Expression for normal and shear stress, Mechanical Engineering

Expression for normal and shear stress:

Derive expression for normal and shear stress on the plane AE inclined at an angle B with AB subjected to the direct stresses of compressive nature (both) of σx and  σy on 2 mutually

perpendicular stresses as shown in the figure given below.
 
Sol.: Consider unit thickness of element. Applying the equations of equilibrium to free body diagram of wedge ABE.

1122_Expression for normal and shear stress.png

Let σn and  τ be normal and shear stresses on plane AE.
67_Expression for normal and shear stress1.png 
By multiplying the equation (iii) by sin θ, (iv) by cos θ and subtracting
505_Expression for normal and shear stress2.png 
Also by multiplying equation (iii) by cos θ and 4 by sin θ and then adding.
1161_Expression for normal and shear stress3.png

Posted Date: 10/23/2012 3:06:58 AM | Location : United States







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