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Unformatted text preview: Question At a point in a loaded member, the stresses relative to an x,y,z coordinate system are given by 30 5 10 5 40 20 10 20 60 MPa. Calculate the magnitude and direction of maximum principal stress. Solution x = 60MPa, y = 40 MPa, z =30 MPa; xy = 20 MPa, xz =10 MPa, yz = 5 MPa; Let us denote the normal stresses in the x, y, z direction as x , y , z respectively and let the corresponding shear stresses be xy , zy , xz , respectively. We first find the stress invariants , I 1 , I 2 , and I 3 I 1 = x + y + z = 60+(40)+30 =50 I 2 =( x y )+( y z )+( y z )( 2 xy + 2 xz + 2 yz ) = 60 (40)+(40) 30+(40) (30)(20 2 + 10 2 + (5) 2 ) =2325 MPa 2 30 5 10 5 40 20 10 20 60 3 = I =83500 MPa 3 Now, we write the Equation (1.28) from the text which when solved would give us three principal stresses 3 2 2 1 3 = + I I I p p p...
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This note was uploaded on 11/22/2011 for the course EML 6653 taught by Professor Law during the Fall '09 term at University of South Florida  Tampa.
 Fall '09
 Law
 Stress

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