Answer to Question #221600 in Mechanical Engineering for Connor

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

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