Validity of bending equations under different conditions

In summary, the bending moment equation σ= M * y / I assumes linear elastic behavior and may not be valid for materials with plasticity, viscoelasticity, nonlinearity, or anisotropy. Different methods must be used for accurate calculations in these cases.
  • #1
mtrl
6
0
Hi all,

I want to ask you a question about the bending moment equation:

σ= M * y / I

Does this equation have the same form if we assume,

-Plasticity instead of elasticity.
-Viscoelasticity instead of elasticity.
-Nonlinearity instead of linearity.
-Anisotropy instead of isotropy.

Can you comment on the validity of the equation with these assumptions please.

Thanks.
 
Engineering news on Phys.org
  • #2
All of the qualities you mentioned (plasticity, viscoelasticity, nonlinearity, ans anisotropy) cause the Euler-Bernoulli bending equation to deviate from an accurate solution.

This equation pre-supposes linear elastic behavior of the beam material with the added requirement that the slope of the beam under bending is also << 1.

The E-B equation, by the fact of its linearity, is quite useful for calculation because it permits the use of superposition when calculating the effect of multiple simultaneous beam loadings.

For materials which are not linearly elastic, different methods must be employed to calculate beam responses.
 

1. What are the different conditions that can affect the validity of bending equations?

The validity of bending equations can be affected by various factors, such as the material properties of the object being bent, the geometry of the object, the applied load, and the boundary conditions.

2. How do material properties impact the validity of bending equations?

Material properties, such as Young's modulus and yield strength, can significantly influence the validity of bending equations. These properties determine how much stress and strain the material can withstand before it undergoes plastic deformation or failure.

3. Are there specific geometries that are more prone to invalidating bending equations?

Yes, certain geometries, such as thin and slender beams, can lead to significant deviations from the predicted bending behavior. This is because these geometries can result in non-uniform stress distributions and buckling, which are not accounted for in the basic bending equations.

4. Can boundary conditions affect the validity of bending equations?

Yes, boundary conditions, such as fixed or simply supported ends, can have a significant impact on the validity of bending equations. These conditions can lead to different stress and strain distributions, which can affect the overall bending behavior of the object.

5. How can one determine the validity of bending equations under different conditions?

The validity of bending equations can be evaluated through experimental testing or finite element analysis. These methods can provide more accurate and detailed information about the bending behavior of a structure, taking into account the different conditions that may affect its validity.

Similar threads

  • Mechanical Engineering
Replies
5
Views
2K
Replies
1
Views
885
  • Mechanical Engineering
Replies
20
Views
7K
  • Mechanical Engineering
Replies
2
Views
839
  • Advanced Physics Homework Help
Replies
4
Views
1K
Replies
1
Views
796
Replies
1
Views
987
Replies
4
Views
807
Replies
1
Views
3K
  • Special and General Relativity
Replies
8
Views
841
Back
Top