The torsional constant J for cross sections made up of joine

The torsional constant J for cross sections made up of joined long narrow rectangles (b_1?10h_1) is defined by J=1/3sigma^e_i=1 (2b_i)(2b_i)^3. Where there is a taper, as in the cross section of a turbine blade, we can use J=1/3 integral (2h)^3 ds where ds is an increment of length along the median line of cross section. Calculate the maximum shear stress in the solid cross section of a turbine blade in terms of an applied torque T.

Solution

HINT:- Maximum shear stress can be calculated by the torsional equation .

Shear stress =T*r/j

Where j=torsional constent which is given in question

T= torque applied

And r= Max distance from neutral fibre/ axis.

In this question Max distance from neutral axis will be where the blade has maximum thickness I.e.at the thickness of 15.