A timber $[E=11$GPa $]$ beam is loaded and supported as shown The cross section of the timber beam is $b=110-mm.$ wide and $h=$

$290-$mm deep. The beam is supported at $B$ by a $11-$mm$-$diameter steel $[E=210$GPa $]$ rod, which has no load before the distributed

load is applied to the beam. After a distributed load of $w=5k\frac{N}{m}$ is applied to the beam, determine:

$($a$)$ the force carried by the steel rod.

$($b$)$ the maximum bending stress in the timber beam.

$($c$)$ the deflection of the beam at $B.$

Assume $L=6\mathrm{.}0m,L_1=7\mathrm{.}0m$

Treat the reaction force from the rod $(1)$ as the redundant, leaving a simply supported beam as the released beam. Determine the

deflection of the wood beam VBu at $B$ due to the distributed load $w=5k\frac{N}{m}.$ An upward deflection is positive, downward is

negative.

Anawer: $v_{Bw}=$

$mm.$

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Part $2$

Determine the deflection VBF of the wood beam due to the unknown upward force $F_1$ the rad $(1)$ exerts on the beam.

Assume $L=6\mathrm{.}0m.$

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Part $3$

Determine the elongation ${}_1$ of the rad $(1)$ due to the farce $F_1.$ Use positive if the rod stretches and negative if it shortens.

Answer: ${}_1=1|$

$m\frac{m}{k}\frac{N}{{?}^{**}}{F}_1$

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Part $4$

Use the compatibility of deflections at point $B$ to solve for the force $F_1$

Anawer: $F_1$

$kN.$

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Part $5$

Draw a shear force and bending moment diagram on paper for the simply supported beam subjected to the loading $w=5k\frac{N}{m}$

and the calculated force $F_1.$ Determine the maximum bending moment in the beam.

Answer: $M_{\text{m}\text{a}\text{x}}=$

$iN-m$