Timber Design Of A Two Storey House

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 FLAMING LAZO

Submitted to Engr. Billy I. Rejuso

1

October, 2015

2

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 fulfillment 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

13

Figure 6. Front Elevation

Figure 7. Rear Elevation

14

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

18

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

85

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.

86

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

89

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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