1. (a) Show that for an isotropic lamina in plane stress, the strain-stress relations are€111S1201S12 S11€62(S11 – S12),where S11 = 1/E and S12 = -v/E.(b) Show thatQ11 Q12€102Q12 Q1106€6whereQ11Q12and Q66 = +v) ·1-v² ,

The generalized Hook's law can be expressed for a three-dimensional elastic anisotropic body as,…

Answered: a) Show that for an isotropic lamina in…

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a) Show that for an isotropic lamina in plane stress, the strain-stress relations are

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 7.7.19P: During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as...

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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.

Question

1. (a) Show that for an isotropic lamina in plane stress, the strain-stress relations are
€1
11
S12
01
S12 S11
€6
2(S11 – S12),
where S11 = 1/E and S12 = -v/E.
(b) Show that
Q11 Q12
€1
02
Q12 Q11
06
€6
where
Q11
Q12
and Q66 = +v) ·
1-v² ,

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