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Question

When a section is subjected to the limiting moment of resistance then the actual stress in steel of a singly reinforced concrete beam of 200 mm width and 400 mm effective depth, with 4 bars of 16 mm diameter of Fe415 steel is ________ N/mm2 [Use M20 grade concrete]
  1. 343.77

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Solution

The correct option is A 343.77
Given data Ast=π4×162×4=804.25mm2

b = 200 mm; d = 400 mm

From equilibrium of forces

T = C
Ast,fst=0.36×fck b xu,lim

fst=0.36×fck b xu,limAst

=0.36×20×200×400×(0.48)804.25

fst=343.77N/mm2

Alternatively,

xu,lim=0.48d=0.48(400)=192mm

Mu,lim=0.138fckbd2=0.138(20)(200)(400)2Nmm

= 88.32 kNm

Mu,lim=fst,Ast(d0.42xu)

88.32×106=fst(804.25)(4000.42×192)

fst=343.86N/mm2

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