A cube of material (E = 15,000 psi, v = 0.25) of side length 2" is shown in the x, y plane. Takex positive to theright and y positive up. Determine the change in length of the cube in the three coordinate directions if4%3Da) The normal stress in the z direction is zero (Ans: 0.0317" in x direction)b) The normal stress in the z direction is 300 psi compression (Ans: 0.0416" in x direction)150 psi100 psi+ 200 psi

Answered: A cube of material (E 15,000 psi, v…

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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Question

A cube of material (E = 15,000 psi, v = 0.25) of side length 2" is shown in the x, y plane. Takex positive to the
right and y positive up. Determine the change in length of the cube in the three coordinate directions if
4
%3D
a) The normal stress in the z direction is zero (Ans: 0.0317" in x direction)
b) The normal stress in the z direction is 300 psi compression (Ans: 0.0416" in x direction)
150 psi
100 psi
+ 200 psi

Expert Solution

Step 1

Change in length of the cube depends on the length of the sides of the cube and the normal stress acting on the cube.

$Change in length in X - direction : L_{X} = [\frac{σ_{x}}{E} - μ \frac{σ_{y}}{E} - μ \frac{σ_{z}}{E}] \times L Change in length in Y - direction : L_{Y} = [\frac{σ_{y}}{E} - μ \frac{σ_{x}}{E} - μ \frac{σ_{z}}{E}] \times L Change in length in Z - direction : L_{Z} = [\frac{σ_{z}}{E} - μ \frac{σ_{x}}{E} - μ \frac{σ_{y}}{E}] \times L$

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