935 ok 2.9213 0.2578 ok 4.3966 0.2998 ok 3.4706 0.3062 ok 2.9213 0.2578 ok 4.3966 0.2998 ok Adjustment due to Slenderness 2.0179 0.2328 ok
11.4263 11.4263 14.5327 11.4263 11.4263 14.5327 8.65332
W (kN/m)
d' (mm)
157.8083 157.8083 201.2396 157.8083 157.8083 201.2396 115.0147
170 170 220 170 170 220 130
Deflection δ
Remarks
18.5621 12.1595 16.4920 14.4461 12.1595 16.4920 7.9240
ok ok ok ok ok ok ok
Ck
F'b (Mpa)
16.2034 16.2034 16.2034 16.2034 16.2034 16.2034 16.2034
22.480536 22.480536 19.215502 22.480536 22.480536 19.215502 23.835726
47
II.C Design of Beams
F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3-B2 F2-B2 F1-B2 FD-B2 FE-B1
FA-B1 FA-B2 FA-B3 FB-B1
Length (m) 5 5 5 5 5 5 5 5 4 4
4 4 5 4
Joist (left) 0 10 10 10 0 10 10 10 8 8
Weight due to Joists and Floor Sheathing Joist (right) W(l-joist) W(r-joist) Resultant (kN) 10 0 4.4594684 44.594684 10 4.4594684 4.4594684 89.189368 10 4.4594684 4.396645 88.561134 0 4.396645 0 43.96645 10 0 4.4594684 44.594684 10 4.4594684 4.4594684 89.189368 10 4.4594684 4.396645 88.561134 0 4.396645 0 43.96645 8 0 2.0178969 16.143175 0 2.0178969 0 16.143175
W (kN/m) 8.9189368 17.8378736 17.7122268 8.79329 8.9189368 17.8378736 17.7122268 8.79329 4.0357938 4.0357938
Beams without joists NO JOIST
48
FB-B2 FB-B3 FD-B1 FD-B3
4 5 4 5
49
From the table shown, looking at the highest axial load (Column 7), the interaction value is 0.617006, which is less than 1, thus using 250 mm x 200 mm as the size of the column is safe for the structure.
Opening A(wall) m2 16
16 16
16 12.8
12.8 12.8 16 12.8
12.8 16
Area A(opening) m2 (m2) 0 16 No Walls No Walls 0 16 0 16 No Walls No Walls 0 16 No Walls 0 12.8
% 100
100 100
100 100
2 3.76 5.3 No Walls 0 No Walls
10.8 9.04 10.7
84.375 70.625 66.875
12.8
100
4.26 5.3
8.54 10.7
66.7187 5 66.875
50
Weight due to Studs h (m) 3.2
s (m) 0.6
b (m) 0.05
d (m) 0.1
3.2 3.2
0.6 0.6
0.05 0.05
0.1 0.1
3.2
0.6
0.05
0.1
3.2
0.6
0.05
0.1
3.2 3.2 3.2
0.6 0.6 0.6
0.05 0.05 0.05
0.1 0.1 0.1
ϒ (kn/m3) quantity (psc) 6.867 9 No Walls No Walls 6.867 9 6.867 9 No Walls No Walls 6.867 9 No Walls 6.867 7
6.867 6.867 6.867
W(i) kN 0.98885
W (kN/m) 0.19777
0.98885 0.98885
0.19777 0.19777
0.98885
0.19777
0.7691
0.19228
7 7 9
0.64893 0.54318 0.66129
0.16223 0.13579 0.13226
7
0.7691
0.19228
7 9
0.51314 0.66129
0.12828 0.13226
No Walls 3.2
0.6
0.05
0.1
6.867
3.2 3.2
0.6 0.6
0.05 0.05
0.1 0.1
6.867 6.867
No Walls
51
3.2
Weight due to Exterior Walls (Wood:Bayok) ϒ t (m) ρ (kg/m3) (kN/m3) W(i) kN/m W (kN/m) 0.0 2 0.44 4.3164 0.27625 0.27625 No Walls No Walls 0.0 2 0.44 4.3164 0.27625 0.27625 0.0 2 0.44 4.3164 0.27625 0.27625 No Walls No Walls 0.0 2 0.44 4.3164 0.27625 0.27625 No Walls 0.0 2 0.44 4.3164 0.27625 0.27625
3.2 3.2 3.2
0.6 0.6 0.6
0.05 0.05 0.05
3.2
0.6
0.05
3.2 3.2
0.6 0.6
0.05 0.05
h (m) 3.2
3.2 3.2
3.2
0.1 0.1 0.1 No Walls 0.1 No Walls 0.1 0.1
0.192 0.192 0.192
0.162 0.1356 0.1284
0.192
0.192
0.192 0.192
0.1281 0.1284
52
Total W WT (kN/m) 9.39296 17.8379 17.7122 9.26731 9.39296 17.8379 17.7122 9.26731 4.03579 4.50432
Design Parameters V (kN) 23.48239 44.594684 44.280567 23.168273 23.48239 44.594684 44.280567 23.168273 8.0715876 9.0086388
M (kNm) 29.35299 55.74336 55.35071 28.96034 29.35299 55.74336 55.35071 28.96034 8.071588 9.008639
b (mm) 200 200 200 200 200 200 200 200 200 200
E (Mpa) 9780 9780 9780 9780 9780 9780 9780 9780 9780 9780
0.32423 0.27139 0.26066 0 0.38428 0 0.25638 0.26066
0.6484658 0.5427899 0.6516461 0 0.768552 0 0.5127683 0.6516461
0.648466 0.54279 0.814558 0 0.768552 0 0.512768 0.814558
200 200 200 200 200 200 200 200
9780 9780 9780 9780 9780 9780 9780 9780
53
Bending
Shearing
Fb (Mpa) 24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
d (mm) 189.5849 261.2607 260.339 188.3126 189.5849 261.2607 260.339 188.3126 99.41618 105.0285
Fv (Mpa) 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49
d (mm) 18.675 18.675 18.675 18.675 18.675 18.675 18.675 18.675 18.675 18.675
Deflection δ(a) (mm) d (mm) 13.8889 323.21288 13.8889 400.25392 13.8889 399.31193 13.8889 321.76523 13.8889 323.21288 13.8889 400.25392 13.8889 399.31193 13.8889 321.76523 11.1111 195.1136 11.1111 202.38933
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
28.17871 25.78063 31.58192 0 30.67709 0 25.05752 31.58192
2.49 2.49 2.49 2.49 2.49 2.49 2.49 2.49
18.675 18.675 18.675 18.675 18.675 18.675 18.675 18.675
11.1111 11.1111 13.8889 11.1111 11.1111 13.8889 11.1111 13.8889
84.190592 79.34358 97.853977 0 89.096157 0 77.852926 97.853977
d' (mm) 340 420 410 340 340 420 410 340 210 220
100 90 110 100 100 100 90 120
54
le (m) 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 7.68 7.68
7.68 7.68 9.6 7.68 7.68 9.6 7.68 9.6
Adjustment due to Slenderness Cs Ck F'b (Mpa) 9.03327 16.2034 24.5 10.0399 16.2034 24.5 9.91968 16.2034 24.5 9.03327 16.2034 24.5 9.03327 16.2034 24.5 10.0399 16.2034 24.5 9.91968 16.2034 24.5 9.03327 16.2034 24.5 6.3498 16.2034 24.5 6.49923 16.2034 24.5
4.38178 4.15692 5.13809 4.38178 4.38178 4.89898 4.15692 5.36656
16.2034 16.2034 16.2034 16.2034 16.2034 16.2034 16.2034 16.2034
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
Adjustment due to Size Factor Cf F'b (Mpa) F'b (Mpa) 0.9861892 24.161636 24.16164 0.9633044 23.600958 23.60096 0.9658871 23.664235 23.66423 0.9861892 24.161636 24.16164 0.9861892 24.161636 24.16164 1 24.5 24.5 0.9658871 23.664235 23.66423 0.9861892 24.161636 24.16164 1 24.5 24.5 1 24.5 24.5
1.1431353 1.1179292 1.129831 1.129831 1.129831 1.1431353 1.1071732 1.1071732
28.006815 27.389264 27.680859 27.680859 27.680859 28.006815 27.125743 27.125743
24.5 24.5 24.5 24.5 24.5 24.5 24.5 24.5
55
Wnew 9.859912 17.837874 17.712227 9.7342652 9.859912 17.837874 17.712227 9.7342652 4.0357938 4.8064674
M 30.8122 55.7434 55.3507 30.4196 30.8122 55.7434 55.3507 30.4196 8.07159 9.61293
Bending fb 7.99625 9.48016 9.87818 7.89435 7.99625 9.48016 9.87818 7.89435 5.49088 5.95843
0.4615729 0.3950009 0.4117324 0.13734 0.521616 0.13734 0.3799901 0.4254664
0.92315 0.79 1.28666 0.27468 1.04323 0.42919 0.75998 1.32958
2.76944 2.92593 3.19008 0.82404 3.1297 1.28756 2.81474 2.76996
Remarks ok ok ok ok ok ok ok ok ok ok
ok ok ok ok ok ok ok ok
V 24.6498 44.5947 44.2806 24.3357 24.6498 44.5947 44.2806 24.3357 8.07159 9.61293
Shearing fv Remarks 0.54375 ok 0.79633 ok 0.81001 ok 0.53682 ok 0.54375 ok 0.79633 ok 0.81001 ok 0.53682 ok 0.28827 ok 0.32771 ok
Deflection δ Remarks 12.5247 ok 12.0206 ok 12.8308 ok 12.3651 ok 12.5247 ok 12.0206 ok 12.8308 ok 12.3651 ok 8.91173 ok 9.23101 ok
0.92315 0.79 1.02933 0.27468 1.04323 0.34335 0.75998 1.06367
0.06924 0.06583 0.07018 0.0206 0.07824 0.02575 0.06333 0.06648
9.43912 11.0806 15.4443 2.80859 10.667 6.85691 10.6595 12.2929
ok ok ok ok ok ok ok ok
ok ok ok ok ok ok ok ok
56
57
3.2 Design Process for Purlins, Truss, and Columns I. Design of Purlins Procedure 1. Determine the details of the truss (height, length, spacing of truss and spacing of purlins) 2. Calculate all the loads that will act on the purlins (Purlin Self Weight, Roof Sheathing Weight, Roof Live Load, and Wind Load). 3. Resolve all the loads into x and y components then sum up. 4. Solve for the bending, shearing, and deflection then check with the allowable (with adjustments).
TRUSS DETAILS Truss Truss Height
Truss Base
Truss Length
1
2.50
10.00
1.50
2
2.50
10.00
3.00
3
2.50
10.00
3.00
4
2.50
10.00
3.50
5
2.50
10.00
2.00
6
1.50
4.00
1.50
7
1.50
4.00
1.50
y/x 0.5 0 0.5 0 0.5 0 0.5 0 0.5 0 0.7 5 0.7 5
Ѳ (degrees) 26.57 26.57 26.57 26.57 26.57 36.87 36.87
Truss length is the tributary length of the truss being considered. y/x is equal to the truss height divided by half of the truss length. Ѳ is the angle of the truss.
58
PURLIN DETAILS b (mm) 150.0 0 150.0 0 150.0 0 150.0 0 150.0 0 150.0 0 150.0 0
d (mm) 100.0 0 100.0 0 100.0 0 100.0 0 100.0 0 100.0 0 100.0 0
spacing (mm)
xspacing
0.40
0.3578
0.40
0.3578
0.40
0.3578
0.40
0.3578
0.40
0.3578
0.40
0.3200
0.40
0.3200
IX
IY
1250000 0 1250000 0 1250000 0 1250000 0 1250000 0 1250000 0 1250000 0
2812500 0 2812500 0 2812500 0 2812500 0 2812500 0 2812500 0 2812500 0
The base (b), depth (d), and spacing (s) are the assumed dimensions of the purlins. X-spacing is the horizontal component of the spacing. Ix is the moment of inertia with respect to x (bd3/12), while Iy is the moment of inertia with respect to y (db3/12)
The loadings considered are the dead loads of the self-weight of the purlins and the roof sheathing, the roof live load, and the wind load acting normal to the roof. Vertical Loads 59
Dead Load Purlin Self-Weight ϒ E W (kN/m3) (MPa) (kN/m)
Live Load Roof Sheathing ϒ t W(kN/m W(LL)kP W(LL)kN/ (kN/m3) (mm) ) a m
6.8670
9780
0.1030
4.3164
20
0.0309
0.7500
0.2683
6.8670
9780
0.1030
4.3164
20
0.0309
0.7500
0.2683
6.8670
9780
0.1030
4.3164
20
0.0309
0.7500
0.2683
6.8670
9780
0.1030
4.3164
20
0.0309
0.7500
0.2683
6.8670
9780
0.1030
4.3164
20
0.0309
0.7500
0.2683
6.8670
9780
0.1030
4.3164
20
0.0276
0.7000
0.2240
6.8670
9780
0.1030
4.3164
20
0.0276
0.7000
0.2240
Total 0.402 2 0.402 2 0.402 2 0.402 2 0.402 2 0.354 6 0.354 6
The Purlin Self-Weight is equal to the product of the unit weight of the concrete and the dimension b and d. The roof sheathing weight is equal to the unit weight of the wood used times the thickness times the horizontal projection of the spacing of purlins. The live load (roof) came from NSCP Table 205-3 – Minimum Roof Live Loads. The value then is multiplied to the horizontal projection of the spacing.
Sloping WIND LOAD WL(kP a) 1.800 0 1.800 0 1.800 0 1.800 0 1.800 0 1.800 0
WL(kN/ m) 0.7200 0.7200 0.7200 0.7200 0.7200 0.7200 60
1.800 0
0.7200
The only sloping load acting on the truss is the wind load. The value of the wind load is assumed. . LOAD COMPONENTS TANGENTIA L
NORMAL Y-WL(kN/m) 0.6440 0.6440 0.6440 0.6440 0.6440 0.5760 0.5760
DL+L L 0.402 2 0.402 2 0.402 2 0.402 2 0.402 2 0.354 6 0.354 6
Total 1.046 2 1.046 2 1.046 2 1.046 2 1.046 2 0.930 6 0.930 6
X-WL(kN/m) 0.3220 0.3220 0.3220 0.3220 0.3220 0.4320 0.4320
The loads in both x and y axes (tangential and normal) are then summed up.
DESIGN PARAMETERS Shear Fv 2.490 0 2.490 0 2.490 0
Vx 0.241 5 0.483 0 0.483 0
Bending Vy 0.784 7 1.569 3 1.569 3
Fb 24.5000 24.5000 24.5000
Mx 0.090 6 0.362 2 0.362 2
Deflection My 0.294 2 1.177 0 1.177 0
δ (mm) 4.1667 8.3333 8.3333 61
2.490 0 2.490 0 2.490 0 2.490 0
0.563 5 0.322 0 0.324 0 0.324 0
1.830 9 1.046 2 0.698 0 0.698 0
24.5000 24.5000 24.5000 24.5000
0.493 1 0.161 0 0.121 5 0.121 5
1.602 0 0.523 1 0.261 7 0.261 7
9.7222 5.5556 4.1667 4.1667
We then get the design parameters from the wood properties, allowable shearing and bending stresses. Formula for beams are used to get the components of the shear and moment to be applied. The allowable deflection is L/360 and actual deflection is equal to 5wl4/384EI.
STRESS ADJUSTMENTS
Stress Adjustments Adjustment due to Other Adjustments Slenderness le F'b (m) Cs Ck (Mpa) 2.8 3.577 Non 8 71 e 24.5 5.7 5.059 Non 6 64 e 24.5 5.7 5.059 Non 6 64 e 24.5 All adjustments factors are equal to 1.0 6.7 5.465 Non 2 04 e 24.5 3.8 4.131 Non 4 18 e 24.5 2.8 3.577 Non 8 71 e 24.5 2.8 3.577 Non 8 71 e 24.5 Formula used for this is already presented in the computation of joists and beams.
62
INVESTIGATION Shearing fVT 0.024 1 0.048 3 0.048 3 0.056 3 0.032 2 0.032 4 0.032 4
fVN 0.078 5 0.156 9 0.156 9 0.183 1 0.104 6 0.069 8 0.069 8
Bending fV 0.082 1 0.164 2 0.164 2 0.191 6 0.109 5 0.077 0 0.077 0
OK! OK! OK! OK! OK! OK! OK!
fbT 0.36 22 1.44 90 1.44 90 1.97 22 0.64 40 0.48 60 0.48 60
fbN 0.784 7 3.138 6 3.138 6 4.272 0 1.394 9 0.698 0 0.698 0
fb 1.14 69 4.58 76 4.58 76 6.24 42 2.03 89 1.18 40 1.18 40
OK ! OK ! OK ! OK ! OK ! OK ! OK !
δT (mm) 0.173 6 2.777 9 2.777 9 5.146 5 0.548 7 0.232 9 0.232 9
Deflection δN δ (mm) (mm) 0.305 0.2507 0 4.879 4.0115 5 4.879 4.0115 5 9.039 7.4318 8 0.963 0.7924 8 0.322 0.2230 5 0.322 0.2230 5
OK! OK! OK! OK! OK! OK! OK!
To get the shearing stress, we get the square root of the sum of the squares of the x and y shearing stresses. To get the bending stress, we add the bending stresses in the x and y directions. To get the deflection, we get the square root of the sum of the squares of the x and y deflections. If the value is less than the allowable, the dimensions are safe, else redesign.
63
II. Design of Truss In this part, only the critical part is subjected to design. The dimension that will be taken will also be applied to all other trusses. Procedure 1. Determine all the loads acting on the truss (consider only the vertical forces). 2. Put all the uniform loads into the joints of the truss. 3. Compute for the reaction and the axial forces in the truss. 4. Check the maximum axial load for the allowable compressive stress (adjusted). TRUSS Length 10
W 2.266 11
Sheathi ng 0.0863 28
PURLINS Quanti Wpurlins ty 0.1030 05 22
LOADS Roof Wind LL Load 1.609968 0.75 94
Roof Beam 0.41202
Ceilin g 0.137 34
RESULTS Corner Load 4.38480 579
Mid Truss 8.311811 573
Mid Ceiling 0.9156
To get the quantity of the purlins, we divide the length of the truss (sloping) to the sum of the spacing and width of a purlin. We then multiply it by 2. To get the vertical loads on the truss, we get the pressures (vertical component) of the sheathing, roof live load, wind load, and weight due to the purlins and multiply it by the length. To get the vertical loads on the ceiling, we get the ceiling load and the roof beam then multiply by the length of that beam. 64
After getting the loads, they are now placed in the joints.
We then solve the reactions and the axial forces in the truss. (The axial forces in each member is shown in the next table.
Truss
b
d
Axial
Directi
Fc
Fc'
P/A
Remark 65
Member
on
AB
75
100
BD
75
100
DF
75
100
AC
75
100
CE
75
100
EG
75
100
45.67 8 44.24 1 38.86 5 40.45 1 36.98 4 28.37 1
JK
75
100
HI
75
FG
s
C
15.8
C
15.8
C
15.8
T
15.8
T
15.8
T
15.8
5.716
C
15.8
100
9.395
C
15.8
75
100
2.603
T
15.8
CD
75
100
T
15.8
FI
75
100
T
15.8
JL
75
100
C
15.8
JH
75
100
C
15.8
HF
75
100
C
15.8
KL
75
100
C
15.8
IK
75
100
C
15.8
GI
75
100
4.756 12.78 7 45.67 8 44.24 1 38.86 5 40.45 1 36.98 4 28.37 1
C
15.8
BC
75
100
5.716
C
15.8
DE
75
100
9.395
C
15.8
HK
75
100
C
15.8
EF
75
100
4.756 12.78 7
C
15.8
10.7595 046 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 8.11323 405 9.53430 476 9.53430 476 9.53430 476 9.53430 476 9.53430 476 9.53430 476 9.53430 476
6.0904
OK!
5.8988
OK!
5.182 5.3934 67
OK!
4.9312
OK!
3.7828 0.7621 33 1.2526 67 0.3470 67 0.6341 33 1.7049 33
OK!
6.0904
OK!
5.8988
OK!
5.182 5.3934 67
OK!
4.9312
OK!
3.7828 0.7621 33 1.2526 67 0.6341 33 1.7049 33
OK!
OK!
OK! OK! OK! OK! OK!
OK!
OK! OK! OK! OK!
After getting all axial forces, we try the dimensions if it is safe for the allowable compressive stress.
66
III. Design of Columns Procedure 1. Compute all the loads that is passed to the columns (from beams and trusses, considering both first and second floors). 2. Design the eccentricities of the loads. 3. Using the assumed dimensions of the columns, compute the actual compressive stress and the actual bending stresses. 4. Use the interaction formula to determine if the dimensions used are adequate for the structure. COLUMN
1st Floor
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3
REACTIONS OF P1 P2 0.615 0.433 0.615 0.537 0.537 35.744 0.807 22.409 0.433 15.298 28.522 0.672 0.672 35.744 22.409 22.409 15.298 0.552
BEAMS (kN) P3 P4 28.522 0.807
14.261 21.483
FROM TRUSS (kN)
Sum (kN) 1.048 29.675 37.088 23.216 15.731 43.455 57.899 44.817 15.850
0.552
14.261
14.746
29.559
14.746
21.483
0.731
36.960
22.409
0.731
11.706
23.140 11.706 67
2nd Floor
1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8
11.706
11.706
0.824
1.030
9.410
11.264
0.824
0.824
1.030
9.410
12.088
0.824
1.030
1.030
9.410
12.294
0.824
1.030
9.410
11.264
1.030
1.030
36.090
38.150
1.030
1.030
36.090
38.150
1.030
1.030
36.090
38.150
1.030
1.030
36.090
38.150
1.030
0.824
9.410
11.264
9.410
12.706
9.410
12.912
0.61 8 0.82 4
0.824
1.030
0.824
0.618
1.030
1.030
1.030
1.030
9.410
11.470
0.618
0.824
9.410
10.852
0.618
0.824
9.410
10.852
The table shows the reactions from the beams (P) and from the truss. The first floor columns carry the loads from the 2 nd floors beams while the second floor columns carry the loads from the roof beams and trusses. The number of P loads indicate the number of beams carried by the column. The loads are obtained from the reaction of beams from the previous chapters. To get the total load acting on the column, we add all these loads.
Load Eccentricities
68
ex = 50 mm ey = 37.5 mm
ex = 0 mm ey = 25 mm
ex = 50 mm ey = 50 mm
69
To solve for the eccentricities of the forces, the contact areas of the beams are first computed. To solve for the centroid of the areas, we use the Varignon’s theorem. We will then know the distance of the centroid of the areas to the centroid of the column. Reaction from the trusses are assumed to be concentric.
Design Parameters Columns 1ST FLR 1 2 3 4 5 6 7
Axial (P)N 1048.0 63 29674. 81 37088. 24 23215. 68 15730. 53 43455. 45 57899. 3
ex (mm)
ey (mm)
Fb (MPa)
Fc (MPa)
E (MPa)
50
37.5
24.5
15.8
9780
0
25
24.5
15.8
9780
0
25
24.5
15.8
9780
50
37.5
24.5
15.8
9780
0
25
24.5
15.8
9780
0 0
0 0
24.5 24.5
15.8 15.8
9780 9780 70
8 9 10 11 12 13 14 15 16 17 18 19 20 2ND FLR
21 22 23 24 25 26 27 28
44817. 47 15850. 3 29559. 35 36959. 69 23139. 55 11706. 23 11706. 23 11264. 09 12088. 13 12294. 14 11264. 09 38150. 1 38150. 1 38150. 1 38150. 1 11264. 09 12706. 16 12912. 17 11470. 1 10852. 07 10852. 07
0
25
24.5
15.8
9780
50
37.5
24.5
15.8
9780
0
0
24.5
15.8
9780
0
0
24.5
15.8
9780
50
37.5
24.5
15.8
9780
50
37.5
24.5
15.8
9780
50
37.5
24.5
15.8
9780
50
37.5
24.5
15.8
9780
0
25
24.5
15.8
9780
0
25
24.5
15.8
9780
50
37.5
24.5
15.8
9780
0
25
24.5
15.8
9780
0
0
24.5
15.8
9780
0
0
24.5
15.8
9780
0
25
24.5
15.8
9780
50
37.5
24.5
15.8
9780
0
0
24.5
15.8
9780
0
0
24.5
15.8
9780
50
37.5
24.5
15.8
9780
50
37.5
24.5
15.8
9780
50
37.5
24.5
15.8
9780
71
Column Properties h (m) 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2
b (mm) 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
d (mm) 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
Ix (mm4) 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667 166666667
Iy (mm4) 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667 260416667
k e
le (mm)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2
The column used in this design is assumed to be simply supported, thus the value of ke is 1. le is equal to ke(lu).
72
Length Type le/ d 18 18 18 18 18 18 18 18 18 18 18 18 18 18 16 16 16 16 16 16
le/b 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 14. 4 12. 8 12. 8 12. 8 12. 8 12. 8 12. 8
K 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2
J 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9 1.22933 9
Type INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE 73
16 16 16 16 16 16 16 16
12. 8 12. 8 12. 8 12. 8 12. 8 12. 8 12. 8 12. 8
16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2 16.6941 2
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
0.8781
INTERMEDIATE
Length type parameters; le < 11, short column 11 < le < k, intermediate column le > k, long column where,
√
E k = 0.671 Fc
,
¿ −11 d j= k −11
Compressive Stress Fc* 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8
KC E
0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3
c' 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8
FCE
Fce/F*
Fc' (MPa)
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027 74
15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8 15. 8
0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3 0. 3
0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8 0. 8
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
9.055556
0.573136
7.63027
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
11.46094
0.725376
9.041658
The formula and specifications for the adjustment of the compressive stress is shown in NSCP 2010, section 618. Bending Stress Cs
Ck
CF(x)
F'bx
CF(y)
F'by 75
3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.3941 13 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2
Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e Non e
1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82
(Mpa) 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07
1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65
(MPa) 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 76
3.2 3.2 3.2 3.2 3.2 3.2
Non e Non e Non e Non e Non e Non e
1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82 1.0460 82
25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07 25.6290 07
1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65 1.0204 65
25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81 25.0013 81
The interaction formula is equal to, fc f bx f by + + ≤ 1.0 F c ' F bx−J F c F by −J F c Where, fc is the compressive stress from the axial load, Fc is the allowable and adjusted compressive stress, fb is the actual bending stresses in x and y direction, Fb is the allowable and adjusted bending stresses in x and y directions.
The value of the interaction formula should be less than 1 for the column to be adequate, else redesign.
Interaction Formula fc 0.0262 02 0.7418 7 0.9272 06 0.5803 92 0.3932 63
fbx 0.0294 77 0.5564 03 0.6954 04 0.6529 41 0.2949 47
fby 0.0393 02 0 0 0.8705 88 0
F c' 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28
Fb'x 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01
Fb'y 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01
Result 0.1039 32 0.3478 67 0.4347 72 0.3409 73 0.1844 03
Remar ks OK! OK! OK! OK! OK! 77
1.0863 86 1.4474 83 1.1204 37 0.3962 58 0.7389 84 0.9239 92 0.5784 89 0.2926 56 0.2926 56 0.2816 02 0.3022 03 0.3073 54 0.2816 02 0.9537 53 0.9537 53 0.9537 53 0.9537 53 0.2816 02 0.3176 54 0.3228 04 0.2867 53 0.2713 02 0.2713 02
0
0
0 0.8403 28 0.4457 9
0 0 0.5943 86
0
0
0
0 0.8677 33 0.4389 83 0.4389 83 0.4224 03
0.6508 0.3292 38 0.3292 38 0.3168 03 0.2266 52 0.2305 15 0.3168 03 0.7153 14
0 0 0.4224 03 0
0
0
0 0.7153 14 0.3168 03
0 0 0.4224 03
0
0
0 0.3225 97 0.3052 14 0.3052 14
0 0.4301 29 0.4069 53 0.4069 53
2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.3726 28 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36 2.9713 36
25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01
25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01 25.629 01
0.4578 83 0.6100 76 0.5253 79 0.2327 96 0.3114 62 0.3894 38 0.3398 54 0.1719 31 0.1719 31 0.1429 65 0.1164 83 0.1184 68 0.1429 65 0.3676 19 0.3209 84 0.3209 84 0.3676 19 0.1429 65 0.1069 06 0.1086 39 0.1455 8 0.1377 36 0.1377 36
OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK! OK!
3.3 Design of Connections
78
The main material used for the joint connections of this structure is a bolt with metal plate. All connections are considered to be in double shear.
Figure 21. Double-Shear (Theoretical)
Figure 22. Double Shear (Actual)
I. Beam-Column Connection The types of connection for beam-column depends on the number of beams which receive support from columns. The figures below show the dimensions of the column and the dimensions to be extracted from it. the
The broken lines show the area to be extracted from the column, and to be added to the beam for connection.
The
first type shows a column with two beams connected in it, which is usually a corner column. The second type is a column with three beams most likely a side column. Lastly, the third type is a column with four beams connected which is most of the time an interior column.
79
FRONT VIEW
SIDE VIEW
The number of bolts is to be solved in the next sections. This figure shows the interaction that will happen in the face of the column.
Figure 23. Beam to Column Connection 80
This figure shows the 3D view (X-ray form) of the connection between the beam and column. Beam-Girder (Beam-Beam)
Figure 24. Beam to Beam Connection
The beam-girder connection is almost the same with beam-column. In this structure, there are only two beam-girder connections and thus no need for type specification.
Truss-Column (Truss-Beam) 81
This figure shows the connection of an inclined member of truss to column. Like the other connections, this is a double shear using bolts. The rafters of the truss will be bolted to the extended part of the column.
Figure 25. Truss to Column Connection
82
I. Beam-Column, Beam-Beam Process 1. Determine the vertical (shear) forces in the member ends to be connected to other members. 2. Determine the length of bolt in main member, the diameter of the bolt, and the allowable loads the bolt could carry. 3. Compute for the number of bolts needed and spacing.
For Second Floor (Beam-Column) Connection F4-B1 C1 FA-B1 FA-B1 C2 F3-B1 FA-B2 FA-B2 C3 F2-B1 FA-B3 FA-B3 C4 F1-B1 F4-B1 C5 F4-B2 FB-B1 FB-B1 F3-B1 C6 F3-B2 FB-B2 FB-B2 F2-B1 C7 F2-B2 FB-B3 FB-B3 C8 F1-B1 F1-B2 F4-B2 C9 FD-B1 FD-B1 F3-B2 C10 FD-B2 F3-B3
Type 1 2
2 1 2
3
3
2 1
3
Beam L 5 4 4 5 4 4 5 5 5 5 5 5 4 4 5 5 4 4 5 5 5 5 5 5 5 4 4 5 4 3
W 6.5826853 0.40068431 0.40068431 11.9753195 0.42320048 0.42320048 14.8984245 0.51162045 0.51162045 9.495686 6.5826853 6.5826853 0.171675 0.171675 11.9753195 6.150751 0.490749 0.490749 14.8984245 9.108191 0.171675 0.171675 9.495686 9.495686 6.5826853 0.43070588 0.43070588 6.150751 7.7678328 0.27468
V 16.45671 0.801369 0.801369 29.9383 0.846401 0.846401 37.24606 1.279051 1.279051 23.73922 16.45671 16.45671 0.34335 0.34335 29.9383 15.37688 0.981498 0.981498 37.24606 22.77048 0.429188 0.429188 23.73922 23.73922 16.45671 0.861412 0.861412 15.37688 15.53567 0.41202
x 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
Φ 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
Q 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84
N 2 1 1 4 1 1 4 1 1 3 2 2 1 1 4 2 1 1 4 3 1 1 3 3 2 1 1 2 2 1 83
C11
C12 C13 C14
FD-B2 F2-B2 FD-B3 F2-B3 FD-B3 F1-B2 F3-B3 FE-B1 F3-B2 FE-B1
4 5 4 3 5 5 3 4 3 4
3
2 2 2
7.7678328 9.108191 0.4811697 0.27468 0.4811697 9.495686 0.27468 6.21363008 0.27468 6.21363008
15.53567 22.77048 0.962339 0.41202 1.202924 23.73922 0.41202 12.42726 0.41202 12.42726
100 100 100 100 100 100 100 100 100 100
16 16 16 16 16 16 16 16 16 16
9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84
2 3 1 1 1 3 1 2 1 2
W is the total weight carried by the beam V is the reaction of the beam (WL/2) x is the length of the main member of the connection Φ is the diameter of the bolt Q is the load perpendicular to the grain N is the number of bolts needed for the connection. (V/Q) *Values of x and Φ are chosen by the designer, resulting to a value of Q (from Table 6.17 NSCP 2010).
For Roof (Beam-Column) Connection F4-B1 C15 FA-B1 FA-B1 C16 F3-B1 FA-B2 FA-B2 C17 F2-B1 FA-B3 FA-B3 C18 F1-B1 F4-B1 C19 F4-B2 FB-B1 FB-B1 C20 F3-B1
Type 1 2
2 1 2 3
Beam L 5 4 4 5 4 4 5 5 5 5 5 5 4 4 5
W 0.6867 0.54936 0.54936 0.6867 0.54936 0.54936 0.6867 0.6867 0.6867 0.6867 0.6867 0.6867 0.54936 0.54936 0.6867
V 1.71675 1.09872 1.09872 1.71675 1.09872 1.09872 1.71675 1.71675 1.71675 1.71675 1.71675 1.71675 1.09872 1.09872 1.71675
x 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
Φ 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
Q 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84
n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 84
C21
C22 C23
C24
C25
C26 C27 C28
Connect ion
F3-B2 FB-B2 FB-B2 F2-B1 F2-B2 FB-B3 FB-B3 F1-B1 F1-B2 F4-B2 FD-B1 FD-B1 F3-B2 FD-B2 F3-B3 FD-B2 F2-B2 FD-B3 F2-B3 FD-B3 F1-B2 F3-B3 FE-B1 F3-B2 FE-B1
Beam L
5 4 4 5 5 5 5 5 5 5 4 4 5 4 3 4 5 4 3 5 5 3 4 3 4
3
2 1
3
3
2 2 2
W
F3-B2 5 F2-B2 5 Beam-Beam (2nd Floor Only) FC-B1
0.6867 0.54936 0.54936 0.6867 0.6867 0.6867 0.6867 0.6867 0.6867 0.6867 0.54936 0.54936 0.6867 0.54936 0.41202 0.54936 0.6867 0.54936 0.41202 0.6867 0.54936 0.41202 0.54936 0.41202 0.54936
V
1.71675 1.09872 1.09872 1.71675 1.71675 1.71675 1.71675 1.71675 1.71675 1.71675 1.09872 1.09872 1.71675 1.09872 0.61803 1.09872 1.71675 1.09872 0.61803 1.71675 1.3734 0.61803 1.09872 0.61803 1.09872
X
2.406962 6.017404 2.406962 6.017404
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
Φ
Q
100 100
16 16
16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84 9.84
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
n 9840 9840
1 1
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II. Truss-Column, Truss-Beam Determine the vertical (shear) forces in the member ends to be connected to other members.
1. Determine the length of bolt in main member, the diameter of the bolt, and the allowable loads the bolt could carry. 2. Compute for the number of bolts needed and spacing.
Truss-Column Connection AB C1 AC FG EG C5 IG JL C9 KL
Type 1 2 1
A 45.678 40.451 2.603 28.371 28.371 45.678 40.451
x 100 100 100 100 100 100 100
Φ 16 16 16 16 16 16 16
P 14.2 0 0 14.2 14.2 14.2 0
Q 9.84 9.84 9.84 0 0 9.84 9.84
Ѳ (rad) cosѲ sinѲ 0.4636 0.8944 0.4472 1 0 1 0 0 1 0 1 0.4636 0.8944 0.4472 1 0
R 13.0441 9.8400 9.8400 14.2000 14.2000 13.0441 9.8400
n 4 5 1 2 2 4 5
A is the axial for from the truss member x is the length of the main member of the connection Φ is the diameter of the bolt P is the load perpendicular to the grain Q is the load perpendicular to the grain R is the resultant of P and Q (Using Hankinson’s Formula) R=
PQ 2 P sin Ѳ+Qcos Ѳ 2
N is the number of bolts needed for the connection. (V/R) *Values of x and Φ are chosen by the designer, resulting to a value of P and Q (from Table 6.17 NSCP 2010). *THIS DESIGN APPLIES TO ALL TRUSSES OF THE STRUCTURE WHOSE MEMBER/S IS/ARE CONNECTED TO A COLUMN.
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Truss-Beam Connection AB FA-B1 AC FG EG FB-B1 IG JL FD-B1 KL
Type 1 2 1
A 45.678 40.451 2.603 28.371 28.371 45.678 40.451
x 100 100 100 100 100 100 100
Φ 16 16 16 16 16 16 16
P 14.2 0 0 14.2 14.2 14.2 0
Q 9.84 9.84 9.84 0 0 9.84 9.84
Ѳ (rad) cosѲ sinѲ 0.4636 0.8944 0.4472 1 0 1 0 0 1 0 1 0.4636 0.8944 0.4472 1 0
R 13.0441 9.8400 9.8400 14.2000 14.2000 13.0441 9.8400
A is the axial for from the truss member x is the length of the main member of the connection Φ is the diameter of the bolt P is the load perpendicular to the grain Q is the load perpendicular to the grain R is the resultant of P and Q (Using Hankinson’s Formula) R=
PQ P sin Ѳ+Qcos2 Ѳ 2
N is the number of bolts needed for the connection. (V/R) *Values of x and Φ are chosen by the designer, resulting to a value of P and Q (from Table 6.17 NSCP 2010).
*THIS DESIGN APPLIES TO ALL TRUSSES OF THE STRUCTURE WHOSE MEMBER/S IS/ARE CONNECTED TO A BEAM.
87
n 4 5 1 2 2 4 5
CHAPTER 4. DESIGN SCHEDULES AND SUMMARY
4.1. Joists
S-1 S-2 S-3 S-4 S-5 S-6 S-7
Computed Actual b d b d Ground Floor 100 170 100 220 100 170 100 220 100 220 100 220 100 170 100 220 100 170 100 220 100 220 100 220 100 130 100 220
o.c. 400 400 400 400 400 400 400
Second Floor S-1 S-2 S-3 S-4 S-5 S-6
100 100 100 100 100 100
170 170 220 170 70 220
100 100 100 100 100 100
220 220 220 220 220 220
S-7
100
140
100
220
400 400 400 400 400 400 400
88
4.2. Beam/Girder Schedule
F4-B1 F3-B1 F2-B1 F1-B1 F4-B2
Computed Actual b d b d Ground Floor 200 340 100 420 200 420 100 420 200 410 100 420 200 340 100 420 200 340 100 420
F3-B2
200
420
100
420
F2-B2 F1-B2 FD-B2 FE-B1 FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
200 200 200 200 200 200 200 200 200 200 200 200
410 340 210 220 100 90 110 100 100 100 90 120
100 100 100 100 100 100 100 100 100 100 100 100
420 420 220 220 120 120 120 120 120 120 120 120
F4-B1 F3-B1 F2-B1 F1-B1 F4-B2 F3B2* F2B2* F1-B2 FC-B1 FD-B2 FE-B1 FA-B1 FA-B2 FA-B3 FB-B1 FB-B2 FB-B3 FD-B1 FD-B3
Computed Actual b d b d Second Floor 200 300 200 390 200 360 200 390 200 390 200 390 200 330 200 390 200 300 200 390 200
290
200
390
200 200 200 200 200 200 200 200 200 200 200 200 200
330 330 170 250 240 90 90 120 100 100 100 90 120
200 200 200 200 200 200 200 200 200 200 200 200 200
390 390 170 250 250 120 120 120 120 120 120 120 120
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4.3. Columns
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Computed Actual b d b d 1st - 2nd Floor 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250
15 16 17 18 19 20 21 22 23 24 25 26 27 28
Computed Actual b d b d 2nd Flr - Roof 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250 250 200 250 250
90
APPENDIX - REFERENCES Books
Association of Structural Engineers of the Philippines. National Structural Code of the Philippines 2010. Quezon City, Philippines: Association of Structural Engineers of the Philippines, Inc. Aghaveree, A. & Vigil, J. Structural and Wood Design – A Practice-Oriented Approach Using the ASD Method.
Websites
http://www.bca.gov.sg/publications/BuildabilitySeries/others/prh_s2.pdf http://elearning.vtu.ac.in/P6/enotes/CV61/Beams-GS.pdf http://www.kultur.gov.tr/EN,35285/wood-as-a-building-material-its-benefitsand-disadvanta-.html www.google.com
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