A cube of material (E 15,000 psi, v 0.25) of side length 2" is shown in the x, y plane. Take x positive to the right and y positive up. Determine the change in length of the cube in the three coordinate directions if 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

Principles of Geotechnical Engineering (MindTap Course List)
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Author:Braja M. Das, Khaled Sobhan
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Chapter10: Stresses In A Soil Mass
Section: Chapter Questions
Problem 10.1CTP: EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on...
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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
Transcribed Image Text: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:LX=σxE-μσyE-μσzE×LChange in length in Y-direction:LY=σyE-μσxE-μσzE×LChange in length in Z-direction:LZ=σzE-μσxE-μσyE×L

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