Shared loading on composite beam section
Shared loading on composite beam section
(OP)
Do you guys agree with the following equation?
Scenario: You have a composite section of two different materials making a beam. The top half (above the geometric centroid) is material 1 & the bottom half (below the geometric centroid) is material 2. Considering equal deflections in both materials, an equation is written to proportion the distributed load based on the relative stiffness of each part.
From W_total, the loading on material 1 (w_matl1) = W_total / [1 + (E2*I2)/(E1*I1)]
and thus, the loading on material 2 (w_matl2) = W_total / [1 + (E1*I1)/(E2*I2)]
QUESTION: I've seen a text reference the equation above then proceed to use each distributed load to calculate the maximum bending stress in each material as though it was a single section beam (Mc/I relative to only the top or bottom section, independently). There was no modular transformation performed (n=E1/E2) or transformed moment of inertia calculated, which provides a very different answer from the typical transformed section method.
Also, what is your approach to finding the overall deflection of this composite section? The problematic equations above are based on equivalent deflections... what is the direct method to finding that overall deflection?
Do any of you know a reference that backs up this load distribution theory?
Thanks!
Scenario: You have a composite section of two different materials making a beam. The top half (above the geometric centroid) is material 1 & the bottom half (below the geometric centroid) is material 2. Considering equal deflections in both materials, an equation is written to proportion the distributed load based on the relative stiffness of each part.
From W_total, the loading on material 1 (w_matl1) = W_total / [1 + (E2*I2)/(E1*I1)]
and thus, the loading on material 2 (w_matl2) = W_total / [1 + (E1*I1)/(E2*I2)]
QUESTION: I've seen a text reference the equation above then proceed to use each distributed load to calculate the maximum bending stress in each material as though it was a single section beam (Mc/I relative to only the top or bottom section, independently). There was no modular transformation performed (n=E1/E2) or transformed moment of inertia calculated, which provides a very different answer from the typical transformed section method.
Also, what is your approach to finding the overall deflection of this composite section? The problematic equations above are based on equivalent deflections... what is the direct method to finding that overall deflection?
Do any of you know a reference that backs up this load distribution theory?
Thanks!






RE: Shared loading on composite beam section
RE: Shared loading on composite beam section
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shared loading on composite beam section
Do you know of any references that expand further on this proportioning of loads through modulus and deflection?
RE: Shared loading on composite beam section
RE: Shared loading on composite beam section
RE: Shared loading on composite beam section
Thanks!
RE: Shared loading on composite beam section
If they are connected, and modulus of elasticity differs the geometric centroid won't be the neutral axis of the combined section. Just pointing this out as you are making this assumption. For them to act independently you will get slip at the interface.
RE: Shared loading on composite beam section
if you don't have analysis software, you can make some conservative estimations with the inverse of the deflection formulas. Otherwise you'll have to do some beam stiffness matrix analysis.