SCHOOL OF ARCHITECTURE . BUILDING & DESIGN Research Unit for Modern Architecture Studies in Southeast Asia (MASSA) Bachelor of Science (Hons) (Architecture)
BUILDING STRUCTURES (ARC 2523) Project 2: Extension of a R.C. Bungalow (Individual Work) Tutor: Ms. Norita Johar
TAN MING LONG (0311069) KONG REN HENG (0316416)
Introduction The proposed extension has a number of 13 beams and 8 columns each for ground floor and first floor, and 10 beams and 8 columns for the roof. All the structures are built with concrete. Ground floor of the extension consists of an outdoor corridor, a gallery, a studio and a dark room, while first floor is made up of a library, an office, a tea house and a void where one can look into ground floor gallery. The extension is accessible through an entrance at the outdoor corridor or an entrance from the original living room. Most of the walls in the extension are full-height walls, with only some of the walls for tea house and void are half-height walls. The material for walls is bricks. The extension was designed for an artist. The gallery is used to display his artwork, ranging from photography, sculpture, painting, and so on. The artist usually works in the studio and the office, and has a dedicated dark room for his photographs. The first floor is used mostly for relaxation, where the artist can read in the library or have some tea in the tea house.
Room Layout Plan
Ground floor room layout
Void
Tea house (Balcony)
Library Office
First floor room layout 2/A-B, B/1-2 and A/2-3 are half-walls.
Foundation, Columns and Beams Plan
Foundation Plan
Ground floor beams and columns
First floor beams and columns
Roof beams and columns
Column Area Distribution
I
II
V
VI
III
IV
VII
VIII
Ground floor area distribution with beams and columns
I
II
V
VI
III
IV
VII
VIII
Ground floor area distribution with room layout
I
II
V
VI
III
IV
VII
VIII
First floor area distribution with beams and columns
I
II
IV
III Tea house (Balcony)
Void
Library Office V
VI
VII
First floor area distribution with room layout
VIII
Dead Load of Structure (constant) Density of concrete = 24kN/m3 Density of brick wall = 19kN/m3 Structure Self-weight calculation Concrete Cross-sectional area = 0.15m x 0.15m beam = 0.0225m2 Self-weight of beam per metre length = Cross-sectional area x density of concrete = 0.0225 x 24 = 0.54 (kN/m) Concrete Thickness of slab = 0.15m slab Self-weight of slab per metre square area = thickness x density of concrete = 0.15 x 24 = 3.6 (kN/m2) Brick Thickness of wall = 0.15m wall Height of full-wall (Ground floor) = 3.6m Height of full-wall (First floor) = 3.3m Height of half-wall = 0.9m Self-weight of full-wall (Ground floor) per metre length = thickness x height x density of brick wall = 0.15 x 3.6 x 19 = 10.26 (kN/m) Self-weight of full-wall (First floor) per metre length = thickness x height x density of brick wall = 0.15 x 3.3 x 19 = 9.41 (kN/m) Self-weight of half-wall per metre length = 0.15 x 0.9 x 19 = 2.57 (kN/m) Dead load factor = 1.4
Live load of rooms according to its function (constant) Room Library Office Tea house (balcony, accessed through library) Studio Gallery Dark room Corridor According to UBBL 2006, schedule 4. Live load factor = 1.6
Live load per metre square area 2.5 kN/m2 2.5 kN/m2 2.5 kN/m2 3.0 kN/m2 4.0 kN/m2 3.0 kN/m2 3.0 kN/m2
TAN MING LONG 0311069 Analysis of Beams Identify One Way or Two Way Slab Ly = Longer side of slab Lx = Shorter side of slab Ly/Lx > 2 or = 2, One way slab Ly/Lx < 2, Two way slab Slab A-B/1-3:
4.2/2.5 =1.68 which is < 2, Two way slab
Slab B-D/1-2:
2.5/2.0 =1.25 which is < 2, Two way slab
Slab B-D/2-3:
2.5/2.2 =1.14 which is < 2, Two way slab
Slab A-C/3-4:
3.8/3.0 =1.26 which is < 2, Two way slab
Slab C-D/3-4:
3.8/2.0 =1.9 which is < 2, Two way slab
Slab A-D/4-5:
6.7/5.0 =1.34 which is < 2, Two way slab
Plan for Beam B-D/2
Beam B-D/2 Dead load on slab B-D/1-2 (Two way slab) Load is transferred to beam B-D/2 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab B-D/1-2 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m Dead load on slab B-D/2-3 (Two way slab) Load is transferred to beam B-D/2 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab B-D/2-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.2m/2) = 3.6kN/m² x 1.1 = 3.96kN/m
Total Dead Load Total dead load B-D/2 = 10.26kN/m + 0.54kN/m + 3.6kN/m + 3.96kN/m = 18.36kN/m
Live load on slab B-D/1-2 (Two way slab) Load is transferred to beam B-D/2 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab B-D/1-2 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.0m/2) = 4.0kN/m² x 1 = 4.0kN/m Live load on slab B-D/2-3 (Two way slab) Load is transferred to beam B-D/2 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab B-D/2-3 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.2m/2) = 3.0kN/m² x 1.1 = 3.3kN/m
Total Live Load Total live load B-D/2
= 4.0kN/m + 3.3kN/m = 7.3kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load B-D/2 = 18.36kN/m x 1.4 = 25.70kN/m Live load B-D/2
= 7.3kN/m x 1.6 = 11.68kN/m
Ultimate load B-D/2
= 25.70kN/m + 11.68kN/m = 37.38kN/m
Reaction UDL to Point Load: 37.38kN/m x 2.5m = 93.45kN In this case the reactions must be equal to half the total load; 93.45kN/2 = 46.73kN both acting up.
Bending Moment Diagram At point B2 there is only a line so no area = 0kN At point D2 = Area of triangle (+ve) + Area of triangle (-ve) = (½ x 46.73 x 1.25) + (-½ x 46.73 x 1.25) = 29.21 – 29.21 =0
Plan for Beam B/1-3
Beam B/1-3 Dead load on slab A-B/1-3 (Two way slab) Load is transferred to beam B/1-3 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab A-B/1-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.5m/2) = 3.6kN/m² x 1.25 = 4.5kN/m Dead load on slab B-D/1-2 (Two way slab) Load is transferred to beam B/1-2 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab B-D/1-2 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab B-D/1-2 = (2/3) x 3.6kN/m = 2.4kN/m Dead load on slab B-D/2-3 (Two way slab) Load is transferred to beam B/2-3 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab B-D/2-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.2m/2) = 3.6kN/m² x 1.1 = 3.96kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab B-D/2-3 = (2/3) x 3.96kN/m = 2.64kN/m
Total Dead Load Total dead load B/1-2
Total dead load B/2-3
= 0.54kN/m + 4.5kN/m + 2.4kN/m = 7.44kN/m = 10.26kN/m + 0.54kN/m + 4.5kN/m + 2.64kN/m = 17.94kN/m
Live load on slab A-B/1-3 (Two way slab) Load is transferred to beam B/1-3 in a trapezoidal form. Convert the trapezoidal load into UDL. Live load from slab A-B/1-3 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.5m/2) = 4.0kN/m² x 1.25 = 5.0kN/m Live load on slab B-D/1-2 (Two way slab) Load is transferred to beam B/1-2 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab B-D/1-2 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.0m/2) = 4.0kN/m² x 1 = 4.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab B-D/1-2 = (2/3) x 4.0kN/m = 2.67kN/m Live load on slab B-D/2-3 (Two way slab) Load is transferred to beam B/2-3 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab B-D/2-3 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.2m/2) = 3.0kN/m² x 1.1 = 3.3kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab B-D/2-3 = (2/3) x 3.3kN/m = 2.2kN/m
Total Live Load Total live load B/1-2
Total live load B/2-3
= 5.0kN/m + 2.67kN/m = 7.67kN/m = 5.0kN/m + 2.2kN/m = 7.2kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load B/1-2 = 7.44kN/m x 1.4 = 10.42kN/m Dead load B/2-3 = 17.94kN/m x 1.4 = 25.12kN/m Live load B/1-2 Live load B/2-3
Ultimate load B/1-2 Ultimate load B/2-3
= 7.67kN/m x 1.6 = 12.27kN/m = 7.2kN/m x 1.6 = 11.52kN/m = 10.42kN/m + 12.27kN/m = 22.69kN/m = 25.12kN/m + 11.52kN/m = 36.64kN/m
Reaction UDL to Point Load: 22.69kN/m x 2.0m = 45.38kN UDL to Point Load: 36.64kN/m x 2.2m = 80.61kN ∑M
RB1
∑Fy RB3
= (RB1 X 4.2m) - (45.38kN X 3.2m) - (46.73kN X 2.2m) - (80.61kN X 1.1m) = 4.2RB1 – 145.22kN – 102.81kN – 88.67kN = 4.2RB1 – 336.7kN = 336.7kN /4.2 = 80.17kN = RB3 + 80.17kN – 45.38kN – 46.73kN – 80.61kN = RB3 – 92.55kN = 92.55Kn
Bending Moment Diagram At point B1 there is only a line so no area = 0kN At point B2 = Area of trapezium = ½ x (80.17 + 34.79) x 2.0 = 114.96 At point B3 = Area of trapezium (+ve) + Area of trapezium (-ve) = 114.96 + [-½ x (11.94 + 92.55) x 2.2] = 114.96 - 114.94 = 0.02
Plan for Beam A-D/1
Beam A-D/1 Dead load on slab A-B/1-3 (Two way slab) Load is transferred to beam A-B/1 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab A-B/1-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.5m/2) = 3.6kN/m² x 1.25 = 4.5kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab A-B/1-3 = (2/3) x 4.5kN/m = 3.0kN/m Dead load on slab B-D/1-2 (Two way slab) Load is transferred to beam B-D/1 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab B-D/1-2 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m
Total Dead Load Total dead load A-B/1 = 10.26kN/m + 0.54kN/m + 3.0kN/m = 13.8kN/m Total dead load B-D/1 = 10.26kN/m + 0.54kN/m + 3.6kN/m = 14.4kN/m
Live load on slab A-B/1-3 (Two way slab) Load is transferred to beam A-B/1 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab A-B/1-3 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.5m/2) = 4.0kN/m² x 1.25 = 5.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab A-B/1-3 = (2/3) x 5.0kN/m = 3.33kN/m Live load on slab B-D/1-2 (Two way slab) Load is transferred to beam B-D/1 in a trapezoidal form. Convert the trapezoidal load into UDL. Live load from slab B-D/1-2 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.0m/2) = 4.0kN/m² x 1 = 4.0kN/m
Total Live Load Total live load A-B/1
= 3.33kN/m
Total live load B-D/1
= 4.0kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load A-B/1 = 13.8kN/m x 1.4 = 19.32kN/m Dead load B-D/1 = 14.4kN/m x 1.4 = 20.16N/m Live load A-B/1 Live load B-D/1
Ultimate load A-B/1 Ultimate load B-D/1
= 3.33kN/m x 1.6 = 5.33kN/m = 4.0kN/m x 1.6 = 6.4kN/m = 19.32kN/m + 5.33kN/m = 24.65kN/m = 20.16kN/m + 6.4kN/m = 26.56kN/m
Reaction UDL to Point Load: 24.65kN/m x 2.5m = 61.63kN UDL to Point Load: 26.56kN/m x 2.5m = 66.4kN ∑M
RA1
∑Fy RD1
= (RA1 X 5.0m) - (61.63kN X 3.75m) - (80.17kN X 2.5m) - (66.4kN X 1.25m) = 5.0RA1 – 231.11kN – 200.43kN – 83.0kN = 5.0RA1 – 514.54kN = 514.54kN /5.0 = 102.91kN = RD1 + 102.91kN – 61.63kN – 80.17kN – 66.4kN = RB3 – 105.29kN = 105.29kN
Bending Moment Diagram At point A1 there is only a line so no area = 0kN At point B1 = Area of trapezium = ½ x (102.91 + 41.28) x 2.5 = 180.24 At point D1 = Area of trapezium (+ve) + Area of trapezium (-ve) = 180.24 + [-½ x (38.89 + 105.29) x 2.5] = 180.24 - 180.23 = 0.01
Plan for Beam C/3-4
Beam C/3-4 Dead load on slab A-C/3-4 (Two way slab) Load is transferred to beam C/3-4 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab A-C/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (3.0m/2) = 3.6kN/m² x 1.5 = 5.4kN/m Dead load on slab C-D/3-4 (Two way slab) Load is transferred to beam C/3-4 in a trapezoidal form. Convert the trapezoidal load into UDL. Dead load from slab C-D/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m
Total Dead Load Total dead load C/3-4
= 10.26kN/m + 0.54kN/m + 4.5kN/m + 3.6kN/m = 18.9kN/m
Live load on slab A-C/3-4 (Two way slab) Load is transferred to beam C/3-4 in a trapezoidal form. Convert the trapezoidal load into UDL. Live load from slab A-C/3-4 = Live load on slab x (Lx/2) = 4.0kN/m² x (3.0m/2) = 4.0kN/m² x 1.5 = 6.0kN/m Live load on slab C-D/3-4 (Two way slab) Load is transferred to beam C/3-4 in a trapezoidal form. Convert the trapezoidal load into UDL. Live load from slab C-D/3-4 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.0m/2) = 3.0kN/m² x 1 = 3.0kN/m
Total Live Load Total live load C/3-4
= 6.0kN/m + 3.0kN/m = 9.0kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load C/3-4 = 18.9kN/m x 1.4 = 26.46kN/m Live load C/3-4
= 9.0kN/m x 1.6 = 14.4kN/m
Ultimate load C/3-4
= 26.46kN/m + 14.4kN/m = 40.86kN/m
Reaction UDL to Point Load: 40.86kN/m x 3.8m = 155.27kN In this case the reactions must be equal to half the total load; 155.27kN/2 = 77.64kN both acting up.
Bending Moment Diagram At point C3 there is only a line so no area = 0kN At point C4 = Area of triangle (+ve) + Area of triangle (-ve) = (½ x 77.64 x 1.9) + (-½ x 77.64 x 1.9) = 73.76 – 73.76 =0
Plan for Beam A-D/3
Beam A-D/3 Dead load on slab A-B/1-3 (Two way slab) Load is transferred to beam A-B/3 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab A-B/1-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.5m/2) = 3.6kN/m² x 1.25 = 4.5kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab A-B/1-3 = (2/3) x 4.5kN/m = 3.0kN/m Dead load on slab B-D/2-3 (Two way slab) Load is transferred to beam B-D/3 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab B-D/2-3 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.2m/2) = 3.6kN/m² x 1.1 = 3.96kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab B-D/2-3 = (2/3) x 3.96kN/m = 2.64kN/m Dead load on slab A-C/3-4 (Two way slab) Load is transferred to beam A-C/3 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab A-C/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (3.0m/2) = 3.6kN/m² x 1.5 = 5.4kN/m
Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab A-C/3-4 = (2/3) x 5.4kN/m = 3.6kN/m Dead load on slab C-D/3-4 (Two way slab) Load is transferred to beam C-D/3 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab C-D/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab C-D/3-4 = (2/3) x 3.6kN/m = 2.4kN/m
Total Dead Load Total dead load A-B/3 = 0.54kN/m + 3.0kN/m + 3.6kN/m = 7.14kN/m Total dead load B-C/3 = 10.26kN/m + 0.54kN/m + 2.64kN/m + 3.6kN/m = 17.04kN/m Total dead load C-D/3 = 10.26kN/m + 0.54kN/m + 2.64kN/m + 2.4kN/m = 15.84kN/m
Live load on slab A-B/1-3 (Two way slab) Load is transferred to beam A-B/3 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab A-B/1-3 = Live load on slab x (Lx/2) = 4.0kN/m² x (2.5m/2) = 4.0kN/m² x 1.25 = 5.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab A-B/1-3 = (2/3) x 5.0kN/m = 3.33kN/m Live load on slab B-D/2-3 (Two way slab) Load is transferred to beam B-D/3 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab B-D/2-3 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.2m/2) = 3.0kN/m² x 1.1 = 3.3kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab B-D/2-3 = (2/3) x 3.3kN/m = 2.2kN/m Live load on slab A-C/3-4 (Two way slab) Load is transferred to beam A-C/3 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab A-C/3-4 = Live load on slab x (Lx/2) = 4.0kN/m² x (3.0m/2) = 4.0kN/m² x 1.5 = 6.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab A-C/3-4 = (2/3) x 6.0kN/m = 4.0kN/m Live load on slab C-D/3-4 (Two way slab) Load is transferred to beam C-D/3 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab C-D/3-4 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.0m/2) = 3.0kN/m² x 1 = 3.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab C-D/3-4 = (2/3) x 3.0kN/m = 2.0kN/m
Total Live Load Total live load A-B/3
= 3.33kN/m + 4.0kN/m = 7.33kN/m
Total live load B-C/3
= 2.2kN/m + 4.0kN/m = 6.2kN/m
Total live load C-D/3
= 2.2kN/m + 2.0kN/m = 4.2kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load A-B/3 = 7.14kN/m x 1.4 = 10.0kN/m Dead load B-C/3 = 17.04kN/m x 1.4 = 23.86kN/m Dead load C-D/3 = 15.84kN/m x 1.4 = 22.18kN/m Live load A-B/3 Live load B-C/3 Live load C-D/3
Ultimate load A-B/3 Ultimate load B-C/3 Ultimate load C-D/3
= 7.33kN/m x 1.6 = 11.73kN/m = 6.2kN/m x 1.6 = 9.92kN/m = 4.2kN/m x 1.6 = 6.72kN/m = 10.0kN/m + 11.73kN/m = 21.73kN/m = 23.86kN/m + 9.92kN/m = 33.78kN/m = 22.18kN/m + 6.72kN/m = 28.9kN/m
Reaction UDL to Point Load: 21.73kN/m x 2.5m = 54.33kN UDL to Point Load: 33.78kN/m x 0.5m = 16.89kN UDL to Point Load: 28.90kN/m x 2.0m = 57.8kN ∑M
RA3
∑Fy RD3
= (RA3 X 5.0m) - (54.33kN X 3.75m) - (92.55kN X 2.5m) - (16.89kN X 2.25m) - (77.64kN X 2.0m) - (57.8kN X 1.0m) = 5.0RA3 – 203.74kN – 231.38kN – 38.0kN – 155.28kN – 57.8kN = 5.0RA3 – 686.2kN = 686.2kN /5.0 = 137.24kN = RD3 + 137.24kN – 54.33kN – 92.55kN – 16.89kN – 77.64kN – 57.8kN = RD3 – 161.97kN = 161.97kN
Bending Moment Diagram At point A3 there is only a line so no area = 0kN At point B3 = Area of trapezium = ½ x (137.24 + 82.91) x 2.5 = 275.19 At point C3 = Area of trapezium (+ve) + Area of trapezium (-ve) = 275.19 + [-½ x (9.64 + 26.53) x 0.5] = 275.19 - 9.04 = 266.15 At point D3 = 266.15 + Area of trapezium (-ve) = 266.15 + [-½ x (104.17 + 161.97) x 2.0] = 266.15 - 266.14 = 0.01
Plan for Beam A-D/4
Beam A-D/4 Dead load on slab A-C/3-4 (Two way slab) Load is transferred to beam A-C/4 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab A-C/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (3.0m/2) = 3.6kN/m² x 1.5 = 5.4kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab A-C/3-4 = (2/3) x 5.4kN/m = 3.6kN/m Dead load on slab C-D/3-4 (Two way slab) Load is transferred to beam C-D/4 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab C-D/3-4 = Dead load on slab x (Lx/2) = 3.6kN/m² x (2.0m/2) = 3.6kN/m² x 1 = 3.6kN/m Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab C-D/3-4 = (2/3) x 3.6kN/m = 2.4kN/m Dead load on slab A-D/4-5 (Two way slab) Load is transferred to beam A-D/4 in a triangular form. Convert the trapezoidal load into UDL. Dead load from slab A-D/4-5 = Dead load on slab x (Lx/2) = 3.6kN/m² x (5.0m/2) = 3.6kN/m² x 2.5 = 9.0kN/m
Convert triangular load to UDL by applying a factor of 2/3 Dead load from slab A-D/4-5 = (2/3) x 9.0kN/m = 6.0kN/m
Total Dead Load Total dead load A-C/4 = 0.54kN/m + 3.6kN/m + 9.0kN/m = 13.14kN/m Total dead load C-D/4 = 10.26kN/m + 0.54kN/m + 2.4kN/m + 9.0kN/m = 22.2kN/m
Live load on slab A-C/3-4 (Two way slab) Load is transferred to beam A-C/4 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab A-C/3-4 = Live load on slab x (Lx/2) = 4.0kN/m² x (3.0m/2) = 4.0kN/m² x 1.5 = 6.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab A-C/3-4 = (2/3) x 6.0kN/m = 4.0kN/m Live load on slab C-D/3-4 (Two way slab) Load is transferred to beam C-D/4 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab C-D/3-4 = Live load on slab x (Lx/2) = 3.0kN/m² x (2.0m/2) = 3.0kN/m² x 1 = 3.0kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab C-D/3-4 = (2/3) x 3.0kN/m = 2.0kN/m Live load on slab A-D/4-5 (Two way slab) Load is transferred to beam A-D/4 in a triangular form. Convert the trapezoidal load into UDL. Live load from slab A-D/4-5 = Live load on slab x (Lx/2) = 3.0kN/m² x (5.0m/2) = 3.0kN/m² x 2.5 = 7.5kN/m Convert triangular load to UDL by applying a factor of 2/3 Live load from slab A-D/4-5 = (2/3) x 7.5kN/m = 5.0kN/m
Total Live Load Total live load A-C/4
Total live load C-D/4
= 4.0kN/m + 5.0kN/m = 9.0kN/m = 2.0kN/m + 5.0kN/m = 7.0kN/m
Ultimate Load Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load A-C/4 = 13.14kN/m x 1.4 = 18.4kN/m Dead load C-D/4 = 22.2kN/m x 1.4 = 31.08kN/m Live load A-C/4 Live load C-D/4
Ultimate load A-C/4 Ultimate load C-D/4
= 9.0kN/m x 1.6 = 14.4kN/m = 7.0kN/m x 1.6 = 11.2kN/m = 18.4kN/m + 14.4kN/m = 32.8kN/m = 31.08kN/m + 11.2kN/m = 42.28kN/m
Reaction UDL to Point Load: 32.8kN/m x 3.0m = 98.4kN UDL to Point Load: 42.28kN/m x 2.0m = 84.56kN ∑M
RA4
∑Fy RD4
= (RA4 X 5.0m) - (98.4kN X 3.5m) - (77.64kN X 2.0m) - (84.56kN X 1.0m) = 5.0RA4 – 344.4kN – 155.28kN – 84.56kN = 5.0RA4 – 584.24 = 584.24kN /5.0 = 116.85kN = RD4 + 116.85kN – 98.4kN – 77.64kN – 84.56kN = RD4 – 143.75kN = 143.75kN
Bending Moment Diagram At point A4 there is only a line so no area = 0kN At point C4 = Area of trapezium = ½ x (116.85 + 18.45) x 3.0 = 202.95 At point D4 = Area of trapezium (+ve) + Area of trapezium (-ve) = 202.95 + [-½ x (59.19 + 143.75) x 2.0] = 202.95 - 202.94 = 0.01
Analysis of Columns Column V
Void Office
Tea house (Balcony)
Library
Area of load acted on the column V= (4.2m/2) x 2.5m = 2.1m x 2.5m = 5.25m2 Ground floor: Dead load Beam: Slab: Wall:
0.54kN/m x (2.1 + 2.5)m 3.6kN/m2 x 5.25m2 10.26kN/m x (2.1 + 2.5)m
= 2.48kN = 18.9kN = 47.2kN
Live load Gallery:
4.0kN/m2 x 5.25m2
= 21.0kN
First floor: Dead load Beam: Slab: Wall:
0.54kN/m x (2.1 + 2.5)m 3.6kN/m2 x 5.25m2 9.41kN/m x (2.1 + 2.5)m
= 2.48kN = 18.9kN = 43.29kN
Live load Office:
2.5kN/m2 x 5.25m2
= 13.13kN
Total load acting on the column V
= 2.48 + 18.9 + 47.2 + 21.0 + 2.48 + 18.9 + 43.29 + 13.13 = 167.38kN
Column VI
Void
Tea house (Balcony)
Office
Area of load acted on the column VI
= [(4.2m/2) + (3.8m/2)] x 2.5m = [2.1 + 1.9]m X 2.5m = 10m2
Ground floor: Dead load Beam: Slab: Wall:
0.54kN/m x (2.1 + 1.9 + 2.5)m 3.6kN/m2 x 10m2 10.26kN/m x (1.9 + 2.5)m
= 3.51kN = 26.0kN = 45.14kN
Live load Corridor: Dark room:
3.0kN/m2 x 10m2 3.0kN/m2 x 10m2
= 30.0kN = 30.0kN
First floor: Dead load Beam: Slab: Wall:
0.54kN/m x (2.1 + 1.9 + 2.5)m 3.6kN/m2 x 10m2 9.41kN/m x (2.1 + 1.9 + 2.5)m
= 3.51kN = 26.0kN = 61.17kN
Live load Office: Library:
2.5kN/m2 x 10m2 2.5kN/m2 x 10m2
= 25.0kN = 25.0kN
Total load acting on the column VI
Library
= 3.51 + 26.0 + 45.14 + 30.0 + 30.0 + 3.51 + 26.0 + 61.17+ 25.0 + 25.0 = 275.33kN
Column IV
Void Office
Area of load acted on the column IV
Library
= (6.7m/2) x 2.5m = 3.35m X 2.5m = 8.38m2
Ground floor: Dead load Beam: Slab: Wall:
0.54kN/m x (3.35 + 2.5)m 3.6kN/m2 x 8.38m2 10.26kN/m x (3.35 + 2.5)m
= 3.16kN = 30.17kN = 60.02kN
Live load Studio:
3.0kN/m2 x 10m2
= 30.0kN
First floor: Dead load Beam: Slab: Wall:
0.54kN/m x (3.35 + 2.5)m 3.6kN/m2 x 8.38m2 9.41kN/m x (3.35+ 2.5)m
= 3.16kN = 30.17kN = 55.05kN
Live load Library:
2.5kN/m2 x 10m2
= 25.0kN
Total load acting on the column IV
Tea house (Balcony)
= 3.16 + 30.17 + 60.02 + 30.0 + 3.16 + 30.17 + 55.05 + 25.0 = 236.73kN
KONG REN HENG 0316416 Analysis of beams Identifying two-way or one-way slabs
Void
II
IV
I
III
V
Slab I, 1-2 / B-D = 4200 / 2500 = 1.68 (< 2, slab I is a two-way slab.) Slab II, 2-3 / A-C = 3800 / 3000 = 1.27 (< 2, slab II is a two-way slab.) Slab III, 2-3 / C-D = 3800 / 2000 = 1.9 (< 2, slab III is a two-way slab.) Slab IV, 3-4 / A-B = 6700 / 2500 = 2.68 (≥ 2, slab IV is a one-way slab.) Slab V, 3-4 / B-D = 6700 / 2500 = 2.68 (≥ 2, slab V is a one-way slab.)
Beam B/1-2
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Slab I: Load is transferred to the beam in a trapezoidal form, (2.5/2) x 3.6 = 4.5 (kN/m) UDL acted on the beam = 4.5 kN/m Half-wall: 2.57 kN/m Live load, Office: Load is transferred to the beam in a trapezoidal form, (2.5/2) x 2.5 = 3.13 (kN/m) UDL acted on the beam = 3.13 kN/m Apply the load factor, Dead load: (0.54 + 4.5 + 2.57) x 1.4 = 7.61 x 1.4 = 10.65 (kN/m) Live load: 3.13 x 1.6 = 5.01 (kN/m)
Load Diagram
Total UDL = 10.65 + 5.01 = 15.66 (kN/m)
15.66 kN/m 2
1 R1
R2 4.2m
Convert UDL to point load: 15.66 x 4.2 = 65.77 (kN) R1 = R2 = 65.77 / 2 = 32.89 (kN)
Shear force diagram
32.89
I 0 II
-32.89
Bending moment diagram Area of I: (32.89 x 2.1) / 2 = 34.53 (m2) 34.53
Area of II: (32.89 x 2.1) / 2 = 34.53 (m2)
0
Beam 1/A-D
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Point load from beam B/1-2 = 32.89 kN Slab I: Load is transferred to the beam in a triangular form, (2.5/2) x 3.6 = 4.5 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 3 (kN/m) Full-wall: 9.41 kN/m Live load, Office: Load is transferred to the beam in a triangular form, (2.5/2) x 2.5 = 3.13 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.13 x (2/3) = 2.08 (kN/m) Apply the load factor, Dead load: (0.54 + 9.41) x 1.4 = 9.95 x 1.4 = 13.93 (kN/m) 3 x 1.4 = 4.2 (kN/m) Live load: 2.08 x 1.6 = 3.33 (kN/m)
Load diagram 32.89 kN
Total UDL (AB) = 13.93 + 3.33 = 17.26 (kN/m) UDL (AD) = 4.2 (kN/m)
17.26 kN/m 4.2 kN/m B
A
Convert UDL to point load: 17.26 x 2.5 = 43.15 (kN) 4.2 x 5 = 21 (kN)
D
RA
RD 2.5m
2.5m
Point load at C = 32.89 kN
32.89 kN
43.15 kN
A
∑M at point A = 0, 5RD – 1.25 (43.15) – 2.5 (21 + 32.89) = 0 RD = 188.66 / 5 = 37.73 (kN)
21 kN
D
B
RA
RD 1.25m
1.25m
2.5m
∑Fy = 0, RA + 37.73 – 43.15 – 32.89 – 21 = 0 RA = 59.31 (kN)
Shear force diagram (17.26 + 4.2) x 2.5 = 53.65 59.31 – 53.65 = 5.66
59.31
5.66 – 32.89 = -27.23
I 5.66 0 -27.23 3.69 -37.73
-27.23 – 4.2 x 2.5 = -37.73 II
-37.73 + 37.73 = 0
Bending moment diagram 81.2
Area of I, (59.31+ 5.66) x 2.5 /2 = 81.2m2 Area of II, (27.23 + 37.73) x 2.5 /2 = 81.2m2
0
Beam C/2-3
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Slab II: Load is transferred to the beam in a trapezoidal form, (3/2) x 3.6 = 5.4 (kN/m) UDL acted on the beam = 5.4 (kN/m) Slab III: Load is transferred to the beam in a trapezoidal form, (2/2) x 3.6 = 3.6 (kN/m) UDL acted on the beam = 3.6 (kN/m) Full-wall: 9.41 kN/m Live load, Tea house: Load is transferred to the beam in a trapezoidal form, (3/2) x 2.5 = 3.75 (kN/m) UDL acted on the beam = 3.75 (kN/m) Library: Load is transferred to the beam in a trapezoidal form, (2/2) x 2.5 = 2.5 (kN/m) UDL acted on the beam = 2.5 (kN/m) Apply the load factor, Dead load: (0.54 + 9.41 + 5.4 + 3.6) x 1.4 = 18.95 x 1.4 = 26.53 (kN/m) Live load: (3.75 + 2.5) x 1.6 = 6.25 x 1.6 = 10 (kN/m)
Load diagram Total UDL = 26.53 + 10 = 36.53 (kN/m)
36.53 kN/m 2
3 R2
R3
Convert UDL to point load: 36.53 x 3.8 = 138.81 (kN)
3.8m
R2 = R3 = 138.81 / 2 = 69.41 (kN)
Shear force diagram
69.41
I 0 II
-69.41
Bending moment diagram
65.94
0
Area of I: (69.41 x 1.9) / 2 = 65.94 (m2) Area of II: (69.41 x 1.9) / 2 = 65.94 (m2)
Beam 2/A-D
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Point load from beam B/1-2 = 32.89 kN Point load from beam C/2-3 = 69.41 kN Slab I: Load is transferred to the beam in a triangular form, (2.5/2) x 3.6 = 4.5 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 3 (kN/m) Slab II: Load is transferred to the beam in a triangular form, (3/2) x 3.6 = 5.4 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 3.6 (kN/m) Slab III: Load is transferred to the beam in a triangular form, (2/2) x 3.6 = 3.6 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 2.4 (kN/m)
Full-wall (B-D): 9.41 kN/m Half-wall (A-B): 2.57 kN/m
Live load, Office: Load is transferred to the beam in a triangular form, (2.5/2) x 2.5 = 3.13 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.13 x (2/3) = 2.08 (kN/m) Tea house: Load is transferred to the beam in a triangular form, (3/2) x 2.5 = 3.75 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.75 x (2/3) = 2.5 (kN/m) Library: Load is transferred to the beam in a triangular form, (2/2) x 2.5 = 2.5 (kN/m) Convert the load to UDL by applying a factor of 2/3, 2.5 x (2/3) = 1.67 (kN/m)
Apply the load factor, Dead load: 0.54 x 1.4 = 0.76 (kN/m) 9.41 x 1.4 = 13.17 (kN/m) 2.57 x 1.4 = 3.6 (kN/m) 3 x 1.4 = 4.2 (kN/m) 3.6 x 1.4 = 5.04 (kN/m) 2.4 x 1.4 = 3.36 (kN/m) Live load: 2.08 x 1.6 = 3.33 (kN/m) 2.5 x 1.6 = 4 (kN/m) 1.67 x 1.6 = 2.67 (kN/m)
Load Diagram
32.89 kN 69.41 kN
Total UDL (BD) = 13.17 + 4.2 + 3.33 = 20.7 (kN/m) Total UDL (CD) = 3.36 + 2.67 = 6.03 (kN/m) Total UDL (AC) = 5.04 + 4 = 9.04 (kN/m)
9.04 kN/m 20.7 kN/m 3.6 kN/m
6.03 kN/m 0.76 kN/m
A
C
B
D
RA 0.5m
2.5m
RD
2m
∑M at point A = 0 5RD – 1.25(9) – 1.5(27.12) – 2.5(32.89) – 2.75(3.8) – 3(69.41) – 3.75(51.75) – 4(12.06) = 0 RD = 595.14 / 5 = 119.03 (kN)
32.89 kN 69.41 kN 9 kN 27.12 kN 3.8 kN
A
51.75 kN 12.06 kN
C
B
D
RA 1.25m
0.25m
RD
0.75m 1m 0.25m 0.25m 0.25m
1m
1m
Shear forcemdiagram 87 53.5
I
20.16 5.36 0
II
III -64.05
-119.03
Convert UDL to point load: 0.76 x 5 = 3.8 (kN) 3.6 x 2.5 = 9 (kN) 6.03 x 2 = 12.06 (kN) 20.7 x 2.5 = 51.75 (kN) 9.04 x 3 = 27.12 (kN)
∑Fy = 0 RA + RD – 9 – 27.12 – 32.89 – 69.41 – 3.8 – 51.75 – 12.06 = 0 RA = 87 (kN)
(0.76 + 3.6 + 9.04) x 2.5 = 33.5 87 – 33.5 = 53.5 53.5 – 32.89 = 20.16 20.61 – (9.04 + 20.7 + 0.76) x 0.5 = 20.61 - 15.25 = 5.36 5.36 – 69.41 = -64.05 -64.05 – (20.7 + 6.03 + 0.76) x 2 = -64.05 – 54.98 = -119.03 -119.03 + 119.03 = 0
Bending moment diagram 182.01 175.63
0
Area of I, (87 + 53.5) x 2.5 /2 = 175.63 Area of II, (20.16 + 5.36) x 0.5 /2 = 6.38 175.63 + 6.38 = 182.01 Area of III, (64.05 + 119.03) x 2 / 2 = 183.08 182.01 – 183.08 ≈ 0
Beam B/3-4
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Slab IV: (2.5/2) x 3.6 = 4.5 (kN/m) Slab V: (2.5/2) x 3.6 = 4.5 (kN/m) Live load, Library: (2/2) x 2.5 = 2.5 (kN/m) Apply the load factor, Dead load: (0.54 + 4.5 + 4.5) x 1.4 = 9.54 x 1.4 = 13.36 (kN/m) Live load: 2.5 x 1.6 = 4 (kN/m)
Load diagram Total UDL = 13.36 + 4 = 17.36 (kN/m)
17.36 kN/m 3
4 R3
R4
Convert UDL to point load: 17.36 x 6.7 = 116.31 (kN)
6.7m
R3 = R4 = 116.31 / 2 = 58.16 (kN)
Shear force diagram
58.16
I 0 II
-58.16
Bending moment diagram 97.42
0
Area of I, 58.16 x 3.35 / 2 = 97.42 Area of II, 58.16 x 3.35 / 2 = 97.42
Beam 3/A-D
Void
II
IV
I
III
V
Dead load, Beam: 0.54 kN/m Point load from beam B/3-4 = 58.16 kN Point load from beam C/2-3 = 69.41 kN Slab II: Load is transferred to the beam in a triangular form, (3/2) x 3.6 = 5.4 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 3.6 (kN/m) Slab III: Load is transferred to the beam in a triangular form, (2/2) x 3.6 = 3.6 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.6 x (2/3) = 2.4 (kN/m) Full-wall (A-C): 9.41 kN/m Live load, Tea house: Load is transferred to the beam in a triangular form, (3/2) x 2.5 = 3.75 (kN/m) Convert the load to UDL by applying a factor of 2/3, 3.75 x (2/3) = 2.5 (kN/m) Library: Load is transferred to the beam in a triangular form, (2/2) x 2.5 = 2.5 (kN/m) Convert the load to UDL by applying a factor of 2/3, 2.5 x (2/3) = 1.67 (kN/m)
Apply the load factor, Dead load: 0.54 x 1.4 = 0.76 (kN/m) 9.41 x 1.4 = 13.17 (kN/m) 3.6 x 1.4 = 5.04 (kN/m) 2.4 x 1.4 = 3.36 (kN/m) Live load: 2.5 x 1.6 = 4 (kN/m) 1.67 x 1.6 = 2.67 (kN/m)
Load diagram 58.16 kN 69.41 kN
Total UDL (AC) = 13.17 + 5.04 + 4 = 22.21 (kN/m) Total UDL (CD) = 3.36 + 2.67 = 6.03 (kN/m)
22.21 kN/m
Convert UDL to point load: 0.76 x 5 = 3.8 (kN) 22.21 x 3 = 66.63 (kN) 6.03 x 2 = 12.06 (kN)
6.03 kN/m 0.76 kN/m A
B
C
D
RA 2.5m
RD
2m
0.5m 69.14 kN 58.16 kN
66.63 kN
3.8 kN
B
A
12.06 kN
C
D
RA 1.5m
1m
0.25m 0.25m
∑M at point A = 0 5RD – 1.5(66.63) – 2.5(58.16) – 2.25(3.8) - 3(69.14) – 4(12.06) = 0 RD = 509.56 / 5 = 101.91 (kN) ∑Fy=0 RA + RD – 66.63 – 58.16 – 3.8 - 69.14 – 12.06 = 0 RA = 107.88 (kN)
RD
1m
1m
Shear force diagram 107.88 – (22.21 + 0.76) x 2.5 = 50.73 50.73 – 58.16 = -7.43 -7.43 – (22.21 + 0.76) x 0.5 = -18.86 -18.86 – 69.41 = -88.27 -88.27 – 2(6.03) = -100.33 -100.33 + 101.91 ≈ 0
107.88 50.73
I
0 -7.43 -18.86
II III
-88.27 -101.91
Bending moment diagram
198.26 190.18
Area of I, (107.88 + 50.73) x 2.5 / 2 = 198.26 Area of II, (7.43 + 18.86) x 0.5 / 2 = 6.57 Area of III, (88.27 + 101.91) x 2 / 2 = 190.18 198.26 – 6.57 – 190.18 ≈ 0
0
Analysis of columns Column I
Void
Tea house (Balcony)
Office
Area of load acted on the column = (4.2 / 2) x 2.5 = 5.25 (m2) First floor: Dead load, Beam: 0.54 x (2.5 + 2.1) = 2.48 (kN) Full-wall: 9.41 x (2.5 + 2.1) = 43.29 (kN) Ground floor: Dead load, Beam: 0.54 x (2.5 + 2.1) = 2.48 (kN) Slab: 3.6 x 5.25 = 18.9 (kN) Full-wall: 10.26 x (2.5 + 2.1) = 47.2 (kN) Live load, Gallery: 4 x 5.25 = 21 (kN) Total load acting on the column = 2.48 + 43.29 + 2.48 + 18.9 + 47.2 + 21 = 135.35 (kN)
Library
Column II
Void
Tea house (Balcony)
Library
Office
Area of load acted on the column = [(4.2 / 2) + (3.8 / 2)] x 2.5 = 10 (m2) First floor: Dead load, Beam: 0.54 x (2.5 + 2.1 + 1.9) = 3.51 (kN) Slab: 3.6 x (1.9 x 2.5) = 17.1 (kN) Full-wall: 9.41 x 2.1 = 19.76 (kN) Half-wall: 2.57 x (2.5 + 1.9) = 11.31 (kN) Live load, Tea house: 2.5 x (1.9 x 2.5) = 11.88 (kN) Ground floor: Dead load, Beam: 0.54 x (2.5 + 2.1 + 1.9) = 3.51 (kN) Slab: 3.6 x 10 = 36 (kN) Full-wall: 10.26 x (2.1 + 1.9) = 41.04 (kN) Live load, Gallery: 4 x 10 = 40 (kN) Total load acting on the column = 3.51 + 17.1 + 19.76 + 11.31 + 11.88 + 3.51 + 36 + 41.04 + 40 = 184.11(kN)
Column III
Void
Tea house (Balcony)
Office
Area of load acted on the column = [(3.8 / 2) + (6.7 / 2)] x 2.5 = 13.13 (m2) First floor: Dead load, Beam: 0.54 x (2.5 + 1.9 + 3.35) = 4.19 (kN) Slab: 3.6 x 13.13 = 47.27 (kN) Full-wall: 9.41 x (2.5 + 3.35) = 55.05 (kN) Half-wall: 2.57 x 1.9 = 4.88 (kN) Live load, Tea house: 2.5 x (2.5 x 1.9) = 11.88 (kN) Library: 2.5 x (2.5 x 3.35) = 20.94 (kN) Ground floor: Dead load, Beam: 0.54 x (2.5 + 1.9 + 3.35) = 4.19 (kN) Slab: 3.6 x 13.13 = 47.27 (kN) Full-wall: 10.26 x (1.9 + 3.35) = 53.87 (kN) Live load, Gallery: 4 x (2.5 x 1.9) = 19 (kN) Studio: 3 x (2.5 x 3.35) = 25.13 (kN) Total load acting on the column = 4.19 + 47.27 + 55.05 + 4.88 + 11.88 + 20.94 + 4.19 + 47.27 + 53.87 + 19 + 25.13 = 293.67 (kN)
Library