Composite Beams

*Example: The simply supported beam shown below supports a load of 1800 lb at

mid-span. The composite beam consists of a wood plank with a x-section 5.5 in

high and 4 in wide as shown. A ½ inch steel plate is laminated to the bottom of

the wood to help carry tensile loads. The ratio of moduli of elasticity of steel to

wood, E_s/E_w = 20. Find the maximum bending stress in the beam.

1. Select the wood to be the “base material”. Therefore E_s / E_w = 20

2. Form the “transformed section” using only the “base material” by multiplying

the width of steel section by 20. The width of the wood is unchanged. The

figure below shows the “transformed” section.

3. Locate the centroid, c, of the “transformed” x-section.

(b₁h₁ + b₂h₂) c = (b₁h₁) (h₁ /2) + (b₂h₂) ( h₁ + h₂ /2)

[(80)(0.5) + (4)(5.5)] c = (80)(0.5)(0.25) + (4)(5.5)(0.5 + 2.75)

So c = 1.315 in.

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