Composite
Beams
*Example: (continued)
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The moment of inertia for
the entire “transformed” section Iyy =
829.5 in4 Use σ = Mc/Iyy to calculate the bending stress. where
c1 = h3/2 + h2 + h1, c2 = h3/2
+ h2 , c3 = h3/2 The bending stresses in
terms of the base material (3) are as follows: At the top of the composite beam σ1 = Mc1/Iyy = (100,000)(9/2) / 829.5 =
542.5 psi At
the interface between (1) and (2)
σ2 = Mc2/Iyy = (100,000)(7/2) / 829.5 =
421.9 psi At
the interface between (2) and (3)
σ3 = Mc3/Iyy = (100,000)(3/2) / 829.5 =
180.8 psi 5.
Finally multiply the stress for material in section (1) by E1/E3
to obtain the actual bending stress at the top of
section (1). σ1 =
3(542.5) = 1630 psi
(result for the maximum bending stress in material (1). and multiply the stress for
material in section (1) by E2/E3 to obtain the actual bending stress at the top of
section (2). σ2 =
(1.5)(421.9) = 633 psi
(result for the maximum bending stress in material (2). σ3 =
180.8 psi (result for the
maximum bending stress in material (3) since it is the base
material) Click here for another
example. |
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