PROBLEM 1 A reinforced concrete beam has a width of 250mm and a total depth of 450mm. It is reinforced with a total steel area of 1875sq.mm placed at an effective depth of 375mm. Assume f'c = 27.6 MPa and fy = 414.7 MPa. Discuss and determine the following: (a) Depth of the compression block (b) Moment capacity reduction factor, (c) B₁

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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PROBLEM 1
A reinforced concrete beam has a width of 250mm and a total depth of 450mm. It is reinforced with a
total steel area of 1875sq.mm placed at an effective depth of 375mm. Assume f'c = 27.6 MPa and fy =
414.7 MPa. Discuss and determine the following:
(a) Depth of the compression block
(b) Moment capacity reduction factor,
(c) B₁
(d) Mn and Mu
(e) Safe uniform live load that the beam could carry in addition to a uniform dead load of 20 kN/m if the
beam span is 6.0m.
PROBLEM 2
A T-beam (internal) for a floor system has a slab thickness of 100mm and a total depth of 550mm. It has
a web thickness of 300mm. The T-beam is casted monolithically with the slab. The beam has a simple span
of 6.0m with a spacing of 2.4m center to center. The beam carries a live load moment of 163 kN.m and a
dead load moment of 84 kN.m. Assume f'c = 20.7 MPa and fy = 413.7 MPa. Assume steel covering to the
centroid of the reinforcement is 65mm. Determine the following and discuss your solution:
(a) Effective width of flange
(b) Depth of compression block
(c) Steel area required
Transcribed Image Text:PROBLEM 1 A reinforced concrete beam has a width of 250mm and a total depth of 450mm. It is reinforced with a total steel area of 1875sq.mm placed at an effective depth of 375mm. Assume f'c = 27.6 MPa and fy = 414.7 MPa. Discuss and determine the following: (a) Depth of the compression block (b) Moment capacity reduction factor, (c) B₁ (d) Mn and Mu (e) Safe uniform live load that the beam could carry in addition to a uniform dead load of 20 kN/m if the beam span is 6.0m. PROBLEM 2 A T-beam (internal) for a floor system has a slab thickness of 100mm and a total depth of 550mm. It has a web thickness of 300mm. The T-beam is casted monolithically with the slab. The beam has a simple span of 6.0m with a spacing of 2.4m center to center. The beam carries a live load moment of 163 kN.m and a dead load moment of 84 kN.m. Assume f'c = 20.7 MPa and fy = 413.7 MPa. Assume steel covering to the centroid of the reinforcement is 65mm. Determine the following and discuss your solution: (a) Effective width of flange (b) Depth of compression block (c) Steel area required
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