Building Structure

Building Structures [ARC 2522/2523] PROJECT 2: EXTENSION OF A R.C. BUNGALOW

Individual Proposal

Name:

Feiven Chee

Student ID:

0312004

Lecturer:

Mr. Adib

1

Table of content 1.0

Design brief

3

2.0

Proposed Extension

4

2.1

Architectural Plans

4

2.2

Structural Plans

7

3.0

Identifying One-Way and Two-Way Slab

11

4.0

Load Distribution Diagram for Beam Analysis

12

5.0

Beam Analysis Calculation

13

5.1

Ground Floor Beam, A1 / 1 – 3

13

5.2

First Floor Beam, A2 - A1 / 2

18

5.3

First Floor Beam, A1 / 1 – 3

25

5.4

First Floor Beam, A2 / 1 – 3

32

5.5

First Floor Beam, B - A1 / 1

41

5.6

First Floor Beam, B - A1 / 3

49

6.0

Load Distribution Diagram for Column Analysis

59

7.0

Column Analysis Calculation

60

7.1

Column A2 / 1

60

7.2

Column A2 / 3

62

7.3

Column B / 1

64

7.4

Column A1 / 3

68 2

1.0

Design brief Through my extension proposal, an extension which includes spaces such as living room,

bathroom, study area and balcony are proposed to be added to the current house. In the current house, the dining area at the ground floor is currently shared with the living room. While the first floor could be extended with a balcony and a bathroom.

For this report, the live loads for the rooms will be assumed, according to UBBL, as follows: Dining room: 2.0kN/m2 Bedroom: 1.5kN/m2 Toilet: 2.0kN/m 2 Roof: 0.5kN/m2

3

2.0

Proposed Extension

2.1 Architectural plans

4

5

6

2.2 Structural plans

7

8

9

10

3.0

Identifying One-Way and Two-Way Slab

Ly = Longer side of slab Lx = Shorter side of slab

When Ly / Lx > 2, it is a One-Way slab.

When Ly / Lx ≤ 2, it is a Two-Way slab.

Ground floor slab B-A1 / 1-3 4.15 m / 3.0 m = 1.38 <2

(Two-Way slab)

First floor slab B-A2 / 1-3 3.0 m / 1.55 m = 1.93 <2

(Two-Way slab)

First floor slab A2-A1 / 1-2 2.60 m / 1.15 m = 2.26 >2

(One-Way slab)

First floor slab A2-A1 / 2-3 2.60 m / 1.85 m = 1.41 <2

(Two-Way slab)

First floor slab A2-A1 / 3-4 2.60 m / 1.08 m = 2.41 >2

(One-Way slab)

11

4.0

Load Distribution Diagram for Beam Analysis

12

5.0 5.1

Beam Analysis Calculation Ground Floor Beam, A1 / 1 – 3 Two-Way slab (triangular)

1) Beam Self weight

( Dead load )

Assuming beam size is 150 mm x 500 mm, Given: Density of concrete = 24 kN/m3

Self weight of beam = Beam size x Density of concrete = 0.15 m x 0.5 m x 24 kN/m3 = 1.8 kN/m

2) Dead load from slab B - A1 / 1 - 3

( Two-Way slab )

Load is transferred to beam A1 / 1–3 in a triangular form

*( L x 1/2 x 2/3 )

*In Two-Way slab, if load is transferred in a trapezoidal form, convert load into UDL by applying factor 1/2, while, if load is transferred in a triangular form, convert load into UDL by applying factor 1/2 x 2/3

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab B-A1 / 1–3 to beam A1 / 1–3 = Slab thickness x density of concrete x [ L x 1/2 x 2/3 ] = 0.15 m x 24 kN/m3 x [ 3 m x 1/2 x 2/3 ] = 3.6 kN/m 13

Total dead load on beam A1 / 1 – 3 = Beam self weight + Dead load from slab B-A1 / 1–3 = 1.8 kN/m + 3.6 kN/m = 5.4 kN/m

Total Dead Load Diagram on Beam A1 / 1-3

14

3) Live load from slab B - A1 / 1 - 3

( Two-Way slab )

Load is transferred to beam A1 / 1–3 in a triangular form

( L x 1/2 x 2/3 ).

Given: Quantify live load for slab B-A1 / 1–3 (Living room) = 2.0 kN/m2

Live load transferred from slab B-A1 / 1–3 to beam A1 / 1–3 = Quantify live load x [ L x 1/2 x 2/3 ] = 2.0 kN/m2 x [ 3 m x 1/2 x 2/3 ] = 2.0 kN/m

Total live load on beam A1 / 1 - 3 = Live load from slab B - A1 / 1 – 3 = 2.0 kN/m

Total Live Load Diagram on Beam A1 / 1-3

15

Ultimate Load *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate load = [Total dead load x 1.4] + [Total live load x 1.6] = [5.4 kN/m x 1.4] + [2.0 kN/m x 1.6] = 10.76 kN/m

Ultimate Load Diagram on Beam A1 / 1-3

16

Reaction Forces * An equivalent point load is put at the middle point to replace the uniformly distributed load over its length

The total load of beam A1 / 1-3 = 10.76 kN/m x 3.0 m = 32.28 kN

Take the moment at point R2 Equilibrium of moments,

â&#x2C6;&#x2018;M=0

(32.28 kN x 1.5 m) = R2 x 3 m R2 = 16.14 kN

Balancing vertical forces Equilibrium of forces,

â&#x2C6;&#x2018;F=0 R1 + R2 = 32.28 kN R1 + 16.14 kN = 32.28 kN R1 = 16.14 kN

Area A1 = Area A2 = 16.14 kN x 1.5 m x 1/2 = 12.11 kNm

17

5.2

First Floor Beam, A2 - A1 / 2 One-Way slab, Two-Way slab (trapezoidal)

1) Beam Self weight

( Dead load )

From the previous calculation, Self weight of beam = 1.8 kN/m

2) Brick wall weight

( Dead load )

Assuming wall height is 3000 mm, wall thickness is 150 mm, Given: Density of brick = 19 kN/m3

Brick wall weight = Wall height x Wall thickness x Density of brick = 3.0 m x 0.15 m x 19 kN/m3 = 8.55 kN/m

3) Dead load from slab A2 - A1 / 1 - 2

( One-Way slab )

*In One-Way slab, Load is transferred only through the longer side of the slab to beam.

*( Lx x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load from slab A2-A1 / 1â&#x20AC;&#x201C;2 to beam A2-A1 / 2 = Slab thickness x density of concrete x [ Lx x 1/2 ] = 0.15 m x 24 kN/m3 x [ 1.15 m x 1/2 ] = 2.07 kN/m

18

4) Dead load from slab A2 - A1 / 2 - 3

( Two-Way slab )

Load is transferred to beam A2-A1 / 3 in a trapezoidal form

( L x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab A2-A1 / 2–3 to beam A2-A1 / 2 = Slab thickness x density of concrete x [ L x 1/2 ] = 0.15 m x 24 kN/m3 x [ 2.6 m x 1/2 ] = 4.68 kN/m

Total dead load on beam A2 - A1 / 2

Total dead load A1 - a = Beam self weight + Brick wall weight + Dead load from slab A2–A1 / 1–2 + Dead load from slab A2-A1 / 2–3 = 1.8 kN/m + 8.55 kN/m + 2.07 kN/m + 4.68 kN/m = 17.1 kN/m

Total dead load a - A2 = Beam self weight + Dead load from slab A2–A1 / 1–2 + Dead load from slab A2-A1 / 2–3 = 1.8 kN/m + 2.07 kN/m + 4.68 kN/m = 8.55 kN/m

19

Total Dead Load Diagram on Beam A2-A1 / 2

20

5) Live load from slab A2 - A1 / 1 - 2

( One-Way slab )

( Lx x 1/2 )

Given: Quantify live load for slab A2-A1 / 1–2 (Extended Bedroom) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 1–2 to beam A2-A1 / 2 = Quantify live load x [ Lx x 1/2 ] = 1.5 kN/m2 x [ 1.15 m x 1/2 ] = 0.86 kN/m

6) Live load from slab A2 - A1 / 2 - 3

( Two-Way slab )

Load is transferred to beam A2-A1 / 3 in a trapezoidal form ( L x 1/2 )

Given: Quantify live load for slab A2-A1 / 2–4 (Study Room) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 2–3 to beam A2-A1 / 2 = Quantify live load x [ L x 1/2 ] = 1.5 kN/m2 x [ 2.6 m x 1/2 ] = 1.95 kN/m

Total live load on beam A2 - A1 / 2 = Live load from slab A2-A1 / 1-2 + Live load from slab A2-A1 / 2-3 = 0.86 kN/m + 1.95 kN/m = 2.81 kN/m

21

Total Live Load Diagram on Beam A2-A1 / 2

Ultimate Load on beam A2 - A1 / 2 *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate Load A1 – a

= [ 1.4 x Total dead load A1 – a ] + [ 1.6 x Total live load A1 - a] = (1.4 x 17.1 kN/m) + (1.6 x 2.81 kN/m) = 28.44kN/m

Ultimate Load a – A2

= [ 1.4 x Total dead load a – A2 ] + [ 1.6 x Total live load A1 - a] = (1.4 x 8.55 kN/m) + (1.6 x 2.81 kN/m) = 16.47 kN/m

22

Ultimate Load Diagram on Beam A2-A1 / 2

23

Reactions

The total load ① of beam A2-A1 / 2 = 28.44 kN/m x 1.5 m = 42.66 kN

The total load ② of beam A2-A1 / 2 = 16.47 kN/m x 1.1 m = 18.12 kN

Take the moment at point R2 Equilibrium of moments,

∑M=0

(42.66 kN x 0.75 m) + (18.12 kN x 2.05 m) = R2 x 2.6 m R2 = 26.59 kN

Balancing vertical forces Equilibrium of forces,

∑F=0 R1 + R2 = 42.66 kN + 18.12kN R1 + 26.59 kN = 60.78 kN R1 = 34.19 kN

Area A1 = 34.19kN x 1.2m x 1/2 = 20.51 kNm Area A2 = - 8.47kN x (1.5-1.21)m x 1/2 = - 1.23 kNm Area A3 = - (8.47+26.59)kN x 1/2 x (2.6-1.5)m = - 19.28 kNm Therefore, A1 + A2 + A3 = 0

24

5.3

First Floor Beam, A1 / 1 – 3 Two-Way slab (triangular), beam-to-beam point load

1) Beam Self weight

( Dead load )

From the previous calculation, Self weight of beam = 1.8 kN/m

2) Brick wall weight

( Dead load )

From the previous calculation, Brick wall weight = 8.55 kN/m

3) Dead load from slab A2 - A1 / 1 - 2

( One-Way slab )

*In One-Way slab, Load is transferred only through the longer side of the slab to beam.

Therefore, in this case, No load is transferred from slab A2-A1 / 1–2 to beam A1 / 1–4.

4) Dead load from slab A2 - A1 / 2 - 3

( Two-Way slab )

Load is transferred to beam A1 / 1–3 in a triangular form

( L x 1/2 x 2/3 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

25

Dead load transferred from slab A2-A1 / 2–3 to beam A1 / 1–3 = Slab thickness x density of concrete x [ L x 1/2 x 2/3 ] = 0.15 m x 24 kN/m3 x [ 1.85 m x 1/2 x 2/3] = 2.22 kN/m

Total dead load on beam A1 / 1 – 3

Total dead load 1 - 2 = Beam self weight + Brick wall weight = 1.8 kN/m + 8.55 kN/m = 10.35 kN/m

Total dead load 2 - 3 = Beam self weight + Brick wall weight + Dead load from slab A2–A1 / 2-3 = 1.8 kN/m + 8.55 kN/m + 2.22 kN/m = 12.57 kN/m

26

Total Dead Load Diagram on Beam A1 / 1 - 3

27

5) Live load from slab A2 - A1 / 2 - 3

( Two-Way slab )

Load is transferred to beam A1 / 1–3 in a triangular form

( L x 1/2 x 2/3 )

Given: Quantify live load for slab A2-A1 / 2-3 (Bedroom) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 2-3 to beam A1 / 1-3 = Quantify live load x [ L x 1/2 ] = 1.5 kN/m2 x [ 1.85m x 1/2 x 2/3 ] = 0.93 kN/m

Total live load on beam A1 / 1 – 3

Total live load 2 - 3 = Total load from slab A2–A1 / 2-3 = 0.93 kN/m

Total Live Load Diagram on Beam A1 / 1 – 3

28

Ultimate Load on beam A1 / 1 - 3 *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate Load 1 – 2

= [ 1.4 x Total dead load 1 – 2 ] + [ 1.6 x Total live load 1 – 2] = (1.4 x 10.35 kN/m) + (1.6 x 0) = 14.49 kN/m

Ultimate Load 2 – 4

= [ 1.4 x Total dead load 2 – 3 ] + [ 1.6 x Total live load 2 – 3 ] = (1.4 x 12.57 kN/m) + (1.6 x 0.93 kN/m) = 19.09 kN/m

Ultimate Load Diagram on Beam A1 / 1 - 3

29

Reactions

The total load ① of beam A1 / 1-3 = 14.49 kN/m x 1.15 m = 16.66 kN

The total load ② of beam A1 / 1-3 = 19.09 kN/m x 1.85 m = 35.32 kN

Point load ③ from beam A2-A1 / 2 = R1 of beam A2-A1 / 2 = 34.19 kN (from previous calculation)

30

Take the moment at point R2 Equilibrium of moments,

∑M=0

(16.66kN x 0.575m) + (34.19kN x 1.15m) + (35.32kN x 2.075m) = R2 x 3.0 m R2 = 40.73 kN

Balancing vertical forces Equilibrium of forces,

∑F=0 R1 + R2 = 16.66 kN + 34.19 kN +35.32 kN R1 + 40.73 kN = 86.17 kN R1 = 45.44 kN

Area A1 = (45.44+28.78)kN x 1/2 x 1.15m = 42.68 kNm

Area A2 = - (5.41+40.73)kN x 1/2 x (3.0-1.15)m = - 42.68 kNm

Therefore, A1 + A2 = 0

31

5.4

First Floor Beam, A2 / 1 – 3 Two-Way slab (triangular), Two-Way slab (trapezoidal), beam-to-beam point load, column-to-beam point loads

1) Beam Self weight

( Dead load )

From the previous calculation, Self weight of beam = 1.8 kN/m

2) Brick wall weight

( Dead load )

From the previous calculation, Brick wall weight = 8.55 kN/m

3) Dead Load from slab B - A2 / 1-3

( Two-Way slab)

Load is transferred to beam A2 / 1–3 in a trapezoidal form

( L x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab B-A2 / 1–3 to beam A2 / 1–3 = Slab thickness x density of concrete x [ L x 1/2 ] = 0.15 m x 24 kN/m3 x [ 3 m x 1/2 ] = 5.4 kN/m

32

4) Dead load from slab A2 - A1 / 1 - 2

( One-Way slab )

*In One-Way slab, Load is transferred only through the longer side of the slab to beam.

Therefore, in this case, No load is transferred from slab A2-A1 / 1–2 to beam A2 / 1–3.

5) Dead load from slab A2 - A1 / 2 - 3

( Two-Way slab )

Load is transferred to beam A2 / 1–3 in a triangular form

( L x 1/2 x 2/3 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab A2-A1 / 2–3 to beam A2 / 1–3 = Slab thickness x density of concrete x [ L x 1/2 x 2/3 ] = 0.15 m x 24 kN/m3 x [ 1.85 m x 1/2 x 2/3 ] = 2.22 kN/m

33

Total dead load on beam A2 / 1 – 3

Total dead load 1 - 2 = Beam self weight + Brick wall weight + Dead load from slab B-A2 / 1–3 = 1.8 kN/m + 8.55 kN/m + 5.4 kN/m = 15.75kN/m

Total dead load 2 - 3 = Beam self weight + Brick wall weight + Dead load from slab B-A2 / 1– + Dead load from slab A2-A1 / 2–3 = 1.8 kN/m + 8.55 kN/m + 5.4 kN/m + 2.22 kN/m = 17.97 kN/m

34

Total Dead Load Diagram on Beam A2 / 1 - 3

35

6) Live load from slab B - A2 / 1-3

( Two-Way slab )

Load is transferred to beam A2 / 1–3 in a trapezoidal form

( L x 1/2 )

Given: Quantify live load for slab B-A2 / 1-3 (Toilet) = 2.0 kN/m2

Live load transferred from slab B-A2 / 1-3 to beam A2 / 1–3 = Quantify live load x [ L x 1/2 ] = 2.0 kN/m2 x [ 3 x 1/2 ] = 3.0 kN/m

7) Live load from slab A2 - A1 / 2-3

( Two-Way slab )

Load is transferred to beam A2 / 1–3 in a triangular form

( L x 1/2 x 2/3 )

Given: Quantify live load for slab A2-A1 / 2-3 (Bedroom) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 2-3 to beam A2 / 1–3 = Quantify live load x [ L x 1/2 x 2/3 ] = 1.5 kN/m2 x [ 1.85 m x 1/2 x 2/3 ] = 0.93 kN/m

36

Total live load on beam A2 / 1 – 3

Total live load 1 - 2 = Live load from slab B-A2 / 1–3 = 3.0 kN/m

Total live load 2 - 3 = Live load from slab B-A2 / 1–3 + Live load from slab A2-A1 / 2–3 = 3.0 kN/m + 0.93 kN/m = 3.93 kN/m

Total Live Load Diagram on Beam A2 / 1 - 3

37

Ultimate Load on beam A2 / 1-3 *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate Load 1 – 2

= [ 1.4 x Total dead load 1 – 2 ] + [ 1.6 x Total live load 1 – 2] = (1.4 x 15.75 kN/m) + (1.6 x 3.0 kN/m) = 26.85 kN/m

Ultimate Load 2 – 4

= [ 1.4 x Total dead load 2 – 4 ] + [ 1.6 x Total live load 2 – 4 ] = (1.4 x 17.97 kN/m) + (1.6 x 3.93 kN/m) = 31.45 kN/m

Ultimate Load Diagram on Beam A2 / 1 - 3

38

Reactions

The total load ① of beam A2 / 1-3 = 26.85 kN/m x 1.15 m = 30.88 kN

The total load ② of beam A2 / 1-3 = 31.45 kN/m x 1.85 m = 58.18 kN

Point load ③ from beam A2-A1 / 2 = R2 of beam A2-A1 / 2 = 26.59 kN (from previous calculation)

Point load ④ from column A2 /1 = 15.87 kN (from calculation of column A2 / 1)

Point load ⑤ from column A2 /3 = 15.87 kN (from calculation of column A2 /3)

39

Take the moment at point R2 Equilibrium of moments,

∑M=0

(15.87kN x 0m) + (30.88kN x 0.575m) + (26.59kN x 1.15m) + (58.18kN x 2.075m) + (15.87kN x 3.0m)

= R2 x 3.0 m 216.67 kNm = R2 x 3.0 m R2 = 72.22 kN

Balancing vertical forces Equilibrium of forces,

∑F=0 R1 + R2 = 15.87 kN + 30.88 kN + 26.59 kN + 58.18 kN + 15.87 kN R1 + 72.22 kN = 147.39 kN R1 = 75.17 kN

Area A1 = (59.3+28.42) kN x 1/2 x 1.15m = 50.44 kNm

Area A2 = 1.83 kN x (1.208-1.15)m x 1/2 = 0.05 kNm

Area A3 = - 56.35 kN x (3.0-1.208) m x 1/2 = - 50.49 kNm

Therefore, A1 + A2 + A3 = 0

40

5.5

First Floor Beam, B - A1 / 1 One-Way slab, Two-Way slab (triangular), beam-to-beam point load, column-to-beam point load

1) Beam Self weight

( Dead load )

From the previous calculation, Self weight of beam = 1.8 kN/m

2) Brick wall weight

( Dead load )

From the previous calculation, Brick wall weight = 8.55 kN/m

3) Dead load from slab B â&#x20AC;&#x201C; A2 / 1-3

( Two-Way slab )

Load is transferred to beam B-A1 / 1 in a triangular form

( L x 1/2 x 2/3 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab B-A2 / 1-3 to beam B-A1 / 1 = Slab thickness x density of concrete x [ L x 1/2 x 2/3 ] = 0.15 m x 24 kN/m3 x [ 1.55 m x 1/2 x 2/3 ] = 1.86 kN/m

41

4) Dead load from slab A2 - A1 / 1 - 2

( One-Way slab )

( Lx x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab A2-A1 / 1–2 to beam B-A1 / 1 = Slab thickness x density of concrete x [ Lx x 1/2 ] = 0.15 m x 24 kN/m3 x [ 1.15 m x 1/2 ] = 2.07 kN/m

Total dead load on beam B-A1 / 1

Total dead load B – A2 = Beam self weight + Brick wall weight + Dead load from slab B-A2 / 1-3 = 1.8 kN/m + 8.55 kN/m + 1.86 kN/m = 12.21 kN/m

Total dead load A2– A1 = Beam self weight + Dead load from slab A2-A1 / 1–2 = 1.8 kN/m + 2.07 kN/m = 3.87 kN/m

42

Total Dead Load Diagram on Beam B1 â&#x20AC;&#x201C; A1 / 1

43

5) Live load from slab B â&#x20AC;&#x201C; A2 / 1 - 3

( Two-Way slab )

Load is transferred to beam B-A1 /1 in a triangular form

( L x 1/2 x 2/3 )

Given: Quantify live load for slab B-A2 / 1-4 (Toilet) = 2.0 kN/m2

Live load transferred from slab B-A2 / 1-3 to beam B-A1 /1 = Quantify live load x [ L x 1/2 x 2/3 ] = 2.0 kN/m2 x [ 1.55 m x 1/2 x 2/3 ] = 1.03 kN/m

6) Live load from slab A2 - A1 / 1 - 2

( One-Way slab )

( Lx x 1/2 )

Given: Quantify live load for slab A2-A1 / 1-2 (Bedroom) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 1-2 to beam B-A1 /1 = Quantify live load x [ Lx x 1/2 ] = 1.5 kN/m2 x [ 1.15 m x 1/2 ] = 0.86 kN/m

44

Total live load on beam B-A1 / 1

Total live load B – A2 = Live load from slab B-A2 / 1-3 = 1.03 kN/m

Total dead load A2 – A1 = Live load from slab A2-A1 / 1-2 = 0.86 kN/m

Total Live Load Diagram on Beam B – A1 / 1

45

Ultimate Load on beam B-A1 / 1 *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate Load B – A2

= [ 1.4 x Total dead load B – A2 ] + [ 1.6 x Total live load B – A2 ] = (1.4 x 12.21 kN/m) + (1.6 x 1.03 kN/m) = 18.74 kN/m

Ultimate Load A2– A1 = [ 1.4 x Total dead load A2– A1 ] + [ 1.6 x Total live load A2– A1 ] = (1.4 x 3.87 kN/m) + (1.6 x 0.86 kN/m) = 6.79 kN/m

Ultimate Load Diagram on Beam B-A1 / 1

46

Reactions

The total load ① of beam B-A1 /1 = 18.74 kN/m x 1.55 m = 29.05 kN

The total load ② of beam B-A1 /1 = 6.79 kN/m x 2.6 m = 17.65 kN

Point load ③ = R1 of beam A2 / 1-3 + load from column A2 / 1 = 75.17 kN + 15.87 kN

(from previous calculation of beam A2/1-3 and calculation of column A2/1 in page __)

= 91.04 kN

47

Take the moment at point R2 Equilibrium of moments,

∑M=0

(29.05 kN x 0.775 m) + (91.04 kN x 1.55 m) + (17.65 kN x 2.85 m) = R2 x 4.15 m 213.93 kNm = R2 x 4.15 m R2 = 51.55 kN

Balancing vertical forces Equilibrium of forces,

∑F=0 R1 + R2 = 29.05 kN + 91.04 kN + 17.65 kN R1 + 51.55 kN = 137.74 kN R1 = 86.19 kN

Area A1 = (86.19+57.14) kN x 1/2 x 1.55m = 111.09 kNm Area A2 = - (33.9+51.55) kN x 1/2 x (4.15-1.55) m = - 111.09 kNm

Therefore, A1 + A2 = 0

48

5.6

First Floor Beam, B - A1 / 3 One-Way slab, Two-Way slab (trapezoidal), Two-Way slab (triangular), beam-to-beam point load, column-to-beam point load

1) Beam Self weight

( Dead load )

From the previous calculation, Self weight of beam = 1.8 kN/m

2) Brick wall weight

( Dead load )

From the previous calculation, Brick wall weight = 8.55 kN/m

3) Dead load from slab B â&#x20AC;&#x201C; A2 / 1-3

( Two-Way slab )

Load is transferred to beam B-A1 / 3 in a triangular form

( L x 1/2 x 2/3 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab B-A2 / 1-3 to beam B-A1 / 3 = Slab thickness x density of concrete x [ L x 1/2 x 2/3 ] = 0.15 m x 24 kN/m3 x [ 1.55 m x 1/2 x 2/3 ] = 1.86 kN/m

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4) Dead load from slab A2-A1 / 2-3

( Two-Way slab )

Load is transferred to beam B-A1 / 3 in a trapezoidal form

( L x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab A2-A1 / 2â&#x20AC;&#x201C;3 to beam B-A1 / 3 = Slab thickness x density of concrete x [ L x 1/2 ] = 0.15 m x 24 kN/m3 x [ 2.6 m x 1/2 ] = 4.68 kN/m

5) Dead load from slab A2-A1 / 3-4

( Cantilevered slab )

( Lx x 1/2 )

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3

Dead load transferred from slab A2-A1 / 3â&#x20AC;&#x201C;4 to beam B-A1 / 3 = Slab thickness x density of concrete x [ Lx x 1/2 ] = 0.15 m x 24 kN/m3 x [ 1.08 m x 1/2 ] = 1.94 kN/m

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Total dead load on beam B-A1 / 3

Total dead load B – A2 = Beam self weight + Brick wall weight + Dead load from slab B-A2 / 1-3 = 1.8 kN/m + 8.55 kN/m + 1.86 kN/m = 12.21 kN/m

Total dead load A2– A1 = Beam self weight + Brick wall weight + Dead load from slab A2-A1 / 2–3 + Dead loads from slab A2-A1 / 3–4 = 1.8 kN/m + 8.55 kN/m + 4.68 kN/m + 1.94 kN/m = 16.97 kN/m

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Total Dead Load Diagram on Beam B1 â&#x20AC;&#x201C; A1 / 3

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6) Live load from slab B â&#x20AC;&#x201C; A2 / 1-3

( Two-Way slab )

Load is transferred to beam B-A1 / 3 in a triangular form

( L x 1/2 x 2/3 )

Given: Quantify live load for slab B-A2 / 1-3 (Toilet) = 2.0 kN/m2

Live load transferred from slab B-A2 / 1-3 to beam B-A1 / 3 = Quantify live load x [ L x 1/2 x 2/3 ] = 2.0 kN/m2 x [ 1.55 m x 1/2 x 2/3 ] = 1.03 kN/m

7) Live load from slab A2-A1 / 2-3 ( Two-Way slab )

Load is transferred to beam B-A1 / 3 in a trapezoidal form

( L x 1/2 )

Given: Density of concrete = 24 kN/m3 Quantify live load for slab A2-A1 / 3-4 (Bedroom) = 1.5 kN/m2

Live load transferred from slab A2-A1 / 3-4 to beam B-A1 / 3 = Quantify live load x [ L x 1/2 ] = 1.5 kN/m2 x [ 2.6 m x 1/2 ] = 1.95 kN/m

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8) Live load from slab A2-A1 / 3-4

( One-Way slab )

( Lx x 1/2 )

Given: Quantify live load for slab A2-A1 / 3-4 (Balcony) = 2.0 kN/m2

Live load transferred from slab A2-A1 / 3-4 to beam B-A1 / 3 = Quantify live load x [ L x 1/2 ] = 2.0 kN/m2 x [ 1.08 m x 1/2 ] = 1.08 kN/m

Total live load on beam B-A1 / 3

Total live load B - A2 = Live load from slab B-A2 / 1-3 = 1.03 kN/m

Total live load A2 â&#x20AC;&#x201C; A1 = Live load from slab A2-A1 / 2-3 + Live load from slab A2-A1 / 3-4 = 1.95 kN/m + 1.08 kN/m = 3.03 kN/m

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Total Live Load Diagram on Beam B â&#x20AC;&#x201C; A1 / 3

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Ultimate Load on beam B-A1 / 3 *Ultimate Load = 1.4 D.L. + 1.6 L.L.

Ultimate Load B – A2

= [ 1.4 x Total dead load B – A2 ] + [ 1.6 x Total live load B – A2 ] = (1.4 x 12.21 kN/m) + (1.6 x 1.03 kN/m) = 18.74 kN/m

Ultimate Load A2– A1 = [ 1.4 x Total dead load A2– A1 ] + [ 1.6 x Total live load A2– A1 ] = (1.4 x 16.97 kN/m) + (1.6 x 3.03 kN/m) = 28.61 kN/m

Ultimate Load Diagram on Beam B – A1 / 3

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Reactions

The total load ① of beam B-A1 / 3 = 18.74 kN/m x 1.55 m = 29.05 kN

The total load ② of beam B-A1 / 3 = 28.61 kN/m x 2.6 m = 74.39 kN

Point load ③ = R2 of beam A2 / 1-3 + load from column A2 / 3 = 72.22 kN + 15.87 kN

(from previous calculation of beam A2/1-3 and calculation of column A2/3 in page __)

= 88.09 kN

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Take the moment at point R2 Equilibrium of moments,

∑M=0

(29.05 kN x 0.775 m) + (88.09 kN x 1.55 m) + (74.39 kN x 2.85 m) = R2 x 4.15 m 371.06 kNm = R2 x 4.15 m R2 = 89.41 kN

Balancing vertical forces Equilibrium of forces,

∑F=0 R1 + R2 = 29.05 kN + 88.09 kN + 74.39 kN R1 + 89.41 kN = 191.53 kN R1 = 102.12 kN

Area A1 = (102.12+73.07) kN x 1/2 x 1.55m = 135.77 kNm

Area A2 = - (15.02+89.41) kN x 1/2 x (4.15-1.55) m = - 135.77 kNm

Therefore, A1 + A2 = 0

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6.0

Load Distribution Diagram for Column Analysis

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7.0

Column Analysis Calculation

7.1

Column A2 / 1

1) Roof slab

( Dead load )

Given: Quantify dead load of roof = 1.0 kN/m2

Dead load from roof B-A2 / 1-3 = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 0.775 m = 1.16 kN Dead load from roof A2-A1 / 1-3 = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 1.3 m = 1.95 kN

2) Roof level beam

( Dead load )

Assuming beam size is 150 mm x 500 mm, Given: Density of concrete = 24 kN/m3

Self weight of beam = Beam size x Density of concrete = 0.15 m x 0.5 m x 24 kN/m3 = 1.8 kN/m Dead load of beam = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 0.775 + 1.3 )m = 6.44 kN

Total dead load = 1.16 kN + 1.95 kN + 6.44 kN = 9.55 kN

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3) Roof slab

( Live load )

Given: Quantify live load of roof = 0.5 kN/m2

Live load from roof B-A2 / 1-3 = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 0.775 m = 0.58 kN Live load from roof A2-A1 / 1-3 = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 1.3 m = 0.98 kN

Total live load = 0.58 kN + 0.98 kN = 1.56 kN

Ultimate load on column A2 / 1 *Ultimate Load = 1.4 D.L. + 1.6 L.L. ( 1.4 x 9.55 kN ) + ( 1.6 x 1.56 kN ) = 15.87 kN

Column size estimation Assuming Fcu = 30 N/mm2 Fy (mild steel) = 250 N/mm2 Ac = ( 150 x 150 )mm2 = 22500 mm2 Asc = 22500 mm2 x 2% = 450 mm2

F = ( 0.4 x Fcu x Ac ) + ( 0.8 x Asc x Fy ) N = ( 0.4 x 30 x 22500 ) + ( 0.8 x 450 x 250 ) N = 360 kN

Therefore, this column can sustains a load of 15.87 kN.

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7.2

Column A2 / 3

1) Roof slab

( Dead load )

Given: Quantify dead load of roof = 1.0 kN/m2

Dead load from roof B-A2 / 1-3 = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 0.775 m = 1.16 kN Dead load from roof A2-A1 / 1-3 = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 1.3 m = 1.95 kN

2) Roof level beam

( Dead load )

Assuming beam size is 150 mm x 500 mm, Given: Density of concrete = 24 kN/m3

Self weight of beam = Beam size x Density of concrete = 0.15 m x 0.5 m x 24 kN/m3 = 1.8 kN/m Dead load of beam = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 0.775 + 1.3 )m = 6.44 kN

Total dead load = 1.16 kN + 1.95 kN + 6.44 kN = 9.55 kN

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3) Roof slab

( Live load )

Given: Quantify live load of roof = 0.5 kN/m2

Live load from roof B-A2 / 1-3 = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 0.775 m = 0.58 kN Live load from roof A2-A1 / 1-3 = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 1.3 m = 0.98 kN

Total live load = 0.58 kN + 0.98 kN = 1.56 kN

Ultimate load on column A2 / 3 *Ultimate Load = 1.4 D.L. + 1.6 L.L. ( 1.4 x 9.55 kN ) + ( 1.6 x 1.56 kN ) = 15.87 kN

Column size estimation Assuming Fcu = 30 N/mm2 Fy (mild steel) = 250 N/mm2 Ac = ( 150 x 150 )mm2 = 22500 mm2 Asc = 22500 mm2 x 2% = 450 mm2

F = ( 0.4 x Fcu x Ac ) + ( 0.8 x Asc x Fy ) N = ( 0.4 x 30 x 22500 ) + ( 0.8 x 450 x 250 ) N = 360 kN

Therefore, this column can sustains a load of 15.87 kN.

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7.3

Column B / 1

1) Slab

( Dead load )

Given: Quantify dead load of roof = 1.0 kN/m2 Dead load from roof slab = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 0.775 m = 1.16 kN

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3 Dead load from first floor slab = 0.15 m x 24 kN/m3 x Area = 0.15 m x 24 kN/m3 x 1.5 m x 0.775 m = 4.19 kN

Dead load from ground floor slab = 0.15 m x 24 kN/m3 x Area = 0.15 m x 24 kN/m3 x 1.5 m x 2.075 m = 11.21 kN

2) Beam

( Dead load )

Assuming beam size is 150 mm x 500 mm, Given: Density of concrete = 24 kN/m3

Self weight of beam = Beam size x Density of concrete = 0.15 m x 0.5 m x 24 kN/m3 = 1.8 kN/m

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Dead load of beam from roof level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 0.775 )m = 4.1 kN

Dead load of beam from first floor level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 0.775 )m = 4.1 kN

Dead load of beam from ground floor level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 2.075 )m = 6.44 kN

3) Brick wall Assuming wall height is 3000 mm, wall thickness is 150 mm, Given: Density of brick = 19 kN/m3

Brick wall weight = Wall height x Wall thickness x Density of brick = 3.0 m x 0.15 m x 19 kN/m3 = 8.55 kN/m

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Dead load of brick wall from first floor level = self weight of brick wall x total length = 8.55 kN/m x ( 1.5 + 0.775 )m = 19.45 kN

Dead load of brick wall from ground floor level = self weight of brick wall x total length = 8.55 kN/m x 1.5 m = 12.83 kN

Total dead load = 1.16 kN + 4.19 kN + 11.21 kN + 4.1 kN + 4.1 kN + 6.44 kN + 19.45 kN + 12.83 kN = 63.48 kN

4) Slab

( Live load )

Given: Quantify live load of roof = 0.5 kN/m2

Live load from roof B-A2 / 1-3 = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 0.775 m = 0.58 kN

Given: Quantify live load of first floor (bathroom 2.0 kN/m2) = 2.0 kN/m2 Live load from first floor slab = 2.0 kN/m2 x Area = 2.0 kN/m2 x 1.5 m x 0.775 m = 2.33 kN

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Given: Quantify live load of ground floor (extended living room 1.5 kN/m2) = 1.5 kN/m2 Live load from ground floor slab = 1.5 kN/m2 x Area = 1.5 kN/m2 x 1.5 m x 2.075 m = 4.67 kN

Total live load = 0.58 kN + 2.33 kN + 4.67 kN = 7.58 kN

Ultimate load on column A2 / 1 *Ultimate Load = 1.4 D.L. + 1.6 L.L. ( 1.4 x 63.48 kN ) + ( 1.6 x 7.58 kN ) = 101.0 kN

Column size estimation Assuming Fcu = 30 N/mm2 Fy (mild steel) = 250 N/mm2 Ac = ( 150 x 150 )mm2 = 22500 mm2 Asc = 22500 mm2 x 2% = 450 mm2

F = ( 0.4 x Fcu x Ac ) + ( 0.8 x Asc x Fy ) N = ( 0.4 x 30 x 22500 ) + ( 0.8 x 450 x 250 ) N = 360 kN

Therefore, this column can sustains a load of 101.0 kN.

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7.4

Column A1 / 3

1) Slab

( Dead load )

Given: Quantify dead load of roof = 1.0 kN/m2 Dead load from roof slab = 1.0 kN/m2 x Area = 1.0 kN/m2 x 1.5 m x 1.3 m = 1.95 kN

Assuming slab thickness is 150mm, Given: Density of concrete = 24 kN/m3 Dead load from first floor slab = 0.15 m x 24 kN/m3 x Area = 0.15 m x 24 kN/m3 x [ (1.5 x 1.3) + ( 1.3 x 1.075) ]m = 12.05 kN

Dead load from ground floor slab = 0.15 m x 24 kN/m3 x Area = 0.15 m x 24 kN/m3 x 1.5 m x 2.075 m = 11.21 kN

2) Beam

( Dead load )

Assuming beam size is 150 mm x 500 mm, Given: Density of concrete = 24 kN/m3

Self weight of beam = Beam size x Density of concrete = 0.15 m x 0.5 m x 24 kN/m3 = 1.8 kN/m

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Dead load of beam from roof level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 1.3 )m = 5.04 kN

Dead load of beam from first floor level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 1.3 )m = 5.04 kN

Dead load of beam from ground floor level = self weight of beam x total length = 1.8 kN/m x ( 1.5 + 2.075 )m = 6.44 kN

3) Brick wall Assuming wall height is 3000 mm, wall thickness is 150 mm, Given: Density of brick = 19 kN/m3

Brick wall weight = Wall height x Wall thickness x Density of brick = 3.0 m x 0.15 m x 19 kN/m3 = 8.55 kN/m

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Dead load of brick wall from first floor level = self weight of brick wall x total length = 8.55 kN/m x ( 1.5 + 1.3 )m = 23.94 kN

Dead load of brick wall from ground floor level = self weight of brick wall x total length = 8.55 kN/m x ( 1.5 + 2.075 ) m = 30.57 kN

Total dead load = 1.95 kN + 12.05 kN + 11.21 kN + 5.04 kN + 5.04 kN + 6.44 kN + 23.94 kN + 30.57 kN = 96.24 kN

4) Slab

( Live load )

Given: Quantify live load of roof = 0.5 kN/m2

Live load from roof = 0.5 kN/m2 x Area = 0.5 kN/m2 x 1.5 m x 1.3 m = 0.98 kN

Given: Quantify live load of first floor (study area 1.5kN/m2) = 1.5 kN/m2 Live load from first floor slab (study area) = 1.5 kN/m2 x Area = 1.5 kN/m2 x 1.5 m x 1.3 m = 2.93 kN

70

Given: Quantify live load of first floor (balcony 1.5kN/m2) = 1.5 kN/m2 Live load from first floor slab (balcony) = 1.5 kN/m2 x Area = 1.5 kN/m2 x 1..075 m x 1.3 m = 2.10 kN

Given: Quantify live load of ground floor (extended living room 1.5 kN/m2) = 1.5 kN/m2 Live load from ground floor slab = 1.5 kN/m2 x Area = 1.5 kN/m2 x 1.5 m x 2.075 m = 4.67 kN

Total live load = 0.98 kN + 2.93 kN + 2.10 kN + 4.67 kN = 10.68 kN

Ultimate load on column A2 / 1 *Ultimate Load = 1.4 D.L. + 1.6 L.L. ( 1.4 x 96.24 kN ) + ( 1.6 x 10.68 kN ) = 151.82 kN

Column size estimation Assuming Fcu = 30 N/mm2 Fy (mild steel) = 250 N/mm2 Ac = ( 150 x 150 )mm2 = 22500 mm2 Asc = 22500 mm2 x 2% = 450 mm2

F = ( 0.4 x Fcu x Ac ) + ( 0.8 x Asc x Fy ) N = ( 0.4 x 30 x 22500 ) + ( 0.8 x 450 x 250 ) N = 360 kN

Therefore, this column can sustains a load of 151.82 kN.

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