Homework Help: Solid Mechanics

Posted by Devi on Friday, August 3, 2012 at 5:55am.

A cast iron block of 5Cm^2 cross section carries an axial compressive load of 50KN.Calculate the magnitude or normal and shear stresses on a plane whose normal is inclined at 30 deg.to the axis of the block,also determine the maximum shear stress in the block?

Solid Mechanics - MathMate, Friday, August 3, 2012 at 6:40am
I'll give it a try.

We have 50kN on 5cm², or 0.0005 m².
So the axial stress
σ_x = 10⁵ kPa
=100 MPa

σ_y=0

So draw the Mohr's circle (in the σ/τ plane) with between (0,0) and (100,0) as a diameter.
The centre is at (50,0).

To find the stresses at θ=30°
draw a diameter passing through the centre at 2*30=60° with the axis.
The stresses in that plane is shown by the extremities of the diameter, namely
σ=50±50cos(60°), and
τ=±50sin(60°).

Maximum shear stress is at θ=45° where
σx=σy=50, and
τxy=50

Hope that helps.

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