# - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.7.26P
Textbook Problem
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## - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?

To determine

The stress along x-direction.

### Explanation of Solution

Given information:

The strain in gauge A is 1100×106, strain in gauge B is 1496×106and strain in gauge C is 39.44×106,.and the Poisson's ratio is 0.33and the Young modulus of the gauge is 70GPa.

Write the expression for transformation for plain strain.

ε=εx+εy2+εx+εy2cos2θ+γxy2sin2θ(I)

Here, strain in gauge is ε, strain along x direction is εx, strain along y-direction is εy, shear strain in x-y plane is γxy,and orientation of gauge is θ.

Write the expression for the stress along x-direction using Hooks law.

σx=E1ν(εx+νεy) (II)

Here, Young modulus is Eand the Poisson's ratio is ν.

Calculation:

Substitute 1100×106for εx, 0for εy, 0°for θin Equation (I) for gauge A.

ε=1100×106+02+1100×106+02cos2(0°)+γxy2sin2(0°)ε=εA=1100×106

Here, strain in gauge A is εA.

Substitute 1496×106for ε, 1100×106for εx, 40°for θin Equation (I) for gauge B.

εB=1100×106+εy2+1100×106+εy2cos2(40°)+γxy2sin2(40°)1496×106=1100×106+εy2+1100×106+εy2cos2(40°)+γxy2sin2(40°)1496×106=645.50×106+0.413εy+0.492γxy0.413εy+0.492γxy=8.5×104(III)

Substitute 39

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