Learning Goal:
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:
$\sum F_x = 0$
$\sum F_y = 0$
$\sum M_O = 0$
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 $P_1 = 504$ lb and $P_2 = 198$ lb and has the dimension $a = 11.0$ ft
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 pounds to three significant figures.
$F_{BC} = $ lbs
