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A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm 2 of steel in tension and 628 mm2 of steel in compression. The effective cover for compressive steel is 50 mm. Assume that both tensioned and compressive steel yield. The grades of concrete and steel used are M-20 and Fe-250 respectively. The stress block parameters (rounded off to first two decimal places) for concrete shall be as per IS : 456-2000.

The depth of neutral axis is

A
205.30 mm
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B
184.56 mm
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C
160.91 mm
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D
145.30 mm
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Solution

The correct option is C 160.91 mm

Grade of concrete = M20
Grade of steel = Fe-250

Effective depth, d = 500 mm
Width, b = 300 mm
Both tension and compressive steel yield .
So stress in both the bar
=0.87fy
=0.87×250
Depth of Neutral Axis (xu),
C = T
0.36fckb.xu+ASC×(0.87fy0.45fck)
=0.87fy.Ast
0.36×20×300×xu+628(0.87×2500.45×20)
=0.87×250×2200
xu=160.908 mm
= 160.91 mm
Maximum depth of Neutral axis
= 0.53 d
=0.53×500
xu max= 265 mm
xu<xu max
Hence O.K.

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