How can we find the maximum normal and maximum shear stress at the point?

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)
Section: Chapter Questions
Problem 8.5.11P: The hollow drill pipe for an oil well (sec figure) is 6,2 in. in outer diameter and 0.75 in. in...
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How can we find the maximum normal and maximum shear stress at the point?

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Step 1

Normal Stress:

Normal stress is the amount of stress that occurred in a member when it is loaded by an axial force. Normal stress will usually occur when the members are either in tension or compression. The magnitude of the normal stress can be calculated by dividing the force or load by the area of cross-section. The area of cross-section is always perpendicular to the applied force.

Consider a bar whose cross-sectional area is subjected to an axial load through the centroid. The average normal stress in an axially loaded bar can be illustrated as follows,

Mechanical Engineering homework question answer, step 1, image 1

 

Step 2

Shear Stress:

Shear stress is the type of stress that actually acts coplanar to the cross-sectional area and it causes deformation of the plane in the direction of the stress. So it is basically perpendicular to the normal stress in the planar stress system.

Mechanical Engineering homework question answer, step 2, image 1

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