ME85-lecture30 - Lecture 30 Mohrs Circle Christian Otto...

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Unformatted text preview: Lecture 30 Mohrs Circle Christian Otto Mohr (1835 1918) Principal stresses The previous equations are combined to yield parametric equations for a circle, ( ) 2 2 2 2 2 2 2 where xy y x y x ave y x ave x R R + = + = = + 2 45 by from offset and 90 by separated angles two defines : Note 2 2 tan 2 o o 2 2 max y x ave p xy y x s xy y x R + = = = + = = Maximum Shear Stress Maximum shearing stress occurs for ave x = 2 45 by from offset and 90 by separated angles two defines : Note 2 2 tan 2 o o 2 2 max y x ave p xy y x s xy y x R + = = = + = = Example 14.1 For the state of plane stress shown, determine (a) the principal planes, (b) the principal stresses, (c) the maximum shearing stress and the corresponding normal stress. SOLUTION: Find the element orientation for the principal stresses from y x xy p = 2 2 tan Determine the principal stresses from 2 2 min max, 2 2 xy y x y x + + = Calculate the maximum shearing stress with 2 2 max 2 xy y x + = 2 y x + = Example 14.1 SOLUTION: Find the element orientation for the principal stresses from ( ) ( ) = = + = = 1 . 233 , 1 . 53 2 333 . 1 10 50 40 2 2 2 tan p y x xy p = 6 . 116 , 6 . 26 p Determine the principal stresses from ( ) ( ) 2 2 2 2 min max, 40 30 20 2 2 + = + + = xy y x y x MPa 30 MPa 70 min max = = MPa 10 MPa 40 MPa 50 = + = + = x xy x Example 14.1 MPa 10 MPa 40 MPa 50 = + = + = x xy x 2 10 50 2 = + = = y x ave The corresponding normal stress is...
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This note was uploaded on 01/21/2012 for the course C 85 taught by Professor Papadopoulos during the Spring '08 term at University of California, Berkeley.

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ME85-lecture30 - Lecture 30 Mohrs Circle Christian Otto...

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