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.

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter6: Introduction To Mechanical Properties

Section: Chapter Questions

Problem 8CQ

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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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