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Question

A 6 m long simply- supported beam is prestressed as shown in the figure.


The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigidity EI = 2 ×104 kNm2 and the effective prestressing force is 200 kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is _______.
  1. 0.12

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Solution

The correct option is A 0.12
Downward UDL, w = 6 kN/m
Eccentricity, e = 50 mm
Prestressing force, P = 200 kN
EI=2×104 kN m2
L = 6 m
Rotation due to Prestress

=PeL2EI

=200×50×103×62×2×104=1.5×103

Rotation due to UDL

=wL324EI

=6×(6)324×2×104=2.7×103

Net rotation = 2.7×1031.5×103
=1.2×103 radian

Elongation of the cable
=2×50×1.2×103 mm
= 0.12 mm

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