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Question

# A circular column of diameter 'd' carries an axial compressive load P at an eccentricity equal to one fourth of radius of column. The ratio between maximum compressive stress and maximum tensile stress is

A
2
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B
2.5
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C
3
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D
None of these
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Solution

## The correct option is D None of these The normal stress, σ=PA±MZ =PA±Pe(πd464)d2 =PA±PeA(d8) =P8⎛⎜ ⎜ ⎜⎝1±ed8⎞⎟ ⎟ ⎟⎠ Maximum compressive stress, σc=PA⎛⎜ ⎜ ⎜⎝1+ed8⎞⎟ ⎟ ⎟⎠ ⎛⎜⎝Sign convection usedCompression→+veTension→→ve⎞⎟⎠ Maximum tensile stress, σt=PA⎛⎜ ⎜ ⎜⎝1−ed8⎞⎟ ⎟ ⎟⎠ σcσt=(1+8e/d1−8e/d)=⎛⎜ ⎜ ⎜ ⎜⎝1+8×d/8d1−8×d/8d⎞⎟ ⎟ ⎟ ⎟⎠=20[Given:e=d8] This implies that tension does not occur anywhere in the column. Hence, option(d) is correct.

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