Validity of bending equations under different conditions


by mtrl
Tags: bending, conditions, equations, validity
mtrl
mtrl is offline
#1
Feb10-13, 09:17 PM
P: 6
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.
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
SteamKing
SteamKing is offline
#2
Feb10-13, 10:28 PM
HW Helper
Thanks
P: 5,599
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.


Register to reply

Related Discussions
boundary conditions bending beam Engineering, Comp Sci, & Technology Homework 0
Range of validity of Maxwell's equations with charges Classical Physics 3
Checking validity of simple tensor equations Calculus & Beyond Homework 0
Query about Range of validity of field equations in Quantum Field Theory General Physics 9
[Thermo] - Maxwells Relations? Prove the Validity of the Equations Engineering, Comp Sci, & Technology Homework 5