TransWikia.com

Stress vector that acts on the plane

Engineering Asked by user28922 on March 14, 2021

enter image description here

A flat plate with dimensions 110×220 mm is subject to the indicated stresses.
Assume that $sigma_{zz} = 120 MPa$.
Determine the stress vector that acts on the plane defined by the z axis and the dashed line segment.

In the solution it is written that

$$theta = 90^o – arctanleft(frac{0.11}{0.22}right)$$

$$n(theta= 63.43^o) = [costheta, sintheta, 0 ] = [0.44730, 0.89440, 0]$$

I thought that θ=0 and therefore n=[0 0 1] since so n is perpendicular to the plane.

Why I am wrong?
Could someone explain me?

One Answer

$vec{n}$ is the normal of the plane which is defined by z (red) , and the dashed line (green).

enter image description here

The direction of the green line can be obtained by the diagonal (apologies for the bad drawing). $theta$ is denoted with blue.

From the right angle you can see that:

$$tantheta = frac{110}{220} Rightarrow$$ $$theta = arctanleft(frac{110}{220}right) $$ Essentially it has the same direction as y' in the figure you are showing.

However, I would have expected the vector to be

$$vec{n}= [-sintheta, costheta, 0]$$

Are you sure, you've written the correct formula?

Answered by NMech on March 14, 2021

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP