Solving Strain in a Box on the X-Y Axis: A Homework Problem

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SUMMARY

The discussion focuses on solving a strain problem involving a box positioned on the x-y axis, with specific dimensions and strain values. The box extends 4 inches in the x direction and 2 inches in the y direction, with strains of +880 microinches/inch in the x direction, +960 microinches/inch in the y direction, and a shear strain of -750 micro radians. The objective is to determine the normal strain along the diagonal AC using the strain equation provided. The correct angle theta for the diagonal AC is identified as approximately 60.15 degrees, leading to a calculated normal strain of 596 microinches/inch.

PREREQUISITES
  • Understanding of strain concepts, specifically normal and shear strain.
  • Familiarity with coordinate systems, particularly the x-y axis.
  • Knowledge of trigonometric functions and their application in engineering problems.
  • Ability to manipulate equations involving strain, such as the provided strain equation.
NEXT STEPS
  • Review the derivation of the strain equation used in the discussion.
  • Study the relationship between angles and strain in two-dimensional systems.
  • Learn about the implications of shear strain in engineering applications.
  • Explore additional examples of strain calculations in structural engineering contexts.
USEFUL FOR

Students studying mechanical engineering, particularly those focusing on materials science and structural analysis, as well as professionals involved in stress analysis and strain measurement in engineering applications.

Bradracer18
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Homework Statement



I've got a problem that I can't figure out. It deals with strain.

I've got a box, sitting on the x-y axis(like normal x-y axis's are). The box extends 4 inches from the origin in the x direction, and 2 inches up. Going clockwise(starting at origin) the corners are labeled A, D, C, B.

epsilon(or strain) in the x direction is = + 880 u in/in.
strain in y direction = + 960 u in/in
and finally, the shear(or gamma) strain in the xy direction is = -750 u radians.

Need to determine the normal strain Eac along the diagonal AC(there is a line from A to C).

u is micro...so x10^-6.

Homework Equations



strain(E) = (Ex +Ey)/2 + (Ex - Ey)/2 *cos2(theta) + gamma(xy)*sin2(theta)


The Attempt at a Solution




Sorry for so many words, I don't know how to make symbols. I hope you get the picture of how I explained it. Basically, I think this box is stretching upwards and to the right(slanted to the right and to the "up", from the origin).

My question is, what is theta...the rest is pretty obvious...I can not find theta.

My answer sheet say the answer is 596 u in/in. And, using that equation, I put in theta's and found about 60.15 degrees to work. I can't for the life of me, find how 60 degrees works though.

I appreciate you help.

Brad
 
Physics news on Phys.org
Is this not understandable?
 
Theta is the angle between the x-axis and the AC diagonal.
 

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