Question

Analytical solutions using force components. Check graphically. One end of a timber roof truss is supported on a brick wall but not securely fastened. The reaction of the brick wall can therefore be only vertical. Assuming that the maximum capacity of either the inclined or horizontal member is 7 kN, determine the maximum magnitudes of F 1 and F 2 so that their resultant is vertical through the brick wall.

CHANGE 7 TO 15lbs

Answer 1

Clearly F₂ can be resolved in two componet such that

$F_{2}\cos 25^{0} = F_{1}$

and

$F_{2}\sin 25^{0} = 15 lbs = 66.7 kN$

$F_{2} = \frac{66.7 kN}{\sin 25^{0}} = 157.83 kN$

$F_{1} = 157.83 kN\cos 25^{0} = 143.04 kN$