## Related questions with answers

The simply supported beam shown in Figure P8.48a/49a carries a uniformly distributed load $w$ on overhang $B C$. The beam is constructed of a Southern pine [ $E=12 \mathrm{GPa}]$ timber that is reinforced on its upper surface by a steel $[E=200 \mathrm{GPa}$ ] plate (Figure P8.48bl $49 b$ ). The beam spans are $L=4 \mathrm{~m}$ and $a=1.25 \mathrm{~m}$. The wood beam has dimensions of $b_w=150 \mathrm{~mm}$ and $d_w=280 \mathrm{~mm}$. The steel plate dimensions are $b_s=230 \mathrm{~mm}$ and $t_s=6 \mathrm{~mm}$. Assume that the allowable bending stresses of the wood and the steel are $9 \mathrm{MPa}$ and $165 \mathrm{MPa}$, respectively. Determine the largest acceptable magnitude for distributed load $w$. (You may neglect the weight of the beam in your calculations.)

Solution

Verified$\bold{Given:}$

- Modulus of elasticity of the Southern pine timber, $E_{\text{w}}$ = $12~\text{GPa}$
- Modulus of elasticity of the steel plate, $E_{\text{st}}$ = $200~\text{GPa}$
- Length of segment $AB$, $L_{AB}$ = $4~\text{m}$
- Length of segment $BC$, $L_{BC}$ = $1.25~\text{m}$
- Base of the wooden beam, $b_{\text{w}}$ = $150~\text{mm}$
- Depth of the wooden beam, $d_{\text{w}}$ = $280~\text{mm}$
- Base of the steel plate, $b_{\text{st}}$ = $230~\text{mm}$
- Thickness of the steel plate, $t_{\text{st}}$ = $6~\text{mm}$
- Allowable bending stress of the wood, $\sigma_{\text{allow (w)}}$ = $9~\text{MPa}$
- Allowable bending stress of the steel, $\sigma_{\text{allow (st)}}$ = $165~\text{MPa}$

$\bold{Required:}$

- Neglecting the weight of the beam, determine the largest acceptable magnitude for distributed load $w$.

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