Part B $-$ Reaction with a known load

Consider a new structure, where the thickness of the bar is reduced to $1$ in $.$ from $C$ to $B($it is still square$)($Figure $2)$ and $x=6\mathrm{.}6ft.$ If the applied load is $F=105$kip

$,$ then what is the reaction at $A?$ Let a positive reaction act to the right. The total length is still $10$ ft

Express your answer with appropriate units to three significant figures.

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Learning Goal:

To solve for forces in statically indeterminate bars with axial loads

When the number of reaction forces is greater than the number of

equilibrium equations, the system is statically indeterminate.

Solving for the reactions requires some additional equations. These

additional equations come from considering compatibility

relationships $($i$.$e$.,$ continuity of displacements and relationships

between displacements and loads$).$

For an axially loaded member, the compatibility relationship for the

deflections can be written by setting the total relative axial

displacement between the ends of the member to a known value.

The load$-$displacement relationship $={\displaystyle \underset{?}{\overset{?}{}}}\frac{NL}{AE}$ gives another

equation for the deflections. Once the internal normal force of each

segment is written in terms of the end reactions and applied loads,

there is enough information to solve for the reactions

Figure

$2$ of $2$