A horizontal bar is attached to a wall. When a force of $1$ kN is applied at point $A($Figure $1),$ the deflection at point $A$ is ${}_{AA}=0\mathrm{.}46mm.$ When a $1$ kN force is applied at point $B($Figure $2),$ the Part C $-$ Required load

If a load of $5\mathrm{.}8$ kN is applied to the right at point $B,$ then what load magnitude must be applied to the left at point $A$ to make the length of the bar remain unchanged?

Express your answer in kN to three significant figures.

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Figure

$1$ of $2$

$\sqrt[\phantom{2}]{}$

$\sqrt[7]{}$

$A$

vec

$?$

$F_A=$

kN

Learning Goal:

To use the principle of superposition to relate external axial loads on a bar to axial

deflections.

Under certain conditions, the effect of complicated loads can be calculated by

combining the effects of simple component loads. This is called the principle of

superposition. This method can only be used when the internal axial force $N$ in a

body is linearly related to the displacement or external loading, and the deflections

are small enough that the body's geometry does not change significantly.

If a complicated load can be expressed as a linear combination of the simpler

loads, then the stress or displacement at a point will be the same linear

combination of the corresponding responses in the simpler loads.

A horizontal bar is attached to a wall. When a force of $1$ kN is applied at point $A($Figure $1),$ the deflection at point $A$ is ${}_{AA}=0\mathrm{.}46mm.$ When a $1$ kN force is applied at point $B($Figure $2),$ the

deflection at point $A$ is ${}_{AB}=0\mathrm{.}2mm.($A given deformation due to a unit load is known as a flexibility factor.$)$

Part A $-$ Larger load

What is the change in the length of the bar if there is a single load of $6\mathrm{.}8$ kN applied to the right at point $A?$ Use a positive value to indicate an increase in length.

Express your answer in mm to three significant figures.

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Part B $-$ Combined loads

What is the change in the length of the bar if a load of $3\mathrm{.}6$ kN is applied to the left at A and a load of $10\mathrm{.}2$ kN is applied to the right at $B?$ Use a positive value to indicate an increase in length.

Express your answer in mm to three significant figures.

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