Q#4: Considering the original state of stress as shown in figure below and recalling the already developed equations for normal and shear stress at an angle O c.c.w from x-axis, mathematically prove that the planes of maximum in-plane shear stress are inclined at 45° to the principal planes.

Q#4: Considering the original state of stress as shown in figure below and recalling the already developed equations for normal and shear stress at an angle O c.c.w from x-axis, mathematically prove that the planes of maximum in-plane shear stress are inclined at 45° to the principal planes.

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 7.4.5P: An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial .is in the and is...

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Question

Considering the original state of stress as shown in figure below and recalling the already developed equations for normal and shear stress at an angle Ɵ c.c.w from x-axis, mathematically prove that the planes of maximum in-plane shear stress are inclined at 45o to the principal planes.

Q#4: Considering the original state of stress as shown in figure below and recalling the already
developed equations for normal and shear stress at an angle O c.c.w from x-axis, mathematically
prove that the planes of maximum in-plane shear stress are inclined at 45° to the principal planes.

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The angle between the planes of maximum in-plane shear stress and the principal planes:

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