Building Structures by kalvinbongjiaying

SCHOOL OF ARCHITECTURE, BUILDING AND DESIGN

BUILDING STRUCTURES (BLD 60103) PROJECT 1: STRUCTURAL DESIGN AND ANALYSIS OF A BUNGALOW

A GROUP EFFORT BY: KALVIN BONG JIA YING // 0327822 KENNETT LIM ROONG XIANG // 0325031 LEE JIA MIN // 0324126 TAN CHIN WERNG // 0324408 YUEN XUAN HUI // 0324292 TUTOR: MR. MOHD. ADIB RAMLI

TABLE OF CONTENT 1.0 Brief Description

2.0 Floor Plans

3.0 Design Brief (Quantity Life and Dead Loads Acting on Structure)

4.0 Structural Plans

5.0 Load Distribution Diagrams

6.0 Tributary Area Diagrams

7.0 Beam & Column Analysis 7.1 Kalvin Bong Jia Ying

7.2 Kennett Lim Roong Xiang

7.3 Lee Jia Min

7.4 Tan Chin Werng

120

7.5 Yuen Xuan Hui

150

1.0 BRIEF DESCRIPTION In this project, we are required to form a group of five, to design a 2-storey bungalow with pitched roof. Our bungalow building layout is a combination of one building outline from category A for ground floor and another from category B for first floor.

Category A (Ground Floor)

Category B (First Floor)

Our bungalow consists of the following component: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

1 entrance 1 living room 2 dining rooms 1 dry kitchen 1 wet kitchen 1 storeroom 1 powder room 1 laundry room 1 family area 1 study room 1 maid room 1 guest bedroom 3 bedrooms 3 bathrooms 1 master bedroom with attached bathroom 2

2.0 FLOOR PLANS

GROUND FLOOR PLAN SCALE 1:150

FIRST FLOOR PLAN SCALE 1:150

ROOF PLAN SCALE 1:150

3.0 DESIGN BRIEF (Quantity Life and Dead Loads Acting on Structure) Dimension of Structure Structure Slab Wall Beam Column

Dimension 0.15m (thickness) 0.15 x 3m (thickness x height) 0.2m x 0.3m (width x depth) 0.3m x 0.3m x 3m (width x length x height)

Standard Weight of Material Material Brickwork Reinforced concrete

Standard Weight (kN/m3) 19 24

Structure Self-Weight Structure Concrete slab Brick wall Beam Column Roof

Calculation 0.15m x 24kN/m3 0.15m x 3m x 19kN/m3 0.2m x 0.3m x 24kN/m3 0.3m x 0.3m x 3m x 24kN/m3 -

Self-Weight 3.6kN/m2 8.55kN/m 1.44kN/m 6.48kN/m 1.0kN/m2

4.0 STRUCTURAL PLANS

FOUNDATION PLAN SCALE 1:150

STRUCTURAL GROUND FLOOR PLAN SCALE 1:150

STRUCTURAL FIRST FLOOR PLAN SCALE 1:150

STRUCTURAL ROOF PLAN SCALE 1:150

5.0 LOAD DISTRIBUTION DIAGRAMS

LOAD DISTRIBUTION GROUND FLOOR PLAN SCALE 1:150

LOAD DISTRIBUTION FIRST FLOOR PLAN SCALE 1:150

LOAD DISTRIBUTION ROOF PLAN SCALE 1:150

6.0 TRIBUTARY AREA DIAGRAMS

TRIBUTARY AREA GROUND FLOOR PLAN SCALE 1:150

TRIBUTARY AREA FIRST FLOOR PLAN SCALE 1:150

TRIBUTARY AREA ROOF PLAN SCALE 1:150

7.0 BEAM AND COLUMN ANALYSIS

KALVIN BONG JIA YING 0327822

Overall first floor location of beams

1. 2. 3. 4. 5.

First floor beam C1/1-2b First floor beam C2/2b-3 First floor beam C1/3-4 First floor beam C-D/2b First floor beam C-D/3

1. First floor beam C1/1-2b

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

2b 4.298m

1.44 kN/m

Slab C-C1/1-2b = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.601m ÷ 2) = 3.6 kN/m2 x 1.3m = 4.68 kN/m

4.68 kN/m

5.158 kN/m

Slab C1-D/1-2b = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (4.298m ÷ 2) x ²/₃ = 3.6 kN/m2 x 2.149m x ²/₃ = 5.158 kN/m

8.55 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For 1-2b = (1.44 + 4.68 + 5.158 + 8.55) kN/m = 19.828 kN/m

19.828 kN/m

1 Live Load Slab C-C1/1-2b (Bathroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.601m ÷ 2) = 1.95 kN/m

2b 4.298m 1.95 kN/m

Slab C1-D/1-2b (Bedroom) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (4.298m ÷ 2) x ²/₃ = 2.149 kN/m

2.149 kN/m

Total Live Load For 1-2b = (1.95 + 2.149) kN/m = 4.099 kN/m

4.099 kN/m

2b 4.298m

Ultimate Load

27.759 kN/m

Ultimate Dead Load = Total dead load x 1.4 = 19.828 kN/m x 1.4 = 27.759 kN/m

6.558 kN/m

Ultimate Live Load = Total live load x 1.6 = 4.099 kN/m x 1.6 = 6.558 kN/m

34.317 kN/m

Total Ultimate Load For 1-2b = (27.759 + 6.558) kN/m = 34.317 kN/m

2b 4.298m

Reaction Forces ∑mb = 0 (Ra x 4.298) – (34.317 x 4.298) x (4.298 ÷ 2) = 0 4.298Ra = 316.966 Ra = 73.747 kN ∑Fy = 0 73.747 – (34.317 x 4.298) + Rb = 0 Rb = 73.747 kN

2.149m

2.149m 34.317 kN/m

Ra = 73.747kN

Rb = 73.747kN

Shear Force Diagram (V)

Ra = 73.747kN

73.747 – (34.317 x 4.298) = -73.747 kN （+） -73.747 + 73.747 = 0 kN

-73.747 + 73.747 = 0 kN

0 kN

（-） 73.747 – (34.317 x 4.298) = -73.747 kN

Bending Moment Diagram (M) Positive area = 73.747 x 2.149 x 1/2 = 79.24 kNm 79.24 kNm

Negative area = 73.747 x 2.149 x 1/2 = 79.24 kNm

∴ Positive Area = Negative Area (79.24 – 79.24) kNm = 0

0 kN

2. First floor beam C2/2b-3

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

3 2.758m

1.44 kN/m

Slab C2-D/2b-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.503m ÷ 2) = 3.6 kN/m2 x 1.252m = 4.5072 kN/m

4.5072 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m

8.55 kN/m

Total Dead Load For 2b-3 = (1.44 + 4.5072 + 8.55) kN/m = 14.4972 kN/m

Live Load

14.4972 kN/m

3 2.758m

Slab C2-D/2b-3 (Bathroom) = Live load (UBBL) x ᴸˣ/₂ =1.5 kN/m2 x (2.503m ÷ 2) = 1.8773 kN/m

1.8773 kN/m

Total Live Load For 2b-3 = 1.8773 kN/m 2b Ultimate Load

2.758m

Ultimate Dead Load = Total dead load x 1.4 = 14.4972 kN/m x 1.4 = 20.2961 kN/m

20.2961 kN/m

Ultimate Live Load = Total live load x 1.6 = 1.8773 kN/m x 1.6 = 3.0037 kN/m

3.0037 kN/m

23.2998 kN/m

Total Ultimate Load For 2b-3 = (20.2961 + 3.0037) kN/m = 23.2998 kN/m

2b 2.758m

Reaction Forces 1.379m

∑mb = 0 (Ra x 2.758) – (23.2998 x 2.758) x (2.758÷ 2) = 0 2.758Ra = 88.6157 Ra = 32.13 kN

23.2998 kN/m

∑Fy = 0 32.13 – (23.2998 x 2.758) + Rb = 0 Rb = 32.13 kN

Shear Force Diagram (V)

1.379m

Ra = 32.13kN

Rb = 32.13kN

Ra = 32.13kN

32.13 – (23.2998 x 2.758) = -32.13 kN （+） -32.13 + 32.13 = 0 kN

-32.13 + 32.13 = 0 kN

0 kN

（-） 32.13 – (23.2998 x 2.758) = -32.13 kN

Bending Moment Diagram (M) Positive area = 32.13 x 1.379 x 1/2 = 22.15 kNm 22.15 kNm

Negative area = 32.13 x 1.379 x 1/2 = 22.15 kNm

∴ Positive Area = Negative Area (22.15 – 22.15) kNm = 0

0 kN

3. First floor beam C1/3-4

Calculation & Analysis

Dead Load

3.945m

Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

1.44 kN/m

Slab C-C1/3-4 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.601m ÷ 2) = 3.6 kN/m2 x 1.3m = 4.68 kN/m

4.68 kN/m

4.734 kN/m

Slab C1-D/3-4 = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (3.945m ÷ 2) x ²/₃ = 3.6 kN/m2 x 1.9725m x ²/₃ = 4.734 kN/m

8.55 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For 3-4 = (1.44 + 4.68 + 4.734 + 8.55) kN/m = 19.404 kN/m

19.404 kN/m

3 Live Load

4 3.945m

Slab C-C1/3-4 (Corridor) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.601m ÷ 2) = 1.9508 kN/m

1.9508 kN/m

Slab C1-D/3-4 (Bedroom) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (3.945m ÷ 2) x ²/₃ = 1.9725 kN/m

1.9725 kN/m

Total Live Load For 3-4 = (1.9508 + 1.9725) kN/m = 3.9233 kN/m

3.9233 kN/m

3.945m

Ultimate Load Ultimate Dead Load = Total dead load x 1.4 = 19.404 kN/m x 1.4 = 27.166 kN/m

27.166 kN/m

Ultimate Live Load = Total live load x 1.6 = 3.9233 kN/m x 1.6 = 6.2773 kN/m

6.2773 kN/m

Total Ultimate Load For 3-4 = (27.166 + 6.2773) kN/m = 33.4433 kN/m

33.4433 kN/m

4 3.945m

Reaction Forces ∑mb = 0 (Ra x 3.945) – (33.4433 x 3.945) x (3.945 ÷ 2) = 0 3.945Ra = 260.239 Ra = 65.967 kN ∑Fy = 0 65.967 – (33.4433 x 3.945) + Rb = 0 Rb = 65.967 kN

1.9725m

33.4433 kN/m

Ra = 65.967kN

Rb = 65.967kN

Shear Force Diagram (V)

Ra = 65.967kN

65.967 – (33.4433 x 3.945) = -65.967 kN （+） -65.967 + 65.967 = 0 kN

-65.967 + 65.967 = 0 kN

0 kN

（-） 65.967 – (33.4433 x 3.945) = -65.967 kN

Bending Moment Diagram (M) Positive area = 65.967 x 1.9725 x 1/2 = 65.06 kNm 65.06 kNm

Negative area = 65.967 x 1.9725 x 1/2 = 65.06 kNm

∴ Positive Area = Negative Area (65.06 – 65.06) kNm = 0

0 kN

4. First floor beam C-D/2b

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

C C1 2.601m

7.76m 2.656m

D 2.503m

1.44 kN/m

Slab C-C1/1-2b = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (2.601m ÷ 2) x ²/₃ = 3.6 kN/m2 x 1.3m x ²/₃ = 3.12 kN/m

3.12 kN/m

7.7364 kN/m

Slab C1-D/1-2b = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (4.298m ÷ 2) = 3.6 kN/m2 x 2.149m = 7.7364 kN/m Slab B-C2/2b-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.758m ÷ 2) = 3.6 kN/m2 x 1.379m = 4.9644 kN/m

4.9644 kN/m

4.5054 kN/m

Slab C2-D/2b-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.503m ÷ 2) = 3.6 kN/m2 x 1.2515m = 4.5054 kN/m 8.55 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For C-C1 = (1.44 + 3.12 + 4.9644 + 8.55) kN/m = 18.0744 kN/m For C1-C2 = (1.44 + 7.7364 + 4.9644 + 8.55) kN/m = 22.6908 kN/m

22.6908 kN/m 18.0744 kN/m

22.2318 kN/m

For C2-D = (1.44 + 7.7364 + 4.5054 + 8.55) kN/m = 22.2318 kN/m

C Live Load Slab C-C1/1-2b (Bathroom) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (2.601m ÷ 2) x ²/₃ = 1.5 kN/m2 x 1.3m x ²/₃ = 1.3 kN/m

C1 C2 C 7.76m 2.601m

2.656m

3.2235 kN/m

2.0685 kN/m

Slab C2-D/2b-3 (Bathroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.503m ÷ 2) = 1.5 kN/m2 x 1.2515m = 1.8773 kN/m

1.8773 kN/m

Total Live Load For C-C1 = (1.3 + 2.0685) kN/m = 3.3685 kN/m For C1-C2 = (3.2235 + 2.0685) kN/m = 5.292 kN/m

2.503m

1.3 kN/m

Slab C1-D/1-2b (Bedroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (4.298m ÷ 2) = 1.5 kN/m2 x 2.149m = 3.2235 kN/m Slab B-C2/2b-3 (Corridor) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.758m ÷ 2) = 1.5 kN/m2 x 1.379m = 2.0685 kN/m

5.292 kN/m 3.3685 kN/m

5.1008 kN/m

For C2-D = (3.2235 + 1.8773) kN/m = 5.1008 kN/m

C Ultimate Load Total Dead Load For C-C1 = Total dead load x 1.4 = 18.0744 kN/m x 1.4 = 25.3042 kN/m

C1 C2 C 7.76m

25.3042 kN/m

Total Dead Load For C1-C2 = Total dead load x 1.4 = 22.6908 kN/m x 1.4 = 31.7671 kN/m

31.7671 kN/m

31.1245 kN/m

Total Dead Load For C2-D = Total dead load x 1.4 = 22.2318 kN/m x 1.4 = 31.1245 kN/m Total Live Load For C-C1 = Total live load x 1.6 = 3.3685 kN/m x 1.6 = 5.3896 kN/m Total Live Load For C1-C2 = Total live load x 1.6 = 5.292 kN/m X 1.6 = 8.4672 kN/m Total Live Load For C2-D = Total live load x 1.6 = 5.1008 kN/m x 1.6 = 8.1613 kN/m

2.503m

2.656m

2.601m

5.3896 kN/m

8.4672 kN/m

8.1613 kN/m

Total Ultimate Load For C-C1 = (25.3042 + 5.3896) kN/m = 30.694 kN/m For C1-C2 = (31.7671 + 8.4672) kN/m = 40.234 kN/m

40.234 kN/m 30.694 kN/m

39.286 kN/m

For C2-D = (31.1245 + 8.1613) kN/m = 39.286 kN/m Point Load For C1/1-2b Rb = 73.747 kN Point load = 73.747 kN

73.747 kN

32.13 kN

40.234 kN/m 30.694 kN/m

39.286 kN/m

Point Load For C2/2b-3 Rb = 32.13 kN Point load = 32.13 kN

C Reaction Forces ∑mb = 0 (Ra x 7.76) – (30.694 x 2.601)(6.4595) – (73.747)(5.159) – (40.234 x 2.656) (3.831) – (32.13)(2.503) – (39.286 x 2.503) (1.2515) = 0 7.76Ra = 1509.026 kN Ra = 194.46 kN ∑Fy = 0 194.46 - (30.694 x 2.601) - 73.747 - (40.234 x 2.656) - 32.13 - (39.286 x 2.503) + Rb = 0 Rb = 196.45 kN

C1 C2 C 7.76m

1.3005m

2.503m

2.656m

2.601m

1.328m 73.747 kN

1.2515m 32.13 kN

40.234 kN/m 30.694 kN/m

Ra = 194.46 kN

39.286 kN/m

Rb = 196.45 kN

Shear Force Diagram (V) 194.46 – (30.694 x 2.601) = 114.625 kN 114.625 – 73.747 = 40.878 kN 40.878 – (40.234 x 2.656) = -65.984 kN -65.984 – 32.13 = -98.114 kN -98.114 – (39.286 x 2.503) = -196.45 kN -196.45 + 196.45 = 0 kN

Ra = 194.46kN 194.46 – (30.694 x 2.601) = 114.625 kN

（+） 0 kN

114.625 – 73.747 = 40.878 kN -196.45 + 196.45 = 0 kN

X 40.878 – (40.234 x 2.656) = -65.984 kN

（-）

-65.984 – 32.13 = -98.114 kN -98.114 – (39.286 x 2.503) = -196.45 kN

Bending Moment Diagram (M) 40.878 / X (40.234 x 2.656)X = 40.878 x 2.656 106.8615X = 108.572 X = 1.016 Positive area = (194.46 + 114.625) x 2.601 x 1/2 + (40.878 x 1.016 x 1/2) = 401.965 + 20.766 = 422.731 kNm Negative area = [65.984 x (2.656 – 1.016) x 1/2] + (196.45 + 98.114) x 2.503 x 1/2 = 54.107 + 368.647 = 422.754 kNm

∴ Positive Area = Negative Area (422.754 - 422.731) kNm = 0.023 ≈ 0 kNm

422.731

0 kN

5. First floor beam C-D/3

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

C C1 2.601m

7.76m 2.656m

D 2.503m

1.44 kN/m

Slab C-C1/3-4 = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (2.601m ÷ 2) x ²/₃ = 3.6 kN/m2 x 1.3m x ²/₃ = 3.12 kN/m

3.12 kN/m

7.101 kN/m

Slab C1-D/3-4 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (3.945m ÷ 2) = 3.6 kN/m2 x 1.9725m = 7.101 kN/m Slab B-C2/2b-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.758m ÷ 2) = 3.6 kN/m2 x 1.379m = 4.9644 kN/m

4.9644 kN/m

4.5054 kN/m

Slab C2-D/2b-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.503m ÷ 2) = 3.6 kN/m2 x 1.2515m = 4.5054 kN/m 8.55 kN/m

22.0554 kN/m 18.0744 kN/m

21.5964 kN/m

For C2-D = (1.44 + 7.101 + 4.5054 + 8.55) kN/m = 21.5964 kN/m

C C1

C Live Load Slab C-C1/3-4 (Corridor) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (2.601m ÷ 2) x ²/₃ = 1.5 kN/m2 x 1.3m x ²/₃ = 1.3 kN/m

2.601m

C2 7.76m 2.656m

2.9588 kN/m

2.0685 kN/m

Slab C2-D/2b-3 (Bathroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.503m ÷ 2) = 1.5 kN/m2 x 1.2515m = 1.8773 kN/m

1.8773 kN/m

Total Live Load For C-C1 = (1.3 + 2.0685) kN/m = 3.3685 kN/m For C1-C2 = (2.9588 + 2.0685) kN/m = 5.0273 kN/m

2.503m

1.3 kN/m

Slab C1-D/3-4 (Bedroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (3.945m ÷ 2) = 1.5 kN/m2 x 1.9725m = 2.9588 kN/m Slab B-C2/2b-3 (Corridor) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.758m ÷ 2) = 1.5 kN/m2 x 1.379m = 2.0685 kN/m

5.0273 kN/m 3.3685 kN/m

4.8361 kN/m

For C2-D = (2.9588 + 1.8773) kN/m = 4.8361 kN/m

C C1

C Ultimate Load Total Dead Load For C-C1 = Total dead load x 1.4 = 18.0744 kN/m x 1.4 = 25.3042 kN/m

7.76m

25.3042 kN/m

Total Dead Load For C1-C2 = Total dead load x 1.4 = 22.0554 kN/m x 1.4 = 30.8776 kN/m

30.8776 kN/m

30.235 kN/m

Total Dead Load For C2-D = Total dead load x 1.4 = 21.5964 kN/m x 1.4 = 30.235 kN/m Total Live Load For C-C1 = Total live load x 1.6 = 3.3685 kN/m x 1.6 = 5.3896 kN/m Total Live Load For C1-C2 = Total live load x 1.6 = 5.0273 kN/m X 1.6 = 8.0437 kN/m Total Live Load For C2-D = Total live load x 1.6 = 4.8361 kN/m x 1.6 = 7.7378 kN/m

2.503m

2.656m

2.601m

5.3896 kN/m

8.0437 kN/m

7.7378 kN/m

Total Ultimate Load For C-C1 = (25.3042 + 5.3896) kN/m = 30.694 kN/m For C1-C2 = (30.8776 + 8.0437) kN/m = 38.921 kN/m

38.921 kN/m 30.694 kN/m

37.973 kN/m

For C2-D = (30.235 + 7.7378) kN/m = 37.973 kN/m Point Load For C1/3-4 Rb = 65.967 kN Point load = 65.967 kN

65.967 kN

32.13 kN

38.921 kN/m 30.694 kN/m

37.973 kN/m

Point Load For C2/2b-3 Rb = 32.13 kN Point load = 32.13 kN

C Reaction Forces ∑mb = 0 (Ra x 7.76) – (30.694 x 2.601)(6.4595) – (65.967)(5.159) – (38.921 x 2.656) (3.831) – (32.13)(2.503) – (37.973 x 2.503) (1.2515) = 0 7.76Ra = 1451.417 kN Ra = 187.04 kN ∑Fy = 0 187.04 - (30.694 x 2.601) – 65.967 - (38.921 x 2.656) - 32.13 - (37.973 x 2.503) + Rb = 0 Rb = 189.31 kN

C1 C2 C 7.76m

1.3005m

2.503m

2.656m

2.601m

1.328m 65.967 kN

1.2515m 32.13 kN

38.921 kN/m 30.694 kN/m

Ra = 187.04 kN

37.973 kN/m

Rb = 189.31 kN

Shear Force Diagram (V) 187.04 – (30.694 x 2.601) = 107.205 kN 107.205 – 65.967 = 41.238 kN 41.238 – (38.921 x 2.656) = -62.136 kN -62.136 – 32.13 = -94.266 kN -94.266 – (37.973 x 2.503) = -189.31 kN -189.31 + 189.31 = 0 kN

Ra = 187.04kN 187.04 – (30.694 x 2.601) = 107.205 kN

（+） 0 kN

107.205 – 65.967 = 41.238 kN -189.31 + 189.31 = 0 kN

X 41.238 – (38.921 x 2.656) = -62.136 kN

（-）

-62.136 – 32.13 = -94.266 kN -94.266 – (37.973 x 2.503) = -189.31 kN

Bending Moment Diagram (M) 41.238 / X (38.921 x 2.656)X = 41.238 x 2.656 103.374X = 109.528 X = 1.06 Positive area = (187.04 + 107.205) x 2.601 x 1/2 + (41.238 x 1.06 x 1/2) = 382.666 + 21.856 = 404.522 kNm Negative area = [62.136 x (2.656 – 1.06) x 1/2] + (189.31 + 94.266) x 2.503 x 1/2 = 49.585 + 354.895 = 404.48 kNm

∴ Positive Area = Negative Area (404.522 - 404.48) kNm = 0.042≈ 0 kNm

404.522

0 kN

Overall location of columns

1. Column C3 2. Column D3

1. Column C3 At Roof Level,

Dead Load Roof Weight = (3.9975 x 5.9225) m2 x 1.0 kN/m2 = 23.675 kN Roof Beam = [(2.0425 + 3.880) + (1.9725 x 2)] m x 1.44 kN/m = 9.8675 m x 1.44 kN/m = 14.209 kN 43

Total Dead Load = (23.675 + 14.209) kN = 37.884 kN Live Load Roof Weight = (3.9975 x 5.9225) m2 x 0.5 kN/m2 = 11.838 kN At First Floor Level,

Dead Load Brick Wall = [(2.0425 + 3.880) + (1.9725 x 2)] m x 8.55 kN/m = 9.8675 m x 8.55 kN/m = 84.367 kN Reinforced Concrete Beam = [(2.0425 + 3.880) + (1.9725 x 2)] m x 1.44 kN/m = 9.8675 m x 1.44 kN/m = 14.209 kN Reinforced Concrete Slab = (3.9975 x 5.9225) m2 x 3.6 kN/m2 = 85.231 kN Total Dead Load = (84.367 + 14.209 + 85.231) kN = 183.807 kN Live Load Reinforced Concrete Slab = (3.9975 x 5.9225) m2 x 1.5 kN/m2 = 35.513 kN

At Ground Floor Level,

Dead Load Brick Wall = [(2.0425 + 3.880) + 1.9725 + (2.5505 x 2)] m x 8.55 kN/m = 12.996 m x 8.55 kN/m = 111.116 kN Reinforced Concrete Beam = [(2.0425 + 3.880) + 1.9725 + (2.5505 x 2)] m x 1.44 kN/m = 12.996 m x 1.44 kN/m = 18.714 kN 46

Reinforced Concrete Slab = (3.9975 x 5.9225) m2 x 3.6 kN/m2 = 85.231 kN Total Dead Load = (111.116 + 18.714 + 85.231) kN = 215.061 kN Live Load Reinforced Concrete Slab = (3.9975 x 5.9225) m2 x 1.5 kN/m2 = 35.513 kN Ultimate Load Total Dead Load = (37.884 + 183.807 + 215.061) kN = 436.75 kN Total Live Load = (11.838 + 35.513 + 35.513) kN = 82.864 kN Ultimate Dead Load = 436.75 x 1.4 = 611.45 kN Ultimate Live Load = 82.864 x 1.6 = 132.58 kN Total Ultimate Load = (611.45 + 132.58) kN = 744.03 kN

2. Column D3 At Roof Level,

Dead Load Roof Weight = (3.9975 x 3.880) m2 x 1.0 kN/m2 = 15.510 kN Roof Beam = (3.880 + 1.9725 + 2.025 + 2.025) m x 1.44 kN/m = 9.9025 m x 1.44 kN/m = 14.260 kN 48

Total Dead Load = (15.510 + 14.260) kN = 39.77 kN Live Load Roof Weight = (3.9975 x 3.880) m2 x 0.5 kN/m2 = 7.755 kN At First Floor Level,

Dead Load Brick Wall = (3.880 + 1.9725 + 2.025 + 2.025) m x 8.55 kN/m = 9.9025 m x 8.55 kN/m = 84.666 kN Reinforced Concrete Beam = (3.880 + 1.9725 + 2.025 + 2.025) m x 1.44 kN/m = 9.9025 m x 1.44 kN/m = 14.260 kN Reinforced Concrete Slab = (3.9975 x 3.880) m2 x 3.6 kN/m2 = 55.830 kN Total Dead Load = (84.666 + 14.260 + 55.830) kN = 154.756 kN Live Load Reinforced Concrete Slab = (3.9975 x 3.880) m2 x 1.5 kN/m2 = 23.265 kN

At Ground Floor Level,

Dead Load Brick Wall = (3.880 + 1.9725) m x 8.55 kN/m = 5.8525 m x 8.55 kN/m = 50.039 kN Reinforced Concrete Beam = (3.880 + 1.9725) m x 1.44 kN/m = 5.8525 m x 1.44 kN/m = 8.428 kN 51

Reinforced Concrete Slab = (3.9975 x 3.880) m2 x 3.6 kN/m2 = 55.837 kN Total Dead Load = (50.039 + 8.428 + 55.837) kN = 114.304 kN Live Load Reinforced Concrete Slab = (3.9975 x 3.880) m2 x 1.5 kN/m2 = 23.265 kN Ultimate Load Total Dead Load = (39.77 + 154.756 + 114.304) kN = 308.83 kN Total Live Load = (7.755 + 23.265 + 23.265) kN = 54.29 kN Ultimate Dead Load = 308.83 x 1.4 = 432.36 kN Ultimate Live Load = 54.29 x 1.6 = 86.86 kN Total Ultimate Load = (432.36 + 86.86) kN = 519.22 kN

KENNETT LIM ROONG XIANG 0325031

Overall ground floor location of beams

1. 2. 3. 4.

Ground floor beam C2/3-4 Ground floor beam C1/2-3 Ground floor beam C-D/2 Ground floor beam C-D/3

1. Ground floor beam C2/3-4

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

4 3.945m

1.44 kN/m

Slab C2-D/3-4 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.503m ÷ 2) = 3.6 kN/m2 x 1.252m = 4.505 kN/m

4.505 kN/m

4.734 kN/m

Slab C-C2/3-4 = Slab self-weight x ᴸˣ/₂ x 2/3 = (0.15m x 24 kN/m3) x (3.945m÷ 2) x 2/3 = 3.6 kN/m2 x 1.9725m x 2/3 = 4.734 kN/m

8.55 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For 3-4 = (1.44 + 4.505 + 4.734 + 8.55) kN/m = 19.229 kN/m

19.229 kN/m

3 Live Load Slab C2-D/3-4 (Bathroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.503m ÷ 2) = 1.877 kN/m

4 3.945m 1.877 kN/m

Slab C-C2/3-4 (Family dining + Dry kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (3.945m ÷ 2) = 2.959 kN/m

2.959 kN/m

Total Live Load For 3-4 = (1.877 + 2.959) kN/m

4.836 kN/m

= 4.836 kN/m Ultimate Load

3.945m 26.921 kN/m

Ultimate Dead Load = Total dead load x 1.4 = 19.229 kN/m x 1.4 = 26.921 kN/m

7.738 kN/m

Ultimate Live Load = Total live load x 1.6 = 4.836 kN/m x 1.6 = 7.738 kN/m

34.659 kN/m

Total Ultimate Load For 3-4 = (26.921 + 7.738) kN/m = 34.659 kN/m

4 3.945m

Reaction Forces ∑mb = 0 (Ra x 3.945) – (34.659 x 3.945) x (3.945 ÷ 2) = 0 3.945Ra = 269.700 Ra = 68.365 kN ∑Fy = 0 68.365 – (34.659 x 3.945) + Rb = 0 Rb = 68.365 kN

1.973m

1.973m 34.659 kN/m

Ra = 68.365 kN

Rb = 68.365 kN

Shear Force Diagram (V)

Ra = 68.365 kN

68.365 – (34.659 x 3.945) = -68.365 kN （+） -68.365 + 68.365 = 0 kN

-95.228 + 95.228 = 0 kN

0 kN 1.973m

（-） 95.228– (36.229 x 5.257) = -95.228 kN

Bending Moment Diagram (M) Positive area = 68.365 x 1.973 x 1/2 = 67.442 kNm Negative area = 68.365 x 1.973 x 1/2 = 67.442 kNm

∴ Positive Area = Negative Area (125.177– 125.177) kNm = 0

67.442 kNm

0 kN

2. Ground floor beam C1/2-3

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

3 5.101m

1.44 kN/m

Slab C1-D/2-3 = Slab self-weight x ᴸˣ/₂ x 2/3 = (0.15m x 24 kN/m3) x (5.101m ÷ 2) x 2/3 = 3.6 kN/m2 x 2.551m x 2/3 = 6.1224kN/m

6.1224 kN/m

4.682 kN/m

Slab C-C1/2-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (2.601m÷ 2) = 3.6 kN/m2 x 1.3005m = 4.6818 kN/m Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m

8.55 kN/m

Total Dead Load For 2-3 = (6.1224 + 4.6818 + 8.55 +1.44) kN/m = 20.7942 kN/m

20.7942 kN/m

2 Live Load Slab C1-D/2-3 (Dining room) = Live load (UBBL) x ᴸˣ/₂x 2/3 = 1.5 kN/m2 x (5.101 m ÷ 2) x 2/3 = 2.5505 kN/m

3 5.101m 2.5505 kN/m

Slab C-C1/2-3 (Guest bedroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (2.601m ÷ 2) = 1.9508 kN/m

1.9508 kN/m

Total Live Load For 2-3 = (1.9508 + 2.5505) kN/m

4.5013 kN/m

= 4.5013 kN/m Ultimate Load

5.101m 29.1119 kN/m

Ultimate Dead Load = Total dead load x 1.4 = 20.7942 kN/m x 1.4 = 29.1119 kN/m

7.2021 kN/m

Ultimate Live Load = Total live load x 1.6 = 4.5013 kN/m x 1.6 = 7.2021 kN/m

36.314 kN/m

Total Ultimate Load For 2-3 = (29.1119 + 7.2021) kN/m = 36.314 kN/m

D 5.101m

Reaction Forces ∑mb = 0 (Ra x 5.101) – (36.314 x 5.101) x (5.101 ÷ 2) = 0

2.5505m

36.314 kN/m

5.101Ra = 472.4488 Ra = 92.6189 kN ∑Fy = 0 92.6189 – (36.314 x 5.101) + Rb = 0 Rb = 92.6189 kN

Ra = 92.6189 kN

Rb = 92.6189 kN

Shear Force Diagram (V)

Ra = 92.6189 kN

92.6189 – (36.314 x 5.101) = -92.6189 kN （+） -92.6189 + 92.6189 = 0 kN

-92.6189 + 92.6189 = 0 kN

0 kN 2.5505m

（-） 35.155 – (28.090 x 2.503) = -35.155 kN

Bending Moment Diagram (M) Positive area = 92.6189 x 2.5505 x 1/2 = 118.323 kNm Negative area = 92.6189 x 2.5505 x 1/2 = 118.323 kNm

∴ Positive Area = Negative Area (118.323 – 118.323) kNm = 0

118.323 kNm

0 kN

3. Ground floor beam C-D/2

Calculation & Analysis

7.760m

Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

C1 2.601m

5.159m 1.44 kN/m

Slab C-C1/2-3 = Slab self-weight x ᴸˣ/₂ x 2/3 = (0.15m x 24 kN/m3) x (2.601m ÷ 2) x 2/3 = 3.6 kN/m2 x 1.3005m = 3.1212 kN/m

3.1212 kN/m

6.1212 kN/m

Slab C1-D/2 = Slab self-weight x ᴸˣ/₂ x 2/3 = (0.15m x 24 kN/m3) x (5.101m÷ 2) x 2/3 = 3.6 kN/m2 x 2.5505m x 2/3 = 6.1212 kN/m

8.55 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For C-C1 = (3.1212 + 8.55 +1.44) kN/m = 13.1112 kN/m

16.1112 kN/m 13.1112 kN/m

For C1-D = (6.1212 + 8.55 +1.44) kN/m = 16.1112 kN/m

Live Load

7.760m 2.601m

Slab C-C1/2 -3 (Dining room) = Live load (UBBL) x ᴸˣ/₂ x 2/3 = 1.5 kN/m2 x (2.601m ÷ 2) x 2/3 = 1.3005 kN/m Slab C-C2/4-4a (Maid room) = Live load (UBBL) x ᴸˣ/₂ x 2/3 = 1.5 kN/m2 x (5.159 ÷ 2) x 2/3 = 2.5795 kN/m

5.159m 1.3005 kN/m

1.252 kN/m

2.5795 kN/m

Total Live Load For C-C1 = 1.3005 kN/m

1.3005 kN/m

For C1-D = 2.5795 kN/m

Ultimate Load

C1 7.760m

Ultimate Dead Load For C-C1 = Total dead load x 1.4 = 13.1112 kN/m x 1.4 = 18.3557 kN/m For C1-D = Total dead load x 1.4 =16.1112 kN/m x 1.4 =22.5568 kN/m

18.3557 kN/m

Ultimate Live Load For C-C1 = Total live load x 1.6 = 1.3005 kN/m x 1.6 = 2.0808 kN/m For C1-D = Total Live Load x 1.6 = 2.5795 kN/m x 1.6 = 4.1272 kN/m

2.0808 kN/m

Total Ultimate Load For C-C1 = (18.3557 + 2.0808) kN/m = 20.4365 kN/m For C1-D = (22.5568 + 4.1272) kN/m = 26.684 kN/m For point load Rb= 92.6189 kN

22.5568 kN/m

4.1272 kN/m

92.6189 kN 26.684 kN/m 20.4365 kN/m

C1 7.760m

C 2.601m

Reaction Forces ∑mb = 0 (Ra x 7.760) – (20.4365 x 2.601) x (7.760 - 2.601 ÷ 2) - (26.684 x 5.159) (5.195 / 2) – (92.6189 x 5.159) = 0 7.760Ra = 1180.644 Ra = 151.58 kN

5.159m

92.6189 kN 26.684 kN/m 20.4365 kN/m

∑Fy = 151.5820 – (20.4365 x 2.601) – (26.684 x 5.159) – (92.6189) Ra = 151.58 kN + Rb = 0 Rb = 131.857 kN

Rb = 131.857 kN

Shear Force Diagram (V)

Ra = 151.58 kN

Ra = 151.58 kN 151.58 – (20.4365 x 2.601) = 98.425 kN 98.425 - 92.6189 = 5.806 kN

（+） 0 kN

5.806 – (26.684 x 5.159) = -131.857 kN

151.58 – (20.4365 x 2.601) = 98.425 kN

98.425 - 92.6189 = 5.806 kN

2.601m

5.159m

（-）

-131.857 + 131.857 = 0 kN

-131.857 + 131.857 = 0 kN kN

5.805 – (26.684 x 5.159) = -131.857 kN

Bending Moment Diagram (M) 5.806/x (26.684 x 5.159) x = 5.806 x 5.159 x = 0.218 Positive area = (151.58 + 98.425) x 2.601 x 1/2 + (5.806 x 0.218 x 0.5) = 325.764 kNm Negative area = 131.857 x (5.159 – 0.218) x 1/2 = 325.753 kNm

∴ Positive Area = Negative Area (325.764 – 325.753) kNm = 0.011 kNm ≈ 0 kNm

325.764 kNm

0 kN

4. Ground floor beam C-D/3

Calculation & Analysis Dead Load Beam Self-Weight = Beam size x Density of concrete = (0.2 x 0.3) m2 x 24 kN/m3 = 1.44 kN/m

C C1

C 2.601m

7.76m 2.656m

D 2.503m

1.44 kN/m

Slab C-C1/2-3 = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (2.601m ÷ 2) x ²/₃ = 3.6 kN/m2 x 1.3m x ²/₃ = 3.12 kN/m

3.12 kN/m

6.1212 kN/m

Slab C1-D/2-3 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (5.101m ÷ 2) x ²/₃ = 3.6 kN/m2 x 2.149m x ²/₃ = 6.1212 kN/m Slab C-C2/3-4 = Slab self-weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x (3.945 ÷ 2) = 3.6 kN/m2 x 1.379m = 7.101 kN/m

7.101 kN/m

3.004 kN/m

Slab C2-D/3-4 = Slab self-weight x ᴸˣ/₂ x ²/₃ = (0.15m x 24 kN/m3) x (2.503m ÷ 2) x ²/₃ = 3.6 kN/m2 x 1.2515m x ²/₃ = 3.0036 kN/m 8.550 kN/m

Brick Wall Self-Weight = Brick wall size x Density of brickwork = (0.15 x 3) m2 x 19 kN/m3 = 8.55 kN/m Total Dead Load For C-C1 = (1.44 + 3.12 + 7.101 + 8.55) kN/m = 20.211 kN/m For C1-C2 = (1.44 + 6.1212 + 7.101 + 8.55) kN/m = 23.212 kN/m

23.212 kN/m 20.211 kN/m

19.115 kN/m

For C2-D = (1.44 + 7.7364 + 4.5054 + 8.55) kN/m = 22.2318 kN/m 69

C Live Load Slab C-C1/2-3 (Dining room) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (2.601m ÷ 2) x ²/₃ = 1.5 kN/m2 x 1.3m x ²/₃ = 1.3005 kN/m

C1 C2 C 7.76m

3.8258 kN/m

2.9588 kN/m kN/m

Slab C2-D/3-4 (Bathroom) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m2 x (2.503m ÷ 2) x ²/₃ = 1.5 kN/m2 x 0.8343m = 1.2515 kN/m

1.2515 kN/m

Total Live Load For C-C1 = (1.3005 + 2.9588) kN/m = 4.2593 kN/m For C1-C2 = (3.8258 + 2.9588) kN/m = 6.7846 kN/m

2.503m

1.3005 kN/m

Slab C1-D/2-3 (Guest bedroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (5.101m ÷ 2) = 1.5 kN/m2 x 2.551m = 3.8258 kN/m Slab C-C2/3-4 (Family kitchen +dry kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m2 x (3.945 ÷ 2) = 1.5 kN/m2 x 1.379m x ²/₃ = 2.9588 kN/m

2.656m

2.601m

6.7846 kN/m 4.2593 kN/m

5.0773 kN/m

For C2-D = (3.8258 + 1.2515) kN/m = 5.0773 kN/m 70

C Ultimate Load Total Dead Load For C-C1 = Total dead load x 1.4 = 20.211 kN/m x 1.4 = 28.2954 kN/m

C1 C2 C 7.76m

28.2954 kN/m

32.4968 kN/m

For C1-C2 = Total dead load x 1.4 = 23.212 kN/m x 1.4 = 32.4968 kN/m

31.1245 kN/m

Total Dead Load For C2-D = Total dead load x 1.4 = 22.2318 kN/m x 1.4 = 31.1245 kN/m Total Live Load For C-C1 = Total live load x 1.6 = 4.2593 kN/m x 1.6 = 6.8149 kN/m Total Live Load For C1-C2 = Total live load x 1.6 = 6.7846 kN/m X 1.6 = 10.8554 kN/m Total Live Load For C2-D = Total live load x 1.6 = 5.0773 kN/m x 1.6 = 8.12368 kN/m

2.503m

2.656m

2.601m

6.8149 kN/m

10.8554 kN/m

8.12368 kN/m

Total Ultimate Load For C-C1 = (28.2954 + 6.8149) kN/m = 35.1103 kN/m For C1-C2 = (32.4968 + 10.8554) kN/m = 43.3522 kN/m

43.3522 kN/m 35.1103 kN/m

39.2858 kN/m

For C2-D = (31.1245 + 8.1613) kN/m = 39.2858 kN/m Point Load For C2/3-4 Rb = 68.3650 kN Point load = 68.3650 kN

92.6189 kN

68.3650 kN

43.3522 kN/m 35.1103 kN/m

39.2858 kN/m

Point Load For C1/2-3 Rb = 92.6189 kN Point load = 92.6189 kN

C Reaction Forces ∑mb = 0 (Ra x 7.76) – (35.1103 x 2.601) (6.4595) – (92.6189) (5.159) – (43.3522 x 2.656) (3.831) – (68.3650) (2.503) – (39.2858 x 2.503) (1.2515) = 0 7.76Ra = 1803.01kN Ra = 232.35 kN

C1 C2 C 7.76m 2.656m

2.601m

92.6189 kN

2.503m

68.3650 kN

43.3522 kN/m 35.1103 kN/m m

39.2858 kN/m

∑Fy = 0 232.35 - (35.1103 x 2.601) – 92.6189 - (43.3522 x 2.656) – 68.3650 - (39.2858 x 2.503) + Rb = 0 Rb = 233.43 kN Ra = 232.35 kN

Rb = 233.43 kN 72

Shear Force Diagram (V)

Ra = 232.35 kN 232.35 – (35.110 x 2.601) = 141.029kN

Ra = 232.35 kN 232.35 – (35.110 x 2.601) = 141.029 kN 141.029 - 92.6189 = 48.410 kN

（+） 0 kN

48.410 – (43.352 x 2.656) = -66.733 kN

2.601m

41.029 - 92.6189 = 48.410 kN x

2.656m 48.410 – (43.352 x 2.656) = -66.733 kN

-66.733 – 68.365 = -135.098 kN

2.503m

（-）

-233.43 + 233.43 = 0 kNkN

-66.733 – 68.365 = -135.098 kN

-135.098 – (39.286 x 2.503) = -233.43 kN -135.098 – (39.286 x 2.503) = -233.43 kN

-233.43 + 233.43 = 0 kN

Bending Moment Diagram (M) 48.410/x = 66.733/y and y=2.656 - x (48.41 x 2.65)- 48.41x = 66.733x x = 1.114m and 2.656m -1.114m=y Positive area = (232.35 + 141.03) x 2.601 x 1/2 + (48.41. x 1.114 x 1/2) = 512.54 kNm Negative area = (233.43 + 135.098) x 2.503 x 1/2 + (2.656 – 1.114) x 66.733 x 1/2 = 512.66 kNm

∴ Positive Area = Negative Area (512.54 – 512.66) kNm = 0.12 kNm ≈ 0 kNm

0 kN

512.54 kNm

0 kN

Overall location of columns

1. Column B3 2. Column B4

1. Column B4 At Roof Level,

Dead Load Roof Weight = (5.120 x 3.998) m2 x 1.0 kN/m2 = 20.467 kN Roof Beam = (3.9975 + 5.12 + 1.9725) m x 1.44 kN/m = 11.09 m x 1.44 kN/m = 15.970 kN 75

Total Dead Load = (20.467 + 15.970) kN = 36.437 kN Live Load Roof Weight = (5.120 x 3.998) m2 x 0.5 kN/m2 = 10.235 kN At First Floor Level,

Dead Load Brick Wall = (3.9975 + 5.12 + 1.9725) m x 8.55 kN/m = 11.0675 m x 8.55 kN/m = 94.627 kN Reinforced Concrete Beam = (3.9975 + 5.12 + 1.9725) m x 1.44 kN/m = 11.090 m x 1.44 kN/m = 15.970 kN Reinforced Concrete Slab = (5.120 x 3.998) m2 x 3.6 kN/m2 = 73.691 kN Reinforced concrete column = 0.3 x 0.3 x 3 x 24kN/m3 = 6.48kN Total Dead Load = (94.627 + 15.9372+ 73.691) kN = 184.255 kN Live Load Reinforced Concrete Slab = (5.120 x 3.998) m2 x 1.5 kN/m2 = 30.705 kN

At Ground Floor Level,

Dead Load Brick Wall = (3.9975 + 5.12 + 1.9725) m x 8.55 kN/m = 11.090 m x 8.55 kN/m = 94.820 kN Reinforced Concrete Beam = (3.9975 + 5.12 + 1.9725) m x 1.44 kN/m = 11.090 m x 1.44 kN/m = 15.970 kN 78

Reinforced Concrete Slab = (5.120 x 3.998) m2 x 3.6 kN/m2 = 73.691 kN Reinforced concrete column = 0.3 x 0.3 x 3 x 24kN/m3 = 6.48kN Total Dead Load = (94.820 + 15.970 + 73.691 + 6.480kN) = 881.27 kN Live Load Reinforced Concrete Slab = (5.120 x 3.998) m2 x 1.5 kN/m2 = 30.705 kN Ultimate Load Total Dead Load = (36.437 + 184.255 + 881.27) kN = 1101.96 kN Total Live Load = (10.235 + 30.705 + 30.705 kN) = 71.645 kN Ultimate Dead Load =1101.96 x 1.4 = 1542.74 kN Ultimate Live Load = 71.645 x 1.6 = 114.632 kN Total Ultimate Load = (1542.74 + 114.632) kN = 1657.376 kN 79

2. Column B3 At Roof Level,

Dead Load Roof Weight = (5.120 x 1.973) m2 x 1.0 kN/m2 = 10.102 kN Roof Beam = (5.919 + 5.120) m x 1.44 kN/m = 11.039 m x 1.44 kN/m = 15.900 kN 80

Total Dead Load = (10.102 + 15.900) kN = 25.998 kN Live Load Roof Weight = (5.120 x 1.973) m2 x 0.5 kN/m2 = 5.051 kN At First Floor Level,

Dead Load Brick Wall = (5.919 + 5.120) m x 8.55 kN/m = 11.039 m x 8.55 kN/m = 94.383 kN Reinforced Concrete Beam = (5.919 + 5.120) m x 1.44 kN/m = 11.039 m x 1.44 kN/m = 15.896 kN Reinforced Concrete Slab = (5.919 + 5.120) m2 x 3.6 kN/m2 = 39.740 kN Reinforced concrete column = 0.3 x 0.3 x 3 x 24kN/m3 = 6.48kN Total Dead Load = (94.383 + 15.896 + 39.740 + 6.48) kN = 156.499 kN Live Load Reinforced Concrete Slab = (5.120 x 1.973) m2 x 1.5 kN/m2 = 15.153kN

At Ground Floor Level,

Dead Load Brick Wall = (3.880 + 1.9725) m x 8.55 kN/m = 5.8525 m x 8.55 kN/m = 50.039 kN Reinforced Concrete Beam = (3.880 + 1.9725) m x 1.44 kN/m = 5.8525 m x 1.44 kN/m = 8.428 kN 83

Reinforced Concrete Slab = (5.120 x 1.973) m2 x 3.6 kN/m2 = 36.366 kN Reinforced concrete column = 0.3 x 0.3 x 3 x 24kN/m3 = 6.48kN Total Dead Load = (50.039 + 8.428 + 55.837) kN = 101.313 kN Live Load Reinforced Concrete Slab = (5.120 x 1.973) m2 x 1.5 kN/m2 = 15.153 kN Ultimate Load Total Dead Load = (25.998 + 156.499 + 101.313) kN = 283.81 kN Total Live Load = (5.051 + 15.153 + 15.153) kN = 35.357 kN Ultimate Dead Load = 283.81 x 1.4 = 397.334 kN Ultimate Live Load = 35.357 x 1.6 = 56.571 kN Total Ultimate Load = (432.36 + 86.86) kN = 519.22 kN

Beam C/ 4-5 Beam C2/ 4-5 Beam C-D/ 5 Beam C-C2/ 4a Beam C2-D/ 4b

Column C5 Column D4

Beam C-C2/ 4a 87

Live Load Slab C-C2/ 4-4a (Dry Kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.206 ÷ 2) = 1.66 kN/m Slab C-C2/ 4a-5 (Wet Kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (3.773 ÷ 2) = 2.83 kN/m Total Live Load = 4.49 kN/m Ultimate Load Ultimate Dead Load = 20.76 kN/m x 1.4 = 29.06 kN/m Ultimate Live Load = 4.49 kN/m x 1.6 = 7.18 kN/m Total Ultimate Load = 36.24 kN/m

5257

1.66 kN/m

2.83 kN/m

4.49 kN/m

29.06 kN/m

7.18 kN/m

36.24 kN/m

∑M=0 (Ra x 5.26) - (36.24 x 5.26)2.63 =0 5.26 Ra = -501.34 Ra = 95.31 kN

5257

36.24 kN/m

∑y=0 95.31 - (36.24 x 5.26) + Rb =0 Rb = 95.31 kN

5257 2628.5

2628.5

190.466kN/m

Positive Area 95.31 x 2.63 x ½ = 125.33 ---(1) Negative Area 95.31 x 2.63 x ½ = 125.33

95.31

(+)

---(2)

-95.31+95.31=0 (-)

∴ Positive Area = Negative Area (125.33 – 125.33) kNm = 0

125.33

Beam C/ 4-5 90

Beam C/ 4-5 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m

5979 3773

2206

1.44 kN/m

4.528 kN/m

Slab C-C2/ 4a-5 = Slab self weight x ᴸˣ/₂ x ²/₃ = 3.6 kN/m x (3.773m ÷ 2) x ²/₃ = 4.528 kN/m

8.55 kN/m

Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m Total Dead Load C/4-4a= 9.99 kN/m C/4a-5= 14.518 kN/m

9.99 kN/m

14.518 kN/m

Live Load Slab C-C2/ 4a-5 (Wet Kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (3.773 ÷ 2) x ²/₃ = 1.887kN/m

5979 2206

3773

1.887 kN/m

Total Live Load C/4a-5= 1.887 kN/m

Ultimate Load

5979 3773

2206

● C-C2/ 4a-5 Ultimate Dead Load = 14.518 kN/m x 1.4 = 20.325 kN/m

20.325 kN/m

3.019 kN/m

Ultimate Live Load = 1.887 kN/m x 1.6 = 3.019 kN/m ● C-C2/ 4-4a Ultimate Dead Load = 9.99 kN/m x 1.4 = 13.986 kN/m

13.986 kN/m

95.31 kN/m

● Total Ultimate Load C-C2/ 4a-5= 23.334 kN/m C-C2/ 4-4a= 13.986 kN/m 95.31 kN/m

● Point Load (Reaction force from Beam C-C2/ 4a) = 95.31 kN

13.989 kN/m

23.334 kN/m

∑M=0 (Ra x 5.979) - (13.986 x 2.206)4.876 - (23.334 x 3.773)1.887 - (95.31 x 3.773) =0 5.979 Ra = -676.174 Ra = 113.09 kN

5979 3773

2206

95.31 kN/m

13.986 kN/m

1103

∑y=0 113.09 - (13.986 x 2.206) - (23.334 x 3.773) - 95.31 + Rb =0 Rb = 101.112 kN

30.853

23.334 kN/m

1886.5

88.039

113.09

Positive Area (82.237+113.09) x 2.206 x ½ = 215.446 = 215.4 Negative Area (101.112+13.073) x 3.773 x ½ = 215.410 = 215.4

113.09-30.853= 82.237

(+) -101.112+101.112= 0

82.237-95.31=-13.073

(-)

-13.073-88.039= -101.112

215.4

Beam C2-D/ 4b 95

Beam C2-D/ 4b Dead Load Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C2-D/ 4-4b = Slab self weight x ᴸˣ/₂ x ²/₃ = 3.6 kN/m x (3.857m ÷ 2) x ²/₃ = 4.63 kN/m Slab C2-D/ 4b-5 = Slab self weight x ᴸˣ/₂ = 3.6 kN/m x (2.122m ÷ 2) = 3.82 kN/m Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m

2503

1.44 kN/m

4.63 kN/m

3.82 kN/m

8.55 kN/m

Total Dead Load = 18.44 kN/m 18.44 kN/m

Live Load Slab C2-D/ 4-4b (Maid Room) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m x (3.857 ÷ 2) x ²/₃ = 1.93 kN/m

2503

1.93 kN/m

1.59 kN/m

Slab C-C2/ 4a-5 (Wet Kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.122 ÷ 2) = 1.59 kN/m 3.52 kN/m

Total Live Load = 3.52 kN/m Ultimate Load Ultimate Dead Load = 18.44 kN/m x 1.4 = 25.82 kN/m Ultimate Live Load = 3.52 kN/m x 1.6 = 5.63 kN/m Total Ultimate Load = 31.45 kN/m

25.82 kN/m

5.63 kN/m

31.45 kN/m

2503

∑M=0 (Ra x 2.5) - (31.45 x 2.5)1.25 =0 2.5 Ra = -98.281 Ra = 39.31 kN

31.45kN/m

∑y=0 39.31 - (31.45 x 2.5) + Rb =0 Rb = 39.31 kN

2503 1251.5

1251.5 78.712kN/m

Positive Area 39.31 x 1.25 x ½ = 24.57

---(1) 95.31

Negative Area 39.31 x 1.25 x ½ = 24.57

(+)

---(2)

-95.31+95.31=0 (-)

∴ Positive Area = Negative Area (24.57 – 24.57) kNm = 0 24.57

Beam C2/ 4-5 99

Beam C2/ 4-5 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C-C2/ 4a-5 = Slab self weight x ᴸˣ/₂ = 3.6 kN/m x (3.773m ÷ 2) x ²/₃ = 4.528 kN/m Slab C2-D/ 4-4b = 3.6 kN/m x (3.857m ÷ 2) = 6.943 kN/m Slab C2-D/ 4b-5 = 3.6 kN/m x (2.122m ÷ 2) x ²/₃ = 2.546 kN/m Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m ● Total Dead Load C2/ 4-4a = 16.933 kN/m C2/ 4a-4b= 14.518 kN/m C2/ 4b-5 = 17.064 kN/m

5979 2206

1651

2122

1.44 kN/m

4.528 kN/m

6.943 kN/m

2.546 kN/m

8.55 kN/m

17.064 kN/m 16.933 kN/m 14.518 kN/m

5979

Live Load

2206

Slab C-C2/ 4a-5 (Wet Kitchen) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m x (3.773 ÷ 2) x ²/₃ = 1.887 kN/m Slab C2-D/ 4-4b (Maid Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (3.857 ÷ 2) = 2.893 kN/m

2122

1.887 kN/m

2.893 kN/m

Slab C2-D/ 4b-5 (Laundry) = Live load (UBBL) x ᴸˣ/₂ x ²/₃ = 1.5 kN/m x (2.122 ÷ 2) x ²/₃ = 1.061 kN/m ● Total Live Load C2/ 4-4a = 2.893 kN/m C2/ 4a-4b= 4.78 kN/m C2/ 4b-5 = 2.948 kN/m

1651

1.061 kN/m

2.893 kN/m

4.78 kN/m 2.948 kN/m

101

Ultimate Load 5979

● C2/ 4-4a Ultimate Dead Load = 16.933 kN/m x 1.4 = 23.706 kN/m Ultimate Live Load = 2.893 kN/m x 1.6 = 4.629 kN/m ● C2/ 4a-4b Ultimate Dead Load = 14.518 kN/m x 1.4 = 20.325 kN/m Ultimate Live Load = 4.78 kN/m x 1.6 = 7.648 kN/m ● C2/ 4b-5 Ultimate Dead Load = 17.064 kN/m x 1.4 = 23.891 kN/m

2206

1651

2122

23.706 kN/m

4.629 kN/m

20.325 kN/m

7.648 kN/m

23.891 kN/m

4.717 kN/m

Ultimate Live Load = 2.948 kN/m x 1.6 = 4.717 kN/m 102

5979

● Total Ultimate Load C2/ 4-4a = 28.335 kN/m C2/ 4a-4b= 27.973 kN/m C2/ 4b-5 = 28.608 kN/m

● Point Load (Reaction force from Beam C-C2/ 4a) = 95.31 kN

2206

1651

2122

95.31 kN/m

39.31 kN/m

● Point Load (Reaction force from Beam C2-D/ 4b) = 39.31 kN 28.608 kN/m 28.335 kN/m 27.973 kN/m

103

∑M=0 (Ra x 5.979) - (62.507 x 4.876) (95.31 x 3.773) - (46.183 x 2.948) -(39.31 x 2.122) - (60.706 x 1.061)=0 5.979 Ra = -948.361 Ra = 158.615 kN

5979 2206

1651

95.31 kN/m

2122

39.31 kN/m 28.608 kN/m

28.335 kN/m

27.973 kN/m

∑y=0 158.615 - 62.507 - 95.31 - 46.183 39.31 - 60.706 + Rb =0 Rb = 145.401 kN

825.5 825.5 1103

1103

62.507

46.183

1061 1061

60.706

1651 0.798 (x) 45.385

0.798/x 46.183x = 0.798 x 1.651 x = 0.029 158.615 158.615 - 62.507= 96.108

Positive Area i.0.798 x 0.029 x ½ = 0.012 ii.(158.615 + 96.108) x 2.206 x ½ = 280.959 Total = 280.971 = 280.9 Negative Area i.(145.401 + 84.695) x 2.122 x ½ = 244.132 ii. 45.385 x (1.651-0.029) x ½ = 36.807 Total = 280.939 = 280.9

(+)

96.108 - 95.31= 0.798 -145.401 + 145.401= 0

0.798 - 46.183= -45.385 (-) -45.385 - 39.31= -84.695

-84.695 - 60.706 =145.401

280.9

104

Beam C-D/ 5 105

Beam C-D/ 5 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C-C2/ 4a-5 = Slab self weight x ᴸˣ/₂ = 3.6 kN/m x (3.773m ÷ 2) = 6.791 kN/m

7760 2503

5257

1.44 kN/m

6.791 kN/m

3.82 kN/m

Slab C2-D/ 4b-5 = Slab self weight x ᴸˣ/₂ = 3.6 kN/m x (2.122m ÷ 2) = 3.82 kN/m Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m Total Dead Load C-C2/5= 16.78 kN/m C2-D/5= 13.81 kN/m

8.55 kN/m

16.78 kN/m

13.81 kN/m

106

Live Load Slab C-C2/ 4a-5 (Wet Kitchen) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (3.773 ÷ 2) = 2.83 kN/m

7760 5257

2503

2.83 kN/m

Slab C2-D/ 4b-5 (Laundry) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.122 ÷ 2) = 1.59 kN/m Total Live Load C-C2/5= 2.83 kN/m C2-D/5= 1.59 kN/m

1.59 kN/m

2.83 kN/m

1.59 kN/m

107

Ultimate Load

7760

● C-C2/ 5 Ultimate Dead Load = 16.78 kN/m x 1.4 = 23.49 kN/m Ultimate Live Load = 2.83 kN/m x 1.6 = 4.53 kN/m

5257

23.49 kN/m

4.53 kN/m

● C2-D/ 5 Ultimate Dead Load = 13.81 kN/m x 1.4 = 19.33 kN/m

19.33kN/m

Ultimate Live Load = 1.59 kN/m x 1.6 = 2.54 kN/m Total Ultimate Load C-C2/5= 28.02 kN/m C2-D/5= 21.87 kN/m

2503

2.54 kN/m

28.02 kN/m

21.87 kN/m

108

∑M=0 (Ra x 7.76) - (147.3 x 5.132) (145.401x 2.5) - (54.741 x 1.252) =0 7.76Ra = -1188.417 Ra = 153.15 kN

7760 5257

2503 145.401 kN/m

28.02 kN/m

∑y=0 153.15 - 147.3 - 145.401 - 54.74 + Rb =0 Rb = 194.291 kN

21.87 kN/m

145.401 kN/m 2628.5

2628.5 1251.5 1251.5

54.74

147.3

153.15 153.15-147.3= 5.85

Positive Area I.(153.15+ 5.85) x 1/2 x 5.257 = 417.932 = 418

(+) -194.291+194.291=0 5.85-145.401=-139.551

(-)

-139.551-54.74=-194.291

Negative Area I.(194.291+139.551) x 2.503 x ½ = 417.803 = 418

418

109

Column D4 --- First Floor 110

Column D4 --- Ground Floor 111

Colum D4 Dead Load Roof Level Weight = 3.88 x (2.99+1.973) x 1.0 kN/m = 19.256 kN Beam = 3.88 x (2.99+1.973) x 1.44 kN/m = 27.729 kN Total = 46.985 kN First Floor Wall = (3.88 + 2.99 + 3.88 + 1.973) x 8.55 kN/m = 108.782 kN Slab = 3.88 x (2.99+1.973) x 3.6 kN/m = 69.323 kN Beam = (3.88+2.99+1.973 + 3.88) x 1.44 kN/m = 18.321 kN Columns = 6.48 kN Total = 202.906 kN

112

Ground Level Wall = (2.99+1.973 +3.88 +1.973+2.99+1.328) x 8.55 kN/m = 129.396 kN Slab = 3.88 x (2.99 + 1.973) x 3.6 kN/m = 69.323 kN Beam = (2.99+1.973 +3.88 +1.973+2.99+1.328) x 1.44 kN/m = 21.792 kN Columns = 6.48 kN Total = 226.991 kN Total Dead Load = 476.882 kN

113

Live Load Roof Level Weight = 3.88 x (2.99 + 1.973) x 0.5 kN/m = 9.628 kN First Floor Slab = 3.88 x (2.99 + 1.973) x 1.5 kN = 28.885 kN Ground Floor Slab = 3.88 x (2.99 + 1.973) x 1.5 kN = 28.885kN Total Live Load = 67.398 kN Ultimate Load Dead Load = 476.882 kN x 1.4 = 667.635 kN Live Load = 67.398 kN x 1.6 = 107.837 kN Total Ultimate Load = 775.472 kN

114

Column C5 --- First Floor 115

Column C5 --- Ground Floor 116

Colum C5 Dead Load Roof Level Weight = 3.88 x (2.99+1.01) x 1.0 kN/m = 15.52 kN Beam = (2.99+1.01) x 1.44 kN/m = 5.76 kN Total = 21.28 kN First Floor Wall = (3.88 + 2.99 + 2.99) x 8.55 kN/m = 84.303 kN Slab = 3.88 x (2.99+1.01) x 3.6 kN/m = 55.872 kN Beam = (3.88+2.99+2.99 + 1.01) x 1.44 kN/m = 15.653 kN Columns = 6.48 kN Total = 162.308 kN

117

Ground Level Wall = (2.99+3.88) x 8.55 kN/m = 58.739 kN Slab = (3.88+2.99) x 3.6 kN/m = 24.732 kN Beam = (3.88+2.99) x 1.44 kN/m = 9.893 kN Columns = 6.48 kN Total = 93.364 kN Total Dead Load = 193.481 kN

118

Live Load Roof Weight = 3.88 x (2.99+1.01) x 0.5 kN/m = 7.76 kN First Floor Slab = 3.88 x (2.99+1.01) x 1.5 kN = 23.28 kN Ground Floor Slab = 3.88 x (2.99+1.01) x 1.5 kN = 23.28 kN Total Live Load = 54.32 kN Ultimate Load Dead Load = 193.481 kN x 1.4 = 270.873 kN Live Load = 54.32 kN x 1.6 = 86.912 kN Total Ultimate Load = 357.785 kN

119

TAN CHIN WERNG 0324408

120

Beam C1-D/ 4a Beam C1/ 4a-5 Beam C-D/ 4 Beam C-D/ 5

Column C4 Column D5

121

Beam C1-D/ 4a 122

Beam C1-D/ 4a Dead Load Beam Self Weight = Beam size x Density of concrete = (0.20 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C1-D/ 4-4a = Slab self weight x ᴸˣ/ = 3.6 kN/m x (2.603m ÷ 2) = 4.68 kN/m Slab C1-D/ 4a-5 = Slab self weight x ᴸˣ/ = 3.6 kN/m x (3.376m ÷ 2) = 6.12 kN/m Brick Wall Self Weight = = 8.55 kN/m

5159

1,44 kN/m

4.68 kN/m

6.12 kN/m

8.55 kN/m

Total Dead Load = 20.79 kN/m 20.79 kN/m

123

Live Load Slab C1-D/ 4-4a (Bathroom) = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (2.6 ÷ 2) = 1.95 kN/m Slab C1-D/ 4a-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (3.4 ÷ 2) = 2.55 kN/m Total Live Load = 4.50 kN/m Ultimate Load Ultimate Dead Load = 20.79 kN/m x 1.4 = 29.11 kN/m Ultimate Live Load = 4.50 kN/m x 1.6 = 7.2 kN/m Total Ultimate Load = 36.31 kN/m

5159

1.95 kN/m

2.55 kN/m

4.50 kN/m

29.11 kN/m

7.2 kN/m

36.31 kN/m

124

Reaction Forces ∑M=0 (Ra x 5.159) - (36.31 x 5.159)2.58 =0 5.159 Ra = 483.388 Ra = 93.680 kN

5159

36.31 kN/m

∑y=0 93.680 - (36.31 x 5.159) + Rb =0 Rb = 93.680 kN

Bending Moment Diagram (M) Positive Area 93.680 x 2.58 x ½ = 120.847 kNm

5159 2579.5

2579.5

187.323 kN/m

93.680

(+) 93.680+93.680=0

Negative Area 93.680 x 2.58 x ½ = 120.847 kNm ∴ Positive Area = Negative Area (120.847 – 120.847) kNm = 0

(-)

120.847

125

Beam C1/ 4a-5 126

Beam C1/ 4-5 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.2 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C-C1/ 4-5 = Slab self weight x ᴸˣ/ = 3.6 kN/m x (2.603m ÷ 2) = 4.68 kN/m Slab C1-D/ 4-4a = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (2.6m ÷ 2) x = 3.12 kN/m Slab C1-D/ 4a-5 = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (3.4m ÷ 2) x = 4.08 kN/m

5979 3376

2603

1,44 kN/m

4.68 kN/m

3.12 kN/m

4.08 kN/m

8.55 kN/m

Brick Wall Self Weight = 8.55 kN/m Total Dead Load C1/ 4-4a= 17.79 kN/m C1/ 4a-5= 10.20 kN/m

17.79 kN/m

10.20 kN/m

Live Load Slab C-C1/ 4-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (2.6 ÷ 2) = 1.95 kN/m Slab C1-D/ 4-4a (Bathroom) = Live load (UBBL) x ᴸˣ/ x = 1.5 kN/m x (2.6 ÷ 2) x = 1.3 kN/m

5979 3376

2603

1.95 kN/m

1.3 kN/m

Slab C1-D/ 4a-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ x = 1.5 kN/m x (3.4 ÷ 2) x = 1.7 kN/m Total Live Load C1/ 4-4a= 3.25 kN/m C1/ 4a-5= 3.65 kN/m

1.7 kN/m

3.25 kN/m

3.65 kN/m

127

Ultimate Load ● C1/ 4-4a Ultimate Dead Load = 17.79 kN/m x 1.4 = 24.906 kN/m Ultimate Live Load = 3.25 kN/m x 1.6 = 5.20 kN/m

5979 2603

3376

24.906 kN/m

5.20 kN/m

● C1/ 4a-5 Ultimate Dead Load = 10.20 kN/m x 1.4 = 14.28 kN/m

14.28 kN/m

Ultimate Live Load = 3.65 x 1.6 = 5.84 kN/m ● Total Ultimate Load C1/ 4-4a= 30.11 kN/m C1/ 4a-5= 20.12 kN/m

5.84 kN/m

30.11 kN/m

20.12 kN/m

● Point Load (Reaction force from Beam C1-D/ 4a) = 93.680 kN 128

Shear Force Diagram (V) ∑M=0 (Ra x 5.979) - (30.11 x 2.603)4.678 (20.12 x 3.376)1.688 - (93.680 x 3.376) =0 5.979 Ra = 797.488 Ra = 133.382 kN

5979

93.680 kN/m 30.11 kN/m

∑y=0 133.382 - (30.11 x 2.603) - (20.12 x 3.376) - 93.680 + Rb =0 Rb = 106.599 kN

Negative Area (106.599+38.704) x 3.376 x ½ = 245.3 kNm = 245 kNm

3376

2603

1301.5

Bending Moment Diagram (M) Positive Area (133.382+54.976) x 2.603 x ½ = 245.1kNm = 245 kNm

1301.5

78.406

20.12 kN/m

1688

67.925

133.382

133.382-78.406= 54.976 106.599-106.599=0

54.976-93.680= -38.704

-38.704-67.925= -106.629

245

∴ Positive Area = Negative Area (245 – 245) kNm = 0 129

Beam C-D/ 4 130

Beam C-D/ 4 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.20 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C-C1/ 3-4 = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (2.601m ÷ 2) x = 3.121 kN/m Slab C-C1/ 4-5 = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (2.601m ÷ 2) x = 3.121 kN/m Slab C1-D/ 3-4 = Slab self weight x ᴸˣ/ = 3.6 kN/m x (3.945m ÷ 2) = 7.101 kN/m Slab C1-D/ 4-5 = Slab self weight x ᴸˣ/ = 3.6 kN/m x (2.603m ÷ 2) = 4.685 kN/m

7760 5159

2601

1,44 kN/m

4.68 kN/m

3.12 kN/m

4.08 kN/m

8.55 kN/m

17.79 kN/m

18.75 kN/m

Brick Wall Self Weight = 8.55 kN/m Total Dead Load C-C1/ 4= 16.232 kN/m C1-D/ 4= 21.776 kN/m Live Load

7760 5159

2601

1.95 kN/m

1.3 kN/m

Slab C-C1/ 3-4 & C-C1/ 4-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ x x2 = 1.5 kN/m x (2.6 ÷ 2) x x2 = 2.601 kN/m Slab C1-D/ 3-4 = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (3.945 ÷ 2) = 2.959 kN/m

1.7 kN/m

3.25 kN/m

3.65 kN/m

Slab C1-D/ 4-4a (Bedroom) = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (2.603÷ 2) = 1.95 kN/m Total Live Load C1/ 4-4a= 2.601 kN/m C1/ 4a-5= 4.909 kN/m

132

Ultimate Load ● C-C1/ 4 Ultimate Dead Load = 16.232 kN/m x 1.4 = 22.725 kN/m Ultimate Live Load = 2.601 kN/m x 1.6 = 4.162 kN/m

7760 2601

5159

24.906 kN/m

5.20 kN/m

● C1-D/ 4 Ultimate Dead Load = 21.776 kN/m x 1.4 = 30.486 kN/m

1.7 kN/m

Ultimate Live Load = 4.909 kN x 1.6 = 7.854 kN/m ● Total Ultimate Load C-C1/ 4= 26.887 kN/m C1-D/ 4= 38.34 kN/m

5.84 kN/m

30.11 kN/m

32.09 kN/m

● Point Load

(Ra from Beam C1/ 4-5 & Rb from C1/ 3-4)

= (133.382 + 65.967) kN = 199.349 kN

133

Shear Force Diagram (V) ∑M=0 (Ra x 7.76) - (26.887 x 2.601)6.46 (38.34 x 5.519)2.58 - (199.349 x 5.159) =0 7.76 Ra = 1990.523 Ra = 256.511kN

7760 5159

2601

199.349 kN/m 26.887 kN/m

∑y=0 256.511 - (26.887 x 2.601) - (38.34 x 5.519) - 199.349 + Rb =0 Rb = 210.567 kN Bending Moment Diagram (M) Positive Area (256.511+186.578) x 2.601 x ½ = 576.237 kNm = 576 kNm

1301.5

69.933

38.34 kN/m

1688

197.796

256.511

256.511-69.933= 186.578

186.578- 199.349 = -12.771

Negative Area (210.567+12.771) x 5.159 x ½ = 576.100 kNm = 576 kNm

-12.771- 197.796= -210.567

576

∴ Positive Area = Negative Area (576– 576) kNm = 0 134

Beam C-D/ 5 135

Beam C-D/ 5 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.20 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab C-C1/ 4-5 = Slab self weight x ᴸˣ/ = 3.6 kN/m x (2.6m ÷ 2) = 4.68 kN/m Slab C1-D/ 4-4a = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (2.6m ÷ 2) x = 3.12 kN/m

7760 5159

2601

1,44 kN/m

4.68 kN/m

3.12 kN/m

4.08 kN/m

Slab C1-D/ 4a-5 = Slab self weight x ᴸˣ/ x = 3.6 kN/m x (3.4m ÷ 2) x = 4.08 kN/m Total Dead Load C-C1/ 5= 8.196 kN/m C1-D / 5= 11.153 kN/m

17.79 kN/m

18.75 kN/m

136

Live Load Slab C-C1/ 4-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ = 1.5 kN/m x (2.6 ÷ 2) = 1.95 kN/m Slab C1-D/ 4-4a (Bathroom) = Live load (UBBL) x ᴸˣ/ x = 1.5 kN/m x (2.6 ÷ 2) x = 1.3 kN/m

7760 5159

2601

1.95 kN/m

1.3 kN/m

Slab C1-D/ 4a-5 (Bedroom) = Live load (UBBL) x ᴸˣ/ x = 1.5 kN/m x (3.4 ÷ 2) x = 1.7 kN/m Total Live Load C1/ 4-4a= 2.95 kN/m C1/ 4a-5= 4.182 kN/m

1.7 kN/m

2.95 kN/m

4.182 kN/m

137

Ultimate Load ● C-C1/ 5 Ultimate Dead Load = 8.196 kN/m x 1.4 = 11.474 kN/m Ultimate Live Load = 2.95 kN/m x 1.6 = 4.72 kN/m

7760 2601

5159

11.474 kN/m

4.72 kN/m

● C1-D/ 5 Ultimate Dead Load = 11.153 kN/m x 1.4 = 15.614 kN/m

15.614 kN/m

Ultimate Live Load = 4.182 x 1.6 = 6.691 kN/m ● Total Ultimate Load C1/ 4-4a= 16.194 kN/m C1/ 4a-5= 22.305 kN/m

6.691 kN/m

16.194 kN/m

22.305 kN/m

● Point Load (Reaction force B from Beam C1/ 4-5) = 106.599 kN 138

Shear Force Diagram (V) ∑M=0 (Ra x 7.76) - (16.194 x 2.601)6.46 (22.305 x 5.159)2.58 - (106.599 x 5.159) =0 7.76 Ra = -1118.927 Ra = 144.191 kN

7760 2601

16.194 kN/m

∑y=0 144.191 - (16.194 x 2.601) - (22.305 x 5.159) - 106.599 + Rb =0 Rb = 119.6 kN

Negative Area (119.6+4.529) x 5.159 x ½ = 320.191 kNm = 320 kNm

5159

106.599 kN/m

1300.5

Bending Moment Diagram (M) Positive Area (144.191+102.07) x 2.601 x ½ = 320.262 kNm = 320 kNm

1301.5

42.121

22.305 kN/m

2579.5

115.071

144.191

144.191-42.121= 102.07

102.07-106.599= -4.529

-4.529-115.071= -119.6

320

∴ Positive Area = Negative Area (320 – 320) kNm = 0 139

Column C4 --- GroundFloor 140

Column C4 --- First Floor 141

Colum C4 Dead Load Roof Level Slab = (1.973 x 5.923) + (3.88 x 2.99) x 1.0 kN/m = 23.287 kN Beam = (3.88 + 2.043 + 2.99) x 1.44 kN/m = 12.835 kN Total = 35.955 kN First Floor Wall = (2.043+1.973+1.973+1.279+1.279+3.88+2.99+ 2.603) x 8.55 kN/m = 154.071 kN Slab = (1.973 x 2.043) + (3.88 x [ 2.99+1.973 ]) x 3.6 kN/m = 83.834 kN Beam = (2.043+1.973+1.973+1.279+1.279+3.88+2.99+ 2.99) x 1.44 kN/m = 26.506 kN Columns = 6.48 kN Total = 264.411 kN

142

Ground Level Wall = (2.043+1.973+3.88+2.99) x 8.55 kN/m = 93.075 kN Slab = (1.973 x 2.043) + (3.88 x [ 2.99+1.973 ]) x 3.6 kN/m = 83.834 kN Beam = (2.043+1.973+3.88+3.88+2.99) x 1.44 kN/m = 15.676 kN Columns = 6.48 kN Total = 192.585 kN Total Dead Load = 492.951 kN

143

Live Load Roof Level Slab = (1.973 x 5.923) + (3.88 x 2.99) x 0.5 kN/m = 11.644 kN First Floor Slab = (1.973 x 5.923) + (3.88 x 2.99) x 1.5 kN = 34.930 kN Ground Floor Slab = (1.973 x 5.923) + (3.88 x 2.99) x 1.5 kN = 34.930 kN Total Live Load = 81.504 kN Ultimate Load Dead Load = 492.951 kN x 1.4 = 690.131 kN Live Load = 81.504 kN x 1.6 = 130.406 kN Total Ultimate Load = 820.537 kN

144

Column D5 --- First Floor 145

Column D5 --- Ground Floor 146

Colum D5 Dead Load Roof Level Slab = 3.88 x (2.99+1.01) x 1.0 kN/m = 15.52 kN Beam = (2.99+1.01) x 1.44 kN/m = 5.76 kN Total = 21.28 kN First Floor Wall = (2.99 + 1.01) x 8.55 kN/m = 25.82 kN Slab = 3.88 x (2.99+1.01) x 3.6 kN/m = 55.872 kN Beam = (3.88+2.99+1.01) x 1.44 kN/m = 11.347 kN Columns = 6.48 kN Total = 99.519 kN

147

Ground Level Wall = (2.99+2.99+3.88+2.503) x 8.55 kN/m = 105.704 kN Slab = (2.99 x 3.88) x 3.6 kN/m = 41.764 kN Beam = (2.99+2.99+2.503+3.88) x 1.44 kN/m = 17.803 kN Columns = 6.48 kN Total = 171.751 kN Total Dead Load = 292.55 kN

148

Live Load Roof Level Slab = 3.88 x (2.99+1.01) x 0.5 kN/m = 3.841 kN First Floor Slab = 3.88 x (2.99+1.01) x 1.5 kN = 23.28 kN Ground Floor Slab = (2.99 x 3.88) x 1.5 kN = 17.402 kN Total Live Load = 44.523 kN Ultimate Load Dead Load = 292.55 kN x 1.4 = 409.57 kN Live Load = 44.523 kN x 1.6 = 71.237 kN Total Ultimate Load = 480.807 kN

149

YUEN XUAN HUI 0324292

150

Beam B1/ 2-3 Beam B-C/ 2 Beam B-C/ 3 Beam B1/ 3-4 Beam A1 / 3-4

Column A3 Column A4 151

Ground Floor Beam B1/ 2-3

152

Ground Floor Beam B1/ 2-3

Dead Load

5101 1051

Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab B-B1/ 2-3 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 1.783m/2 = 3.6 kN/m x (0.8915m) = 3.2094 kN/m Slab B1-C/ 2-3 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.302m/2 = 3.6 kN/m x (1.151m) = 4.1436kN/m

1292

2758

1,44 kN/m

3.2094 kN/m

4.1436 kN/m

Brick Wall Self Weight

= 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m Total Dead Load = Beam self weight + slab B-B1/2-3 self weight + slab B1-C/2-3 self weight = 1.44kN/m + 3.2094 kN/m + 4.1436 kN/m + 8.55 kN/m = 17.343kN/m

8.55 kN/m

8.793 kN/m

153

Live Load

5101 1051

Slab B-B1/ 2-3 (Living Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (1.783m ÷ 2) = 1.33725kN/m Slab B1-C/ 2-3 (Dining Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.302 ÷ 2) = 1.7265 kN/m Total Live Load =Slab B-B1/ 2-3 (Living Room) + Slab B1-C/ 2-3 (Dining Room) =1.33725kN/m + 1.7265kN/m =3.06375kN/m =3.064kN/m

1292

2758

1.33725kN/m

1.7265kN/m

3.064 kN/m

154

Ultimate Load Ultimate Dead Load = Total dead load x dead load factor = 17.343kN/m x 1.4 = 24.2802 kN/m = 24.28 kN/m

5101 1051

1292

2758

24.28kN/m

4.902kN/m

Ultimate Live Load = Total live load x live load factor = 3.064kN/m x 1.6 = 4.9024kN/m =4.902 kN/m 29.212 kN/m

Ultimate Load = Ultimate dead load + ultimate live load = 24.28 kN/m + 4.902 kN/m = 29.212 kN/m

155

Shear Force Diagram (V) ∑M=0 =(Ra x 5.101) - (29.182 x 5.101) x 5.101/2 =5.101 Ra - 148.857 x 2.5505 =5.101 Ra - 379.66 5.101 Ra = 379.66 Ra = 74.429kN =74.43kN

5101 1051

1292

2758

29.212 kN/m

2550.5

2550.5 148.86kN/m

∑y=0 Ra-(29.182 x 5.101) + Rb =0 74.429 - 148.857 + Rb = 0 Rb = 74.428kN = 74.43 kN

74.43

(+)

Bending Moment Diagram (M)

-74.73+74.43=0

Positive Area (1)74.43 x 5.101/2 x 1/2 =94.917 Negative Area (2)74.43 x 5.101/2 x 1/2 =94.917

(-)

94.917

(1)=(2)

156

Ground Floor Beam B-C/ 2

157

Ground Floor Beam B-C/ 2 B1

Dead Load 4085

1783

2302

1,44 kN/m

3.2094 kN/m

Slab B1-C/ 2-3 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.302m/2 = 3.6 kN/m x (1.151m) = 4.1436kN/m Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m Total Dead Load B-B1/2 = Beam self weight + slab B-B1/2-3 self weight + Brick Wall Self Weight = 1.44kN/m + 3.2094 kN/m + 8.55 kN/m = 13.1994kN/m B1-C/2 = Beam self weight + slab B1-C/2-3 self weight + Brick Wall Self Weight = 1.44kN/m + 4.1436 kN/m + 8.55 kN/m = 14.1336 kN/m

4.1436 kN/m

8.55 kN/m

13.1994 kN/m

14.1336 kN/m

158

Live Load

4085 1783

Slab B-B1/ 2-3 (Living Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (1.783m ÷ 2) = 1.33725kN/m

2302

1.33725 kN/m

Slab B1-C/ 2-3 (Dining Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.302 ÷ 2) = 1.7265 kN/m Total Live Load =Slab B-B1/ 2-3 (Living Room) + Slab B1-C/ 2-3 (Dining Room) =1.33725kN/m + 1.7265kN/m =3.06375kN/m =3.064kN/m

1.7265 kN/m

1.33725 kN/m

1.7265 kN/m

Ultimate Load Ultimate Dead Load B-B1/2 = Total dead load x dead load factor = 13.1994kN/m x 1.4 = 18.47916 kN/m = 18.479 kN/m B1-C/2 = Total dead load x dead load factor = 14.1336kN/m x 1.4 = 19.78704kN/m = 19.787kN/m

18.479 kN/m

19.787 kN/m

159

4085 1783

Ultimate Live Load B-B1/2 = Total live load x live load factor = 1.33725kN/m x 1.6 = 2.1396kN/m = 2.14 kN/m

2302

2.14 kN/m

2.762 kN/m

B1-C/2 = Total live load x live load factor = 1.7265kN/m x 1.6 = 2.7624kN/m = 2.762kN/m Ultimate Load B-B1/2 = Ultimate dead load + ultimate live load = 18.479 kN/m + 2.14 kN/m = 20.619 kN/m

43.899 kN/m

43.899 kN/m 22.549 kN/m

Ultimate Load B1-C/2 = Ultimate dead load + ultimate live load = 19.787 kN/m + 2.762 kN/m = 22.549 kN/m

20.619 kN/m

Point load (Reaction force B from Beam B1/ 2-3) =43.899 kN

160

Shear Force Diagram (V) ∑M=0 =(Ra x 4.085) - (20.619 x 1.783) x (1.783/2 + 2.302 ) - (22.549 x 2.302) x 2.302/2 - ( 43.899 x 2.302 ) = 4.085Ra - (36.764x 3.1935)(51.908x1.151)-101.0555 = 4.085Ra - 117.406- 59.746-101.0555 4.085Ra= 278.2075 Ra= 68.105kN

4085 1783

2302

43.899 kN/m 22.549 kN/m 20.619 kN/m

891.5 891.5

1151

43.899kN/m

∑y=0 Rb +68.105 - (20.619 x 1.783) - (22.549 kN/m x 2.302) - 43.899 =0 Rb + 68.105 - 36.764 - 51.908 - 43.899 Rb = 64.466kN

36.764kN/m

51.908kN/m

68.105

Bending Moment Diagram (M) Positive Area (1)(31.341 + 68.105) x 1.783 x 1/2 =88.656 =88.7

68.105 -36.764=31.341

(+) -64.466+64.466= 0

31.341-43.899=-12.558

Negative Area (2)(12.558 + 64.466) x 2.303 x ½ =88.69 =88.7

(-)

-12.558-51.908=-64.466

88.7

(1)=(2)

161

Ground Floor Beam B-C/ 3

162

Beam B-C/ 3

Dead Load

4085 1783

Beam Self Weight = Beam size x Density of concrete = (0.20 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab B-B1/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 1.783m/2 = 3.6 kN/m x (0.8915m) = 3.2094 kN/m

2302

1,44 kN/m

3.2094 kN/m

Slab B1-C/ 2-3 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.302m/2 = 3.6 kN/m x (1.151m) = 4.1436kN/m Slab B-B1/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 1.783m/2 = 3.6 kN/m x (0.8915m) = 3.2094 kN/m Slab B1-C/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.302m/2 = 3.6 kN/m x (1.151m) = 4.1436kN/m Brick Wall Self Weight = 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m

4.1436 kN/m

3.2094 kN/m

4.1436 kN/m

8.55kN/m

163

Total Dead Load B-B1/3 = Beam self weight + slab B-B1/2-3 self weight + slab B-B1/ 3-4 self weight + Brick Wall Self Weight = 1.44kN/m + 3.2094 kN/m + 3.2094 kN/m + 8.55 kN/m = 16.4088kN/m

4085 1783

2302

16.4088 kN/m

18.2772 kN/m

B1-C/3 = Beam self weight + slab B1-C/2-3 self weight + slab B1-C/3-4 self weight + Brick Wall Self Weight = 1.44kN/m + 4.1436 kN/m + 4.1436 kN/m + 8.55 kN/m = 18.2772 kN/m Live Load Slab B-B1/2-3 (Living Room) & Slab B-B1/3-4 (Storeroom) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (1.783m ÷ 2) = 1.33725kN/m

1.33425 kN/m

Slab B1-C/2-3 (Dining Room) & Slab B1-C/3-4 ( Powder Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.302 ÷ 2) = 1.7265 kN/m Total live load B-B1/3 =1.33725kN/m B1-c /3=1.7265 kN/m

1.7265 kN/m

1.33725kN/m

1.7265 kN/m

149

164

Ultimate Load

4085 1783

● B-B1/3 Ultimate Dead Load = 16.4088kN/m x 1.4 = 22.97232 kN/m = 22.972 kN/m Ultimate Live Load = 1.33725kN/m x 1.6 = 2.1396 kN/m = 2.14 kN/m

2302

22.972 kN/m

2.14 kN/m

● B1-C/3 Ultimate Dead Load = 18.2772 kN/m x 1.4 = 25.58808 kN/m = 25.588 kN/m

25.588 kN/m

Ultimate Live Load = 1.7265 kN/m x 1.6 = 2.7624 kN/m = 2.762 kN/m ● Total Ultimate Load B-B1/3 =22.972 kN/m + 2.14 kN/m =25.112 kN/m

2.762 kN/m

25.112 kN/m

28.35 kN/m

B1-C/3 =25.588 kN/m + 2.762 kN/m =28.35kN/m 165

● Point Load =Ra from Beam B1/ 2-3 + Rb from B1/ 3-4

Ground Floor Beam B1/ 3-4

166

Ground Floor Beam B1/ 3-4

Dead Load

3945

Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab B-B1/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 1.783m/2 = 3.6 kN/m x (0.8915m) = 3.2094 kN/m Slab B1-C/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.302m/2 = 3.6 kN/m x (1.151m) = 4.1436kN/m

Brick Wall Self Weight

= 3.0m x 0.15m x 19 kN/m = 8.55 kN/m

1,44 kN/m

3.2094 kN/m

4.1436 kN/m

8.55 kN/m

Total Dead Load = Beam self weight + Slab B-B1/ 3-4 self weight + Slab B1-C/ 3-4 self weight + Brick Wall Self Weight = 1.44kN/m + 3.2094 kN/m + 4.1436 kN/m + 8.55 kN/m = 17.343kN/m

17.343kN/m

167

Live Load Slab B-B1/ 3-4 (Store Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (1.783m ÷ 2) = 1.33725kN/m Slab B1-C/ 3-4 (Powder Room) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.302 ÷ 2) = 1.7265 kN/m Total Live Load =Slab B-B1/ 3-4 (Store Room) + Slab B1-C/ 3-4 (powder Room) =1.33725kN/m + 1.7265kN/m =3.06375kN/m =3.064kN/m

3945

1.33725kN/m

1.7265kN/m

3.064 kN/m

168

Ultimate Load Ultimate Dead Load = Total dead load x dead load factor = 17.343kN/m x 1.4 = 24.2802 kN/m = 24.28 kN/m

3945

24.28kN/m

4.902kN/m

Ultimate Live Load = Total live load x live load factor = 3.064kN/m x 1.6 = 4.9024kN/m =4.902 kN/m 29.212 kN/m

Ultimate Load = Ultimate dead load + ultimate live load = 24.28 kN/m + 4.902 kN/m = 29.212 kN/m

169

Shear Force Diagram (V) ∑M=0 =(Ra x 3.945) - (29.182 x 3.945) x 3.945/2 =3.945 Ra - 115.123 x 1.9725 =3.945 Ra - 227.08 3.945 Ra = 227.08 Ra = 57.561kN =57.56kN

3945

29.212 kN/m

1972.5

1972.5 57.62kN

∑y=0 Ra-(29.182 x 3.945) + Rb =0 57.56 - 115.123 + Rb = 0 Rb = 57.563kN = 57.56 kN

57.56

(+)

Bending Moment Diagram (M)

-57.56+57.56=0

Positive Area (1)57.56 x 3.945/2 x 1/2 =113.5371 Negative Area (2)57.56 x 3.945/2 x 1/2 =113.5371

(-)

94.917

(1)=(2) ● Point Load =Ra from Beam B1/ 2-3 + Rb from B1/ 3-4 =74.43 kN + 57.56 kN

=131.99 kN

170

Shear Force Diagram (V) ∑M=0 (Ra x 4.085) - (25.112 x 1.783)x(2.302 +0.8915) - (28.35 x 2.302)x 1.151 - (131.99 x 2.302) =0 4.085 Ra - ( 44.775 x 3.1935) - (65.2617 x 1.151)- 303.841=0 4.085 Ra - 142.989 - 75.116 -303.841 4.085 Ra= 521.946 Ra = 127.771kN

4085 1783

2302

131.99 kN/m 25.112kN/m

891.5

44.775

∑y=0 127.771 - (25.112 x 1.783) - (28.35x 2.302) 131.99 + Rb =0 127.771- 44.775- 65.2617-131.99+ Rb Rb = 114.2557 kN

28.35 kN/m

1151

65.2617

127.771

Bending Moment Diagram (M) Positive Area (127.771 + 82.996) x 1.783 x ½ = 187.899 =187.9

127.771-44.775=82.996

-114.2557+114.2557=0 82.996- 131.99 = -48.994

-48.994- 65.2617= -114.2557

Negative Area (48.994+114.2557) x 2.302 x ½ = 187.9 187.9

∴ Positive Area = Negative Area 187.9– 187.9) kNm = 0

171

Ground Floor Beam A1/ 3-4

171

Ground Floor Beam A1/ 3-4 Dead Load Beam Self Weight = Beam size x Density of concrete = (0.15 x 0.30)m² x 24 kN/m3 = 1.44 kN/m Slab A-A1/ 2-3 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 3.412m/2 = 3.6 kN/m x (1.706m) = 6.1416 kN/m Slab A1-B/ 3-4 = Slab self weight x ᴸˣ/₂ = (0.15m x 24 kN/m3) x 2.743m/2 = 3.6 kN/m x (1.3715m) = 4.9374kN/m

3945

1,44 kN/m

6.1416 kN/m

4.9374 kN/m

Brick Wall Self Weight

= 3.0m x 0.15m x 19 kN/m3 = 8.55 kN/m Total Dead Load = Beam self weight + slab A-A1/2-3 self weight + slab A1-B/ 3-4 self weight = 1.44kN/m + 6.1416 kN/m + 4.9374 kN/m + 8.55 kN/m = 21.069kN/m

8.55 kN/m

21.069 kN/m

172

Live Load Slab A-A1/ 3-4 (Entrance) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (3.412m ÷ 2) = 2.559kN/m Slab A1-B/ 3-4 (Stairs) = Live load (UBBL) x ᴸˣ/₂ = 1.5 kN/m x (2.743 ÷ 2) = 2.05725 kN/m =2.057kN/m Total Live Load =Slab A-A1/ 3-4 (Entrance) + Slab A1-B/ 3-4 (Stairs) =2.559kN/m + 2.057kN/m =4.616kN/m

3945

2.559kN/m

2.057kN/m

4.616 kN/m

173

Ultimate Load Ultimate Dead Load = Total dead load x dead load factor = 21.069kN/m x 1.4 = 29.4966 kN/m Ultimate Live Load = Total live load x live load factor = 4.616kN/m x 1.6 = 7.3856kN/m Ultimate Load = Ultimate dead load + ultimate live load = 29.4966 kN/m + 7.3856 kN/m = 36.8822 kN/m = 36.882 kN/m

3945

20.4966kN/m

7.3856kN/m

36.882 kN/m

174

Shear Force Diagram (V) ∑M=0 =(Ra x 3.945) - (36.882 x 3.945) x 3.945/2 =3.945 Ra - 145.499 x 1.9725 =3.945 Ra - 286.997 3.945 Ra = 286.997 Ra = 72.75kN

3945

36.882 kN/m

1972.5

1972.5 72.75kN/m

∑y=0 Ra-(36.882 x 3.945) + Rb =0 72.75 - 145.499 + Rb = 0 Rb = 72.75kN 72.75

Bending Moment Diagram (M)

Positive Area (1)72.75 x 3.945/2 x 1/2 =71.75

(+) -72.75+72.75=0 (-)

Negative Area (2)72.75 x 3.945/2 x 1/2 =71.75 (1)=(2)

71.75

175

Column A3 --- First Floor 176

Column A3 --- Ground Floor 177

COLUMN A3 First Floor Structure

Live Load Analysis

Slab

1.5 kN/m2x (4.503m x 2.954m) = 19.953 kN

Dead Load Analysis 3.6 kN/m2x (4.503m x 2.954m) = 47.887 kN

Brick Wall

8.55 kN/m2x (4.503m + 2.954m) = 63.757 kN

Beam self weight

1.44 kN/m2x (4.503m + 2.954m) = 10.738kN

Column self weight

6.48kN

Total

19.953 kN

128.862 kN

Ultimate load = 1.6(19.953kN) + 1.4(128.862kN) = 212.33 kN

Ground Floor Structure

Live Load Analysis

Slab

1.5 kN/m2x (4.503m x 2.954m) = 19.953 kN

Dead Load Analysis 3.6 kN/m2x (4.503m x 2.954m) = 47.887 kN

Brick Wall

8.55 kN/m2x 4.503m = 38.2755 kN

Beam self weight

1.44 kN/m2x (4.503m + 2.954m) = 10.738kN

Column self weight

6.48kN

Total

19.953 kN

Ultimate load = 1.6(19.953) + 1.4(103.3805) = 176.66 kN

103.3805 kN 178

COLUMN A3 Roof Level Structure

Live Load Analysis

Roof

0.5kN/m2 x (4.503m x 2.954m) = 6.65 kN

Beam self weight

Total

6.65 kN

Dead Load Analysis 1 kN/m2x (4.503m x 2.954m) = 13.302 kN 1.44 kN/m2x (4.503m + 2.954m) = 10.7381kN 24.0401 kN

Ultimate load = 1.6(6.65kN) + 1.4(24.01kN) = 44.254 kN Total column load for column E2 = 212.33 kN + 176.66 kN+ 44.254 kN = 433.244 kN

179

Column A4 --- First Floor 180

Column A4 --- Ground Floor 181

COLUMN A4 First Floor Structure

Live Load Analysis

Slab

1.5 kN/m2x (1.944m x 2.954m) = 8.615 kN

Dead Load Analysis 3.6 kN/m2x (1.944m x 2.954m) = 20.675 kN

Brick Wall

8.55 kN/m2x (1.944m + 2.954m) = 41.8779 kN

Beam self weight

1.44 kN/m2x (1.944m + 2.954m) = 7.053kN

Column self weight

6.48kN

Total

8.615 kN

76.086 kN

Ultimate load = 1.6(8.615kN) + 1.4(76.086kN) = 120.304 kN

Ground Floor Structure

Live Load Analysis

Slab

1.5 kN/m2x (1.944m x 2.954m) = 8.615 kN

Dead Load Analysis 3.6 kN/m2x (1.944m x 2.954m) = 20.675 kN

Brick Wall

8.55 kN/m2x (1.944m + 2.954m) = 41.8779 kN

Beam self weight

1.44 kN/m2x (1.944m + 2.954m) = 7.053kN

Column self weight

6.48kN

Total

8.615 kN

76.086 kN 182

Ultimate load = 1.6(8.615kN) + 1.4(76.086kN) = 120.304 kN

COLUMN A4 Roof Level Structure

Live Load Analysis

Roof

0.5kN/m2 x (1.944m x 2.954m) = 2.872 kN

Beam self weight

Total

2.872 kN

Dead Load Analysis 1 kN/m2x (1.944m x 2.954m) = 5.743 kN 1.44 kN/m2x (1.944m + 2.954m) = 7.053kN 12.796 kN

Ultimate load = 1.6(2.872kN) + 1.4(12.796kN) = 22.5096 kN Total column load for column E2 = 120.304 kN + 120.304 kN + 22.5096 kN = 263.12 kN

183