(a) Explanation Given information: The modulus of elasticity E x is 50 GPa . The modulus of elasticity E y is 15.2 GPa . The modulus of elasticity E z is 15.2 GPa . The strain along xz axis is 0.254. The strain along xy axis is 0.254 The strain along zy axis is 0.428. Calculation: Write the stress to strain Equation along x direction as follows: ε x = σ x E x − ν y x σ y E y − ν z x σ z E z (1) Here, σ x , σ y , σ z is normal stress along x , y, z axis respectively. Write the stress to strain Equation along y direction as follows: ε y = − ν x y σ x E x + σ y E y − ν z y σ z E z (2) Write the stress to strain Equation along z direction as follows: ε z = − ν x z σ x E x − ν y z σ y E y + σ z E z (3) Equate the stress Equation along xy axis. ν x y E x = ν y x E y (4) Equate the stress Equation along yz axis. ν y z E y = ν z y E z (5) Equate the stress Equation along zx axis. ν z x E z = ν x z E x (6) Apply the constraint conditions as follows: ε z = 0 Apply the load conditions as follows: σ y = 0 Substitute 0 for ε y in Equation (3). 0 = − ν x z σ x E x − ν y z ( 0 ) E y + σ z E z 0 = − ν x z E x σ x + 1 E z σ z σ z = ν x z E z E x σ x (7) Substitute 0.254 for ν x z , 15.2 GPa for E z , and 50 GPa for E x in Equation (7). σ z = 0.254 × 15.2 50 σ x = 0.077216 σ x Substitute 0 for σ y in Equation (1). ε x = σ x E x − ν y x ( 0 ) E y − ν z x σ z E z = σ x E x − ν z x σ z E z = 1 E x σ x − ν x z E x σ z (8) Substitute 0 (b) To determine Find the change in dimension in y direction.

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 2.9, Problem 92P

(a)

To determine

Find the stresse values σx,σy,σz.

(b)

To determine

Find the change in dimension in y direction.

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Chapter 2.9, Problem 91P

Chapter 2.13, Problem 93P

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Chapter 2 Solutions

Mechanics of Materials, 7th Edition

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Find the stresse values σ x , σ y , σ z .

Solution Summary: The author calculates the stress to strain Equation along x, y, and z axis.