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Stress state in a beam 
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#1
Mar1309, 03:09 AM

P: 45

Hello!
If I know the deflection (w) of a beam subjected to a point load in the middle, can I calculate the stress in that beam by calculating the shear force or moment ? or use a 2d plane strain state ? What is the best way to do it ? Thanks 


#2
Mar1309, 02:10 PM

P: 86

Yes. You need three equations:
deflection of beam as a function of (P,L,E,I) bending stress of beam as a function of moment. shear stress of beam as a function of shear. Then you need to add the two stresses together, but they almost always don't add linearly. Bending stress is varies with the height, y, within the section; ie: high at both top and bottom fibers, and zero at the mid section. Shear stress is parabolic, with its maximum at the mid section. A bit of reading will reveal what shear stress engineers usually use at the extreme fibers (it is not zero). This is all in most books on "Mechanics of Materials". 


#3
Mar1309, 03:38 PM

P: 723

Shear stress is linear and is zero at the mid plane. Bending stress is parabolic.
You had them backwards 


#4
Mar1409, 06:09 AM

P: 45

Stress state in a beam
Ok.
So the bending stress sigma_B = M_max *Z/I , right? I=moment of inertia. What about the stress due to shear then? With the equation for deflection I could integrate and get the shear force, but how do I get the shear stress ? 


#5
Mar1409, 10:58 PM

P: 86

What you said is true but for longitudinal stress along the length. 


#6
Mar1509, 02:26 AM

P: 735

I think I didn't get the question.
Yeah if you know the deflection, you can apply hooks law and figure out the stress. But for that you also need to know 'sigma'; the constant. 


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