Using transformation equations of plane stress, determine the normal and shear stress components for X’-axis located 0.5 radians clockwise from x-axis. The non-zero stress components are given as follows, σx= 200 MPa, σy= 100 MPa, τxy= -50 MPa.

Using transformation equations of plane stress, determine the normal and shear stress components for X’-axis located 0.5 radians clockwise from x-axis. The non-zero stress components are given as follows, σx= 200 MPa, σy= 100 MPa, τxy= -50 MPa.

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 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec...

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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

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Expert Solution

Given data:

The clockwise angle between the x’-axis and the x-axis is, $θ = 0.5 rad \times (\frac{180 °}{π}) = 28.65 °$
The stress component in the x-axis is, $σ_{x} = 200 MPa$
The stress component in the y-axis is, $σ_{y} = 100 MPa$
The shear stress in the xy plane is, $τ_{x y} = - 50 MPa$

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