WHy is shear stress soooo small!!? HELP!?

Question

Hey,

What's the engineering reasoning behind why sometimes shear stress is neglected if it is significantly smaller than,say, bending stress. So I guess what I am asking is that why does shear stress come out soo small?

like for example, a bike pedal with crank has 300lbs vertical only force applied to it, and made a cut and analyzed it. The bending stress due to bending moment was 50kpsi while shear stress was 1.7 kpsi.

We also made that assumption when I took streghts of materials for many of the cases. I still don't know why it is safe to make that assumption.

Thanks

Answer 1

A simple model for this is the cantilever, supported at one end (bearing of crank) and with load on the other end. I guess this is what you used. Yes it is common for bending to be more significant than shear.

You generate two stresses:
a) shear stress; from the shear force
b) bending stress (tensile&compression); from moment = force x distance

Bending stress becomes more significant since it multiplies with distance, the moment arm. Shear stress however remains constant no matter how long the arm. Imagine load at one end of a very long moment arm, bending would be huge, while shear remains no different from load being close to support. Hence bending is much greater.

When doe shear become more critical: say shear on a bolt clamping two plates tightly together. Moment arm may be small (thickness of plates), so bending moment is small. Shear becomes more significant, as pulling the plates hard may shear the bolt.

As for when it is “safe” to make that assumption, well you have calculated yourself. I would say when moment arm is relatively long. Also when you apply a sufficiently large safety factor: say safety factor is 2.0 (100% higher) and your shear stress is only 3% of bending, you may be safe. If you are deisgining aircraft parts with tight sf than go after every load.

Answer 2

Your units are peculiar: shear is never in psi or kpsi. Shear is always calculated in lbs or kips, and along with moment, it is used in design.