At a point in a stressed body, the cartesian components of stress are oxx = 60 MPa, Oyy = -40 MPa, Ozz = 20 MPa, Txy = -40 MPa, Tyz = 20 MPa, and Txz = 30 MPa. Determine: (a) The principle stresses and their direction cosines. (b) The normal and shear stresses on a plane whose outer normal has the following direction cosines: cos (n. x) = 0,429 : cos (n. v) = 0,514: cos (n. z) = 0.743

At a point in a stressed body, the cartesian components of stress are oxx = 60 MPa, Oyy = -40 MPa, Ozz = 20 MPa, Txy = -40 MPa, Tyz = 20 MPa, and Txz = 30 MPa. Determine: (a) The principle stresses and their direction cosines. (b) The normal and shear stresses on a plane whose outer normal has the following direction cosines: cos (n. x) = 0,429 : cos (n. v) = 0,514: cos (n. z) = 0.743

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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Planar Stresses

Question

At a point in a stressed body, the cartesian components of stress are oxx = 60 MPa, ơyy = -40
MPa, Ozz = 20 MPa, Txy = -40 MPa, Tyz = 20 MPa, and Txz = 30 MPa. Determine:
(a)
The principle stresses and their direction cosines.
(b)
The normal and shear stresses on a plane whose outer normal has the following
direction cosines:
cos (n, x) = 0.429 ; cos (n, y) = 0.514; cos (n, z) = 0.743

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