Please help Learning Goal: Part C $-$ Calculate the deflection

What is the deflection of the end of the rod, $D?$ Let a positive deflection be to the right.

Express your answer with appropriate units to three significant figures.

Figure

$1$ of $1$

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${}_D=$

$||$

To calculate the elastic deflection in an axially

loaded member

For a bar subject to axial loading, the change in

length, or deflection, between two points A and $B$

is $={\displaystyle \underset{0}{\overset{L}{}}}\frac{N(x)dx}{A(x)E(x)},$ where $N$ is the internal

normal force, $A$ is the cross$-$sectional area, $E$ is

the modulus of elasticity of the material, $L$ is the

original length of the bar, and $x$ is the position

along the bar. This equation applies as long as the

response is linear elastic and the cross section

does not change too suddenly.

In the simpler case of a constant cross section,

homogenous material, and constant axial load, the

integral can be evaluated to give $=\frac{NL}{AE}.$ This

shows that the deflection is linear with respect to

the internal normal force and the length of the bar.

In some situations, the bar can be divided into

multiple segments where each one has uniform

internal loading and properties. Then the total

deflection can be written as a sum of the deflections

for each part, $={\displaystyle \underset{?}{\overset{?}{}}}\frac{NL}{AE}.$

The circular rod shown $($Figure $1)$ has dimensions $d_1=6\mathrm{.}6cm,L_1=6m,d_2=3\mathrm{.}2cm,$ and $L_2=5m$ with applied loads $F_1=150kN$ and $F_2=55kN.$ The modulus of elasticity is $E=80$GPa. Use the following steps to find

the deflection at point $D.$ Point $B$ is halfway between points A and $C.$

Part A $-$ Reaction force

What is the reaction force at $A?$ Let a positive reaction force be to the right.

Express your answer with appropriate units to three significant figures.

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Part B $-$ Segment the rod

For the given rod, which segments must, at a minimum, be considered in order to use $={\displaystyle \underset{?}{\overset{?}{}}}\frac{NL}{AE}$ to calculate the deflection at $D?$

Check all that apply.

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$CD$

$BC$

$AB$

$BD$

$AC$

$AD$