The known stress components at a point in a body, relative to the (x, y, z) axes, are ox = 20MPA, Oy = 10 MPa, txy= 30 MPa, txz = -10 MPa, and tyz = 80 MPa. Also, the second stress invariant is I2 = -7800 MPa. (a) Determine the stress component o,. Then determine the stress invariants I, and I3, and the three principal stresses. (b) Show that I1, I2, and I3, 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 ox = 20MPA, Oy = 10 MPa, txy= 30 MPa, txz = -10 MPa, and tyz = 80 MPa. Also, the second stress invariant is I2 = -7800 MPa. (a) Determine the stress component o,. Then determine the stress invariants I, and I3, and the three principal stresses. (b) Show that I1, I2, and I3, are the same relative to (x, y, z) axes and relative to principal axes (1,2,3).

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.4.21P: -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see...

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Q1/
The known stress components at a point in a body, relative to the (x, y, z) axes, are ox = 20MPA,
Oy = 10 MPa, txy= 30 MPa, Txz = -10 MPa, and tyz = 80 MPa. Also, the second stress invariant
is I2 = -7800 MPa.
(a) Determine the stress component o,. Then determine the stress invariants I, and I3, and
the three principal stresses.
(b) Show that I1, I2, and I3, are the same relative to (x, y, z) axes and relative to principal
axes (1,2,3).

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