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Question

A prestressed concrete beam 150 mm × 300 mm supports a live load 5 kN/m over a simple span of 8 m. It has a parabolic cable having an eccentricity of 75 mm at mid-span and zero at the ends. The prestressing force required to maintain the net resultant stress at the bottom fibre at mid-span as zero under the action of DL + LL + prestress is

A
239 kN
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B
293 kN
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C
302 kN
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D
392 kN
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Solution

The correct option is D 392 kN
Area,A=45×103 mm2Section modulus,Z=Bd26=150×30026=2.25×106mm2Dead load=0.15×0.30×1×25=1.125KN/mFor bottom fibre stress to be zeroPA+PeZ=MDL+MLLZMDL+MLL=(1.25+5)×828=49kNme=75 mmP=49×1062.25×106[145×103+752.25×106]=392 kN

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