Question

8: A rectangular concrete beam 100 mm wide by
250mm deep spanning over 8m is pre-stressed by a
straight cable carrying an effective pre-stressing force
of 250 kN located at an eccentricity of 40 mm. The
beam supports a live load of 1.2 kN/m. The density of
concrete is 24 kN/m2. The resultant stress at top of
fiber is
2937352686
109.2 N/mm2
14.2 N/mm2
99.2 N/mm2
89.2 N/mm2​

Answer 1

Answer:

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Answer 2

Answer:

14 2N/mm^2

Explanation:

P=250kN

A=100 × 250 = 25×10^3 mm^2

e=40mm

Self weight of the beam = 0.1×0.25×24=0.6kN/m

LL on the beam = 1.2kN/m

Total load = Self weight + LL = 1.2+0.6=1.8kN/m

Section modulus , Z=bd^2/6=1.04×10^6mm^3

M=wl^2/8=14.4kN/m

Stress due to loads = M/Z = 13.8N/mm^2

Pre-stress at top and bottom fibres = [P/A+Pe/Z]/[P/A-Pe/Z]=[10+9.6]/[10-9.6]N/mm^2

Resultant stress at

Top fibre = 10 - 9.6 + 13.8 = 14.2N/mm^2(comp)

Bottom fibre = 10 + 9.6 - 13.8 = 5.8N/mm^2(comp)