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Question

A rectangular concrete beam 250 mm wide and 600 mm deep is pre-stressed by means of 16 high tensile wires, each of 7 mm diameter, located at 200 mm from the bottom face of the beam at a given section. If the effective pre-stress in the wires is 700 MPa, what is the maximum sagging bending moment (in kNm)(correct to 1-decimal place) due to live load that this section of the beam can withstand without causing tensile stress at the bottom face of the beam? Neglect the effect of dead load of beam .______
  1. 86.16

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Solution

The correct option is A 86.16

Area of pre-stressed steel
=16×π×724 mm2

Force of prestress

=16×π× 49×700N4

= 430.808 kN

The moment caused by prestress,
F x e = 43.0808 kNm

The various stress diagrams are; Taking tension (+)ve and compression (-)ve,



F/A=430.808×103N250×600mm2

=2.872N/mm2

Flexural stress due to moment caused by pre-stress i.e.,

M = 43.0808 kN-m

fmax=Mz,

z=Iy=112×250×(600)3300mm3=15×106mm3

=2.872N/mm2

The net stress diagram;



The additional sagging moment that can be applied without causing tensile stress at the bottom face of the beam should generate the maximum tensile stress of 5.744 MPa.

M=f×z

=5.744N/mm2×15×106mm3

M = 86.16 kN-m

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