Question

Calculate the forces in members BE and BD of the loaded truss. The forces are positive if in tension, negative if in compression. Assume F = 4.4 kN, a = 2.3 m, b = 3 m, c = 2 m, and d = 2 m.

Answer 1

In order to find BE we will resolve force at point E

$\sum F_y=0\\ F_{BE}=0$

Force in member BE = 0

In order to find force in BD, we can resolve force along a vertical direction at point B

$\sum F_y=0\\ F_{BE}+F_{AB} cos \theta+F_{BD} cos \theta=0\\ Since \space F_{BE} =0\\ F_{AB} cos \theta = -F_{BD} cos \theta \\ F_{AB}=-F_{BD}-------(1)$

Now we need to find F_AB

At point A resolving along the vertical direction

$F= F_{AB}sin \theta\\ F= F_{AB} \frac{3}{\sqrt{13}}\\ F_{AB}= \frac{\sqrt{13}}{3}(4.4)\\ F= 5.28814kN (Tension)$

Substituting in equation 1

$F_{AB}= -F_{BD}\\ 5.28814= -F_{BD}\\ F_{BD}=-5.28814(Compression)$