The pin$-$connected structure shown in the figure consists of a rigid bar ABCD and two aluminum alloy $E=70$GPa bars, each with a Part $4$

Determine the compatibility equation and rearrange it find the ratio of $F_1$ to $F_2,$ where $F_1$ is the magnitude of the internal force in

bar $(1)$ and $F_2$ is the magnitude of the internal force in bar $(2).$

$\frac{F_1}{F_2}=1$

eTextbook and Media

Attempts: unlimited

Part $5$

The allowable normal stress in bars $(1)$ and $(2)$ must be limited to $140$MPa. Determine the allowable internal force for each bar.

The allowable force is the same for both bars.

$F_{\text{a}\text{l}\text{l}\text{o}\text{w}}=kN$

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Attempts: unlimited

Part $6$

When the maximum load $P$ is applied, determine $F_1$ and $F_2,$ the magnitudes of the internal forces in bars $(1)$ and $(2),$ respectively.

$F_1=$

$F_2=kN$

Attempts: unlimited

Part $7$

Determine the magnitude of the maximum load $P$ that may be applied to the rigid bar at $D.$

$P=$

$kN$

eTextbook and Media Part $8$

When the maximum load $P$ is applied, determine the elongation of bar $(1).$

${}_1=,mm$

eTextbook and Media

Attempts: unlimited

Part $9$

When the maximum load $P$ is applied, determine the magnitude of the downvard deflection at $D.$ Since the magnitude is

required, enter a positive value.

$v_D=1,mm$

eTextbook and Media

cross$-$sectional area of $350m{m}^2.$ Bar $(1)$ has a length of $L_1=815mm$ and bar $(2)$ has a length of $L_2=980mm.$ Assume dimensions

of $a=480mm.b=390mm.$ and $c=590mm.$ If the allowable normal stress in bars $(1)$ and $(2)$ must be limited to $140$MPa.

determine:

$($a$)$ the maximum load $P$ that may be applied to the rigid bar at $D.$

$($b$)$ the deflection at $D$ for the load determined in part $($a$).$

Part $1$

Part $2$

Determine geometry$-$of$-$deformation relationships. Find the ratio of $u_A$ to $u_B,$ where $u_A$ is the magnitude of the horizontal

deflection of pin A and $u_B$ is the magnitude of the horizontal deflection of pin $B.$ Also, find the ratio of $u_A$ to $v_D.$ where $vD$ is the

magnitude of the vertical deflection of point $D.$

$\frac{u_A}{u_B}=$

$\frac{u_A}{v_D}=1$

Attempts: unlimited

Part $3$

What is the ratio of ${}_1$ to ${}_2,$ where ${}_1$ is the magnitude of the deformation of bar $(1)$ and ${}_2$ is the magnitude of the deformation

of bar $(2)?$

$\frac{{}_1}{{}_2}=$