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Question

# Assume straight line instead of parabola for stress strain curve of concrete as follows and partial factor of safety as 1.0 A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M-20 The depth of the neutral axis obtained as per IS: 456-2000 differs from the depth of neutral axis obtained in case of from compression fibre is

A
15 mm
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B
20 mm
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C
25 mm
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D
32 mm
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Solution

## The correct option is C 25 mm For depth of Neutral Axis xu C= T Area of stress diagram × width = T 12[37xu+xu]×0.67fck×300=0.87fy.Ast 12×107xu×0.67×20×300 =0.87×415×3×π×1624 xu=75.844 mm xu≃ 76mm Depth of NA as per IS : 456 C = T 0.36fckb.xu=0.87fyAst 0.36×20×300xu=0.87×415×3×π×1624 xu=100.824 mm Neutral axis differs by (100.824-75.84) = 24.98 = 25 mm

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