An element is subject to the following normal and shear strains: €x = -350 x 10-6 €y = 200 x 10-6 Yxy = 300 X 10-6 If the element were oriented at an angle of 15° counterclockwise: a) Determine the normal and shear strains Ex', ', and Yx'y'. b) The principal strains and the orientation upon which they act. c) The maximum in-plane shear strain and the orientation upon which they act.

An element is subject to the following normal and shear strains: €x = -350 x 10-6 €y = 200 x 10-6 Yxy = 300 X 10-6 If the element were oriented at an angle of 15° counterclockwise: a) Determine the normal and shear strains Ex', ', and Yx'y'. b) The principal strains and the orientation upon which they act. c) The maximum in-plane shear strain and the orientation upon which they act.

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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Design of structures using FEA

An arrangement, in which various members are interconnected with their constrained relative motion, the whole arrangement is then known as a structure. The degree of freedom of such a structure is zero. In such a structure, the load can act throughout the length of the structure or at the joints.

Question

An element is subject to the following normal and shear strains:
Ex = -350 × 10-6
€y = 200 x 10-6
Yxy = 300 X 10-6
If the element were oriented at an angle of 15° counterclockwise:
a) Determine the normal and shear strains €¸', €', and Yx'y'.
b) The principal strains and the orientation upon which they act.
c) The maximum in-plane shear strain and the orientation upon which they act.

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Step 1: (a) Determination of normal strain

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Step 2: (b) Determination of principal strain

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Step 3: (c) Determination of maximum shear strain

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Step 4: orientation

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