EM 319 - Mohr's Circle Example 2

EM 319 - Mohr's Circle Example 2 - An example of Mohrs...

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Given a stress state as shown in the figure, construct its Mohr’s circle and finish the following: Construct the Mohr’s circle : Read coordinates for point A and B : ) 5000 , 30000 ( A and ) 5000 , 6000 ( B , plot them on stress plane. (Note: Don’t forget to alter the sign of shear stress for point B !) Connect AB . Intersection of AB and x -axis ( σ axis) is C, whose coordinate is ) 0 , 18000 ( C . Find radius : 13000 5000 ) 18000 30000 ( 2 2 2 2 = + = + = AE CE R . Find angle α : ( ) ( ) ° = = = = 62 . 22 12000 5000 tan tan 1 1 CE AE ACE α . Find the stresses acting on an element oriented at an angle ° = 60 θ and show these stresses on a sketch of an element oriented at the angle . Rotate ° 120 on the circle, find point A . The angle ° = ° ° = 38 . 37 120 180 2 CP A . 28330 7670 38 . 37 cos 13000 18000 cos 1 1 2 1 = + = = ° = = x y x y x CP A R C . 7890 38 . 37 sin 1 1 = ° = R y x τ . Principal stresses :
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