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The known stress components at a point in a body. relative to the (x. y. z) axes, are o. = 20MPA. o, = 10 MPa. ty= 30 MPa. Tu = -10 MPa, and t,, = 80 MPa. Also, the second stress invariant is l: = -7800 MPa. (a) Determine the stress component a,. Then determine the stress invariants I,, and I, and the three principal stresses. (b) Show that I,. I;, and Is, are the same relative to (x. y. z) axes and relative to principal axes (1.2.3).

The known stress components at a point in a body. relative to the (x. y. z) axes, are o. = 20MPA. o, = 10 MPa. ty= 30 MPa. Tu = -10 MPa, and t,, = 80 MPa. Also, the second stress invariant is l: = -7800 MPa. (a) Determine the stress component a,. Then determine the stress invariants I,, and I, and the three principal stresses. (b) Show that I,. I;, and Is, are the same relative to (x. y. z) axes and relative to principal axes (1.2.3).

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The known stress components at a point in a body, relative to the (x. y. z) axes, are o, = 20MP.. o, = 10 MPa, tay= 30 MPa, T = -10 MPa, and t,, = 80 MPa. Also, the second stress invariant is l = -7800 MPa. (a) Determine the stress component a,. Then determine the stress invariants I, and I, and the three principal stresses. (b) Show that I1, I2, and Is, are the same relative to (x, y. z) axes and relative to principal axes (1,2,3).
Transcribed Image Text:The known stress components at a point in a body, relative to the (x. y. z) axes, are o, = 20MP.. o, = 10 MPa, tay= 30 MPa, T = -10 MPa, and t,, = 80 MPa. Also, the second stress invariant is l = -7800 MPa. (a) Determine the stress component a,. Then determine the stress invariants I, and I, and the three principal stresses. (b) Show that I1, I2, and Is, are the same relative to (x, y. z) axes and relative to principal axes (1,2,3).
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