Basic Strength of Materials Calculation ???? 2

[dtwo]

I am working on a shaft failure and I came across something that puzzles me.

If I look at Mechanical Engineers handbook it lists a formula for maximum stress in center of a beam where the load is applied in the center with supports on the two ends being: WL / 4Z

W: weight
L: over all length
Z: section modulus

However from strength of materials class many moons ago I remember using Mc / I for stress due to bending. What is the difference?

 

[Twoballcane]

Well the units work out, do you know if you get the same answer?

Tobalcane
"If you avoid failure, you also avoid success."

 

[Airmack]

WL/4Z is derived from Mc/I...

The section modulus is defined as Z = I/c

Also, (for a beam of length L, simply supported on each end with a load, W, applied at the center) the maximum moment is

M = WL/4 (at dist = L/2)

If we insert these into your standard Mc/I equation, this leads to the equation,

WL/4Z

The difference is that this equation is specific for this loading configuration and Mc/I still holds for *any* bending loading configuration.

 

[Heckler]

I would suggest getting a copy of Roark's Formulas for Stress & Strain.

Heckler
Sr. Mechanical Engineer
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[40818]

Probably read timoshenkos basic books, as they would also give a good refresher to the grey matter.

 

[imok2]

This may be of some help:

http://www.jniosh.go.jp/english/publication/SRR/abst/SRR-91.htm