Structural Analysis

SCHOOL OF ARCHITECTURE, BUILDING AND DESIGN

BUILDING STRUCTURES BLD61003 STRUCTURAL ANALYSIS OF A BUNGALOW

REST, RELAXATION AND COMMERCIAL CENTRE IN SEBANGKOI, SARIKEI, SARAWAK

TUTOR:

Mr Mohamed Rizal Mohamed

GROUP Chong Xian Jun Loi Chi Wun Ng Zien Loon Nicholas Wong Raemi Safri Yew Jey Yee

CONTENTS 1.0

INTRODUCTION

2.0

DRAWINGS

3.0

SUMMARY OF SPECIFICATIONS

4.0

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

1.0

INTRODUCTION

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

1.0 STRUCTURAL ANALYSIS OF BUNGALOW In a group of six, we were tasked to select and obtain drawings of a 2-3 storey bungalow, using our knowledge of structural theory to produce structural plans for the building. From the structural plans produced, we were then required to analyze the beams and columns of the building.

We chose the Rest, Relaxation and Commercial Centre (RRCC), a 3 storey building located in Sebangkoi, Sarikei, Sarawak. The building includes separate dormitories for both male and female occupants, and a seminar hall on the 2nd floor.

STRUCTURAL ANALYSIS OF A BUNGALOW

02

2.0

DRAWINGS ARCHITECTURAL FLOOR PLANS STRUCTURAL PLANS LOAD DISTRIBUTION PLANS COLUMN TRIBUTARY AREAS COLUMN AND BEAM DISTRIBUTION

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.1 ARCHITECTURAL DRAWINGS

GROUND FLOOR ARCHITECTURAL PLAN

1:300

FIRST FLOOR ARCHITECTURAL PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

04

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.1 ARCHITECTURAL DRAWINGS

SECOND FLOOR ARCHITECTURAL PLAN

ROOF ARCHITECTURAL PLAN

STRUCTURAL ANALYSIS OF A BUNGALOW

1:300

1:300

05

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.2 STRUCTURAL DRAWINGS

GROUND FLOOR STRUCTURAL PLAN

FIRST FLOOR STRUCTURAL PLAN

STRUCTURAL ANALYSIS OF A BUNGALOW

1:300

1:300

06

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.2 STRUCTURAL DRAWINGS

SECOND FLOOR STRUCTURAL PLAN

1:300

ROOF STRUCTURAL PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

07

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.3 LOAD DISTRIBUTION DRAWINGS

GROUND FLOOR LOAD DISTRIBUTION PLAN 1:300

FIRST FLOOR LOAD DISTRIBUTION PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

08

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.3 LOAD DISTRIBUTION DRAWINGS

SECOND FLOOR LOAD DISTRIBUTION PLAN 1:300

ROOF LOAD DISTRIBUTION PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

09

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.4 COLUMN TRIBUTARY DRAWINGS

GROUND FLOOR COLUMN TRIBUTARY PLAN 1:300

FIRST FLOOR COLUMN TRIBUTARY PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

10

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.4 COLUMN TRIBUTARY DRAWINGS

SECOND FLOOR COLUMN TRIBUTARY PLAN 1:300

ROOF COLUMN TRIBUTARY PLAN 1:300

STRUCTURAL ANALYSIS OF A BUNGALOW

11

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2.5 COLUMN AND BEAM DISTRIBUTION

FIRST FLOOR LOAD DISTRIBUTION PLAN

CHONG XIAN JUN LOI CHI WUN NG ZIEN LOON NICHOLAS WONG YEW KHUNG RAEMI SAFRI YEW JEY YEE

STRUCTURAL ANALYSIS OF A BUNGALOW

12

3.0

SUMMARY OF SPECIFICATIONS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

3.0 SUMMARY OF SPECIFICATIONS BEAM Dimension (width x length)

0.25m x 0.60m or 0.20m x 0.50m (refer to structural plans)

Material Density

24kN/m³ (reinforced concrete)

COLUMN Dimension (width x length x height)

0.30m x 0.30m x 3.00m

Material Density

24kN/m³ (reinforced concrete)

WALL Dimension (width x height)

0.15m x 3.00m

Material Density

19kN/m³ (brick)

SLAB Dimension (thickness)

0.125m

Material Density

24kN/m³ (reinforced concrete)

Live Load

1.50k/Nm²

ROOF Dead Load

1.00kN/m²

Live Load

0.50kN/m²

STRUCTURAL ANALYSIS OF A BUNGALOW

14

4.0

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

CHONG XIAN JUN 0332605 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM ANALYSIS BEAM B/2-3 (Uniformly Distributed Load) BEAM B-D/3 (Uniformly Distributed Load and Point Load from Beam B/2-4)

COLUMN ANALYSIS COLUMN A8 (Perimeter Column) COLUMN C6 (Interior Column)

STRUCTURAL ANALYSIS OF A BUNGALOW

17

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM B/2-3

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/2-3 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline B/2-3 : Gridline B/2-3 : Gridline B-C/2-3 : Gridline B-C/2-3

18

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

2 3600

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab B-C/2-3 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

16.35 kN/m

Total Dead Load For 2-3 = (2.40 + 8.55 + 5.40) kN/m = 16.35 kN/m

LIVE LOAD

2

Ultimate Dead Load = Total dead load x Load factor = 16.35 kN/m x 1.4 = 22.89 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3 3600

Slab B-C/2-3 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

ULTIMATE LOAD

3

2.70 kN/m

2

3 3600

22.89 kN/m

19

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 2.70 kN/m x 1.6 = 4.32 kN/m

2

3 4.32 kN/m

Total Ultimate Load For B/2-3 = (22.89 + 4.32) kN/m = 27.21 kN/m

REACTION FORCES

27.21 kN/m

2

3 3600

Total Load = 27.21 kN/m x 3.6 m = 97.96 kN

1800

1800

97.96 kN ΣM = 0 0 = M3B2 + (-M3B1) = (Ra x 3.6) - (97.96 x 1.8) = 3.6 Ra - 176.32 3.6 R2B = 176.32 R2B= 48.98 kN

ΣF = 0 0 = R2B +R3B + (-97.96) 0 = 48.98 + R3B -97.96 R3B = 97.96 - 48.98 = 48.98 kN

M3B2 M3B1

R2B

R3B

27.21 kN/m

48.98 kN

48.98 kN

SHEAR FORCES 48.98 - 97.96 = -48.98 kN -48.98 + 48.98 = 0 kN

48.98 kN -48.98 + 48.98 = 0kN

48.98 - 97.96 = -48.98 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

20

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 48.98 kN x 1.8 m x ½ = 44.08 kNm 44.08 kNm Negative Area = -48.98 kN x 1.8 m x ½ = -44.08 kNm

∴ Positive area = Negative area 44.08 kNm + (-44.08 kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

44.08-44.08 = 0 kNm

21

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM C/2-4

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM C/2-4 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

: Gridline C/2-3, C/3-4 : Gridline C/ 2-3. C/3-4 : Gridline B-C/2-3, C-D/2-3, B-C/3-4, C-D/3-4 : Gridline B-C/2-3, C-D/2-3, B-C/3-4, C-D/3-4

2 DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 7.20 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3

4

7200

7.20 kN/m

22

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2 Brick Wall Self Weight = Wall thickness x Height x Density of reinforced concrete = (0.15 x 3) m² x 19 kN/m³ = 8.55 kN/m

Slab B-C/2-3 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

Slab C-D/2-3 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

Slab B-C/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

Slab C-D/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3

4

8.55 kN/m

5.40 kN/m

5.40 kN/m

5.40 kN/m

5.40 kN/m

23

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2

3

4

7200

Total Dead Load For 5-6 = (7.20 + 8.55 + 5.40 + 5.40) kN/m = 26.55 kN/m

26.55 kN/m

LIVE LOAD Slab B-C/2-3 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

Slab C-D/2-3 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

Slab B-C/3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

Slab C-D/3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

Total Live Load For 2-3 = (2.70 + 2.70 ) kN/m = 5.40 kN/m

2.70 kN/m

2.70 kN/m

5.40 kN/m

For 3-4 = (2.70 + 2.70) kN/m = 5.40 kN/m STRUCTURAL ANALYSIS OF A BUNGALOW

24

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD

2

3

4

Ultimate Dead Load For 2-3 = Total dead load x Load factor = 26.55 kN/m x 1.4 = 37.17 kN/m For 3-4 = Total dead load x Load factor = 26.55 kN/m x 1.4 = 37.17 kN/m

3600

3600

37.17 kN/m

37.17 kN/m

Ultimate Live Load For 2-3 = Total dead load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m For 3-4 = Total dead load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m

8.64 kN/m

8.64 kN/m

45.81 kN/m

45.81 kN/m

164.91 kN

164.91 kN

7200

Total Ultimate Load For 2-3 = (37.17 + 8.64) kN/m = 45.81 kN/m For 3-4 = (37.17 + 8.64) kN/m = 45.81 kN/m

REACTION FORCES Total Load For 2-3 = 45.81 kN/m x 3.6 m = 164.91 kN For 3-4 = 45.81 kN/m x 3.6m = 164.91 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

R2C

R3C

R4C

25

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

2

3

4

7200 3600

For C/ 2-3, About Point C3, ΣM = 0 (164.91 x 1.8 - 3.6 RC2 ) kNm = 0 R2C = (164.91 x 1.8)/3.6 kN = 82.46 kN ΣF = 0 164.91kN - RC2 - RC3 = 0 R3C = (164.91 - 82.46) kN = 82.46 kN

3600

164.91 kN M3C1 M3C2

R2C

R3C 45.81 kN/m

82.46 kN

82.46 kN

164.91 kN

For C/ 3-4 ΣM = 0 (164.91 x 1.8 - 3.6 R2C ) kNm = 0 R4C = (164.91 x 1.8)/3.6 kN = 82.46 kN

M3C4

M3C3

R3C

ΣF = 0 164.91kN - RC4 - RC3 = 0 R3C = (164.91 - 82.46) kN = 82.46 kN

R4C 45.81 kN/m

82.46 kN

45.81 kN/m

Total Reaction Forces R3C (Total) = R3C (From C/ 2-3) + R3C (from C/ 3-4) = (82.46 + 82.46) kN = 164.92 kN 82.46 kN STRUCTURAL ANALYSIS OF A BUNGALOW

82.46 kN

164.92 kN

82.46 kN 26

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM B-D/3

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B-D/3 CARRIES: Dead Load from beam self weight Dead Load from slab self weight Live Load from slab Point Load from B/2-4

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline B-C/3, C-D/3 : Gridline B-C/2-3, C-D/2-3, B-C/3-4, C-D/3-4 : Gridline B-C/2-3, C-D/2-3, B-C/3-4, C-D/3-4 : Gridline B/2-4

27

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

B

C 7200

2.40 kN/m

Slab B-C/2-3 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab B-C/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab C-D/2-3 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

Slab C-D/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

D

5.40kN/m

5.40 kN/m

28

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total dead load from slab For B-C/3 = ( 5.40 + 5.40) kN = 10.80 kN

B

C

D

7200

10.80 kN/m

10.80 kN/m

For C-D/3 = ( 5.40 + 5.40) kN = 10.80 kN

Total uniformly distributed load = 2.40 + 10.80 = 13.20 kN/m

164.92 kN 10.80 kN/m

10.80 kN/m

Total point load from beams C/ 2-4 = R3C (Total) = 164.92 kN

LIVE LOAD Slab B-C/2-3 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

Slab B-C/3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

Slab C-D/2-3 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

2.70 kN/m

2.70 kN/m

2.70 kN/m

29

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

B

C

D

7200

Slab C-D/3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

Total Live Load For B-C = (2.70 + 2.70 ) kN/m = 5.40 kN/m

2.70 kN/m

5.40 kN/m

For C-D = (2.70 + 2.70 ) kN/m = 5.40 kN/m

ULTIMATE LOAD

18.48 kN/m

Ultimate uniformly distributed dead load (UDL) = ( 13.20 x 1.4 ) kN = 18.48 kN 8.64 kN/m Ultimate live load = ( 5.40 x 1.6 ) kN = 8.64 kN

Total Ultimate Load = ( 18.48 + 8.64 ) kN = 27.12 kN Ultimate dead point load = ( 164.92 x 1.4 ) kN = 230.89 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

230.89 kN 27.12 kN/m

30

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

B

Total Load = 27.12 kN/m x 7.2 m + Point Load = ( 195.26 + 230.89) kN = 426.15 kN About point 3D ΣM = 0 0 = M3D1 + (-M3D2)) = (R3B x 7.2) - (426.15 x 3.6) = 7.2 R3B - 1534.14 7.2 R3B = 1534.14 R3B = 213.08 kN

C

D

7200

426.15 kN MD3 (1) MD3 (2)

R3B

R3D

230.89 kN 27.12 kN/m

ΣF = 0 0 = R3B +R3D + (-426.15) 0 = 213.08 + R3D - 426.15 R3D = 426.15 - 213.08 = 213.07 kN

SHEAR FORCES

213.08 kN

213.08 kN

27.12 x 3.6 = 97.63 kN 213.08 - 97.63 = 115.45 kN 115.45 - 230.89 = -115.44 kN -115.44 - 97.63 = -213.07 kN -213.07 + 213.07 = 0 kN

213.07 kN

213.08 - 97.63 = 115.45kN

115.45 - 230.89 = -115.44kN

BENDING MOMENT Positive Area = (213.08 + 115.45) kN x ½ x 3.6 m = 591.35 kNm

-213.07+213.07 = 0kN

-115.44-97.63 = -213.07 kN

591.35 kNm

Negative Area = (-115.45 - 213.07) kN x ½ x 3.6 m = -591.35 kNm ∴ Positive area = Negative area 591.35 kNm + (-591.35 kNm) = 0 STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

591.35 - 591.35

= 0 kNm

31

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN B2

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (1.8 x 1.8) m² x 1.0 kN/m² = 3.24 kN

Roof Weight = (1.8 x 1.8) m² x 0.5 kN/m² = 1.62kN

Roof Beam = (1.8 + 1.8) m x 1.44 kN/m = 5.18 kN

Total Dead Load = (3.24 + 5.18) kN = 8.42 kN STRUCTURAL ANALYSIS OF A BUNGALOW

32

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD Roof Self Weight = (3.60 x 2.70) m² x 1.0 kN/m² = 9.72 kN

LIVE LOAD Total Live Load from Roof = (3.60 x 2.70) m² x 0.5 kN/m² = 4.86 kN

Beam Self Weight = (1.80 + 1.80 + 3.60 + 0.90) m x 1.44 kN/m + 2.7 m x 1.44 kN/m x ½ = 11.66 kN + 1.94 kN = 13.60 kN

Brick Wall Self Weight = ( 1.80 + 1.80 )m x 10 kN/m = 36.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

33

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (9.72 + 13.60 + 36.00 + 6.48) kN = 65.80 kN

FIRST FLOOR TRIBUTARY AREA

STRUCTURAL ANALYSIS OF A BUNGALOW

34

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.70 x 3.60) m² x 3.6 kN/m² = 34.99 kN

Total Live Load = (2.70 x 3.60) m² x 1.5 kN/m² = 14.58 kN

Beam Self Weight = (1.80 + 1.80 + 0.90 + 3.60) m x 1.44 kN/m + 2.70 m x 1.44 kN/m x ½ = 13.61 kN

Brick Wall Self Weight = (1.80 + 1.80 + 0.90) m x 10 kN/m = 45.00 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (34.99 + 13.61 + 45.00 + 6.48) kN = 100.08 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

35

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (5.40 x 1.80 + 0.90 x 3.60) m² x 3.6 kN/m² = 46.66 kN

Total Live Load = (5.40 x 1.80 + 0.90 x 3.60) m² x 1.5 kN/m² = 19.44 kN

Beam Self Weight = (1.80 + 1.80 + 0.90 + 3.60) m x 1.44 kN/m + 2.70 m x 1.44 kN/m x ½ = 11.66 kN + 1.94 kN = 13.60 kN

Brick Wall Self Weight = (1.80 + 1.80 + 0.90) m x 10 kN/m = 45.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

36

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (46.66 + 13.60 + 45.00 + 6.48) kN = 111.74 kN

ULTIMATE LOAD Total Dead Load = (8.42 + 65.80 + 100.08 + 111.74) kN = 286.04 kN Ultimate Dead Load = 286.04 kN x 1.4 = 400.46 kN

Total Live Load = (1.62 + 4.86 + 14.88 + 19.94) kN = 41.00 kN Ultimate Live Load = 41.00 x 1.6 = 65.60 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (400.46 + 65.60) kN = 466.06 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

37

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN D3

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Roof Self Weight = (7.20 x 4.50) m² x 1.0 kN/m² = 32.40 kN

Total Live Load from Roof = (7.20 x 4.50) m² x 0.5 kN/m² = 16.20 kN

Beam Self Weight = 4.5 m x 1.44 kN/m + 4.5 m x 2 x 1.44 kN/m x ½ = 12.96 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

38

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load = (32.40 + 12.96 + 6.48) kN = 51.84 kN

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (7.20 x 4.50) m² x 3.6 kN/m² = 116.64 kN

Total Live Load = (7.20 x 4.50) m² x 1.5 kN/m² = 48.60 kN

Beam Self Weight = 4.50 m x 1.44 kN/m + 4.50 m x 2 x 1.44 kN/m x ½ = 12.96 kN Brick Wall Self Weight = 4.50 m x 10 kN/m + 4.50m x 2 x 10 kN/m x ½ = 90.00 kN STRUCTURAL ANALYSIS OF A BUNGALOW

39

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (116.64 + 12.96 + 90.00 + 6.48) kN = 226.08 kN

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (7.20 x 4.50) m² x 3.6 kN/m² = 116.64 kN

Total Live Load = (7.20 x 4.50) m² x 1.5 kN/m² = 48.60 kN

Beam Self Weight = 4.50 m x 1.44 kN/m + 4.50 m x 2 x 1.44 kN/m x ½ = 12.96 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

40

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Brick Wall Self Weight = 4.50 m x 10 kN/m + 4.50m x 2 x 10 kN/m x ½ = 90.00 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (116.64 + 12.96 + 90.00 + 6.48) kN = 226.08 kN

ULTIMATE LOAD Total Dead Load = (51.84 + 226.08 + 226.08) kN = 504.00 kN Ultimate Dead Load = 504.00 kN x 1.4 = 705.60 kN

Total Live Load = (16.20 + 48.60 + 48.60) kN = 113.40 kN Ultimate Live Load = 113.40 kN x 1.6 = 181.44 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (705.60 + 113.40) kN = 819.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

41

LOI CHI WUN 0328652 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM E/6-8

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM A/5-6 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 6-8 : Gridline 6-8 : Gridline D-E/6-8 , E-F/6-8 : Gridline D-E/6-8 , E-F/6-8

43

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

5 4200

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab A-B/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

17.55 kN/m

Total Dead Load For 5-6 = (3.60 + 8.55 + 5.40) kN/m = 17.55 kN/m

LIVE LOAD

5

Ultimate Dead Load = Total dead load x Load factor = 17.55 kN/m x 1.4 = 24.57 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

6 4200

Slab A-B/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

ULTIMATE LOAD

6

2.70 kN/m

5

6 4200

24.57 kN/m

44

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 2.70 kN/m x 1.6 = 4.32 kN/m

4.32 kN/m

28.89 kN/m

Total Ultimate Load For 5-6 = (24.57 + 4.32) kN/m = 28.89 kN/m

REACTION FORCES

5

6 4200

Total Load = 28.89 kN/m x 4.2 m = 121.34 kN By using 6A as reference point, ΣM = 0 0 = M6A1 + (-M6A2) = (R5A x 4.2) - (121.34 x 2.1) = 4.2 R5A - 254.81 4.2 R5A = 254.81 R5A = 60.67 kN

ΣFy = 0 0 = R5A +R6A + (-121.34) 0 = 60.67 + R6A -121.34 R6A = 121.34 - 60.67 = 60.67 kN

2100

M6A1

2100

121.34 kN

M6A2 R5A

R6A

28.89 kN/m

60.67 kN

60.67 kN

SHEAR FORCES 60.67 - 121.34 = -60.67 kN -60.67 + 60.67 = 0 kN

60.67 kN -60.67 + 60.67 = 0kN

60.60 - 121.34 = -60.67 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

45

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 60.67 kN x 2.1 m x ½ = 63.70 kNm 63.70 kNm Negative Area = -60.67 kN x 2.1 m x ½ = -63.70 kNm

∴ Positive area = Negative area 63.70 kNm + (-63.70 kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

63.70 - 63.70 = 0 kNm

46

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

6 4800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab D-E/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab E-F/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

22.95 kN/m

Total Dead Load For 6-8 = (3.60 + 8.55 + 5.40 + 5.40 ) kN/m = 22.95 kN/m

LIVE LOAD Slab D-E/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

8

6

8 4800

2.70 kN/m

47

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Slab D-E/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

5.40 kN/m

Total Live Load For 6-8 = (2.70 + 2.70) kN/m = 5.40 kN/m

ULTIMATE LOAD

6

4800

Ultimate Dead Load = Total dead load x Load factor = 22.95 kN/m x 1.4 = 32.13 kN/m

32.13 kN/m

Ultimate Live Load = Total live load x Load Factor = 5.4 kN/m x 1.6 = 8.64 kN/m

2.70 kN/m

Total Ultimate Load For 6-8 = (32.13 + 8.64) kN/m = 40.77 kN/m

40.77 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

8

48

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

6

8 4800

Total Load = 40.77 kN/m x 4.8 m = 195.70 kN By using 6E as reference point, ΣM = 0 0 = M6E1 + (-M6E2) = (R6E x 4.8) - (195.70 x 2.4) = 4.8 R6E - 469.68 4.8 R6E = 469.68 R6E = 97.85 kN

ΣFy = 0 0 = R6E +R8E + (-195.70) 0 = 97.85 + R6A -195.70 R6A = 195.70 - 97.85 = 97.85 kN

SHEAR FORCES

2400

M6E1

2400

195.70 kN

M6E2 R6E

R8E

40.77 kN/m

97.85 kN

97.85 kN

97.85 kN -97.85 + 97.85 = 0kN

97.85 - 195.70 = -97.85 kN -97.85 + 97.85 = 0 kN

97.85 - 195.70 = -97.85 kN

BENDING MOMENT Positive Area = 97.85 kN x 2.1 m x ½ = 102.74 kNm 102.74 kNm

Negative Area = -97.85 kN x 2.1 m x ½ = -102.74 kNm

∴ Positive area = Negative area 102.74 kNm + ( -102.74 kNm ) = 0 STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

102.74-102.74 = 0 kNm 49

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM F/6-8

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM F/6-8 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 6-8 : Gridline 6-8 : Gridline E-F/6-8, F-G/6-8 : Gridline E-F/6-8, F-G/6-8

50

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

6 4800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab E-F/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab F-G/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

21.75 kN/m

Total Dead Load For 6-8 = (2.40 + 8.55 + 5.40 + 5.40) kN/m = 21.75 kN/m

LIVE LOAD Slab E-F/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

8

6

8 4800

2.70 kN/m

51

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Slab F-G/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

5.40 kN/m

Total Live Load For 6-8 = (2.70 + 2.70) kN/m = 5.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 21.75 kN/m x 1.4 = 30.45 kN/m

Ultimate Live Load = Total live load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m

6

8 4800

30.45 kN/m

8.64 kN/m

39.09 kN/m Total Ultimate Load For 6-8 = (30.45 + 8.64) kN/m = 39.09 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

52

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

6

8 4800

Total Load = 39.09 kN/m x 4.8 m = 187.63 kN By using 6F as reference point, ΣM = 0 0 = M6F1 + (-M6F2) = (R6F x 4.8) - (187.63 x 2.4) = 4.8 R6F - 450.32 4.2 R6F = 450.32 R5B = 93.82 kN

ΣFy = 0 0 = R6B +R8B + (-187.63) 0 = 93.82 + R8B -187.63 R8B = 187.63 - 93.82 = 93.82 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

2400

M6F1

2400

187.63 kN

M6F2

R6F

R8F

39.09 kN/m

93.82 kN

93.82 kN

53

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM F/5-6

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM F/5-6 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 5-6 : Gridline 5-6 : Gridline E-F/5-6, F-G/5-6 : Gridline E-F/5-6, F-G/5-6

54

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

5

6 4200

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab E-F/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab F-G/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

21.75 kN/m

Total Dead Load For 5-6 = (2.40 + 8.55 + 5.40 + 5.40 ) kN/m = 21.75 kN/m

LIVE LOAD

5

6 4200

Slab E-F/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m Slab F-G/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m STRUCTURAL ANALYSIS OF A BUNGALOW

2.70 kN/m

2.70 kN/m

55

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Live Load For 5-6 = (2.70 + 2.70) kN/m = 5.40 kN/m

ULTIMATE LOAD

5.40kN/m

5

6

Ultimate Dead Load = Total dead load x Load factor = 21.75 kN/m x 1.4 = 30.45 kN/m

4200

30.45 kN/m

Ultimate Live Load = Total live load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m

8.64 kN/m

39.09 kN/m

Total Ultimate Load For 5-6 = (30.45 + 8.64) kN/m = 39.09 kN/m REACTION FORCES Total Load = 39.09 kN/m x 4.2 m = 689.56 kN By using 6F as reference point, ΣM = 0 0 = M5F1 + (-M5F2) = (R5F x 4.2) - (689.56 x 2.1) = 4.2 R5F - 1448.07 4.2 R5F = 1448.07 R5F = 344.78 kN ΣFy = 0 0 = R5F +R6F + (-689.56) 0 = 344.78 + R6F -689.56 R6F = 689.56 - 344.78 = 344.78 kN STRUCTURAL ANALYSIS OF A BUNGALOW

5

6 4200 2100

M5F1

2100

689.56 kN

M5F2 R5F

R6F

39.09 kN/m

344.78 kN

344.78 kN 56

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM 6/E-G

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 6/E-G CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline E-F : Gridline E-F : Gridline E-F/6-8, E-F/5-6, F-G/6-8, F-G/5-6 : Gridline E-F/6-8, E-F/5-6, F-G/6-8, F-G/5-6

57

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

Slab E-F/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m

Slab E-F/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m

E

F 7200 3600

3600

2.40 kN/m

3.60 kN/m

3.60 kN/m

3.60 kN/m

Slab F-G/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m

3.60 kN/m

Slab F-G/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m Total Dead Load For E-F = (2.40 + 3.60 + 3.60) kN/m = 9.60 kN/m For F-G = (2.40 + 3.60 + 3.60) kN/m = 9.60 kN/m STRUCTURAL ANALYSIS OF A BUNGALOW

G

9.60 kN/m

9.60 kN/m

58

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

LIVE LOAD

E

Slab E-F/6-8 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

F

G

7200 3600

3600

1.80 kN/m

Slab E-F/5-6 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

1.80 kN/m

Slab F-G/6-8 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

1.80 kN/m

Slab F-G/5-6 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

1.80 kN/m

Total Live Load For E-F = (1.80 + 1.80) kN/m = 3.60 kN/m For F-G = (1.80 + 1.80) kN/m = 3.60 kN/m

ULTIMATE LOAD Ultimate Dead Load For E-F = Total dead load x Load factor = 9.60 kN/m x 1.4 = 13.44 kN/m For F-G = Total dead load x Load factor = 9.60 kN/m x 1.4 = 13.44 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3.60 kN/m

E

3.60 kN/m

F

G

7200 3600

3600

13.44 kN/m

13.44 kN/m

59

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load For E-F = Total live load x Load factor = 3.60 kN/m x 1.6 = 5.76 kN/m For F-G = Total live load x Load factor = 3.60 kN/m x 1.6 = 5.76 kN/m

Total Ultimate Load For E-F = (13.44 + 5.76) kN/m = 19.20 kN/m For F-G = (13.44 + 5.76) kN/m = 19.20 kN/m

5.76 kN/m

5.76 kN/m

19.20 kN/m

19.20 kN/m

438.60 kN

Point Load = R6F (from Beam F/6-8) + R6F (from Beam F/5-6) = (93.82 + 344.78) kN = 438.60 kN

19.20 kN/m

19.20 kN/m

REACTION FORCES Total Load For E-F = 19.20 kN/m x 3.6 m = 69.12 kN For F-G = 19.20 kN/m x 3.6 m = 69.12 kN By using 6G as reference point, ΣM = 0 0 = M6G1 + (-M6G2) + (-M6G3) + (-M6G4) = (R6E x 7.2) - (69.12 x 5.4) - (438.60 x 3.6) - (69.12 x 1.8) = 7.2 R6E - 373.25 - 1578.96 - 124.42 7.2 R6E = 2076.73 R6E = 288.42 kN ΣFy = 0 0 = R6E +R6G + (-69.12) + (-438.60) + (-69.12) 0 = 288.42 + R6G - 69.12 - 438.60 - 69.12 R6G = -288.42 +69.12 +438.60 +69.12 = 288.42 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

F

E

G

7200 1800

1800

1800

1800

438.60 kN 69.12 kN 69.12 kN M6G1 M6G2

M6G3

M6G4

R6E

R6G 438.60 kN 19.20 kN/m

288.42 kN

19.20 kN/m

288.42 kN

60

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SHEAR FORCES 288.42 - 69.12 = 219.30 kN 219.30 - 438.60 = -219.30 kN -219.30 - 69.12 = -288.42 kN -288.42+ 288.42 = 0 kN

1288.42 kN

288.42 - 69.12 = 219.30 kN

BENDING MOMENT Positive Area = (288.42 + 219.30) kN x ½ x 3.6 m = 913.90 kNm

219.30 - 438.60 = -219.30 kN

Negative Area = (-219.30 -288.42) kN x ½ x 3.6 m = -913.90

-288.42+ 288.42 = 0 kN

-219.30 - 69.12 = -288.42 kN

913.90 kNm

∴ Positive area ≈ Negative area 913.90 kNm + (-913.90) = 0 0 kNm

STRUCTURAL ANALYSIS OF A BUNGALOW

913.90 - 913.90

= 0 kNm

61

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN E8

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (1.5 x 7.2) m² x 1.0 kN/m² = 16.20 kN

Roof Weight = (1.5 x 7.2) m² x 0.5 kN/m² = 5.4 kN

Roof Beam = (1.5 + 7.2) m x 1.44 kN/m = 12.53 kN

Total Dead Load = (16.20 + 12.53) kN = 28.73 kN STRUCTURAL ANALYSIS OF A BUNGALOW

62

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (1.5 x 7.2) m² x 3.6 kN/m² = 38.88 kN

Total Live Load = (1.50 x 7.2) m² x 1.5 kN/m² = 16.20 kN

Beam Self Weight = (1.5 + 7.2) m x 1.44 kN/m + [ (1.5+1.5)m x 1.44 kN/m x ½ ] = 12.53 kN + 2.16 kN = 14.69

Brick Wall Self Weight = 7.2 m x 10 kN/m = 72.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

63

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (38.88 + 14.69 + 72 + 6.48 )kN = 132.05 kN

FIRST FLOOR TRIBUTARY AREA

STRUCTURAL ANALYSIS OF A BUNGALOW

64

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (1.5 x 7.2) m² x 3.6 kN/m² = 38.88 kN

Total Live Load = (1.50 x 7.2) m² x 1.5 kN/m² = 16.20 kN

Beam Self Weight = (1.5 + 7.2) m x 1.44 kN/m + [ (1.5+1.5)m x 1.44 kN/m x ½ ] = 12.53 kN + 2.16 kN = 14.69

Brick Wall Self Weight = 7.2 m x 10 kN/m = 72.00 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (38.88 + 14.69 + 72 + 6.48) kN = 132.05 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

65

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (1.5 x 7.2) m² x 3.6 kN/m² = 38.88 kN

Total Live Load = (1.50 x 7.2) m² x 1.5 kN/m² = 16.20 kN

Beam Self Weight = (1.5 + 7.2) m x 1.44 kN/m + [ (1.5+1.5)m x 1.44 kN/m x ½ ] = 12.53 kN + 2.16 kN = 14.69

Brick Wall Self Weight = 7.2 m x 10 kN/m = 72.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

66

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (38.88 + 14.69 + 72 + 6.48) kN = 132.05 kN

ULTIMATE LOAD Total Dead Load = (28.73+132.05+132.05+132.05) kN = 424.88 kN Ultimate Dead Load = 424.88 kN x 1.4 = 594.83 kN

Total Live Load = (5.40 + 8.10 + 8.10 + 8.10 ) kN = 29.70 kN Ultimate Live Load = 29.70 x 1.6 = 47.52 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (594.83 + 47.52) kN = 642.34 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

67

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN G6

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 1.0 kN/m² = 28.35 kN

Roof Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 0.5 kN/m² = 14.18 kN

Roof Beam = { (2.4+2.1) [ (5.4/2) + 3.6 } m x 1.44 kN/m = 40.82 kN Total Dead Load =[ { (2.4+2.1) [ (5.4/2) + 3.6 } + 14.69 ] kN = 69.17 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

68

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 3.6 kN/m² = 102.06 kN

Total Live Load = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 1.5 kN/m² = 42.53 kN

Beam Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 15.55 kN + 3.24 kN = 18.79 kN Brick Wall Self Weight = 4.5 m x 10 kN/m = 45.00 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN STRUCTURAL ANALYSIS OF A BUNGALOW

69

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load = (102.06 + 18.79 + 45.00 + 6.48) kN = 172.33 kN

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 3.6 kN/m² = 102.06 kN

Total Live Load = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 1.5 kN/m² = 42.53 kN

Beam Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 15.55 kN + 3.24 kN = 18.79 kN Brick Wall Self Weight = 4.5 m x 10 kN/m = 45.00 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN STRUCTURAL ANALYSIS OF A BUNGALOW

70

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load = (102.06 + 18.79 + 45.00 + 6.48) kN = 172.33 kN

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

Slab Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 3.6 kN/m² = 102.06 kN

LIVE LOAD Total Live Load = { (2.4+2.1) [ (5.4/2) + 3.6 } m² x 1.5 kN/m² = 42.53 kN

Beam Self Weight = { (2.4+2.1) [ (5.4/2) + 3.6 } m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 15.55 kN + 3.24 kN = 18.79 kN Brick Wall Self Weight = 4.5 m x 10 kN/m = 45.00 kN STRUCTURAL ANALYSIS OF A BUNGALOW

71

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (102.06 + 18.79 + 45.00 + 6.48) kN = 172.33 kN

ULTIMATE LOAD Total Dead Load = (69.17+ 172.33 + 172.33 + 172.33) kN = 586.17 kN Ultimate Dead Load = 586.17 kN x 1.4 = 820.64 kN Total Live Load = (14.18 + 42.53 + 42.53 + 42.53) kN = 141.77 kN Ultimate Live Load = 141.77 x 1.6 = 226.83 kN Total Ultimate Load = Ultimate dead load + Ultimate live load = (820.64 + 226.83) kN = 1047.44 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

72

NG ZIEN LOON 0328565 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM ANALYSIS BEAM A/5-6 (Uniformly Distributed Load) BEAM 5-A/C (Uniformly Distributed Load and Point Load from Beam B/5-6 & Beam B/4-5)

COLUMN ANALYSIS COLUMN A6 (Perimeter Column) COLUMN C5 (Interior Column)

STRUCTURAL ANALYSIS OF A BUNGALOW

74

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM A/5-6

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM A/5-6 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 5-6 : Gridline 5-6 : Gridline A-B/5-6 : Gridline A-B/5-6

75

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

5 4200

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab A-B/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

17.55 kN/m

Total Dead Load For 5-6 = (3.60 + 8.55 + 5.40) kN/m = 17.55 kN/m

LIVE LOAD

5

Ultimate Dead Load = Total dead load x Load factor = 17.55 kN/m x 1.4 = 24.57 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

6 4200

Slab A-B/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

ULTIMATE LOAD

6

2.70 kN/m

5

6 4200

24.57 kN/m

76

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 2.70 kN/m x 1.6 = 4.32 kN/m

4.32 kN/m

28.89 kN/m

Total Ultimate Load For 5-6 = (24.57 + 4.32) kN/m = 28.89 kN/m

REACTION FORCES

5

6 4200

Total Load = 28.89 kN/m x 4.2 m = 121.34 kN By using 6A as reference point, ΣM = 0 0 = M6A1 + (-M6A2) = (R5A x 4.2) - (121.34 x 2.1) = 4.2 R5A - 254.81 4.2 R5A = 254.81 R5A = 60.67 kN

ΣFy = 0 0 = R5A +R6A + (-121.34) 0 = 60.67 + R6A -121.34 R6A = 121.34 - 60.67 = 60.67 kN

2100

M6A1

2100

121.34 kN

M6A2 R5A

R6A

28.89 kN/m

60.67 kN

60.67 kN

SHEAR FORCES 60.67 - 121.34 = -60.67 kN -60.67 + 60.67 = 0 kN

60.67 kN -60.67 + 60.67 = 0kN

60.60 - 121.34 = -60.67 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

77

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 60.67 kN x 2.1 m x ½ = 63.70 kNm 63.70 kNm Negative Area = -60.67 kN x 2.1 m x ½ = -63.70 kNm

∴ Positive area = Negative area 63.70 kNm + (-63.70 kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

63.70 - 63.70 = 0 kNm

78

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM B/5-6

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/5-6 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 5-6 : Gridline 5-6 : Gridline A-B/5-6, B-C/5-6 : Gridline A-B/5-6, B-C/5-6

79

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

5 4200

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab A-B/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab B-C/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

21.75 kN/m

Total Dead Load For 5-6 = (2.40 + 8.55 + 5.40 + 5.40) kN/m = 21.75 kN/m

LIVE LOAD Slab A-B/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

6

5

6 4200

2.70 kN/m

80

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Slab B-C/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

5.40 kN/m

Total Live Load For 5-6 = (2.70 + 2.70) kN/m = 5.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 21.75 kN/m x 1.4 = 30.45 kN/m

Ultimate Live Load = Total live load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m

5

6 4200

30.45 kN/m

8.64 kN/m

39.09 kN/m Total Ultimate Load For 5-6 = (30.45 + 8.64) kN/m = 39.09 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

81

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

5

6 4200

Total Load = 39.09 kN/m x 4.2 m = 164.18 kN By using 6B as reference point, ΣM = 0 0 = M6B1 + (-M6B2) = (R5B x 4.2) - (164.18 x 2.1) = 4.2 R5B - 344.78 4.2 R5B = 344.78 R5B = 82.09 kN

ΣFy = 0 0 = R5B +R6B + (-164.18) 0 = 82.09 + R6B -164.18 R6B = 164.18 - 82.09 = 82.09 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

2100

M6B1

2100

164.18 kN

M6B2

R5B

R6B

39.09 kN/m

82.09 kN

82.09 kN

82

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM B/4-5

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/4-5 CARRIES: Dead Load from beam self weight

: Gridline 4-5

DEAD LOAD

4 1800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 2.40 kN/m x 1.4 = 3.36 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

5 2.40 kN/m

4

5 1800

3.36 kN/m

83

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

4

5 1800

Total Load = 3.36 kN/m x 1.8 m = 6.05 kN By using 5B as reference point, ΣM = 0 0 = M5B1 + (-M5B2) = (R4B x 1.8) - (6.05 x 0.9) = 1.8 R4B - 5.45 1.8 R4B = 5.45 R4B = 3.03 kN

ΣFy = 0 0 = R4B +R5B + (-6.05) 0 = 3.03 + R5B -6.05 R5B = 6.05 - 3.03 = 3.02 kN (≈3.03 kN)

STRUCTURAL ANALYSIS OF A BUNGALOW

900

900

6.05 kN M5B1 M5B2

R4B

R5B

39.09 kN/m

3.03 kN

3.02 kN

84

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM 5/A-C

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 5/A-C CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline A-C : Gridline A-C : Gridline A-B/5-6, A-B/4-5, B-C/5-6 & B-C/4-5 : Gridline A-B/5-6, A-B/4-5, B-C/5-6 & B-C/4-5

85

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

Slab A-B/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m

Slab A-B/4-5 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125 m x 24 kN/m³) x 1.8/2 = 3 kN/m² x 0.9 m = 2.70 kN/m

Slab B-C/5-6 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8m x 2/3 = 3.60 kN/m

Slab B-C/4-5 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125 m x 24 kN/m³) x 1.8/2 = 3 kN/m² x 0.9 m = 2.70 kN/m STRUCTURAL ANALYSIS OF A BUNGALOW

A

B

C

7200 3600

3600

2.40 kN/m

8.55 kN/m

3.60 kN/m

2.70 kN/m

3.60 kN/m

2.70 kN/m

86

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load For A-B = (2.40 + 8.55 + 3.60 + 2.70) kN/m = 17.25 kN/m For B-C = (2.40 + 8.55 + 3.60 + 2.70) kN/m = 17.25 kN/m

LIVE LOAD Slab A-B/5-6 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

Slab A-B/4-5 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 1.8/2 = 1.35 kN/m

17.25 kN/m

A

17.25 kN/m

B

C

7200 3600

3600

1.80 kN/m

1.35 kN/m

Slab B-C/5-6 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

1.80 kN/m

Slab B-C/4-5 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 1.8/2 = 1.35 kN/m

1.35 kN/m

Total Live Load For A-B = (1.80 + 1.35) kN/m = 3.15 kN/m For B-C = (1.80 + 1.35) kN/m = 3.15 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3.15 kN/m

3.15 kN/m

87

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Ultimate Dead Load For A-B = Total dead load x Load factor = 17.25 kN/m x 1.4 = 24.15 kN/m For B-C = Total dead load x Load factor = 17.25 kN/m x 1.4 = 24.15 kN/m

Ultimate Live Load For A-B = Total live load x Load factor = 3.15 kN/m x 1.6 = 5.04 kN/m For B-C = Total live load x Load factor = 3.15 kN/m x 1.6 = 5.04 kN/m

Total Ultimate Load For A-B = (24.15 + 5.04) kN/m = 29.19 kN/m For B-C = (24.15 + 5.04) kN/m = 29.19 kN/m

A

B

C

7200 3600

3600

24.15 kN/m

24.15 kN/m

5.04 kN/m

5.04 kN/m

29.19 kN/m

29.19 kN/m

85.11 kN Point Load = R5B (from Beam B/5-6) + R5B (from Beam B/4-5) = (82.09 + 3.02) kN = 85.11 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

29.19 kN/m

29.19 kN/m

88

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES Total Load For A-B = 29.19 kN/m x 3.6 m = 105.08 kN For B-C = 29.19 kN/m x 3.6 m = 105.08 kN By using 5C as reference point, ΣM = 0 0 = M5C1 + (-M5C2) + (-M5C3) + (-M5C4) = (R5A x 7.2) - (105.08 x 5.4) - (85.11 x 3.6) - (105.8 x 1.8) = 7.2 R5A - 567.43 - 306.40 - 189.14 7.2 R5A = 1062.97 R5A = 147.63 kN

ΣFy = 0 0 = R5A +R5C + (-105.08) + (-85.11) + (-105.08) 0 = 147.63 + R5C - 105.08 - 85.11 - 105.08 R5C = 105.08 + 85.11 + 105.08 - 147.63 = 147.64 kN (≈147.63 kN)

SHEAR FORCES

B

A

C

7200 1800

1800

1800

85.11 kN 105.08 kN 105.08 kN M5C1 M5C2

M5C3

R5C 85.11 kN 29.19 kN/m

29.19 kN/m

147.63 kN

147.63 kN

147.64 kN

147.63 - 105.08 = 42.55kN

42.55 - 85.11 = -42.56kN

BENDING MOMENT Positive Area = (147.63 + 42.55) kN x ½ x 3.6 m = 342.32 kNm

∴ Positive area ≈ Negative area 342.32 kNm + (-342.36 kNm) = -0.04 (≈0)

STRUCTURAL ANALYSIS OF A BUNGALOW

M5C4

R5A

147.63 - 105.08 = 42.55 kN 42.55 - 85.11 = -42.56 kN -42.56 - 105.08 = -147.64 kN -147.64 + 147.64 = 0 kN

Negative Area = (-42.56 - 147.64) kN x ½ x 3.6 m = -342.36 kNm (≈342.32 kNm)

1800

-147.64 + 147.64 = 0kN

-42.56 - 105.08 = -147.64 kN

342.32 kNm

0 kNm

342.32 - 342.35

≈ 0 kNm

89

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A6

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (4.5 x 3.6) m² x 1.0 kN/m² = 6.48 kN

Roof Weight = (4.5 x 3.6) m² x 0.5 kN/m² = 8.10 kN

Roof Beam = (4.5 + 3.6) m x 1.44 kN/m = 11.66 kN

Total Dead Load = (6.48 + 11.66) kN = 18.14 kN STRUCTURAL ANALYSIS OF A BUNGALOW

90

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 3.6) m² x 3.6 kN/m² = 58.32 kN

Total Live Load = (4.5 x 3.6) m² x 1.5 kN/m² = 24.30 kN

Beam Self Weight = (4.5 + 3.6) m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 11.66 kN + 3.24 kN = 14.90 kN

Brick Wall Self Weight = 4.5 m x 10 kN/m = 45.00 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

91

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (58.32 + 14.90 + 45.00 + 6.48) kN = 124.70 kN

FIRST FLOOR TRIBUTARY AREA

STRUCTURAL ANALYSIS OF A BUNGALOW

92

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 3.6) m² x 3.6 kN/m² = 58.32 kN

Total Live Load = (4.5 x 3.6) m² x 1.5 kN/m² = 24.30 kN

Beam Self Weight = (4.5 + 3.6) m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 11.66 kN + 3.24 kN = 14.90 kN

Brick Wall Self Weight = 4.5 m x 10 kN/m + 4.5 m x 10 kN/m x ½ = 45.00 kN + 22.5 kN = 67.50 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (58.32 + 14.90 + 67.50 + 6.48) kN = 147.20 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

93

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 3.6) m² x 3.6 kN/m² = 58.32 kN

Total Live Load = (4.5 x 3.6) m² x 1.5 kN/m² = 24.30 kN

Beam Self Weight = (4.5 + 3.6) m x 1.44 kN/m + 4.5 m x 1.44 kN/m x ½ = 11.66 kN + 3.24 kN = 14.90 kN

Brick Wall Self Weight = 4.5 m x 10 kN/m + 4.5 m x 10 kN/m x ½ = 45.00 kN + 22.5 kN = 67.50 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

94

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (58.32 + 14.90 + 67.50 + 6.48) kN = 147.20 kN

ULTIMATE LOAD Total Dead Load = (27.86 + 124.70 + 147.20 + 147.20) kN = 446.96 kN Ultimate Dead Load = 446.96 kN x 1.4 = 645.74 kN

Total Live Load = (8.10 + 24.30 + 24.30 + 24.30) kN = 81.00 kN Ultimate Live Load = 81.00 x 1.6 = 129.60 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (625.74 + 129.60) kN = 755.34 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

95

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN C5

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (3.0 x 7.2) m² x 1.0 kN/m² = 21.60 kN

Roof Weight = (3.0 x 7.2) m² x 0.5 kN/m² = 10.80 kN

Roof Beam = (3.0 + 7.2)m x 1.44 kN/m = 14.69 kN Total Dead Load = (21.60 + 14.69) kN = 36.29 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

96

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (3.0 x 7.2) m² x 3.6 kN/m² = 77.76 kN

Total Live Load = (3.0 x 7.2) m² x 1.5 kN/m² = 32.40 kN

Beam Self Weight = (3.0 + 7.2) m x 1.44 kN/m + (3.0 + 3.0) m x 1.44 kN/m x ½ = 14.69 kN + 4.32 kN = 19.01 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (77.76 + 19.01 + 6.48) kN = 103.25 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

97

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (3.0 x 7.2) m² x 3.6 kN/m² = 77.76 kN

Total Live Load = (3.0 x 7.2) m² x 1.5 kN/m² = 32.40 kN

Beam Self Weight = (3.0 + 7.2) m x 1.44 kN/m + (3.0 + 3.0) m x 1.44 kN/m x ½ = 14.69 kN + 4.32 kN = 19.01 kN Brick Wall Self Weight = (2.1 + 7.2) m x 10 kN/m + (2.1 + 2.1) m x 10 kN/m x ½ = 93.00 kN + 21.00 kN = 114.00 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN STRUCTURAL ANALYSIS OF A BUNGALOW

98

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load = (77.76 + 19.01 + 114.00 + 6.48) kN = 217.25 kN

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (3.0 x 7.2) m² x 3.6 kN/m² = 77.76 kN

Total Live Load = (3.0 x 7.2) m² x 1.5 kN/m² = 32.40 kN

Beam Self Weight = (3.0 + 7.2) m x 1.44 kN/m + (3.0 + 3.0) m x 1.44 kN/m x ½ = 14.69 kN + 4.32 kN = 19.01 kN Brick Wall Self Weight = (2.1 + 7.2) m x 10 kN/m + (2.1 + 2.1) m x 10 kN/m x ½ = 93.00 kN + 21.00 kN = 114.00 kN STRUCTURAL ANALYSIS OF A BUNGALOW

99

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (77.76 + 19.01 + 114.00 + 6.48) kN = 217.25 kN

ULTIMATE LOAD Total Dead Load = (36.29 + 103.25 + 217.25 + 217.25) kN = 574.04 kN Ultimate Dead Load = 574.04 kN x 1.4 = 803.66 kN Total Live Load = (10.80 + 32.40 + 32.40 + 32.40) kN = 108..00 kN Ultimate Live Load = 108.00 x 1.6 = 172.80 kN Total Ultimate Load = Ultimate dead load + Ultimate live load = (803.66 + 172.80) kN = 976.46 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

100

NICHOLAS WONG 0328559 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM ANALYSIS BEAM A/3-4 (Uniformly Distributed Load) BEAM 4/A-C(Uniformly Distributed Load and Point Load from Beam B/4-5 & Beam B/3-4)

COLUMN ANALYSIS

STRUCTURAL ANALYSIS OF A BUNGALOW

102

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM A/3-4

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM A/3-4 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 3-4 : Gridline 3-4 : Gridline A-B/3-4 : Gridline A-B/3-4

103

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

3

4 3600

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

8.55 kN/m Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

12.15 kN/m

Total Dead Load For 3-4 = (3.60 + 8.55) kN/m = 12.15 kN/m

ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 12.15 kN/m x 1.4 = 17.01 kN/m

3

4 3600

17.01 kN/m

Total Ultimate Load For 3-4 = 17.01 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

104

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

3

4 3600

Total Load = 24.57 kN/m x 3.6 m = 88.452 kN By using 6A as reference point, ΣM = 0 0 = M3A1 + (-M3A2) = (R3A x 3.6) - (88.452 x 1.8) = 3.6 R3A - 159.2136 -3.6 R3A = -159.213 R3A = 44.226kN

1800

M3A1

88.452 kN

M3A2 R3A

R4A

28.89 kN/m

ΣFy = 0 0 = R3A +R4A + (-44.226) 0 = 44.226+ R4A -88.452 R6A = 88.452-44.226 = 44.226 kN

44.226kN

SHEAR FORCES

44.226 kN

44.226-88.452 = -44.226 kN

1800

44.226kN

-44026 +44.226 = 0kN

-44.226+44.226 = 0 kN

44.226-88.452 = -44.226 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

105

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 44.226 kN x 1.8 m x ½ = 39.803 kNm 44.226 kNm

Negative Area = -44.226 kN x 1.8 m x ½ = -39.803 kNm

∴ Positive area = Negative area 39.803 kNm + (-39.803kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

44.226-44.226 = 0 kNm

106

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM A/3-4

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/4-5 CARRIES: Dead Load from beam self weight

: Gridline 4-5

DEAD LOAD

4 1800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 2.40 kN/m x 1.4 = 3.36 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

5 2.40 kN/m

4

5 1800

3.36 kN/m

107

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

4 1800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 2.40 kN/m x 1.4 = 3.36 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

5 2.40 kN/m

4

5 1800

3.36 kN/m

108

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

4

5 1800

Total Load = 3.36 kN/m x 1.8 m = 6.05 kN By using 5B as reference point, ΣM = 0 0 = M5B1 + (-M5B2) = (R4B x 1.8) - (6.05 x 0.9) = 1.8 R4B - 5.45 1.8 R4B = 5.45 R4B = 3.03 kN

ΣFy = 0 0 = R4B +R5B + (-6.05) 0 = 3.03 + R5B -6.05 R5B = 6.05 - 3.03 = 3.02 kN (≈3.03 kN)

STRUCTURAL ANALYSIS OF A BUNGALOW

900

900

6.05 kN M5B1 M5B2

R4B

R5B

39.09 kN/m

3.03 kN

3.02 kN

109

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM A/3-4

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/3-4 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 3-4 : Gridline 3-4 : Gridline B-C/3-4 : Gridline B-C/3-4

110

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

3 3600

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab B-C/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

17.55 kN/m

Total Dead Load For 3-4 = (3.60 + 8.55 + 5.40) kN/m = 17.55 kN/m

LIVE LOAD

3

Ultimate Dead Load = Total dead load x Load factor = 17.55 kN/m x 1.4 = 24.57 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

4 3600

Slab B-C/3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

ULTIMATE LOAD

4

2.70 kN/m

3

4 3600

24.57 kN/m

111

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 2.70 kN/m x 1.6 = 4.32 kN/m

4.32 kN/m

28.89 kN/m Total Ultimate Load For 3-4 = (24.57 + 4.32) kN/m = 28.89 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

112

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

3

4 3600

Total Load = 28.89 kN/m x 3.6 m = 104.004 kN By using 4A as reference point, ΣM = 0 0 = M3B1 + (-M3B2) = (R3B x 3.6) - (104.004 x 1.8) = 3.6 R3B - 187.2072 -3.6 R3B = -187.2072 R3B = 52.002 kN

ΣFy = 0 0 = R3B +R4B + (-104.004) 0 = 52.002+ R4B -104.004 R4B = 104.004-52.002 = 52.002 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

1800

M3B1

1800

104.004 kN

M3B2 R3B

R4B

28.89 kN/m

52.002 kN

52.002kN

113

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM 4/A-C

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 4/A-C CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 3-4 : Gridline 3-4 : Gridline A-B/4-5 , B-C 4-5, B-C/3-4 : Gridline A-B/4-5 , B-C 4-5, B-C/3-4

114

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

Slab A-B/4-5 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 1.8/2 = 3 kN/m² x 0.9m = 2.70 kN/m

A

B 7200 3600

3600

3.6 kN/m

8.55 kN/m

2.70 kN/m

Slab B-C/4-5 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 1.8/2 = 3 kN/m² x 0.9m = 2.70 kN/m

2.70 kN/m

Slab B-C/3-4 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 0.9m = 5.40 kN/m

Total Dead Load For A-B = (3.60+8.55+2.7) kN/m = 14.85 kN/m

C

5.40 kN/m

14.85 kN/m

20.25 kN/m

For B-C = (3.60+8.55+2.7+5.40) kN/m = 20.25 kN/m STRUCTURAL ANALYSIS OF A BUNGALOW

115

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

LIVE LOAD Slab A-B/4-5 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 1.8/2 = 1.35 kN/m

A

B 7200 3600

1.35 kN/m

Slab B-C /3-4 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3600

1.35 kN/m

Slab B-C/4-5 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 1.8/2 = 1.35 kN/m

Total Live Load For A-B = 1.35 kN/m For B-C = (2.70 + 1.35) kN/m = 4.05 N/m

C

2.70 kN/m

1.35 kN/m

4.05 kN/m

116

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Ultimate Dead Load For A-B = Total dead load x Load factor = 14.85 kN/m x 1.4 = 20.79 kN/m For B-C = Total dead load x Load factor = 20.25 kN/m x 1.4 = 28.35 kN/m

Ultimate Live Load For A-B = Total live load x Load factor = 1.35 kN/m x 1.6 = 2.16 kN/m For B-C = Total live load x Load factor = 4.05 kN/m x 1.6 = 6.48 kN/m

Total Ultimate Load For A-B = (20.79+2.16) kN/m = 22.95 kN/m For B-C = (28.35+6.48) kN/m = 34.83 kN/m

A

B

C

7200 3600

3600

24.15 kN/m

24.15 kN/m

2.16 kN/m

6.48kN/m

22.95kN/m

34.83 kN/m

55.022 kN Point Load = R5B (from Beam B/5-6) + R5B (from Beam B/4-5) = (52.002 + 3.02) kN = 55.022 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

22.95kN/m

34.83 kN/m

117

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES Total Load = 28.89 kN/m x 7.2 m = 208.01 kN By using 4C as reference point, ΣM = 0 0 = M4A1 + (-M4A2) = (R4A x 7.2) - (263.03 x3.6) = 7.2 R4A - 946.91 -7.2 R4A = -946.91 R4A = 131.51 kN

ΣFy = 0 0 = R4A +R4C + (-104.004) 0 = 52.002+ R4C -104.004 R4A = 104.004-52.002 = 52.002 kN

A

C 7200 3600

3600

263.03 kN

M4A1

M4A2 R4A

R4C 55.022kN 28.89 kN/m

131.51kN

131.51 kN

SHEAR FORCES 131.51 kN 131.51-104.00 = 27.51kN 27.51-55.02 = -27.51kN -27.51-104.00= -131.51 kN -131.51 + 131.51 = 0 kN

131.51-104.00 = 27.51kN

-11.51+131.51 = 0kN

27.51-55.02

=

STRUCTURAL ANALYSIS OF A BUNGALOW

--27.51kN

-27.51-104.00 = -131.51 kN

118

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = (131.51+27.51) kN x 3.6 m x ½ = 329.58 kNm 329.58 kNm

Negative Area = (-131.51-27.51)kN x 3.6 m x ½ = -329.58 kNm

∴ Positive area = Negative area 329.58 kNm + (-329.58kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

329.58-329.58 = 0 kNm

119

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (2.7 x 3.6) m² x 1.0 kN/m² = 9.72 kN

Roof Weight = (2.7x 3.6) m² x 0.5 kN/m² = 4.86 kN

Roof Beam = (2.7 + 3.6) m x 1.44 kN/m = 6.3 kN

Total Dead Load = (9.72+6.3) kN = 16.02 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

120

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

SECOND FLOOR

SECOND FLOOR TRIBUTARY AREA

DEAD LOAD Slab Self Weight = (0.9 x 3.6) m² x 3.6 kN/m² = 11.66 kN

Beam Self Weight = (0.9 + 3.6) m x 1.44 kN/m + 0.9 m x 1.44 kN/m x ½ = 6.48 kN + 1.3 kN = 7.78 kN

Brick Wall Self Weight = 0.9 m x 10 kN/m = 9 kN STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (0.9 x 3.6) m² x 1.5 kN/m² = 4.86 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (11.66 + 7.78 + 9+ 6.48) kN = 34.92kN

121

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

FIRST FLOOR

FIRST FLOOR TRIBUTARY AREA

DEAD LOAD

LIVE LOAD

Slab Self Weight = (0.9 x 3.6) m² x 3.6 kN/m² = 11.66 kN

Total Live Load = (0.9 x 3.6) m² x 1.5 kN/m² = 4.86 kN

Beam Self Weight = (0.9 + 3.6) m x 1.44 kN/m + 0.9 m x 1.44 kN/m x ½ = 6.48 kN + 1.3 kN = 7.78 kN

Brick Wall Self Weight = 0.9 m x 10 kN/m + 0.9 m x 10 kN/m x ½ = 13.5 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (11.66 + 7.78 + 13.5+ 6.48) kN = 39.42 kN

122

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (1.8x 3.6) m² x 3.6 kN/m² = 23.32 kN

Total Live Load = (1.8 x 3.6) m² x 1.5 kN/m² = 9.72 kN

Beam Self Weight = (1.8+ 3.6) m x 1.44 kN/m + 1.8m x 1.44 kN/m x ½ = 7.77 kN + 1.3 kN = 9.07 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (23.32+9.07+27+ 6.48) kN = 65.87 kN

Brick Wall Self Weight = 1.8 m x 10 kN/m +1.8 m x 10 kN/m x ½ = 27 kN STRUCTURAL ANALYSIS OF A BUNGALOW

123

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS ULTIMATE LOAD Total Dead Load = (16.02+34.92+39.42+65.87) kN = 156.23 kN Ultimate Dead Load = 156.23 kN x 1.4 = 162.64 kN

Total Live Load = (4.86+4.86+4.86+9.72) kN = 24.3kN Ultimate Live Load = 24.3 x 1.6 = 30.13 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (162.64+30.13) kN = 192.77 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

124

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN C5

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (0.9 x 7.2) m² x 1.0 kN/m² = 6.48 kN

Roof Weight = (0.9 x 7.2) m² x 0.5 kN/m² = 3.24 kN

Roof Beam = (0.9 + 7.2) m x 1.44 kN/m = 11.664 kN

Total Dead Load = (6.48+11.664) kN = 18.144 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

125

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN C5

SECOND FLOOR DEAD LOAD Slab Self Weight = (0.9 x 7.2 m² x 3.6 kN/m² = 23.33 kN

Beam Self Weight = (0.9 + 7.2) m x 1.44 kN/m + 0.9 m x 1.44 kN/m x ½ = 11.66 kN + 1.3 kN = 12.96 kN

Brick Wall Self Weight = 0.9 m x 10 kN/m = 9 kN STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (0.9 x 7.2) m² x 1.5 kN/m² = 9.72 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (23.33 + 12.96 + 9+ 6.48) kN = 51.77 kN

126

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

FIRST FLOOR DEAD LOAD

FIRST FLOOR TRIBUTARY AREA

Slab Self Weight = (2.7x 7.2) m² x 3.6 kN/m² = 69.98 kN

Beam Self Weight = (2.7+ 7.2) m x 1.44 kN/m + 2.7m x 1.44 kN/m x ½ = 14.25 kN + 3.88 kN =18.13 kN

Brick Wall Self Weight =2.7 m x 10 kN/m + 2.7 m x 10 kN/m x ½ = 40.5 kN STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (2.7 x 7.2) m² x 1.5 kN/m² = 29.16 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (69.98+18.13+40.5+6.48) kN = 135.09 kN

127

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4

GROUND FLOOR

GROUND FLOOR TRIBUTARY AREA

DEAD LOAD Slab Self Weight = (2.7x 7.2) m² x 3.6 kN/m² = 69.98 kN

Beam Self Weight = (2.7+ 7.2) m x 1.44 kN/m + 2.7m x 1.44 kN/m x ½ = 14.25 kN + 3.88 kN =18.13 kN

Brick Wall Self Weight =2.7 m x 10 kN/m + 2.7 m x 10 kN/m x ½ = 40.5 kN STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (2.7 x 7.2) m² x 1.5 kN/m² = 29.16 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (69.98+18.13+40.5+6.48) kN = 135.09 kN

128

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A4 ULTIMATE LOAD Total Dead Load = (18.144+51.77+135.09+135.09) kN = 340.1 kN Ultimate Dead Load = 340.1 kN x 1.4 = 476.14 kN

Total Live Load = (3.24+9.72+29.16+29.16) kN = 71.28kN Ultimate Live Load = 71.28 x 1.6 = 114.05 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (476.14+114.05) kN = 590.19 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

129

RAEMI SAFRI 0328385 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM ANALYSIS BEAM A/6-8 (Uniformly Distributed Load) BEAM A-C/8 (Uniformly Distributed Load and Point Load from Beam B/6-8)

COLUMN ANALYSIS COLUMN A8 (Perimeter Column) COLUMN C6 (Interior Column)

STRUCTURAL ANALYSIS OF A BUNGALOW

131

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM A/6-8

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM A/6-8 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 6-8 : Gridline 6-8 : Gridline A-B/6-8 : Gridline A-B/6-8

132

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

6 4800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab A-B/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

17.55 kN/m

Total Dead Load For 6-8 = (3.60 + 8.55 + 5.40) kN/m = 17.55 kN/m

LIVE LOAD

6

Ultimate Dead Load = Total dead load x Load factor = 17.55 kN/m x 1.4 = 24.57 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

8 4800

Slab A-B/5-6 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

ULTIMATE LOAD

8

2.70 kN/m

6

8 4800

24.57 kN/m

133

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 2.70 kN/m x 1.6 = 4.32 kN/m

4.32 kN/m

28.89 kN/m

Total Ultimate Load For 6-8 = (24.57 + 4.32) kN/m = 28.89 kN/m

REACTION FORCES

6

8 4800

Total Load = 28.89 kN/m x 4.8 m = 138.67 kN By using 8A as reference point, ΣM = 0 0 = M8A1 + (-M8A2) = (R6A x 4.8) - (138.67 x 2.4) = 4.8 R6A - 332.81 4.8 R6A = 332.81 R6A = 69.34 kN

ΣFy = 0 0 = R6A +R8A + (138.67) 0 = 69.34 + R8A -138.67 R8A = 138.67 - 69.34 = 69.33 (≈69.34 kN)

2400

M8A1

2400

138.67

M8A2 R6A

R8A

28.89 kN/m

69.34 kN

69.33 kN

SHEAR FORCES 69.34 - 138.67 = -69.33 kN -69.33 + 69.33 = 0 kN

69.34 kN -69.33 + 69.33 = 0kN

69.34 - 138.67 = -69.33 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

134

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 69.34 kN x 2.4 m x ½ = 83.21 kNm 83.21 kNm Negative Area = -69.33 kN x 2.4 m x ½ = -83.20 kNm

∴ Positive area = Negative area 83.21 kNm + (-83.20 kNm) = 0.1 (≈0)

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

83.21 - 83.20

≈ 0 kNm

135

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM B/6-8

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM B/6-8 CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 6-8 : Gridline 6-8 : Gridline A-B/6-8, B-C/6-8 : Gridline A-B/6-8, B-C/6-8

136

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

6 4800

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.50) m² x 24 kN/m³ = 2.40 kN/m

2.40 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab A-B/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

Slab B-C/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 3.6/2 = 3 kN/m² x 1.8m = 5.40 kN/m

5.40 kN/m

21.75 kN/m

Total Dead Load For 6-8 = (2.40 + 8.55 + 5.40 + 5.40) kN/m = 21.75 kN/m

LIVE LOAD Slab A-B/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

8

6

8 4200

2.70 kN/m

137

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Slab B-C/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 3.6/2 = 2.70 kN/m

2.70 kN/m

5.40 kN/m

Total Live Load For 6-8 = (2.70 + 2.70) kN/m = 5.40 kN/m ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 21.75 kN/m x 1.4 = 30.45 kN/m

Ultimate Live Load = Total live load x Load factor = 5.40 kN/m x 1.6 = 8.64 kN/m

6

8 4800

30.45 kN/m

8.64 kN/m

39.09 kN/m Total Ultimate Load For 5-6 = (30.45 + 8.64) kN/m = 39.09 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

138

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

6

8 4800

Total Load = 39.09 kN/m x 4.8 m = 187.63 kN

2400

187.63 kN

By using 8b as reference point; ΣM = 0 0 = M8b1 + (-M8b2) = (R6b x 4.8) - (187.63 x 2.4) = 4.8 R6b - 450.31 4.8 R6b = 450.31 R6b = 93.81 kN

ΣFy = 0 0 = R6b +R8b + (-187.63) 0 = 93.81 + R8b -187.63 R8b = 187.63 - 93.81 = 93.82 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

2400

M8b1 M8b2

R6b

R8b

187.63 kN/m

93.81 kN

93.82 kN

139

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM 8/A-C

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 8/A-C CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline A-C : Gridline A-C : Gridline A-B/6-8 & B-C/6-8 : Gridline A-B/6-8 & B-C/6-8

140

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

Slab A-B/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8 m x 2/3 = 3.60 kN/m

A

B 7200 3600

3600

3.60 kN/m

8.55 kN/m

3.60 kN/m

Slab B-C/7-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125m x 24 kN/m³) x 3.6/2 x 2/3 = 3 kN/m² x 1.8m x 2/3 = 3.60 kN/m

Total Dead Load For A-B = (3.60 + 8.55 + 3.60) kN/m = 15.75 kN/m For B-C = (3.60 + 8.55 + 3.60) kN/m = 15.75 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

C

3.60 kN/m

15.75 kN/m

15.75 kN/m

141

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

LIVE LOAD Slab A-B/6-8 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

A

B 7200 3600

STRUCTURAL ANALYSIS OF A BUNGALOW

3600

1.80 kN/m

1.80 kN/m

Slab B-C/6-8 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 3.6/2 x 2/3 = 1.80 kN/m

Total Live Load For A-B = 1.80 kN/m For B-C = 1.80 kN/m

C

1.80 kN/m

1.80 kN/m

142

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Ultimate Dead Load For A-B = Total dead load x Load factor = 15.75 kN/m x 1.4 = 22.05 kN/m For B-C = Total dead load x Load factor = 15.75 kN/m x 1.4 = 22.05 kN/m

Ultimate Live Load For A-B = Total live load x Load factor = 1.80 kN/m x 1.6 = 2.88 kN/m For B-C = Total live load x Load factor = 1.80 kN/m x 1.6 = 2.88 kN/m

Total Ultimate Load For A-B = (22.05 + 2.88) kN/m = 24.93 kN/m For B-C = (22.05 + 2.88) kN/m = 24.93 kN/m

A

B

C

7200 3600

3600

22.05 kN/m

22.05 kN/m

2.88 kN/m

2.88 kN/m

24.93 kN/m

24.93 kN/m

93.82 kN Point Load = R8b = 93.82 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

24.93 kN/m

24.93 kN/m

143

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES Total Load For A-B = 24.93 kN/m x 3.6 m = 89.75 kN For B-C = 24.93 kN/m x 3.6 m = 89.75 kN

B

A

C

7200 1800

1800

1800

1800

93.82 kN 89.75 kN 89.75 kN M8c1

By using 8c as reference point, ΣM = 0 0 = M8c1 + (-M8c2) + (-M8c3) + (-M8c4) = (R8a x 7.2) - (89.75 x 5.4) - (93.82 x 3.6) - (89.75 x 1.8) = 7.2 R5a - 484.65 - 337.75 - 161.55 7.2 R8a = 983.95 R8a = 136.66 kN

ΣFy = 0 0 = R8a +R8c + (-89.75) + (-93.82) + (-89.75) 0 = 136.66 + Rb - 89.75 - 93.82 - 89.75 R8c = 89.75 + 93.82 + 89.75 - 136.66 = 136.66 kN

M8c2

M8c3

M8c4

R8a

R8c 93.82 kN 24.93 kN/m

24.93 kN/m

136.66 kN

136.66 kN SHEAR FORCES 136.66 - 89.75 = 46.91 kN 46.91 - 93.82 = -46.91 kN -46.91 - 89.75 = -136.66 kN -136.66 + 136.66 = 0 kN

136.66 kN

136.66 - 89.75 = 46.91kN

46.91 - 93.82 = -46.91kN

BENDING MOMENT Positive Area = (136.66 + 46.91) kN x ½ x 3.6 m = 221.01 kNm

-136.66 + 136.66 = 0kN

-46.91 - 89.75 = -136.66 kN

221.01 kNm

Negative Area = (-46.91 - 136.66) kN x ½ x 3.6 m = -221.01 kNm ∴ Positive area = Negative area 0 STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

221.01 - 221.01

= 0 kNm

144

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN A8

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (2.4 x 3.6) m² x 1.0 kN/m² = 8.64 kN

Roof Weight = (2.4 x 3.6) m² x 0.5 kN/m² = 4.32 kN

Roof Beam = (2.4 + 3.6) m x 1.44 kN/m = 8.64 kN

Total Dead Load = (8.64 + 8.64) kN = 17.28 kN STRUCTURAL ANALYSIS OF A BUNGALOW

145

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.4 x 3.6) m² x 3.6 kN/m² = 31.10 kN

Total Live Load = (2.4 x 3.6) m² x 1.5 kN/m² = 12.96 kN

Beam Self Weight = (2.4 + 3.6) m x 1.44 kN/m + 2.4 m x 1.44 kN/m x ½ = 8.64 kN + 1.73 kN = 10.37 kN

Brick Wall Self Weight = (2.4 + 3.6) x 10 kN/m = 60 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

146

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (31.10 + 10.37 + 60 + 6.48) kN = 107.95 kN

FIRST FLOOR TRIBUTARY AREA

STRUCTURAL ANALYSIS OF A BUNGALOW

147

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.4 x 3.6) m² x 3.6 kN/m² = 31.10 kN

Total Live Load = (2.4 x 3.6) m² x 1.5 kN/m² = 12.96 kN

Beam Self Weight = (2.4 + 3.6) m x 1.44 kN/m + 2.4 m x 1.44 kN/m x ½ = 8.64 kN + 1.73 kN = 10.37 kN

Brick Wall Self Weight = (2.4+3.6) m x 10 kN/m + 2.4 x 10 kN/m x ½ = 72 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (31.10 + 10.37 + 72 + 6.48) kN = 119.95 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

148

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.4 x 3.6) m² x 3.6 kN/m² = 31.10 kN

Total Live Load = (2.4 x 3.6) m² x 1.5 kN/m² = 12.96 kN

Beam Self Weight = (2.4 + 3.6) m x 1.44 kN/m + 2.4 m x 1.44 kN/m x ½ = 8.64 kN + 1.73 kN = 10.37 kN

Brick Wall Self Weight = (2.4+3.6) m x 10 kN/m + 2.4 x 10 kN/m x ½ = 72 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

149

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (31.10 + 10.37 + 72 + 6.48) kN = 119.95 kN

ULTIMATE LOAD Total Dead Load = (17.28 + 107.95 + 119.95 + 119.95) kN = 365.13 kN Ultimate Dead Load = 365.13 kN x 1.4 = 511.18 kN

Total Live Load = (4.32 + 12.96 + 12.96 + 12.96) kN = 43.2 kN Ultimate Live Load = 43.2 x 1.6 = 69.12 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (511.18 + 69.12) kN = 580.30 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

150

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN C6

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (4.5 x 7.2) m² x 1.0 kN/m² = 32.4 kN

Roof Weight = (4.5 x 7.2) m² x 0.5 kN/m² = 16.2 kN

Roof Beam = (4.5 + 7.2)m x 1.44 kN/m = 16.85 kN Total Dead Load = (32.4 + 16.85) kN = 49.25 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

151

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 7.2) m² x 3.6 kN/m² = 116.64 kN

Total Live Load = (4.5 x 7.2) m² x 1.5 kN/m² = 48.6 kN

Beam Self Weight = (4.5 + 7.2) m x 1.44 kN/m + (4.5 + 4.5) m x 1.44 kN/m x ½ = 16.85 kN + 6.48 kN = 23.33 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (116.64 + 23.33 + 6.48) kN = 146.45 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

152

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 7.2) m² x 3.6 kN/m² = 116.64 kN

Total Live Load = (4.5 x 7.2) m² x 1.5 kN/m² = 48.6 kN

Beam Self Weight = (4.5 + 7.2) m x 1.44 kN/m + (4.5 + 4.5) m x 1.44 kN/m x ½ = 16.85 kN + 6.48 kN = 23.33 kN Brick Wall Self Weight = 4.5 m x 10 kN/m + (4.5 + 4.5) m x 10 kN/m x ½ = 45 kN + 45 kN = 90 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN STRUCTURAL ANALYSIS OF A BUNGALOW

153

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Total Dead Load = (116.64 + 23.33 + 90 + 6.48) kN = 236.45 kN

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.5 x 7.2) m² x 3.6 kN/m² = 116.64 kN

Total Live Load = (4.5 x 7.2) m² x 1.5 kN/m² = 48.6 kN

Beam Self Weight = (4.5 + 7.2) m x 1.44 kN/m + (4.5 + 4.5) m x 1.44 kN/m x ½ = 16.85 kN + 6.48 kN = 23.33 kN Brick Wall Self Weight = 4.5 m x 10 kN/m + (4.5 + 4.5) m x 10 kN/m x ½ = 45 kN + 45 kN = 90 kN STRUCTURAL ANALYSIS OF A BUNGALOW

154

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Total Dead Load = (116.64 + 23.33 + 90 + 6.48) kN = 236.45 kN

ULTIMATE LOAD Total Dead Load = (49.25 + 146.45 + 236.45 + 236.45) kN = 668.6 kN Ultimate Dead Load = 668.6 kN x 1.4 = 936.04 kN Total Live Load = (16.20 + 48.60 + 48.60 + 48.60) kN = 162 kN Ultimate Live Load = 162 x 1.6 = 259.20 kN Total Ultimate Load = Ultimate dead load + Ultimate live load = (936.04 + 259.20) kN = 1195.24 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

155

YEW JEY YEE 0327708 STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM ANALYSIS BEAM 8/G-H (Uniformly Distributed Load) BEAM H/6-8 (Uniformly Distributed Load and Point Load from Beam 7/H-I)

COLUMN ANALYSIS COLUMN G8 (Perimeter Column) COLUMN H6 (Interior Column)

STRUCTURAL ANALYSIS OF A BUNGALOW

157

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM ANALYSIS BEAM 8/G-H

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 8/G-H CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline G-H : Gridline G-H : Gridline G-H/6-8 : Gridline G-H/6-8

158

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

G 5400

Beam Self Weight = Beam size x Density of reinforced concrete = (0.25 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab G-H/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 = (0.125m x 24 kN/m³) x 4.8/2 = 3 kN/m² x 2.4m = 7.20 kN/m

7.20 kN/m

19.35 kN/m

Total Dead Load For G-H = (3.60 + 8.55 + 7.20) kN/m = 19.35 kN/m

LIVE LOAD

G

Ultimate Dead Load = Total dead load x Load factor = 19.35 kN/m x 1.4 = 27.09 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

H 5400

Slab G-H/6-8 = Live load (UBBL) x Lx/2 = 1.5 kN/m² x 4.8/2 = 3.60 kN/m

ULTIMATE LOAD

H

3.60 kN/m

G

H 5400

27.09 kN/m

159

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

Ultimate Live Load = Total live load x Load factor = 3.60 kN/m x 1.6 = 5.76 kN/m

5.76 kN/m

32.85 kN/m

Total Ultimate Load For G-H = (27.09 + 5.76) kN/m = 32.85 kN/m

REACTION FORCES

G

H 5400

Total Load = 32.85 kN/m x 5.4 m = 177.39 kN By using 8H as reference point, ΣM = 0 0 = M8H1 + (-M8H2) = (R8G x 5.4) - (177.39 x 2.7) = 5.4 R8G - 478.95 5.4 R8G = 478.95 R8G = 88.70 kN

ΣFy = 0 0 = R8G +R8G + (-177.39) 0 = 88.70 + R8G - 177.39 R8G = 177.39 - 88.70 = 88.70 kN

2700

M8H1

2700

177.39 kN

M8H2 R8G

R8H

32.85 kN/m

88.70 kN

88.70 kN

SHEAR FORCES 88.70 - 177.39 = -88.70 kN -88.70 + 88.70 = 0 kN

88.70 kN -88.70 + 88.70 = 0kN

88.70 - 177.39 = -88.70 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

160

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT Positive Area = 88.70 kN x 2.7 m x ½ = 119.74 kNm 119.74 kNm Negative Area = -88.70 kN x 2.7 m x ½ = -119.74 kNm

∴ Positive area = Negative area 119.74 kNm + (-119.74 kNm) = 0

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

119.74 - 119.74 = 0 kNm

161

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM 7/H-I

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 7/H-I CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline H-I : Gridline H-I

162

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

H

I 3000

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Total Dead Load For H-I = (3.60 + 8.55) kN/m = 12.15 kN/m

12.15 kN/m

H ULTIMATE LOAD Ultimate Dead Load = Total dead load x Load factor = 12.15 kN/m x 1.4 = 17.01 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

I 3000

17.01 kN/m

163

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

H

I 3000

Total Load = 17.01 kN/m x 3 m = 51.03 kN By using 7I as reference point, ΣM = 0 0 = M7I1 + (-M7I2) = (R7H x 3) - (51.03 x 1.5) = 3 R7H - 76.55 3 R7H = 76.55 R7H = 25.52 kN

ΣFy = 0 0 = R7H +R7I + (-51.03) 0 = 25.52 + R7I -51.03 R7I = 51.03 -25.52 = 25.52 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

1500

M7I1

1500

51.03 kN

M7I2

R7H

R7I

17.01 kN/m

25.52 kN

25.52 kN

164

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BEAM H/6-8

FIRST FLOOR LOAD DISTRIBUTION PLAN

BEAM 5/A-C CARRIES: Dead Load from beam self weight Dead Load from brick wall self weight Dead Load from slab self weight Live Load from slab

STRUCTURAL ANALYSIS OF A BUNGALOW

: Gridline 6-8 : Gridline 6-8 : Gridline G-H/6-8 : Gridline G-H/6-8

165

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

DEAD LOAD

6

Beam Self Weight = Beam size x Density of reinforced concrete = (0.20 x 0.60) m² x 24 kN/m³ = 3.60 kN/m

8

4800 3300

1500

3.60 kN/m

Brick Wall Self Weight = Wall height x Wall thickness x Density of brick = (3.00 x 0.15) m² x 19 kN/m³ = 8.55 kN/m

8.55 kN/m

Slab G-H/6-8 Self Weight = Slab thickness x Density of reinforced concrete x Lx/2 x 2/3 = (0.125 m x 24 kN/m³) x 5.4/2 x 2/3 = 3 kN/m² x 2.7 m x 2/3 = 5.40 kN/m

5.40 kN/m

15.55 kN/m

Total Dead Load For 6-8 = (3.60 + 8.55 + 5.40) kN/m = 15.55 kN/m

LIVE LOAD

7

6

7

8

4800

Slab G-H/6-8 = Live load (UBBL) x Lx/2 x 2/3 = 1.5 kN/m² x 5.4/2 x 2/3 = 2.7 kN/m

STRUCTURAL ANALYSIS OF A BUNGALOW

3300

1500

5.40 kN/m

166

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Ultimate Dead Load For 6-8 = Total dead load x Load factor = 15.55 kN/m x 1.4 = 21.77 kN/m

Ultimate Live Load For 6-8 = Total live load x Load factor = 2.7 kN/m x 1.6 = 4.32 kN/m

Total Ultimate Load For 6-8 = (21.77 + 4.32) kN/m = 26.09 kN/m

Point Load = R7H (from Beam 7/H-I) = 21.52 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

6

7

8

4800 3300

1500

21.77 kN/m

4.32 kN/m

26.09 kN/m

21.52 kN 26.09 kN/m

167

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

REACTION FORCES

7

6

Total Load For 6-7 = 26.09 kN/m x 3.3 m = 125.22

By using 8H as reference point, ΣM = 0 0 = M8H1 + (-M8H2) + (-M8H3) = (R8H x 4.8) - (125.22 x 2.4) - (25.52 x 1.5) = 4.8 R6H - 300.53 - 38.28 4.8 R6H = 338.81 R6H = 70.59 kN

ΣFy = 0 0 = R6H +R8H + (-86.10) + (-39.12) + (-25.52) 0 = 70.59 + R8H - 150.73 R8H = 150.74 - 70.59 = 80.15

8

4800 2400

800

1500

25.52 kN M8H1

125.22 kN

M8H2

M8H3

R6H

R8H 25.52 kN 26.09 kN/m

70.59 kN

80.15 kN

SHEAR FORCES 70.59 - 86.10 = -15.51 kN -15.51 - 25.52 = -41.03 kN -41.03 - 39.13 = -80.16 kN -80.16 + 80.15 = -0.01 kN (≈0 kN)

70.59 kN 70.59 - 86.10 = -15.51kN

-41.03 - 39.13 = -80.15 kN

Positive Area = (147.63 + 42.55) kN x ½ x 3.6 m = 342.32 kNm 342.32 kNm

Negative Area = (-42.56 - 147.64) kN x ½ x 3.6 m = -342.36 kNm (≈342.32 kNm)

STRUCTURAL ANALYSIS OF A BUNGALOW

≈ 0 kN

-15.51 - 25.52 = -41.03kN

BENDING MOMENT

∴ Positive area ≈ Negative area 342.32 kNm + (-342.36 kNm) = -0.04 (≈0)

-80.16 - 80.10

0 kNm

342.32 - 342.35

≈ 0 kNm

168

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

BENDING MOMENT 3.3 - 0.8

Positive Area 15,51/70.59 = x/3.30 x = 0.80

= 2.50

x = 0.8

3.3 - 0.80 = 2.50 = ½(70.59 x 2.50) + ½(15.51 x 0.73) = 88.23 + 5.66 = 93.09 kNm

80.15 - 41.03

= 39.12

Negative Area 80.15 - 41.03 = 39.12

93.09 kNm

= (1.5 x 41.03) + ½(1.5 x 39.12) = 61.77 + 31.34 = 93.11 ∴ Positive area ≈ Negative area 93.09 kNm + (-93.11 kNm) = -0.02 (≈0)

STRUCTURAL ANALYSIS OF A BUNGALOW

0 kNm

93.09 - 93.11

≈ 0 kNm

169

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN G8

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (6.3 x 2.4) m² x 1.0 kN/m² = 15.12 kN

Roof Weight = (6.3 x 2.4) m² x 0.5 kN/m² = 7.56 kN

Roof Beam = (6.3 + 2.4) m x 1.44 kN/m = 12.53 kN

Total Dead Load = (15,12 + 12.53) kN = 27.65 kN STRUCTURAL ANALYSIS OF A BUNGALOW

170

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD Slab Self Weight = (6.3 x 2.4) m² x 3.6 kN/m² = 54.43 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Beam Self Weight = (6.3 + 2.4) m x 1.44 kN/m + (2.4 m x 1.44 kN/m x ½) = 12.53 kN + 1.73 kN = 14.26 kN

Total Dead Load = (54.43 + 14.26 + 97.20 + 6.48) kN = 172.47 kN

Brick Wall Self Weight = (3.6 + 2.7) m x 10 kN/m = 97.20 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (6.3 x 2.4) m² x 1.5 kN/m² = 22.68 kN

171

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD Slab Self Weight = (6.3 x 2.4) m² x 3.6 kN/m² = 54.43 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Beam Self Weight = (6.3 + 2.4) m x 1.44 kN/m + (2.4 m x 1.44 kN/m x ½ ) = 12.53 kN + 1.73 kN = 14.26 kN

Total Dead Load = (54.43 + 14.26 + 114 + 6.48) kN = 189.17 kN

Brick Wall Self Weight = (6.3 + 2.7 + 2.4) m x 10 kN/m = 114 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

LIVE LOAD Total Live Load = (6.3 x 2.4) m² x 1.5 kN/m² = 22.68 kN

172

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD Slab Self Weight = (6.3 x 2.4) m² x 3.6 kN/m² = 54.43 kN

Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN

Beam Self Weight = (6.3 + 2.4) m x 1.44 kN/m + (2.4 m x 1.44 kN/m x ½ ) = 12.53 kN + 1.73 kN = 14.26 kN

Total Dead Load = (54.43 + 14.26 + 87 + 6.48) kN = 162.27 kN

LIVE LOAD Brick Wall Self Weight = (6.3+2.4) m x 10 kN/m = 87 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

Total Live Load = (6.3 x 2.4) m² x 1.5 kN/m² = 22.68 kN

173

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Total Dead Load = (27.65 + 172.47 + 189.17 + 162.27) kN = 551.56 kN Ultimate Dead Load = 551.56 kN x 1.4 = 772.18 kN

Total Live Load = (7.56 + 22.68 + 22.68 + 22.68) kN = 75.60 kN Ultimate Live Load = 75.60 x 1.6 = 120.96 kN

Total Ultimate Load = Ultimate dead load + Ultimate live load = (772.18 + 120.96) kN = 893.14 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

174

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

COLUMN ANALYSIS COLUMN H6

ROOF LEVEL TRIBUTARY AREA

ROOF LEVEL DEAD LOAD

LIVE LOAD

Roof Weight = (4.2 x 3.75) m² x 1.0 kN/m² = 15.75 kN

Roof Weight = (4.2 x 3.75) m² x 0.5 kN/m² = 7.88 kN

Roof Beam = (4.2 + 3.75)m x 1.44 kN/m = 11.45 kN Total Dead Load = (15.75 + 11.45) kN = 27.20 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

175

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

SECOND FLOOR TRIBUTARY AREA

SECOND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.7 x 3.75) m² x 3.6 kN/m² = 23.22 kN

Total Live Load = (2.7 x 3.75) m² x 1.5 kN/m² = 15.19 kN

Beam Self Weight = (2.7 + 3.75) m x 1.44 kN/m = 9.28 kN Brick Wall Self Weight = (3.75 + 2.7) m x 10 kN/m = 64.50 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (23.22 + 9.28 + 64.50 + 6.48) kN = 103.48 kN STRUCTURAL ANALYSIS OF A BUNGALOW

176

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

FIRST FLOOR TRIBUTARY AREA

FIRST FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (2.7 x 3.75) m² x 3.6 kN/m² = 23.22 kN

Total Live Load = (2.7 x 3.75) m² x 1.5 kN/m² = 15.19 kN

Beam Self Weight = (2.7 + 3.75) m x 1.44 kN/m = 9.28 kN Brick Wall Self Weight = 3.75 m x 10 kN/m = 37.50 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (23.22 + 9.28 + 37.50 + 6.48) kN = 76.48 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

177

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

GROUND FLOOR TRIBUTARY AREA

GROUND FLOOR DEAD LOAD

LIVE LOAD

Slab Self Weight = (4.2 x 3.75) m² x 3.6 kN/m² = 56.7 kN

Total Live Load = (4.2 x 3.75) m² x 1.5 kN/m² = 23.63 kN

Beam Self Weight = (4.2 + 3.75) m x 1.44 kN/m = 11.45 kN Brick Wall Self Weight = 3.75 m x 10 kN/m = 37.50 kN Column Self Weight = (0.3 x 0.3 x 3.0) m³ x 24 kN/m³ = 6.48 kN Total Dead Load = (56.7 + 11.45 + 37.50 + 6.48) kN = 112.13 kN STRUCTURAL ANALYSIS OF A BUNGALOW

178

STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

ULTIMATE LOAD Total Dead Load = (27.20 + 103.48 + 76.48 + 112.13) kN = 319.29 kN Ultimate Dead Load = 319.29 kN x 1.4 = 447 kN Total Live Load = (7.88 + 15.19 + 15.19 + 23.63) kN = 61.89 kN Ultimate Live Load = 61.89 x 1.6 = 99.02 kN Total Ultimate Load = Ultimate dead load + Ultimate live load = (447 + 99.02) kN = 546.02 kN

STRUCTURAL ANALYSIS OF A BUNGALOW

179