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For a prestressed cantilever beam of size 200mm×400mm with prestressing force of 500kN. The beam is subjected to uniformly distributed load (inclusive of self weight) of 4kN/m. The span of beam is 6m. The distance (in mm, rounded off to two decimal places) of the cable from the soffit of the beam at the fixed end for no tensile stress in during service conditions is _______.
  1. 277

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Solution

The correct option is A 277
Let the eccentricity of cable from centre line be e.Tensile stress at top fibre =0
In cantilever beam, tensile stress may be generated at top fibre side.
PA+PeZMZ=0
M=wl22=4×622=72kNm
Z=bd26=200×(400)26=5333333.33mm2
P=500kN
500×103200×400+500×103×e5333333.3372×1065333333.33=0
e=77.33mm
Distance of cable from soffit =200+77.33=277.33mm

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