The state of stress at a point in an elastic body is defined by the stress components, G11 = 2000; O22 = -2000; 612 = 1000; 623 = -400; 613 = 033 = 0. A plane that passes through the point has unit normal vector (1/5, 3/5, 3/V5) in relation to the x, y, z axes. (A) Find the stress vector components of the x, y, z axes acting on the plane. (B) Find the magnitude stress vector components of the x, y, z axes acting on the plane. (C) Find the magnitude of the normal stress acting on the plane.
The state of stress at a point in an elastic body is defined by the stress components, G11 = 2000; O22 = -2000; 612 = 1000; 623 = -400; 613 = 033 = 0. A plane that passes through the point has unit normal vector (1/5, 3/5, 3/V5) in relation to the x, y, z axes. (A) Find the stress vector components of the x, y, z axes acting on the plane. (B) Find the magnitude stress vector components of the x, y, z axes acting on the plane. (C) Find the magnitude of the normal stress acting on the plane.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The state of stress at a point in an elastic body is defined by the stress components, O11 = 2000;
O22 = -2000; o12 = 1000; G23 = -400; 013 = 033 = 0. A plane that passes through the point has
unit normal vector (1/5, 3/5, 3/V5) in relation to the x, y, z axes.
(A) Find the stress vector components of the X, y, z axes acting on the plane.
(B) Find the magnitude stress vector components of the x, y, z axes acting on the plane.
(C) Find the magnitude of the normal stress acting on the plane.
(D) Find the magnitude shear stress acting on the plane.
(E) Construct the 3D Mohr's circle. (You can use the graphical paper to construct the
circle and then take photo or by scanner to attach it with your answer).
(F) Based on the Mohr's circle, determine the principal stresses and the maximum
shear stress.
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