Structural Design
QUESTION 1 / SOALAN 1
The reinforced concrete beam shown in Figure 1 carries an imposed live load of 12kN/m2 and a dead load of 12 kN/m2 as shown in the diagram. Given, fcu = 30 N/mm2, fy = 460 N/mm2, fy, links = 250 N/mm2. The beam is exposed to a mild condition. a) Determine whether the beam is singly or doubly reinforced beam. b) Determine the main reinforcement for the beam using a design chart. c) Determine the shear reinforcement for the beam. d) Check whether the deflection of the beam is acceptable. e) Sketch the detailed cross section of the beam indicating the reinforcements in (b) and (c).
a) Determine whether the beam is singly or doubly reinforced beam.
Solution
i) Characteristic Loads
Dead loads Superimposed load = 12.00kN/m
Before we find the selfweight we need to find the size of beam. The thickness of the concrete cover is determined by using Table 3.2 and Table 3.3 of BS8110. The condition is mild, therefore the thickness of the concrete cover is 25mm. Assumed the reinforcement bar is 25mmØ and link is 10mmØ.
225
400
448
Hence h = d + ½ Ø bar + link + cover h = 400 + ½ (25) + 10 + 25 = 448mm
Selfweight (24 X 0.225 X 0.448) = 2.4kN/m Total dead load = 14.4kN/m
Live loads Imposed live load = 12kN/m
ii) Design Loads
Design load, w = 1.4gk + 1.6qk = 1.4(14.4) + 1.6(12) = 39.36kN/m
iii) Ultimate Bending Moment, M
M= wl28
M= 39.36(6)28 = 177.12kN/m
iv) Ultimate Moment of Resistance, Mu Mu = 0.156 fcu bd2 Mu = 0.156 (30) (225) (400)2 = 168.48kN/m M > Mu Therefore it is doubly reinforced beam. b) Determine the main reinforcement for the beam using a design chart.
Solution
Compresses Reinforcement, A’s
Assume compressed reinforcement (A’s) is 12mmØ. d’ = cover + ½ Ø bar + link
For mild condition by using Table 3.2 and Table 3.3 of BS8110 the thickness of the concrete cover is 25mm and link size are as assumed in the Solution
The reinforced concrete beam shown in Figure 1 carries an imposed live load of 12kN/m2 and a dead load of 12 kN/m2 as shown in the diagram. Given, fcu = 30 N/mm2, fy = 460 N/mm2, fy, links = 250 N/mm2. The beam is exposed to a mild condition. a) Determine whether the beam is singly or doubly reinforced beam. b) Determine the main reinforcement for the beam using a design chart. c) Determine the shear reinforcement for the beam. d) Check whether the deflection of the beam is acceptable. e) Sketch the detailed cross section of the beam indicating the reinforcements in (b) and (c).
a) Determine whether the beam is singly or doubly reinforced beam.
Solution
i) Characteristic Loads
Dead loads Superimposed load = 12.00kN/m
Before we find the selfweight we need to find the size of beam. The thickness of the concrete cover is determined by using Table 3.2 and Table 3.3 of BS8110. The condition is mild, therefore the thickness of the concrete cover is 25mm. Assumed the reinforcement bar is 25mmØ and link is 10mmØ.
225
400
448
Hence h = d + ½ Ø bar + link + cover h = 400 + ½ (25) + 10 + 25 = 448mm
Selfweight (24 X 0.225 X 0.448) = 2.4kN/m Total dead load = 14.4kN/m
Live loads Imposed live load = 12kN/m
ii) Design Loads
Design load, w = 1.4gk + 1.6qk = 1.4(14.4) + 1.6(12) = 39.36kN/m
iii) Ultimate Bending Moment, M
M= wl28
M= 39.36(6)28 = 177.12kN/m
iv) Ultimate Moment of Resistance, Mu Mu = 0.156 fcu bd2 Mu = 0.156 (30) (225) (400)2 = 168.48kN/m M > Mu Therefore it is doubly reinforced beam. b) Determine the main reinforcement for the beam using a design chart.
Solution
Compresses Reinforcement, A’s
Assume compressed reinforcement (A’s) is 12mmØ. d’ = cover + ½ Ø bar + link
For mild condition by using Table 3.2 and Table 3.3 of BS8110 the thickness of the concrete cover is 25mm and link size are as assumed in the Solution