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The effective depth of a singly reinforced rectangular beam is 400 mm. The section is over-reinforced and the neutral axis is 180 mm below the top. If the maximum stress attained by concrete is 5 N/mm2 and the modular ratio is 18, then the stress developed in the steel will be


1.

110 N/mm2


2.

135 N/mm2


3.

160 N/mm2


4. 180 N/mm2

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Best answer
Correct Answer - Option 1 :

110 N/mm2


d = 400 mm

xu = 180 mm

C = 5 N/mm2

m = 18

\(\frac{{\rm{c}}}{{\frac{{\rm{t}}}{{\rm{m}}}}}{\rm{ = }}\frac{{{{\rm{x}}_{\rm{u}}}}}{{{\rm{d - }}{{\rm{x}}_{\rm{u}}}}}\)

\({\rm{t = }}\frac{{{\rm{18 \times 5}}}}{{{\rm{180}}}}{\rm{ \times }}\left( {{\rm{400 - 180}}} \right)\)

t = 220/2

t = 110 N/mm2

Hence the tensile stress developed in the steel is 110 N/mm2

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