HW03.pdf - Elasticity (I) Homework 3 date: due: 1....

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Elasticity (I)Homework 3date:3/23/2020due:3/30/20201.The state of stress throughout a body is given by the stress tensor331100000ijCxCxCxCxwhereCisanarbitraryconstant.(a)Determine the body force applied to the body.(b)At the point P(1, 1, 2) calculate the stress vector on the plane23222xxx, and onthe sphere2212349xxx.(c)Find the maximum normal and shear stresses and the planes on which they occur at P, anddraw the Mohr’s circles.(d)At point P, use the principal directions to define a new coordinate system. Then, determinethe stress tensor in the new coordinate system by tensor transformation.2.The stress state at a certain point in a body is given by21202120Tσ,whereTis a constant.(a)DetermineTsuch that there is a traction-free plane and determine the normal to thetraction-free plane.(e)If a new Cartesian coordinate system23,,xxxis employed such that the1xaxis is inthe direction121
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