Stress state in a beam

  • Thread starter ladil123
  • Start date
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
 
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".
 
Last edited:
Shear stress is linear and is zero at the mid plane. Bending stress is parabolic.

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

You had them backwards
I guess I wasn't clear. I was referring to the transverse stress level within a SECTION of the beam, and not referring along its length.

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

Related Threads for: Stress state in a beam

  • Posted
Replies
6
Views
1K
Replies
10
Views
21K
  • Posted
Replies
7
Views
2K
Replies
2
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top