Question

For a long narrow cross-section (i.e., ratio of b/t, breadth b and thickness t above 10) bar subjected to torsion T, the value of maximum shear stress will be

• A. $$T/bt^2$$
• B. $$T/4bt^2$$
• C. $$2T/bt^2$$
• D. $None of these$

Answer 1

Answer:

$None of these$

$\frac TJ =\frac {\tau}{R}$ $J=I_{XX} +I_{YY} =\frac {bt^ 3}{2} +\frac {tb^ 3}{12} =\frac {bt(b^ 2 +t^ 2 )}{12}$ (Given b/t ratio greater than10 hence b is very large than t) Hence neglecting $t ^ 2$ since it is very small compared to b. $J = \frac{tb ^ 3}{12}$

R = b / 2 Substitute the values of J and R in the equation of torsion$\tau =\frac{T \times \frac{b}{2}}{\frac{t b ^ 3}{12}} = \frac{6T}{t b ^ 2}$