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Question

A composite beam is made of two brass $[E=110 \mathrm{GPa}]$ bars to two aluminum $[E=70 \mathrm{GPa}]$ bars, as shown in Figure P8.44. The beam is subjected to a bending moment of $380 \mathrm{~N}$-m acting about the $z$ axis. Using $a=5 \mathrm{~mm}, b=40 \mathrm{~mm}, c=10 \mathrm{~mm}$, and $d=$ $25 \mathrm{~mm}$, calculate (a) the maximum bending stresses in the aluminum bars. (b) the maximum bending stress in the brass bars.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 7$\bold{Given:}$

- Length of the aluminum bars, $L_{al}$ = $40~\text{mm}$
- Height of the aluminum bars, $H_{al}$ = $5~\text{mm}$
- Length of the brass bars, $L_{br}$ = $10~\text{mm}$
- Height of the brass bars, $H_{br}$ = $25~\text{mm}$
- Bending-moment acting about the z-axis of the beam, $M = 380~\text{N} \cdot \text{m}$
- Modulus of elasticity of the aluminum bars, $E_1$ = $70~\text{GPa}$
- Modulus of elasticity of the brass bars, $E_2$ = $110~\text{GPa}$

$\bold{Required:}$

- Maximum bending stress in the aluminum bars, $\sigma_{\text{max (al)}}$
- Maximum bending stress in the brass bars, $\sigma_{\text{max (br)}}$

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