Building Structure Project 2

BUILDING STRUCTURES (BLD61003) ASSIGNMENT 2 : STRUCTURAL ANALYSIS OF A BUNGALOW

AKANAKA RESIDENCE, JAKARTA, INDONESIA (RAW ARCHITECTS)

TUTOR: MR. MOHD. ADIB RAMLI

CHEN LIAN LIAN (AGNES) CHONG MIN (CADENCE) LEE JIA YEE (REBECCA) NG JING YUAN NANG AYE MYAT MON SIM LI MEI

0333357 0333339 0333311 0331472 0328627 0328623

TABLE OF CONTENTS

1.0

Introduction

2.0

Architectural Plans 2.1 2.2 2.3

Ground Floor Plan First Floor Plan Roof Plan

3.0

Structural Brief

4.0

Structural Plans 4.1 4.2 4.3

5.0

9

10 11 12

Ground Floor Load Distribution Plan First Floor Load Distribution Plan Roof Load Distribution Plan

13 14 15

Column Tributary Area Diagrams 6.1 6.2 6.3

7.0

6 7 8

Load Distribution Plans 5.1 5.2 5.3

6.0

Ground Floor Structural Plan First Floor Structural Plan Roof Structural Plan

5

Ground Floor Columns Tributary Area Diagram First Floor Columns Tributary Area Diagram Roof Columns Tributary Area Diagram

16 17 18

Sim Li Mei - Beam and Column Analysis

19

7.1

Selected Beams and Columns

20

7.2

Beam Analysis 7.2.1 Uniform Distribution Load 7.2.2 Point Load & UDL

21 25

Column Analysis 7.3.1 Perimeter Column 7.3.2 Internal Column

31 35

7.3

2

8.0

Nang Aye Myat Mon - Beam and Column Analysis

39

8.1

Selected Beams and Columns

40

8.2

Beam Analysis 8.2.1 Uniform Distribution Load 8.2.2 Point Load & UDL

41 45

Column Analysis 8.3.1 Perimeter Column 8.3.2 Internal Column

51 55

8.3

9.0

Ng Jing Yuan - Beam and Column Analysis

59

9.1

Selected Beams and Columns

60

9.2

Beam Analysis 9.2.1 Uniform Distribution Load 9.2.2 Point Load & UDL

61 65

Column Analysis 9.3.1 Perimeter Column 9.3.2 Internal Column

71 75

9.3

10.0 Lee Jia Yee - Beam and Column Analysis

79

10.1 Selected Beams and Columns

80

10.2 Beam Analysis 10.2.1 Uniform Distribution Load 10.2.2 Point Load & UDL

81 85

10.3 Column Analysis 10.3.1 Perimeter Column 10.3.2 Internal Column

91 95

3

11.0 Chong Min - Beam and Column Analysis

99

11.1 Selected Beams and Columns

100

11.2 Beam Analysis 11.2.1 Uniform Distribution Load 11.2.2 Point Load & UDL

101 105

11.3 Column Analysis 11.3.1 Perimeter Column 11.3.2 Internal Column

113 117

12.0 Chen Lian Lian - Beam and Column Analysis

121

12.1 Selected Beams and Columns

122

12.2 Beam Analysis 12.2.1 Uniform Distribution Load 12.2.2 Point Load & UDL

123 127

12.3 Column Analysis 12.3.1 Perimeter Column 12.3.2 Internal Column

133 137

4

1.0

INTRODUCTION

Exterior (above) and interior (right) view of Akanaka Residence, Jakarta, Indonesia. (Archdaily, 2016)

In this group cum individual assignment, we were given to task to obtain a set of architectural drawings for a 2-storey bungalow. We were then required to redraw and simplify the plans to only grid lines, dimensions and room labels.

The bungalow plan drawings used in this assignment was obtained from an online source: https://www.archdaily.com/791281/akanaka-raw-architecture. This bungalow, named Akanaka, is located in Jakarta, Indonesia designed by RAW Architects.

The architectural plan was redrawn and modified in AutoCAD requirements of the assignment.

in order to suit the

Among the lists of drawings produced were ground floor structural plan, first floor structural plan and the roof structural plan.The subsequent structural plans were then duplicated in order to be turned into load distribution plans and columns tributary area, 2 beams and 2 columns were chosen among the group members, prior in conducting the structural analysis and respective calculations: - One (1) beam with point load and uniformly distributed load - One (1) beam with only uniformly distributed load - One internal column (from roof to ground level) - One perimeter column (from roof to ground level) Along with the calculations, we were also required to produce load diagrams, shear force diagrams and bending moment diagrams, whereas for the column, the ultimate load for the column is analysed.

5 Images above shows the interior spaces of the house. (Archdaily, 2016)

2.0

ARCHITECTURAL PLANS 2.1

GROUND FLOOR PLAN

Ground Floor Plan Scale 1:200 6

2.0

ARCHITECTURAL PLANS 2.2

FIRST FLOOR PLAN

First Floor Plan Scale 1:200 7

2.0

ARCHITECTURAL PLANS 2.3

ROOF PLAN

Roof Plan Scale 1:200 8

3.0

STRUCTURAL BRIEF

(Quantity Life and Dead Loads Acting on Structure) Dimension of structure Structure

Dimension

Slab

0.15m (thickness)

Wall

0.15m X 3.0m (thickness X height)

Beam

0.2m X 0.3 m (width X depth)

Column

0.3m X 0.3m X 3.0m (width X length X height)

Standard Weight of Material Material

Standard Weight (kN/m³)

Brickwork

19

Reinforced concrete

24

Structure Self-Weight Structure

Calculation

Self-weight

Concrete slab

0.15m X 24kN/m³

3.6kN/m²

Brick wall

0.15m X 3.0m X 19kN/m³

8.6kN/m

Beam

0.2m X 0.3m X 24kN/m³

1.4kN/m

Column

0.3m X 0.3m X 3.0m X 24kN/m³

6.5kN/m²

Roof

-

1.0kN/m² 9

4.0

STRUCTURAL PLANS 4.1

GROUND FLOOR STRUCTURAL PLAN

Ground Level Structural Plan Scale 1:200

10

4.0

STRUCTURAL PLANS 4.2

FIRST FLOOR STRUCTURAL PLAN

First Level Structural Plan Scale 1:200

11

4.0

STRUCTURAL PLANS 4.3

ROOF STRUCTURAL PLAN

Roof Structural Plan Scale 1:200

12

5.0

LOAD DISTRIBUTION PLANS 5.1

GROUND FLOOR LOAD DISTRIBUTION PLAN

Ground Level (Load Distribution Plan) Scale 1:200

13

5.0

LOAD DISTRIBUTION PLANS 5.2

FIRST FLOOR LOAD DISTRIBUTION PLAN

First Level (Load Distribution Plan) Scale 1:200

14

5.0

LOAD DISTRIBUTION PLANS 5.3

ROOF LOAD DISTRIBUTION PLAN

Roof Level (Roof Load Distribution Plan) Scale 1:200

15

6.0

COLUMNS TRIBUTARY AREA DIAGRAM 6.1

GROUND FLOOR COLUMNS TRIBUTARY AREA DIAGRAM

Ground Level (Columns Tributary Area Diagram) Scale 1:200

16

6.0

COLUMNS TRIBUTARY AREA DIAGRAM 6.2

FIRST FLOOR COLUMNS TRIBUTARY AREA DIAGRAM

First Level (Columns Tributary Area Diagram) Scale 1:200

17

6.0

COLUMNS TRIBUTARY AREA DIAGRAM 6.3

ROOF LEVEL COLUMNS TRIBUTARY AREA DIAGRAM

Roof Level (Columns Tributary Area Diagram) Scale 1:200

18

7.0

SIM LI MEI

BEAM AND COLUMN ANALYSIS 7.1

Selected Beams and Columns

7.2 Beam Analysis 7.2.1 Uniform Distribution Load -First Floor Beam B-C / 14a 7.2.2 Point Load & UDL -First Floor Beam B/13-15 7.3 Column Analysis 7.3.1 Perimeter Column -Column C/13 7.3.2 Internal Column -Column B/13

19

7.1

SELECTED BEAMS AND COLUMNS

Perimeter Column - Column B / 13

Point Load & UDL - Beam B/ 13-15

Internal Column - Column C / 13

Uniform Distribution Load Beam Beam B-C / 14a

20

7.2

BEAM ANALYSIS 7.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 14a First Floor Beam B-C / 14a carries: -

Dead load from beam self weight: gridline B-C/14a

-

Dead load from brick wall weight: gridline B-C/14a

-

Dead load from slab: gridline B-C/13-14a & B-C/14a - 15

-

Live load from slab: gridline B-C/13-14a & B-C/14a-15

First floor structural plan

First floor load distributary plan

21

7.2

BEAM ANALYSIS 7.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 14a B Dead Load

C 3.43m 1.4kN/m

Beam self weight = (0.2 X 0.3) m² X 24kN/m³ = 1.44kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² X 19kN/m³ = 8.6kN/m

Slab B-C/13-14a = (2.77m/2) X (0.15m X 24kN/m³) = 1.385m X 3.6kN/m³ = 5kN/m

5kN/m

2.7kN/m Slab B-C/14a-15 = (1.48m/2)X (0.15m X 24kN/m³) = 0.74m X 3.6kN/m³ = 2.7kN/m

17.7kN/m Total Dead Load = 1.4kN/m + 8.6kN/m + 5kN/m + 2.7kN/m = 17.7kN/m

22

7.2

BEAM ANALYSIS 7.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 14a Live Load Slab B-C/13-14a = (2.77m/2) X 1.5kN/m² = 1.385m X 1.5kN/m² = 2.1kN/m

Slab B-C/14a - 15 = (1.48m/2) X 1.5kN/m² = 0.74m X 1.5kN/m² = 1.1kN/m

Total live load = 2.1kN/m + 1.1kN/m = 3.3kN/m

B

C 3.43m 2.1kN/m

1.1kN/m

3.3kN/m

Ultimate Load 24.8kN/m Ultimate dead load = 17.7kN/m X 1.4 = 24.8kN/m

5.3kN/m Ultimate live load = 3.3kN/m X 1.6 = 5.3kN/m

30.1kN/m Total ultimate load = 24.8kN/m + 5.3kN/m = 30.1kN/m 23

7.2

BEAM ANALYSIS 7.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 14a B

C

3.43m

Resultant Force

30.1kN/m

= 30.1kN/m X 3.43m = 103.2kN

3.43m Reaction Force ∑MD = 0 = Rb (3.43) – 103.2(3.43/2) = 3.43Rb – 177 Rb = 51.6kN

1.715m

1.715m

Fᵣ = 103.2kN

∑Fy = 0 = Rc + 51.6 - 103.2 Rc = 51.6kN

Rb

Ra

3.43m 1.715m

1.715m

30.1kN/m

Rb = 51.6kN

Rc = 51.6kN

Shear force diagram 51.6kN - 103.2kN = -51.6kN

51.6kN -51.6kN+51.6kN = 0kN

+

-51.6kN + 51.6kN = 0kN 0kN

Bending moment diagram 44.2kNm

Positive area 51.6kN X 1.715m X (½) = 44.2kNm Negative area 51.6kN X 1.715m X (½) = 44.2kNm Hence, Positive area = Negative area

0kN

51.6kN - 103.2kN = -51.6kN

0kN 24

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

First Floor Beam B / 13-15

First Floor Beam B/13-15 carries: -

Dead load from beam self weight: gridline B/13-15

-

Dead load from brick wall weight: gridline B/13-14a

-

Dead load from slab: gridline B-C/13-14a

-

Live load from slab: gridline B-C/13-14a

-

Point load at point B/14a from beam B-C/14a

First floor structural plan

First floor load distributary plan

25

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

First Floor Beam B / 13-15 Dead Load

13

14a 4.25m 2.77m

15 1.48m

1.4kN/m

Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.4kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.6kN/m

3.2kN/m Slab B-C/13-14a = [(2.77m / 2) (⅔)] x (0.15m x 24kN/m³) = 0.9m x 3.6kN/m³ = 3.2kN/m 13.2kN/m Total Dead Load

1.4kN/m

Beam B/13-14a = 1.4kN/m + 8.6kN/m + 3.2kN/m = 13.2kN/m Beam B/14a-15 = 1.4kN/m

26

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

First Floor Beam B / 13-15 13 Live Load Slab B-C/13-14a = [(2.77m / 2) (⅔)] x 1.5kN/m² = 0.9m x 1.5kN/m² = 1.4kN/m

14a 4.25m 2.77m 1.4kN/m

15 1.48m

1.4kN/m Total Live Load Beam B/13-14a = 1.4kN/m

27

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

First Floor Beam B / 13-15 Ultimate Load

13

14a 4.25m 2.77m

15 1.48m

Ultimate dead load Beam B/13-14a = 13.2kN/m x 1.4 = 18.5kN/m

18.5kN/m 2kN/m

Beam B/14a-15 = 1.4kN/m x 1.4 = 2kN/m

2.7kN/m Ultimate live load Beam B/13-14a = 1.4kN/m x 1.6 = 2.7kN/m

Total ultimate load

21.2kN/m 2kN/m

Beam B/13-14a = 18.5kN/m + 2.7kN/m = 21.2kN/m Beam B/14a-15 = 2kN/m

51.6kN 21.2kN/m Point Load from beam B-C/14a = 51.6kN

2kN/m

28

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

First Floor Beam B / 13-15

13

14a 4.25m 2.77m

Resultant Force Point load at point B/14a = 51.6kN

15 1.48m

51.6kN/m 21.2kN/m

Resultant Force, Fr1 = 21.2kN/m x 2.77m = 58.7kN

2kN/m

Resultant Force, Fr2 = 2kN/m x 1.48m = 3kN

Reaction Force ∑M =0 = Ra(4.25) + [-58.7 (2.865)] + [-51.6(1.48)] + [-3(0.74)] = 4.25Ra – 168.176 – 76.368– 2.22 4.25Ra = 246.764 Ra = 58.1kN

4.25m 2.77m 1.385m

1.48m

1.385m

0.74m 0.74m

51.6kN/m 21.2kN/m 2kN/m

∑Fy = 0 = 58.1 + Rb + (–58.7) + (–51.6) + (–3) Rb = 55.2kN Ra = 58.1kN

Rb = 55.2kN

29

7.2

BEAM ANALYSIS 7.2.2 POINT LOAD & UDL

13

14a

15

First Floor Beam B / 13-15 4.25m 2.77m

Shear force diagram 58.1kN - [21.2kN/m (2.77m)] = 58.1kN - 58.7kN = -0.6kN

1.385m

1.48m

1.385m

0.74m 0.74m

51.6kN/m

– 0.6kN – 51.6kN = –52.2kN

21.2kN/m

2kN/m

– 52.2kN – [2kN/m (1.48m)] = – 52.2kN – 3kN = – 55.2kN – 55.2kN + 55.2kN = 0kN Ra = 58.1kN

Rb = 55.2kN

2.77

58.1

58.1kN

x

–55.2kN + 55.2kN = 0kN

+

0.6 0kN

Triangular proportion method x / 2.77 = 0.6 / (0.6+58.1) x = 0.028

58.1kN - 58.7kN = – 0.6kN

– -0.6kN - 51.6kN = – 52.2kN

Bending moment diagram Positive area = 0.5 X 58.1 X (2.77 - 0.028 ) = 0.5 X 58.1 X 2.742 = 79.7 kNm Negative area = [0.5 (0.6) (0.028)] + [0.5(52.2 + 55.2)(1.48)] = 0.008 + 77.4 = 79.5 kNm Positive area - negative area = 79.7kNm - 79.5kNm = 0.2kNm ≈ 0kNm

– 52.2kN – 3kN = – 55.2kN

79.5kNm

30

7.3

COLUMN ANALYSIS 7.3.1 PERIMETER COLUMN - Column B/13

ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (3.175m x 1.715m) x 1.0kN/m² = 5.4kN

Total dead load = 5.4kN + 6.8kN = 12.2kN

Live Load Roof beam = (3.175 + 1.715)m x 1.4kN/m = 6.8kN

Roof weight = (3.175m x 1.715m) x 0.5kN/m² = 2.7kN

31

7.3

COLUMN ANALYSIS 7.3.1 PERIMETER COLUMN - Column B/13

FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = (3.175m x 1.715m) x 3.6kN/m² = 19.6kN

Total dead load = 19.6kN + 6.8kN + 27.3kN + 6.5kN = 60.2kN

Beam self weight = (3.175 + 1.715)m x 1.4kN/m = 6.8kN

Live Load

Brick wall = 3.175m x 8.6kN/m = 27.3kN

Concrete slab = (3.175m x 1.715m) x 1.5kN/m² = 8.2kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 32

7.3

COLUMN ANALYSIS 7.3.1 PERIMETER COLUMN - Column B/13

GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = (3.175m x 1.715m) x 3.6kN/m² = 19.6kN Beam self weight = (3.175 + 1.715)m x 1.44kN/m = 6.8kN

Total dead load = 19.6kN + 6.8kN + 27.3kN + 6.5kN = 60.2kN

Live Load Brick wall = 3.175m x 8.6kN/m = 27.3kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = (3.175m x 1.715m) x 1.5kN/m² = 8.2kN

33

7.3

COLUMN ANALYSIS 7.3.1 PERIMETER COLUMN - Column B/13

Ultimate Load Total dead load = 12.2kN + 60.2kN + 60.2kN = 132.6kN Total live load = 2.7kN + 8.2kN + 8.2kN = 19.1kN

Ultimate dead load = 132.6kN x 1.4 = 185.6kN

Ultimate live load = 19.1kN x 1.6 = 30.6kN

Total ultimate load = 185.6kN + 30.6kN = 216.2kN

34

7.3

COLUMN ANALYSIS 7.3.1 INTERNAL COLUMN - Column C/13

ROOF LEVEL

Dead load Roof weight = (3.42m x 4.08m) x 1.0kN/m² = 14kN

Total dead load = 14kN + 10.5kN = 24.5kN

Live Load Roof beam = (3.42m + 4.08m) x 1.4kN/m = 10.5kN

Roof weight = (3.42m x 4.08m) x 0.5kN/m² = 7kN

35

7.3

COLUMN ANALYSIS 7.3.1 INTERNAL COLUMN - Column C/13

FIRST LEVEL

Dead load Concrete slab = [(3.42m x 4.08m)]x 3.6kN/m² = 14m² x 3.6kN/m² = 50.4kN Beam self weight = (3.42m + 4.08m) x 1.4kN/m = 10.5kN Brick wall = 4.08m x 8.6kN/m = 35.1kN

Total dead load = 50.4kN + 10.5kN + 35.1kN + 6.5kN = 102.3kN

Live Load Concrete slab = [(3.42m x 4.08m)] x 1.5kN/m² = 14m² x 1.5 kN/m² = 21kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 36

7.3

COLUMN ANALYSIS 7.3.1 INTERNAL COLUMN - Column C/13

GROUND LEVEL

Dead load Concrete slab = (3.42m x 4.08m) x 3.6kN/m² = 50.2kN

Total dead load = 50.2kN + 10.5kN + 35.1kN + 6.5kN = 102.3kN

Beam self weight = (3.42m + 4.08m)x 1.4kN/m = 10.5kN

Live Load

Brick wall = 4.08m x 8.6kN/m = 35.1kN

Concrete slab = (3.42m x 4.08m) x 1.5kN/m² = 20.9kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 37

7.3

COLUMN ANALYSIS 7.3.1 INTERNAL COLUMN - Column C/13

Ultimate Load Total dead load = 24.5kN + 102.3kN + 102.3kN = 229.1kN Total live load = 7kN + 21kN + 20.9kN = 48.9kN

Ultimate dead load = 229.1kN x 1.4 = 320.7kN

Ultimate live load = 48.9kN x 1.6 = 78.2kN

Total ultimate load = 320.7kN + 78.2kN = 398.9kN

38

8.0

NANG AYE MYAT MON

BEAM AND COLUMN ANALYSIS 8.1 Selected Beams and Columns 8.2 Beam Analysis 8.2.1 Uniform Distribution Load -First Floor Beam B-C / 3a 8.2.2 Point Load & UDL -First Floor Beam B/3-4 8.3 Column Analysis 8.3.1 Perimeter Column -Column C/3 8.3.2 Internal Column -Column B/3

39

8.1

SELECTED BEAMS AND COLUMNS

Perimeter Column - Column B / 3

Point Load & UDL - Beam B/ 3-4

Internal Column - Column C / 3

Uniform Distribution Load Beam Beam B-C / 3a

40

8.2

BEAM ANALYSIS 8.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 3a First Floor Beam B-C / 3a carries: -

Dead load from beam self weight: gridline B-C/3a

-

Dead load from brick wall weight: gridline B-C/3a

-

Dead load from slab: gridline B-C/3-3a & B-C/3a - 4

-

Live load from slab: gridline B-C/3-3a & B-C/3a - 4

First floor structural plan

First floor load distributary plan

41

8.2

BEAM ANALYSIS 8.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 3a

Dead Load

B

3.43m

C

1.4kN/m Beam self weight = (0.2 X 0.3) m² X 24kN/m³ = 1.44kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² X 19kN/m³ = 8.6kN/m

Slab B-C/3-3a = (1.83m/2) X (0.15m X 24kN/m³) = 0.915m X 3.6kN/m³ = 3.3kN/m

3.3kN/m

2.61kN/m Slab B-C/4-4a = (1.45m/2)X (0.15m X 24kN/m³) = 0.725m X 3.6kN/m³ = 2.61kN/m

15.9kN/m Total Dead Load = 1.4kN/m + 8.6kN/m +3.3kN/m + 2.61kN/m = 15.9kN/m

42

8.2

BEAM ANALYSIS 8.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 3a Live Load Slab B-C/3-3a = (1.83m/2) X 1.5kN/m² = 0.915m X 1.5kN/m² = 1.4kN/m

Slab B-C/3a - 4 = (1.45m/2) X 1.5kN/m² = 0.725m X 1.5kN/m² = 1.1kN/m

Total live load = 1.4kN/m + 1.1kN/m = 2.5kN/m

B

C 3.43m 1.4kN/m

1.1kN/m

2.5kN/m

Ultimate Load 22.3kN/m Ultimate dead load = 15.9kN/m X 1.4 = 22.3kN/m

4kN/m Ultimate live load = 2.5kN/m X 1.6 = 4kN/m

26.3kN/m Total ultimate load = 22.3kN/m + 4kN/m = 26.3kN/m 43

8.2

BEAM ANALYSIS 8.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 3a B

C

3.43m

Resultant Force

26.3kN/m

= 26.3kN/m X 3.43m = 90.2kN

3.43m Reaction Force ∑MD = 0 = Rb (3.43) – 90.2(3.43/2) = 3.43Rb – 154.7 Rb = 45.1kN

1.715m

1.715m

Fᵣ = 90.2kN

∑Fy = 0 = Rc + 45.1 - 90.2 Rc = 45.1kN

Rb

Ra

3.43m 1.715m

1.715m

26.3kN/m

Rb = 45.1kN

Rc = 45.1kN

Shear force diagram 45.1kN - 90.2kN = -45.1kN

45.1kN -45.1kN+45.1kN = 0kN

+

-45.1kN + 45.1kN = 0kN 0kN

Bending moment diagram 38.7kNm

Positive area 45.1kN X 1.715m X (½) = 38.7kNm Negative area 45.1kN X 1.715m X (½) = 38.7kNm Hence, Positive area = Negative area

0kN

45.1kN - 90.2kN = -45.1kN

0kN 44

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL

First Floor Beam B / 3-4

First Floor Beam B/3-4 carries: -

Dead load from beam self weight: gridline B/3-4

-

Dead load from brick wall weight: gridline B/3-4

-

Dead load from slab: gridline B-C/3-4

-

Live load from slab: gridline B-C/3-4

-

Point load at point B/3a from beam B-C/3a

First floor structural plan

First floor load distributary plan

45

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL

First Floor Beam B / 3-4 Dead Load

3

3a 3.28m 1.83m

4 1.45m

1.4kN/m

Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.4kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.6kN/m

2.2kN/m Slab B-C/3-3a = [(1.83m / 2) (⅔)] x (0.15m x 24kN/m³) = 0.61m x 3.6kN/m³ = 2.2kN/m 12.2kN/m Total Dead Load

1.4kN/m

Beam B/3-3a = 1.4kN/m + 8.6kN/m + 2.2kN/m = 12.2kN/m Beam B/3a-4 = 1.4kN/m

46

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL

First Floor Beam B / 3-4 3 Live Load Slab B-C/3-3a = [(1.83m / 2) (⅔)] x 1.5kN/m² = 0.61m x 1.5kN/m² = 0.9kN/m

3a 3.28m 1.83m 0.9kN/m

4 1.45m

0.9kN/m Total Live Load Beam B/3-3a = 0.9kN/m

47

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL

First Floor Beam B / 3-3a Ultimate Load

3

3a 3.28m 1.83m

4 1.45m

Ultimate dead load Beam B/13-14a = 12.2kN/m x 1.4 = 17.1kN/m

17.1kN/m 2kN/m

Beam B/14a-15 = 1.4kN/m x 1.4 = 2kN/m

1.3kN/m Ultimate live load Beam B/3-3a =0.9kN/m x 1.6 = 1.3kN/m

Total ultimate load

18.4kN/m 2kN/m

Beam B/3-3a = 17.1kN/m + 1.3kN/m = 18.4kN/m Beam B/3a-4 = 2kN/m

45.1kN 18.4kN/m Point Load from beam B-C/3a = 45.1kN

2kN/m

48

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL

First Floor Beam B / 3-4

3

3a 3.28m 1.83m

Resultant Force Point load at point B/3a = 45.1kN

4 1.45m

45.1kN/m 17.1kN/m

Resultant Force, Fr1 = 17.1kN/m x 1.83m = 31.3kN

2kN/m

Resultant Force, Fr2 = 2kN/m x 1.45m = 3kN

Reaction Force ∑M =0 = Ra(3.28) + [-31.3 (2.365)] + [-45.1(1.45)] + [-3(0.725)] = 3.28Ra – 74 – 65.4– 2.175 3.28Ra = 141.575 Ra = 43.2kN

3.28m 1.83m 0.915m

1.45m

0.915m 0.725m 0.725m 45.1kN/m

17.1kN/m 2kN/m

∑Fy = 0 = 43.2 + Rb + (–31.3) + (–45.1) + (–3) Rb = 36.2kN Ra = 43.2kN

Rb = 36.2kN

49

8.2

BEAM ANALYSIS 8.2.2 POINT LOAD & UDL 3

First Floor Beam B / 3-4

3a

4

3.28m 1.83m

Shear force diagram 43.2kN - [17.1kN/m (1.83m)] = 43.2kN - 31.3kN = 11.9kN

0.915m

1.45m

0.915m

0.725m 0.725m

45.1kN/m

11.9kN – 45.1kN = –33.2kN

17.1kN/m

2kN/m

– 33.2kN – [2kN/m (1.45m)] = – 33.2kN – 3kN = – 36.2kN Ra = 43.2kN

Rb = 36.2kN

– 36.2kN + 36.2kN = 0kN 43.2KN

(43.2-31.3) 11.9KN

+

Bending moment diagram

0KN

0KN Positive area (43.2kN + 11.9kN)X 1.83m X (½) = 50.4kNm

-33.2KN (11.9-45.1)

Negative area (-33.2kN + (-36.2kN)X 1.45m X (½) = 50.3 kNm

-

Shear Force DIagram

Positive area - Negative area =50.4 kNm - 50.3 kNm =0.1kNm

-36.2KN (-33.2-3)

50.4KNm

0.1kNm ≈ 0kNm Hence, Positive Area = Negative Area 0KN

0KN

Bending Moment DIagram

50

8.3

COLUMN ANALYSIS 8.3.1 PERIMETER COLUMN - Column B/3

ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (3.35m x 1.715m) x 1.0kN/m² = 5.7kN

Total dead load = 5.7kN + 8.3kN = 14kN

Live Load Roof beam = (3.35 + 1.715)m x 1.44kN/m = 8.3kN

Roof weight = (3.35m x 1.715m) x 0.5kN/m² = 2.85kN

51

8.3

COLUMN ANALYSIS 8.3.1 PERIMETER COLUMN - Column B/3

FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = (3.35m x 1.715m) x 3.6kN/m² = 20.7kN

Total dead load = 20.7kN + 7.1kN + 28.8kN + 6.5kN = 63.1kN

Beam self weight = (3.35 + 1.715)m x 1.4kN/m = 7.1kN

Live Load

Brick wall = 3.35m x 8.6kN/m = 28.8kN

Concrete slab = (3.35m x 1.715m) x 1.5kN/m² = 8.6kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 52

8.3

COLUMN ANALYSIS 8.3.1 PERIMETER COLUMN - Column B/3

GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = (3.35m x 1.715m) x 3.6kN/m² = 20.7kN Beam self weight = (3.35 + 1.715)m x 1.44kN/m = 7.1kN

Total dead load = 20.7kN + 7.1kN + 28.8kN + 6.5kN = 63.1kN

Live Load Brick wall = 3.35m x 8.6kN/m = 28.8kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = (3.35m x 1.715m) x 1.5kN/m² = 8.6kN

53

8.3

COLUMN ANALYSIS 8.3.1 PERIMETER COLUMN - Column B/3

Ultimate Load Total dead load = 14kN + 63.1kN + 63.1kN = 140.2kN Total live load = 2.85kN + 8.6kN + 8.6kN = 20kN

Ultimate dead load = 140.2kN x 1.4 = 196.3kN

Ultimate live load = 20kN x 1.6 = 32kN

Total ultimate load = 196.3kN + 32kN = 228.3kN

54

8.3

COLUMN ANALYSIS 8.3.1 INTERNAL COLUMN - Column C/3

ROOF LEVEL

Dead load Roof weight = (3.35m x 3.42m) x 1.0kN/m² = 11.5kN

Total dead load = 11.5kN + 9.7kN = 21.2kN

Live Load Roof beam = (3.435m + 3.42m) x 1.44kN/m = 9.7kN

Roof weight = (3.35m x 3.42m) x 0.5kN/m² = 5.7kN

55

8.3

COLUMN ANALYSIS 8.3.1 INTERNAL COLUMN - Column C/3

FIRST LEVEL

Dead load Concrete slab = [(3.35m x 3.42m) - (1.715m x 1.705m)]x 3.6kN/m² = (11.5 - 2.9)m² x 3.6kN/m² = 8.6m² x 3.6 kN/m² = 31kN

Total dead load = 31kN + 9.5kN + 28.8kN + 6.5kN = 75.8kN

Beam self weight = (3.35m + 3.42m) x 1.4kN/m = 9.5kN

Live Load

Brick wall = 3.35m x 8.6kN/m = 28.8kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = [(3.35m x 3.42m) - (1.715m x 1.705m)] x 1.5kN/m² = (11.5 - 2.9)m² x 1.5kN/m² = 8.6m² x 1.5 kN/m² = 12.9kN 56

8.3

COLUMN ANALYSIS 8.3.1 INTERNAL COLUMN - Column C/3

GROUND LEVEL

Dead load Concrete slab = (3.35m x 3.42m) x 3.6kN/m² = 41.2kN

Total dead load = 41.2kN +16kN + 29.4kN + 6.5kN = 93.1kN

Beam self weight = (3.35m x 3.42m)x 1.4kN/m = 16kN

Live Load

Brick wall = 3.42m x 8.6kN/m = 29.4kN

Concrete slab = (3.35m x 3.42m) x 1.5kN/m² = 17.2kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 57

8.3

COLUMN ANALYSIS 8.3.1 INTERNAL COLUMN - Column C/3

Ultimate Load Total dead load = 21.2kN + 75.8kN + 93.1kN = 190.1kN Total live load = 5.7kN + 12.9kN + 17.2kN = 35.8kN

Ultimate dead load = 190.1kN x 1.4 = 266.14kN

Ultimate live load = 35.8kN x 1.6 = 57.3kN

Total ultimate load = 266.14kN + 57.3kN = 323.44kN

58

9.0

NG JING YUAN

BEAM AND COLUMN ANALYSIS 9.1 Selected Beams and Columns 9.2 Beam Analysis 9.2.1 Uniform Distribution Load -First Floor Beam E-F/14a 9.2.2 Point Load & UDL -First Floor Beam E/12-15 9.3 Column Analysis 9.3.1 Perimeter Column -Column G/14 9.3.2 Internal Column -Column F/14

59

9.1

SELECTED BEAMS AND COLUMNS

First floor structural plan Scale 1:200

Perimeter Column - Column G / 14

Point Load & UDL - Beam E/12-15

Internal Column - Column F/ 14

Uniform Distribution Load Beam Beam E-F/14a

60

9.2

BEAM ANALYSIS 9.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam E-F/14a First Floor Beam E-F/14a carries: -

Dead load from beam self weight: gridline E-F/14a

-

Dead load from brick wall weight: gridline E-F/14a

-

Dead load from slab: gridline E-F/12-14a & E-F/14a - 15

-

Live load from slab: gridline E-F/12-14a & E-F/14a - 1

First floor structural plan

First floor load distributary plan

61

9.2

BEAM ANALYSIS 9.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam E-F/14a E Dead Load

F 3.75.m 1.4kN/m

Beam self weight = Beam size x density of concrete = (0.2 X 0.3) m² X 24kN/m³ = 1.4kN/m

Brick wall self weight = Brick wall size x density of brickwork = (0.15 x 3.0) m² X 19kN/m³ = 8.6kN/m

Slab E-F/12-14a =( ᴸˣ/₂ X ²/₃ ) X slab self-weight = ( 3.75/₂ X ²/₃ ) X (0.15m X 24kN/m³) = 4.5kN/m

8.6kN/m

4.5kN/m

2.7kN/m Slab E-F/14a - 15 = ( ᴸˣ/₂ ) X slab self-weight = ( 1.48/₂ ) X (0.15m X 24kN/m³) = 2.7kN/m

17.2kN/m Total Dead Load = 1.4kN/m + 8.6kN/m + 4.5kN/m + 2.7kN/m = 17.2kN/m

62

9.2

BEAM ANALYSIS 9.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam E-F/14a Live Load Slab E-F/12-14a =( ᴸˣ/₂ X ²/₃ ) X live load (UBBL) = ( 3.75/₂ X ²/₃ ) X 1.5kN/m² = 1.9kN/m

E

F 3.75m 1.9kN/m

1.1kN/m Slab E-F/14a - 15 = ( ᴸˣ/₂ ) X live load (UBBL) = ( 1.48/₂ ) X 1.5kN/m² = 1.1 kN/m

3.0kN/m Total live load = 1.9kN/m + 1.1kN/m = 3.0kN/m

Ultimate Load

24.1kN/m

Ultimate dead load = 17.2kN/m X 1.4 = 24.1kN/m

4.8kN/m Ultimate live load = 3.0kN/m X 1.6 = 4.8kN/m

28.9kN/m Total ultimate load = 24.1kN/m + 4.8kN/m = 28.9kN/m 63

9.2

BEAM ANALYSIS 9.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam E-F/14a E

F

3.75m

Resultant Force

28.9kN/m

= 28.9kN/m X 3.75m =108.4kN

3.75m Reaction Force ∑MF = 0 (Ra x 3.75 ) - (108.4 x 1.875) = 0 3.75Ra = 203.25 Ra = 54.2kN

∑Fy = 0 54.2 - 108.4 + Rb = 0 Rb = 54.2kN

1.875m

1.875m

Fᵣ = 108.4kN

Rb =54.2kN

Ra=54.2kN

54.2kN

Shear force diagram (V) 54.2kN - 108.4kN = -54.2kN

-54.2kN+54.2kN = 0kN

+ 0kN

-

-54.2kN + 54.2kN = 0kN 54.2kN - 108.4kN = -54.2kN

Bending moment diagram (M) Positive area 54.2kN X 1.875m X (½) = 50.8kNm

50.8kNm

Negative area 54.2kN X 1.875m X (½) = 50.8kNm Hence, Positive area = Negative area (50.8-50.8)kNm = 0

0kN

0kN

64

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

First Floor Beam E/ 12-15

First Floor Beam E/12-15 carries: -

Dead load from beam self weight: gridline E/12-15

-

Dead load from brick wall weight: gridline E/12-14a

-

Dead load from slab: gridline E-F/12-14a

-

Live load from slab: gridline E-F/12-14a

-

Point load at point E/14a from beam E-F /14a

First floor structural plan

First floor load distributary plan

65

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

First Floor Beam E/ 12-15 Dead Load

12

14a 5.07m

Slab E-F/12-14a = ( ᴸˣ/₂ ) X slab self-weight = ( 3.75/₂ ) x (0.15m x 24kN/m³) = 6.8kN/m

Total Dead Load

6.55m

1.48m

1.4kN/m

Beam self weight = Beam size x density of concrete = (0.2 x 0.3) m² x 24kN/m³ = 1.4kN/m

Brick wall self weight = Brick wall size x density of brickwork = (0.15 x 3.0) m² x 19kN/m³ = 8.6kN/m

15

8.6kN/m

6.8kN/m

16.8kN/m

1.4kN/m

Beam E/12-14a = 1.4kN/m + 8.6kN/m + 6.8kN/m = 16.8kN/m Beam E/14a-15 = 1.4kN/m

66

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

First Floor Beam E/ 12-15 12

14a

Live Load Slab E-F/12-14a = ( ᴸˣ/₂ ) X live load (UBBL) = ( 3.75/₂ ) X 1.5kN/m² = 2.8 kN/m

Total Live Load Beam E/ 12-14a = 2.8 kN/m

15

6.55m 5.07m 1.8kN/m

1.48m

1.4kN/m

67

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

First Floor Beam E/ 12-15

12

14a

15

6.55m

Ultimate Load 5.07m

1.48m

Ultimate dead load Beam E/12-14a = 16.8kN/m x 1.4 = 23.5kN/m

23.5kN/m 2.0kN/m

Beam E/14a-15 = 1.4kN/m x 1.4 = 2.0kN/m

4.5kN/m Ultimate live load Beam E/ 12-14a = 2.8kN/m x 1.6 = 4.5kN/m

Total ultimate load

28.0kN/m 2.0kN/m

Beam E/12-14a = 23.5kN/m + 4.5kN/m = 28.0kN/m Beam E/14a-15 = 2.0kN/m

54.2kN 28.0kN/m Point Load from beam E-F /14a = 54.2kN

2.0kN/m

68

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

First Floor Beam E/ 12-15

12

14a 6.55m

Resultant Force 5.07m Point load at point E/14a = 54.2kN Resultant Force, Fr1 = 28.0kN/m x 5.07m = 142.0kN

15 1.48m

54.2kN/m 28.0kN/m 28.0kN/m

2.0kN/m

Resultant Force, Fr2 = 2.0kN/m x 1.48m = 3.0kN

Reaction Force ∑M15 = 0 (Ra x 6.55) - [142.0 x (2.535+1.48)] - (54.2 x 1.48) - (3.0 x 0.74) = 0 6.55Ra = 652.566 Ra = 99.6kN

5.07m 2.535m

6.55m 1.48m

2.535m

0.74m 0.74m

54.2kN/m 28.0kN/m 2.0kN/m

∑Fy = 0 99.6 - 142.0 - 54.2 - 3.0 + Rb = 0 Rb = 99.6kN Ra = 99.6kN

Rb = 99.6kN

69

9.2

BEAM ANALYSIS 9.2.2 POINT LOAD & UDL

12

14a

First Floor Beam E/ 12-15 5.07m Shear force diagram (V) 99.6kN - [28.0kN/m x (5.07m)] =99.6kN - 141.96kN = -42.4kN

2.535m

15

6.55m 1.48m

2.535m

0.74m 0.74m

54.2kN/m 28.0kN/m

– 42.4kN – 54.2kN = –96.6kN

2.0kN/m

– 96.6kN – [2.0kN/m (1.48m)] =-96.6kN - 2.96kN = – 99.6kN – 99.6kN + 99.6kN = 0kN 5.07

Ra = 99.6kN

Rb = 99.6kN

x 99.6kN 99.6 –99.6kN + 99.6kN = 0kN

+

42.4 0kN

99.6kN - 141.96kN = – 42.4kN

Triangular proportion method x / 5.07 = 42.4 / (99.6 + 42.4) x = 1.5 m

Bending moment diagram (M) Positive area = 0.5 X 99.6 X (5.07 - 1.5 ) = 177.6kNm

-42.4kN - 54.2kN = – 96.6kN

–

– 96.6kN – 2.96kN = – 99.6kN

177.8kNm

Negative area = (0.5 x 42.4 x 1.5) + [0.5(96.6+99.6) x 1.48] = 177.0kNm Positive area - negative area = 177.6kNm - 177.0kNm = 0.6kNm ≈ 0kNm 70

9.3

COLUMN ANALYSIS 9.3.1 PERIMETER COLUMN - Column G/14

ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (3.175m x 2.0m) x 1.0kN/m² = 6.4kN

Total dead load = 6.4kN + 7.5kN = 13.9kN

Live Load Roof beam = (3.175 + 2.0 )m x 1.44kN/m = 7.5kN

Roof weight = (3.175m x 2.0m) x 0.5kN/m² = 3.2kN

71

9.3

COLUMN ANALYSIS 9.3.1 PERIMETER COLUMN - Column G/14

FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = (3.175m x 2.0m) x 3.6kN/m² = 22.9kN

Total dead load = 22.9kN + 7.5kN + 17.2kN + 6.5kN = 54.1kN

Beam self weight = (3.175 + 2.0)m x 1.44kN/m = 7.5kN

Live Load

Brick wall = 2.0m x 8.6kN/m = 17.2kN

Concrete slab = (3.175m x 2.0m) x 1.5kN/m² = 9.5kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 72

9.3

COLUMN ANALYSIS 9.3.1 PERIMETER COLUMN - Column G/14

GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = (3.175m x 2.0m) x 3.6kN/m² = 22.9kN Beam self weight = (3.175 + 2.0)m x 1.44kN/m = 7.5kN

Total dead load = 22.9kN + 7.5kN + 34.4kN + 6.5kN = 71.3kN

Live Load Brick wall = ( 2.0m x2 ) x 8.6kN/m = 34.4kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = (3.175m x 2.0m) x 1.5kN/m² = 9.5kN

73

9.3

COLUMN ANALYSIS 9.3.1 PERIMETER COLUMN - Column G/14

Ultimate Load Total dead load = 13.9kN + 54.1kN + 71.3kN = 139.3kN Total live load = 3.2kN + 9.5kN + 9.5kN = 22.2kN

Ultimate dead load = 139.3kN x 1.4 = 195.0kN

Ultimate live load = 22.2kN x 1.6 = 35.5kN

Total ultimate load = 195.0kN + 35.5kN = 230.5kN

74

9.3

COLUMN ANALYSIS 9.3.1 INTERNAL COLUMN - Column F/14

ROOF LEVEL

Dead load Roof weight = (3.875m x 3.175m) x 1.0kN/m² = 12.3kN

Total dead load = 12.3kN + 7.5kN = 19.8kN

Live Load Roof beam = (3.175m + 2.0m) x 1.44kN/m = 7.5kN

Roof weight = (3.875m x 3.175m) x 0.5kN/m² = 6.1kN

75

9.3

COLUMN ANALYSIS 9.3.1 INTERNAL COLUMN - Column F/14

FIRST LEVEL

Dead load Concrete slab = (3.875m x 3.175m) x 3.6kN/m² = 44.3kN

Total dead load = 44.3kN + 7.5kN + 47.1kN + 6.5kN = 105.4kN

Beam self weight = (2.0 + 3.175)m x 1.4kN/m = 7.5kN

Live Load

Brick wall = (1.875 + 1.6 + 2.0)m x 8.6kN/m = 47.1kN

Concrete slab = (3.875m x 3.175m) x 1.5kN/m² = 18.5kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 76

9.3

COLUMN ANALYSIS 9.3.1 INTERNAL COLUMN - Column F/14

GROUND LEVEL

Dead load Concrete slab = (3.875m x 3.175m) x 3.6kN/m² = 44.3kN

Total dead load = 44.3kN + 7.5kN + 60.6kN + 6.5kN = 118.9kN

Beam self weight = (2.0 + 3.175)m x 1.44kN/m = 7.5kN

Live Load

Brick wall = (2.0 + 3.175 + 1.875)m x 8.6kN/m = 60.6kN

Concrete slab = (3.875m x 3.175m) x 1.5kN/m² = 18.5kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 77

9.3

COLUMN ANALYSIS 9.3.1 INTERNAL COLUMN - Column F/14

Ultimate Load Total dead load = 19.8kN + 105.4kN + 118.9kN =244.1kN Total live load = 6.1kN + 18.5kN + 18.5kN = 43.1kN

Ultimate dead load = 244.1kN x 1.4 = 341.7kN

Ultimate live load = 43.1kN x 1.6 = 69.0kN

Total ultimate load = 341.78kN + 69.0kN = 410.7kN

78

10.0

LEE JIA YEE

BEAM AND COLUMN ANALYSIS 10.1 Selected Beams and Columns 10.2 Beam Analysis 10.2.1 Uniform Distribution Load -First Floor Beam E-F / 14a 10.2.2 Point Load & UDL -First Floor Beam E/12-15 10.3 Column Analysis 10.3.1 Perimeter Column -Column E/12 10.3.2 Internal Column -Column F/12

79

10.1 SELECTED BEAMS AND COLUMNS Ground Floor Plan

Perimeter Column - Column E/ 12

Point Load & UDL - Beam E/ 12-15

Internal Column - Column F / 12

Uniform Distribution Load Beam Beam E-F / 14a

80

10.2 BEAM ANALYSIS 10.2.1 UNIFORM DISTRIBUTION LOADS

Ground Floor Beam E-F / 14a Ground Floor Beam E-F / 14a carries: -

Dead load from beam self weight: gridline E-F /14a

-

Dead load from brick wall weight: gridline E-F /14a

-

Dead load from slab: gridline E-F /12-14a & E-F /14a-15

-

Live load from slab: gridline E-F /12-14a & E-F /14a-15

Ground floor structural plan

Ground floor load distributary plan

81

10.2 BEAM ANALYSIS 10.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam E-F / 14a

Dead Load

E

3.75m

F

1.4kN/m Beam self weight = (0.2 X 0.3) m² X 24kN/m³ = 1.4kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² X 19kN/m³ = 8.6kN/m

Slab E-F/12-14a = (4.87m/2) X (0.15m X 24kN/m³) = 2.4m X 3.6kN/m³ = 8.6kN/m

8.6kN/m

2.5kN/m Slab E-F/14a-15 = (1.48m/2)X (0.15m X 24kN/m³) = 0.7m X 3.6kN/m³ = 2.5kN/m

21.1kN/m Total Dead Load = 1.4kN/m + 8.6kN/m + 8.6kN/m + 2.5kN/m = 21.1kN/m

82

10.2 BEAM ANALYSIS 10.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam E-F / 14a Live Load Slab E-F/12-14a = (4.87m/2) X 1.5kN/m² = 2.4m X 1.5kN/m² = 3.6kN/m

Slab E-F/14a-15 = (1.48m/2) X 1.5kN/m² = 0.74m X 1.5kN/m² = 1.1kN/m

Total live load = 3.6kN/m + 1.1kN/m = 4.7kN/m

E

F 3.75m 3.6kN/m

1.1kN/m

4.7kN/m

Ultimate Load 29.5kN/m Ultimate dead load = 21.1kN/m X 1.4 = 29.5kN/m

7.5kN/m Ultimate live load = 4.7kN/m X 1.6 = 7.5kN/m

37kN/m Total ultimate load = 29.5kN/m + 7.5kN/m = 37kN/m 83

10.2 BEAM ANALYSIS 10.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam E-F / 14a E

F

3.75m

Resultant Force

37kN/m

= 37kN/m X 3.75m = 138.8kN

3.75m Reaction Force ∑MD = 0 = Rb (3.75) – 138.8(3.75/2) = 3.75Rb – 260.25 Rb = 69.4kN

1.875m

1.875m

Fᵣ = 138.8kN

∑Fy = 0 = Rc + 69.4 - 138.8 Rc = 69.4kN

Rb

Ra

3.75m 1.875m

1.875m

138.8kkN/m

Rb = 69.4kN

Rc = 69.4kN

Shear force diagram 69.4kN - 138.8kN = -69.4kN

69.4kN -69.4kN + 69.4kN = 0kN

+

-69.4kN + 69.4kN = 0kN 0kN

Bending moment diagram 65kNm

Positive area 69.4kN X 1.875m X (½) = 65kNm Negative area 69.4kN X 1.875m X (½) = 65kNm Hence, Positive area = Negative area

0kN

69.4kN - 138.8kN = -69.4kN

0kN 84

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL Ground Floor Beam E / 12-15

Ground Floor Beam E / 12-15 carries: -

Dead load from beam self weight: gridline E/12-15

-

Dead load from brick wall weight: gridline E/12-14a

-

Dead load from slab: gridline E-F/12-14a

-

Live load from slab: gridline E-F/12-14a

-

Point load at point E/14a from beam E-F/14a

Ground floor structural plan

Ground floor load distributary plan

85

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL Ground Floor Beam E / 12-15 Dead Load Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.4kN/m

Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.6kN/m

Slab E-F/12-14a = [(4.87m / 2) x (2/3)] x (0.15m x 24kN/m³) = 1.6m x 3.6kN/m³ = 5.8kN/m

12

14a 6.35m 4.87m

15 1.48m

1.4kN/m

8.6kN/m

5.8kN/m

Total Dead Load Beam E/12-14a = 1.4kN/m + 8.6kN/m + 5.8kN/m = 15.8kN/m

15.8kN/m

1.4kN/m

Beam E/14a-15 = 1.4kN/m

86

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL Ground Floor Beam E / 12-15 12 Live Load Slab E-F/12-14a = [(4.87m / 2) x (2/3)] x 1.5kN/m² = 1.6m x 1.5kN/m² = 2.4kN/m

14a 6.35m 4.87m 2.4kN/m

15 1.48m

2.4kN/m Total Live Load Beam E/12-14a = 2.4kN/m

87

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL Ground Floor Beam E / 12-15 Ultimate Load

12

14a 6.35m 4.87m

15 1.48m

Ultimate dead load Beam E/12-14a = 15.8kN/m x 1.4 = 22.1kN/m

22.1kN/m 2kN/m

Beam E/14a-15 = 1.4kN/m x 1.4 = 2kN/m

3.8kN/m Ultimate live load Beam E/12-14a = 2.4kN/m x 1.6 = 3.8kN/m

Total ultimate load

25.9kN/m 2kN/m

Beam E/12-14a = 22.1kN/m + 3.8kN/m = 25.9kN/m Beam E/14a-15 = 2kN/m

69.4kN 25.9kN/m Point Load from beam E-F/14a = 69.4kN

2kN/m

88

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL Ground Floor Beam E / 12-15

12

14a 6.35m 4.87m

Resultant Force Point load at point E/14a = 69.4kN

15 1.48m

69.4kN/m 25.9kN/m

Resultant Force, Fr1 = 25.9kN/m x 4.87m = 126.1kN

2kN/m

Resultant Force, Fr2 = 2kN/m x 1.48m = 3kN

Reaction Force ∑M =0 = Ra(6.35) + [-126.1 (3.9)] + [-69.4(1.48)] + [-3(0.74)] = 6.35Ra – 491.8 – 102.7– 2.2 6.35Ra = 596.7 Ra = 94kN

6.35m 4.87m 2.435m

1.48m

2.435m

0.74m 0.74m

69.4kN/m 25.9kN/m 2kN/m

∑Fy = 0 = 94 + Rb + (–126.1) + (–69.4) + (–3) Rb = 104.5kN Ra = 94kN

Rb = 104.5kN

89

10.2 BEAM ANALYSIS 10.2.2 POINT LOAD & UDL

12

14a

15

Ground Floor Beam E / 12-15 6.35m 4.87m

Shear force diagram 94kN - [25.9kN/m (4.87m)] = 94kN - 126.1kN = -32.1kN

2.435m

1.48m

2.435m

0.74m 0.74m

69.4kN/m

– 32.1kN – 69.4kN = –101.5kN

25.9kN/m

2kN/m

– 101.5N – [2kN/m (1.48m)] = – 101.5kN – 3kN = – 104.5kN – 104.5N + 104.5kN = 0kN Ra = 94kN

Rb = 104.5kN

4.87

94kN 94.4 x

– 104.5N + 104.5kN = 0kN

+ 31.7 0kN

Triangular proportion method x / 4.87 = 32.1 / (32.1+94) x = 1.2

94kN - 126.1kN = –32.1kN

– -32.1kN - 69.4kN = – 101.5kN

Bending moment diagram Positive area = (½) X [94 (4.87 - 1.2)] = (½) X 345 = 172.5 kNm Negative area = [½ X (32.1 X 1.2)] + [½ X 1.48 X (101.1+104.1)] = 19.3 + 152.4 = 171.7 kNm Positive area - negative area = 172.5 kNm - 171.7 kNm = 0.8kNm ≈ 0kNm

–101.5kN – 3kN = – 104.5kN

171.7kNm

90

10.3 COLUMN ANALYSIS 10.3.1 PERIMETER COLUMN - Column E/12 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (4.5 x 1.76)m x 1.0kN/m² = 7.9kN

Total dead load = 7.9kN + 9kN = 16.9kN

Live Load Roof beam = (4.5 + 1.76)m x 1.44kN/m = 9kN

Roof weight = (4.5 x 1.76)m x 0.5kN/m² = 4kN

91

10.3 COLUMN ANALYSIS 10.3.1 PERIMETER COLUMN - Column E/12 FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = (4.5 x 1.76)m x 3.6kN/m² = 28.5kN

Total dead load = 28.5kN + 11.1kN + 53.8kN + 6.5kN = 99.9kN

Beam self weight = (4.5 + 1.76)m x 1.4kN/m = 11.1N

Live Load

Brick wall = (4.5 + 1.76)m x 8.6kN/m = 53.8kN

Concrete slab = (4.5 x 1.76)m x 1.5kN/m² = 11.9kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 92

10.3 COLUMN ANALYSIS 10.3.1 PERIMETER COLUMN - Column E/12 GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = (4.5 x 1.76)m x 3.6kN/m² = 28.5kN

Total dead load = 28.5kN + 11.1kN + 6.5kN = 46.1kN

Beam self weight = (4.5 + 1.76)m x 1.4kN/m = 11.1N

Live Load

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = (4.5 x 1.76)m x 1.5kN/m² = 11.9kN

93

10.3 COLUMN ANALYSIS 10.3.1 PERIMETER COLUMN - Column E/12

Ultimate Load Total dead load = 16.9kN + 99.9kN + 46.1kN = 162.9kN Total live load = 4kN + 11.9kN + 11.9kN = 27.8kN

Ultimate dead load = 162.9kN x 1.4 = 228.1kN

Ultimate live load = 27.8kN x 1.6 = 44.5kN

Total ultimate load = 228.1kN + 44.5kN = 272.6kN

94

10.3 COLUMN ANALYSIS 10.3.2 INTERNAL COLUMN - Column F/12 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (4.4m x 3.9m) x 1.0kN/m² = 17.2kN

Total dead load = 17.2kN + 11.6kN = 28.8kN

Live Load Roof beam = (4.4m + 3.9m) x 1.4kN/m = 11.6kN

Roof weight = (4.4m x 3.9m) x 0.5kN/m² = 8.6kN

95

10.3 COLUMN ANALYSIS 10.3.2 INTERNAL COLUMN - Column F/12 FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = [(2.9m x 3.9m)]x 3.6kN/m² = 11.3m² x 3.6kN/m² = 40.7kN Beam self weight = (2.9m + 3.9m) x 1.4kN/m = 9.5kN Brick wall = (2.9m + 3.9m)x 8.6kN/m = 58.5kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Total dead load = 40.7kN + 9.5kN + 58.5kN + 6.5kN = 115.2kN

Live Load Concrete slab = [(2.9m x 3.9m)] x 1.5kN/m² = 11.3m² x 1.5 kN/m² = 17kN

96

10.3 COLUMN ANALYSIS 10.3.2 INTERNAL COLUMN - Column F/12 GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = [(2.9m x 3.9m)]x 3.6kN/m² = 11.3m² x 3.6kN/m² = 40.7kN Beam self weight = (2.9m + 3.9m) x 1.4kN/m = 9.5kN Brick wall = (2.9m + 1.9m)x 8.6kN/m = 41.3kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Total dead load = 40.7kN + 9.5kN + 41.3kN + 6.5kN = 98kN

Live Load Concrete slab = [(2.9m x 3.9m)] x 1.5kN/m² = 11.3m² x 1.5 kN/m² = 17kN

97

10.3 COLUMN ANALYSIS 10.3.2 INTERNAL COLUMN - Column F/12

Ultimate Load Total dead load = 28.8kN + 115.2kN + 98kN = 242kN Total live load = 8.6kN + 17kN + 17kN = 42.6kN

Ultimate dead load = 242kN x 1.4 = 338.8kN

Ultimate live load = 42.6kN x 1.6 = 68.2kN

Total ultimate load = 338.8kN + 68.2kN = 407kN

98

11.0

CHONG MIN

BEAM AND COLUMN ANALYSIS 11.1 Selected Beams and Columns 11.2 Beam Analysis 11.2.1 Uniform Distribution Load Ground Floor Beam B-C / 7 11.2.2 Point Load & UDL -Ground Floor Beam B/4-7 11.3 Column Analysis 11..3.1 Perimeter Column -Column B/7 11.3.2 Internal Column -Column C/7

99

11.1 SELECTED BEAMS AND COLUMNS

Perimeter Column - Column B / 7

Point Load & UDL - Beam B/ 4-7

Internal Column - Column C / 7

Uniform Distribution Load Beam Beam B-C / 7

100

11.2 BEAM ANALYSIS 11.2.1 UNIFORM DISTRIBUTION LOADS

Ground Floor Beam B-C / 7 First Floor Beam B-C / 3a carries: -

Dead load from beam self weight: gridline B-C / 7

-

Dead load from brick wall weight: gridline B-C / 7

-

Dead load from slab: gridline Slab B-C/5-7 & Slab B-C/7-9

-

Live load from slab: gridline Slab B-C/5-7 & Slab B-C/7-9

Ground floor structural plan

Ground floor load distributary plan

101

11.2 BEAM ANALYSIS 11.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam B-C / 7

Dead Load

Beam self weight = (0.2 X 0.3) m² X 24kN/m³ = 1.44kN/m

Brick wall self weight = (0.15 x 3.0) m² X 19kN/m³ = 8.55kN/m

Slab B-C/5-7 = (3m/2) X (0.15m X 24kN/m³) = 1.5m X 3.6kN/m³ = 5.4kN/m

Slab B-C/7-9 = (3.4m/2) X (2/3) X (0.15m X 24kN/m³) = 1.1m X 3.6kN/m³ = 4.1kN/m

Total Dead Load = 1.4kN/m + 8.55kN/m +5.4kN/m + 4.1kN/m = 19.5kN/m

102

11.2 BEAM ANALYSIS 11.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam B-C / 7 Live Load Slab B-C/5-7 = (3m/2) X 1.5kN/m² = 1.5m X 1.5kN/m² = 2.3kN/m

Slab B-C/7-9 = (3.4m/2) X (2/3) X 1.5kN/m² = 1.1m X 1.5kN/m² = 1.7kN/m

Total live load = 2.3kN/m + 1.7kN/m = 4.0kN/m

Ultimate Load

Ultimate dead load = 19.5N/m X 1.4 = 27.3kN/m

Ultimate live load = 4.0kN/m X 1.6 = 6.4kN/m

Total ultimate load = 27.3kN/m + 6.4kN/m = 33.7kN/m 103

11.2 BEAM ANALYSIS 11.2.1 UNIFORM DISTRIBUTION LOADS Ground Floor Beam B-C / 7

Resultant Force = 33.7kN/m X 3.4m = 115kN

Reaction Force ∑MD = 0 Rb (3.4) = 115(1.7) Rb = 57.5kN ∑Fy = 0 Rc + Rb = 115 Rc = 57.5kN

Shear force diagram 57.5kN -115kN = -57.5N -57.5kN + 57.5kN = 0kN

Bending moment diagram Positive area 57.5kN X 3.4m X (½) = 97.8kNm Negative area 45.1kN X 1.715m X (½) = 38.7kNm Hence, Positive area = Negative area 104

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Ground Floor Beam B/4-7

Ground Floor Beam B/4-7 carries: -

Dead load from beam self weight: gridline B/4-7

-

Dead load from brick wall weight: gridline B/4-7

-

Dead load from slab: gridline B-C/4-5

-

Live load from slab: gridline B-C/5-7

-

Point load at point B/5 from beam B-C/5

Ground floor structural plan

Ground floor load distributary plan

105

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Ground Floor Beam B/4-7 Dead Load

Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.44kN/m

Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.55kN/m

Slab B-C/4-5 = (1.5m / 2) x (0.15m x 24kN/m³) = 2.7kN/m

Slab B-C/5-7 = (3m / 2) x (2/3) X (0.15m x 24kN/m³) = 3.6kN/m

Total Dead Load Slab B-C/4-5 = 1.4kN/m + 8.6kN/m + 2.7kN/m = 12.3kN/m Slab B-C/5-7 = 1.4kN/m + 8.6kN/m + 3.6kN/m = 13.4kN/m

106

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Ground Floor Beam B/4-7

Total Live Load Slab B-C/4-5 = (1.5m / 2) x 1.5kN/m² = 1.1kN

Slab B-C/5-7 = (3m / 2) x (2/3) 1.5kN/m² = 1.5kN

107

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Ground Floor Beam B/4-7 Ultimate Load Ultimate dead load Beam B/4-5 = 12.3kN/m x 1.4 = 17.2kN/m Beam B/5-7 = 13.4kN/m x 1.4 = 18.8kN/m

Ultimate live load Beam B/4-5 =1.1kN/m x 1.6 = 1.8kN/m Beam B/5-7 =1.5kN/m x 1.6 = 2.4kN/m

Total ultimate load BeamB/4-5 = 17.2kN/m + 1.8kN/m = 19.0kN/m Beam B/5-7 = 18.8kN/m + 2.4kN/m = 21.2kN/m

Point Load from beam B-C/3a = 45.1kN

108

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Point Load at Point B/5 Dead Load

Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.44kN/m

Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.55kN/m

Slab B-C/4-5 = (1.5m / 2) x (0.15m x 24kN/m³) = 2.7kN/m

Slab B-C/5-7 =(3m / 2) x (0.15m x 24kN/m³) = 5.4kN/m

Total Dead Load Slab B-C/4-5 = 1.4kN/m + 8.6kN/m + 2.7kN/m + 5.4kN/m = 18.1kN/m Live Load Slab B-C/4-5 = (1.5m / 2) x 1.5kN/m² = 1.1kN

Slab B-C/5-7 = (3m / 2) x 1.5kN/m² = 2.3kN Total Live Load = 1.1kN + 2.3kN = 3.4kN 109

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL Point Load at Point B/5

Ultimate Load

Ultimate dead load = 18.1N/m X 1.4 = 25.3kN/m

Ultimate live load = 3.4N/m X 1.6 = 5.5kN/m

Total ultimate load = 25.3kN/m + 5.5kN/m = 30.8kN/m

Resultant Force = 30.8kN/m X 3.4m = 105kN

110

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL First Floor Beam B / 3-4 Resultant Force Point load at point B/5 = 105kN Resultant Force, Fr1 = 19kN/m x 1.5m = 28.5kN Resultant Force, Fr2 = 21.1kN/m x 3m = 63.6kN

Fr=105 kN

Reaction Force ∑MD = 0 {28.5 [4.5-(1.5/2)]} + [63.6(3/2)] + (105X3)= 4. Rb Rb = 115.3kN ∑Fy = 0 Rc + Rb = 28.5+63.6+105 Rc = 81.8kN

111

11.2 BEAM ANALYSIS 11.2.2 POINT LOAD & UDL First Floor Beam B / 3-4 Shear force diagram 115.3kN -28.5kN=86.8kN 86.8kN -105kN=-18.2kN -18.2kN+63.6kN=-81.8kN -81.8kN + 81.1kN=0

Bending moment diagram Positive area (115.3kN + 86.8kN)X 1.5m X (½) = 151 kNm Negative area (81.8kN + 18.2kN)X 3m X (½) = 150 kNm Positive area - Negative area =151 kNm - 150 kNm =1kNm 1kNm ≈ 0kNm Hence, Positive area = Negative area

112

11.3 COLUMN ANALYSIS 11.3.1 PERIMETER COLUMN - Column B/7 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (1.7mX4.2m) x 1.0kN/m² =7.1kN

Total dead load = 7.1kN + 9.5kN =16.6kN

Live Load Roof beam = (1.7m+4.2m) x 1.44kN/m = 9.5kN

Roof weight = (1.7m+4.2m) x 0.5kN/m² =2.95kN

113

11.3 COLUMN ANALYSIS 11.3.1 PERIMETER COLUMN - Column B/7 FIRST LEVEL

First floor columns tributary area diagram

Dead load Concrete slab = (1.7mx4.2m) x 3.6kN/m² = 25.7kN

Total dead load = 25.7kN +8.3kN + 50.7kN + 6.5kN = 91.2kN

Beam self weight = (4.2m+1.7m) x 1.4kN/m = 8.3kN

Live Load

Brick wall =(4.2m+1.7m) x 8.6kN/m = 50.7kN

Concrete slab = (1.7mx4.2m) x 1.5kN/m² = 10.7kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 114

11.3 COLUMN ANALYSIS 11.3.1 PERIMETER COLUMN - Column B/7 GROUND LEVEL

Ground floor columns tributary area diagram

Dead load Concrete slab = (1.7mx4.2m) x 3.6kN/m² = 25.7kN

Total dead load = 25.7kN +8.3kN + 50.7kN + 6.5kN = 91.2kN

Beam self weight = (4.2m+1.7m) x 1.4kN/m = 8.3kN

Live Load

Brick wall =(4.2m+1.7m) x 8.6kN/m = 50.7kN

Concrete slab = (1.7mx4.2m) x 1.5kN/m² = 10.7kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 115

11.3 COLUMN ANALYSIS 11.3.1 PERIMETER COLUMN - Column B/7

Ultimate Load Total dead load = 16.6kN + 91.2kN + 91.2kN = 199kN Total live load =2.95KN +10.7kN +10.7kN = 24.4kN

Ultimate dead load = 199kN x 1.4 = 278.6

Ultimate live load = 24.4kN x 1.6 = 39.0kN

Total ultimate load = 278.6kN + 39.0kN = 317.6kN

116

11.3 COLUMN ANALYSIS 11.3.2 INTERNAL COLUMN - Column C/7 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (3.4mX4.2m) x 1.0kN/m² =14.3kN

Total dead load = 14.3kN + 11kN = 25.3kN

Live Load Roof beam = (3.4m+4.2m)m x 1.44kN/m = 11.0kN

Roof weight = (3.4m x 4.2m) x 0.5kN/m² = 7.14kN

117

11.3 COLUMN ANALYSIS 11.3.2 INTERNAL COLUMN - Column C/7 FIRST LEVEL

First floor columns tributary area diagram

Dead load Concrete slab = (3.4mx4.2m) x 3.6kN/m² = 51.4kN

Total dead load = 51.4kN +10.6kN + 65.4kN + 6.5kN = 133.9kN

Beam self weight = (3.4m+4.2m) x 1.4kN/m = 10.6kN

Live Load

Brick wall = (3.4m+4.2m) x 8.6kN/m = 65.4kN

Concrete slab = (3.4mx4.2m) x 1.5kN/m² = 21.4kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 118

11.3 COLUMN ANALYSIS 11.3.2 INTERNAL COLUMN - Column C/7 GROUND LEVEL

Ground floor columns tributary area diagram

Dead load Concrete slab = (3.4mx4.2m) x 3.6kN/m² = 51.4kN

Total dead load = 51.4kN +10.6kN + 65.4kN + 6.5kN = 133.9kN

Beam self weight = (3.4m+4.2m) x 1.4kN/m = 10.6kN

Live Load

Brick wall = (3.4m+4.2m) x 8.6kN/m = 65.4kN

Concrete slab = (3.4mx4.2m) x 1.5kN/m² = 21.4kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 119

11.3 COLUMN ANALYSIS 11.3.2 INTERNAL COLUMN - Column C/7

Ultimate Load Total dead load = 25.3kN + 104.6kN + 104.6kN = 234.5kN Total live load =7.14N + 21.4kN +21.4kN = 50.0kN

Ultimate dead load = 234.5kN x 1.4 = 328.3kN

Ultimate live load = 50.0kN x 1.6 = 80.0kN

Total ultimate load = 328.3kN + 80.0kN = 408.3kN

120

12.0

CHEN LIAN LIAN

BEAM AND COLUMN ANALYSIS

12.1 Selected Beams and Columns 12.2 Beam Analysis 12.2.1 Uniform Distribution Load -First Floor Beam B-C/8a 12.2.2 Point Load & UDL -First Floor Beam B/7-9 12.3 Column Analysis 12.3.1 Perimeter Column -Column B/7 12.3.2 Internal Column -Column C/7

121

12.1 SELECTED BEAMS AND COLUMNS First Floor Plan

Perimeter Column - Column B / 9

Point Load & UDL - Beam B/ 7-9

Internal Column - Column C / 7

Uniform Distribution Load Beam Beam B-C / 9

122

12.2 BEAM ANALYSIS 12.2.1 UNIFORM DISTRIBUTION LOADS

First Floor Beam B-C / 8a First Floor Beam B-C / 8a carries: -

Dead load from beam self weight: gridline B-C/8a

-

Dead load from brick wall weight: gridline B-C/8a

-

Dead load from slab: gridline B-C/7-8a & B-C/8a-9

-

Live load from slab: gridline B-C/7-8a & B-C/8a-9

First floor structural plan

First floor load distributary plan

123

12.2 BEAM ANALYSIS 12.2.1 UNIFORM DISTRIBUTION LOADS First Floor Beam B-C / 8a B Dead Load

C 3.43m 1.4kN/m

Beam self weight = (0.2 X 0.3) m² X 24kN/m³ = 1.4kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² X 19kN/m³ = 8.6kN/m

Slab B-C/ 7-8a = [(2.35m/2) X (⅔)] X (0.15m X 24kN/m³) = 0.78m X 3.6kN/m³ = 2.8kN/m

2.8kN/m

2.5kN/m Slab B-C/ 8a-9 = (1.4m/2)X (0.15m X 24kN/m³) = 0.7m X 3.6kN/m³ = 2.5kN/m

15.3kN/m Total Dead Load = 1.4kN/m + 8.6kN/m + 2.8kN/m + 2.5kN/m = 15.3kN/m

124

12.2 BEAM ANALYSIS 12.2.1 UNIFORM DISTRIBUTION LOADS First Floor Beam B-C / 8a Live Load Slab B-C/ 7-8a = [(2.35m/2) X (⅔)] X 1.5kN/m² = 0.78m X 1.5kN/m² = 1.2kN/m

Slab B-C/ 8a-9 = (1.4m/2) X 1.5kN/m² = 0.7m X 1.5kN/m² = 1.1kN/m

Total live load = 1.2kN/m + 1.1kN/m = 2.3kN/m

B

C 3.43m 1.2kN/m

1.1kN/m

2.3kN/m

Ultimate Load 21.4kN/m Ultimate dead load = 15.3kN/m X 1.4 = 21.4kN/m

3.7kN/m Ultimate live load = 2.3kN/m X 1.6 = 3.7kN/m

25.1kN/m Total ultimate load = 21.4kN/m + 3.7kN/m = 25.1kN/m 125

12.2 BEAM ANALYSIS 12.2.1 UNIFORM DISTRIBUTION LOADS First Floor Beam B-C / 8a B

C

3.43m

Resultant Force

25.1kN/m

= 25.1kN/m X 3.43m = 86kN

3.43m Reaction Force ∑MD = 0 = Rb (3.43) – 86(3.43/2) = 3.43Rb – 147.5 Rb = 43kN

1.715m

1.715m

Fᵣ = 86kN

∑Fy = 0 = Rc + 43 - 86 Rc = 43kN

Rb

Ra

3.43m 1.715m

1.715m

25.1kN/m

Rb = 43kN

Rc = 43kN

Shear force diagram 43kN - 86kN = -43kN

43kN -43kN+43kN = 0kN

+

-43kN + 43kN = 0kN 0kN

Bending moment diagram 36.9kNm

Positive area 43kN X 1.715m X (½) = 36.9kNm Negative area 43kN X 1.715m X (½) = 36.9kNm Hence, Positive area = Negative area

0kN

43kN - 86kN = -43kN

0kN 126

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL First Floor Beam B / 7-9

First Floor Beam B/ 7-9 carries: -

Dead load from beam self weight: gridline B/ 7-9

-

Dead load from brick wall weight: gridline B/ 7-8a

-

Dead load from slab: gridline B-C/ 7-8a

-

Live load from slab: gridline B-C/ 7-8a

-

Point load at point B/ 8a from beam B-C/ 8a

First floor structural plan

First floor load distributary plan

127

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL First Floor Beam B / 7-9 Dead Load

7

8a 4.17m 2.77m

9 1.4m

1.4kN/m

Beam self weight = (0.2 x 0.3) m² x 24kN/m³ = 1.4kN/m

8.6kN/m Brick wall self weight = (0.15 x 3.0) m² x 19kN/m³ = 8.6kN/m

5kN/m Slab B-C/ 7-8a = (2.77m/2)x (0.15m x 24kN/m³) = 1.39m x 3.6kN/m³ = 5kN/m 15kN/m Total Dead Load

1.4kN/m

Beam B/ 7-8a = 1.4kN/m + 8.6kN/m + 5kN/m = 15kN/m Beam B/ 8a-9 = 1.4kN/m

128

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL First Floor Beam B / 7-9 7 Live Load Slab B-C/ 7-8a = (2.77m / 2) x 1.5kN/m² = 1.39m x 1.5kN/m² = 2.1kN/m

8a 4.17m 2.77m 2.1kN/m

9 1.4m

2.1kN/m Total Live Load Beam B/ 7-8a = 2.1kN/m

129

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL First Floor Beam B / 7-9 Ultimate Load

7

8a 4.17m 2.77m

9 1.4m

Ultimate dead load Beam B/ 7-8a = 15kN/m x 1.4 = 21kN/m

21kN/m 2kN/m

Beam B/ 8a-9 = 1.4kN/m x 1.4 = 2kN/m

3.7kN/m Ultimate live load Beam B/ 7-8a = 2.1kN/m x 1.6 = 3.7kN/m

Total ultimate load

24.7kN/m 2kN/m

Beam B/ 7-8a = 21kN/m + 3.7kN/m = 24.7kN/m Beam B/ 8a-9 = 2kN/m

43kN 24.7kN/m Point Load from beam B-C/ 8a = 43kN

2kN/m

130

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL First Floor Beam B / 7-9

7

8a

9

4.17m 2.77m

Resultant Force Point load at point B/ 8a = 43kN

1.4m 43kN/m

21kN/m

Resultant Force, Fr1 = 21kN/m x 2.77m = 58.2kN

2kN/m

Resultant Force, Fr2 = 2kN/m x 1.4m = 2.8kN

Reaction Force ∑M =0 = Ra(4.17) + [-58.2 (2.77)] + [-43(1.4)] + [-2.8(0.7)] = 4.17Ra – 161.21 – 6.02– 1.98 4.17Ra = 169.21 Ra = 40.6kN

4.17m 2.77m 1.385m

1.4m

1.385m

0.7m

0.7m

43kN/m 21kN/m 2kN/m

∑Fy = 0 = 40.6 + Rb + (–58.2) + (–43) + (–2.8) Rb = 63.4kN

Ra = 40.6kN

Rb = 63.4kN

131

12.2 BEAM ANALYSIS 12.2.2 POINT LOAD & UDL

7

8a

First Floor Beam B / 7-9

9

4.17m

Shear force diagram 40.6kN - (21kN/m X 2.77m) = 40.6kN - 58.2kN = -17.6kN

2.77m 1.385m

1.4m

1.385m

0.7m 0.7m

43kN/m

– 17.6kN – 43kN = –60.6kN

21kN/m

2kN/m

– 60.6kN – (2kN/m X 1.4m) = – 60.6kN – 2.8kN = – 63.4kN – 63.4kN + 63.4kN = 0kN

Ra = 40.6kN

Rb = 63.4kN

2.77

40.6

40.6kN

x

–63.4kN + 63.4kN = 0kN

+

17.6 0kN

40.6kN - 58.2kN = – 17.6kN

Triangular proportion method x / 2.77 = 17.6 / (17.6+40.6) x = 0.84

– -17.6kN - 43kN = – 60.6kN

Bending moment diagram Positive area = (½) X [40.6 (2.77 - 0.84)] = (½) X (112.5 X 34.1) = (½) X 78.4 = 39.2 kNm Negative area = [½ X (-17.6 X 0.84)] + [½ X 1.4 X 63.4] = -7.4 + 46.4 = 39 kNm Positive area - negative area = 39.2kNm - 39kNm = 0.2kNm ≈ 0kNm

– 60.6kN – 2.8kN = – 63.4kN

39kNm

132

12.3 COLUMN ANALYSIS 12.3.1 PERIMETER COLUMN - Column B/7 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (4.15m x 1.715m) x 1.0kN/m² = 7.1kN

Total dead load = 7.1kN + 10.3kN = 17.4kN

Live Load Roof beam = (4.15 x 1.715)m x 1.44kN/m = 10.3kN

Roof weight = (4.15m x 1.715m) x 0.5kN/m² = 3.6kN 133

12.3 COLUMN ANALYSIS 12.3.1 PERIMETER COLUMN - Column B/7 FIRST LEVEL

First floor columns tributary area diagram Dead load Concrete slab = (4.15m x 1.715m) x 3.6kN/m² = 25.6kN

Total dead load = 25.6kN + 8.2kN + 41.5kN + 6.5kN = 81.8kN

Beam self weight = (4.15 + 1.715)m x 1.4kN/m = 8.2kN

Live Load

Brick wall = 4.15m x 10kN/m = 41.5kN

Concrete slab = (4.15m x 1.715m) x 1.5kN/m² = 10.7kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

134

12.3 COLUMN ANALYSIS 12.3.1 PERIMETER COLUMN - Column B/7 GROUND LEVEL

Ground floor columns tributary area diagram Dead load Concrete slab = (4.17m x 1.715m) x 3.6kN/m² = 25.7kN Beam self weight = (4.17 + 1.715)m x 1.44kN/m = 8.5kN

Total dead load = 25.7kN + 8.5kN + 41.7kN + 6.5kN = 75.9kN

Live Load Brick wall = 4.17m x 8.6kN/m = 41.7kN Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

Concrete slab = (4.17m x 1.715m) x 1.5kN/m² = 10.7kN

135

12.3 COLUMN ANALYSIS 12.3.1 PERIMETER COLUMN - Column B/7

Ultimate Load Total dead load = 17.4kN + 81.8kN + 75.9kN = 175.1kN Total live load = 3.6kN + 10.7kN + 10.7kN = 25kN

Ultimate dead load = 178.7kN x 1.4 = 245.1kN

Ultimate live load = 25kN x 1.6 = 40kN

Total ultimate load = 245.1kN + 40kN = 285.1kN

136

12.3 COLUMN ANALYSIS 12.3.1 INTERNAL COLUMN - Column C/7 ROOF LEVEL

Roof level columns tributary area diagram

Dead load Roof weight = (4.15m x 3.42m) x 1.0kN/m² = 14.2kN

Total dead load = 14.2kN + 20.4kN = 34.6kN

Live Load Roof beam = (4.15m x 3.42m) x 1.44kN/m = 20.4kN

Roof weight = (4.15m x 3.42m) x 0.5kN/m² = 7.1kN

137

12.3 COLUMN ANALYSIS 12.3.1 INTERNAL COLUMN - Column C/7 FIRST LEVEL

First level columns tributary area diagram Dead load Concrete slab = (4.15m X 3.42m) X 3.6kN/m² = 51.1kN

Total dead load = 51.1kN + 10.6kN + 41.5kN + 6.5kN = 109.7kN

Beam self weight = (4.15m + 3.42m) x 1.4kN/m = 10.6kN

Live Load

Brick wall = 4.15m x 10kN/m = 41.5kN

Concrete slab = (4.15m x 3.42m) x 1.5kN/m² = 21.3kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN

138

12.3 COLUMN ANALYSIS 12.3.1 INTERNAL COLUMN - Column C/7 GROUND LEVEL

Ground level columns tributary area diagram Dead load Concrete slab = (4.16m x 3.42m) x 3.6kN/m² = 51.2kN

Total dead load = 51.2kN + 10.6kN + 41.6kN + 6.5kN = 110kN

Beam self weight = (4.16m + 3.42m)x 1.4kN/m = 10.6kN

Live Load

Brick wall = 4.16m x 10kN/m = 41.6kN

Concrete slab = (4.16m x 3.42m) x 1.5kN/m² = 21.3kN

Column self weight = (0.3 x 0.3 x 3.0)m x 24kN/m³ = 6.5kN 139

12.3 COLUMN ANALYSIS 12.3.1 INTERNAL COLUMN - Column C/7

Ultimate Load Total dead load = 34.6kN + 109.7kN + 110kN = 254.3kN Total live load = 7.1kN + 21.3kN + 21.3kN = 49.7kN

Ultimate dead load = 254.3kN x 1.4 = 356kN

Ultimate live load = 49.7kN x 1.6 = 79.5kN

Total ultimate load = 356kN + 79.5kN = 435.5kN

140