Answered: What is the Maximum In-Plane Shear…

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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Question

What is the Maximum In-Plane Shear Strain?

Expert Solution

Step 1

The Maximum in-plane shear stress is explained as below,

The maximum shear stress of the plane that will be present at 45°. It is placed parallel to the principal planes. The one half differences of the principal stresses give the maximum shear stress value.The principal planes give the value of 2θp. Hence, 0° and 360° gives the angle between them.

Step 2

It defines the small area in which the maximum concentrated value of the shear force gives the maximum shear stress.

The Principal Stresses formula is given as based on the Shear Stress = 0 as,

$σ_{1} = \frac{σ_{x} + σ_{y}}{2} + \sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + {τ_{x y}}^{2}} σ_{2} = \frac{σ_{x} + σ_{y}}{2} + \sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + {τ_{x y}}^{2}}$

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