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Question

A beam of rectangular cross-section (b×d) is subjected to a torque T. What is the maximum torsional stress induced in the beam (b < d and α is a constant)?

A
Tαb2d
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B
Tαbd2
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C
Tαbd
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D
Tbd
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Solution

The correct option is A Tαb2d
Torsional constant of a rectangular,section of width b and depth d (b < d) may be expressed as
J=b3d
For T, L and I sections torsion,canstant,
J=13b3idi

where bi and di are the-dimensions of e.ach of the component rectangles into which the:s.ection may be divided.
Torsional shear stress for rectangular section
τ=Tαb2d
For T, L and.J,sections torsional shear stress may be calculated for each component rectangle by considering them subjected to torsional moment

Ti=T[b3idib3idi]

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