Part A

Learning Goal:

To apply the method of sections to find the forces in specific members of a truss.

The method of sections is used to find the force in a specific member of a truss and is based on the principle that, if a body is in equilibrium, then every part of that body is also in equilibrium. When applied, the method of sections "cuts" or sections the members of a truss and exposes their internal forces. To find the unknown internal member forces, the free$-$body diagram of a section is drawn and the equations of equilibrium are applied:

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_O=0$

Because there are only three independent equilibrium equations, section cuts should be made such that there are not more than three members that have unknown forces.

As shown, a truss is loaded by the forces $P_1=2\mathrm{.}27kN$ and $P_2=0\mathrm{.}950kN$ and has the dimension $a=3\mathrm{.}40m.$

Determine $F_{BC},$ the magnitude of the force in member $BC,$ using the method of sections. Assume for your calculations that each member is in tension, and include in your response the sign of each force that you obtain by applying this assumption

Express your answer numerically in kilonewtons to three significant figures.

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