KML 7/9/09
Bending of beams made of two materials
(Chapter 6 in Gere)
The purpose of this analysis is to transform a beam’s section of two materials into an imaginary
section of one equivalent material and then calculate the bending stresses.
Since the moment load
supported by a material is proportional to its modulus, E, and to its width, b, for rectangular beams
(
29
)
EI
/(
M
=
κ
, the effective width of a material can be imaginarily changed to represent an
effective change in modulus.
The stresses in the two materials can be computed with one of the
two options described below.
See Gere pp. 457469 for a full derivation.
***Whichever material has its width changed will have the same factor in its stress equation***
Define the modular ratio:
1
2
E
E
n
≡
> 1
(by definition let
2
E denote the higher modulus of the two materials)
Option 1: Transform the effective width of material two (the one with higher E)

enlarge the width of the stiffer material2 (
1
2
E
E
) by factor n (
nb
b
T
=
)

compute the vertical centroid of transformed cross section

compute the centroidal second moment of area for the transformed
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 Fall '08
 Sharpe
 Second moment of area, Tensile strength, Compressive stress, effective width

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