Calculating Stress in Beam Under Point Load: Best Methods

In summary, the conversation is about calculating the stress in a beam subjected to a point load in the middle. The best way to do this is by using three equations: deflection of beam as a function of (P,L,E,I), bending stress of beam as a function of moment, and shear stress of beam as a function of shear. These stresses are then added together, but do not add linearly. Bending stress varies with the height within the section, while shear stress is parabolic with its maximum at the mid section. Engineers typically use a specific shear stress at the extreme fibers. This information can be found in books on "Mechanics of Materials". Additionally, the conversation clarifies that shear stress is linear and zero at
  • #1
ladil123
45
0
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
 
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  • #2
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:
  • #3
Shear stress is linear and is zero at the mid plane. Bending stress is parabolic.

You had them backwards
 
  • #4
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
CFDFEAGURU said:
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.
 
  • #6
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.
 

1. What is the formula for calculating stress in a beam under point load?

The formula for calculating stress in a beam under point load is σ = F/A, where σ is the stress, F is the applied force, and A is the cross-sectional area of the beam.

2. How do I determine the maximum stress in a beam under point load?

The maximum stress in a beam under point load can be determined by finding the point of maximum deflection, which occurs at the center of the beam, and then using the formula σ = F/A to calculate the stress at that point.

3. Can I use the same method to calculate stress in any type of beam under point load?

Yes, the formula σ = F/A can be used to calculate stress in any type of beam under point load, as long as the beam is linearly elastic and the load is acting at a single point.

4. What are the assumptions made when calculating stress in a beam under point load?

The main assumptions made when calculating stress in a beam under point load are that the beam is linearly elastic, the load is acting at a single point, and the beam is homogeneous and isotropic.

5. Are there any other methods for calculating stress in a beam under point load?

Yes, there are other methods for calculating stress in a beam under point load, such as using the bending moment equation, the moment-area method, or finite element analysis. Each method may be more suitable for different types of beams or loading scenarios.

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