Can Maximum Bending Strain Be Calculated Without Knowing Young's Modulus?

In summary, it is possible to determine bending stress in a beam without knowing the Young's modulus of the material used. The Euler's model of beam bending and the Euler-Timoshenko model both provide equations that involve stress, moment, and the 2nd moment of area, but do not explicitly require the Young's modulus. However, the amount of deflection of the beam does depend on Young's modulus. Therefore, to solve for the maximum bending strain, it is necessary to use the known stresses and Young's modulus.
  • #1
maniaciswicke
7
0
Very simply put.
Is it possible to determine bending stress in a beam without knowing the young's modulus of the material used? All equations I've seen seem to include in some form an E value ( young's modulus), which is used in conjunction with a stress value to evaluate the strain.
 
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  • #2
The forces and therefore the stresses in many beams are statically determinate so they do not depend on the material. Euler's model of beam bending gives.

[tex]\frac \sigma y = \frac M I [/tex]

Where [itex]\sigma[/itex] is the stress, y is the offset from the neutral axis, M is the bending moment and I is the 2nd moment of area.

The Euler-Timoshenko model also includes shear stresses.

The strains, and therefore the amount of deflection of the beam, DO depend on Young's modulus.
 
  • #3
This is what i thought.
It is a homework problem but i wasn't asking for the answer, merely if it was possible to solve. The dimensions of the beam are known so i agree the stresses are quite straightforward. The question very clearly asks for the "maximum bending strain" though. Could i perhaps give the answer in terms of the known stresses and E?
 

1. What is bending strain in a beam?

Bending strain in a beam is a measure of the deformation or change in shape of a beam when subjected to a bending force or moment. It is the ratio of the change in length of a beam to its original length.

2. How is bending strain calculated?

Bending strain can be calculated using the formula ε = (M*y)/I, where ε is the bending strain, M is the bending moment, y is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the beam cross-section.

3. What factors affect bending strain in a beam?

The magnitude and distribution of the bending force or moment, the material properties of the beam, and the geometry of the beam cross-section all affect the bending strain in a beam. Other factors such as temperature, loading duration, and boundary conditions may also have an impact.

4. How is bending strain different from axial strain?

Bending strain occurs when a beam is subjected to a bending force or moment, causing it to deform and change shape. Axial strain, on the other hand, is the change in length of a beam due to being pulled or compressed along its axis. Bending strain is a result of a combination of axial and shear strains.

5. Why is bending strain important in engineering?

Bending strain is important in engineering because it helps engineers determine the strength and stability of a beam and whether it can withstand the applied loads without failing. It is also a key factor in the design and analysis of various structures such as bridges, buildings, and mechanical components.

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