Since it is assumed the pin at B will fail first, the force at B is set at 4.909 kip with an unknown angle of θ, as shown at the left. Notice the x-y coordinates are orientated in the handbrake direction. There are three unknowns, F, T and θ. Summing all forces in x direction, ΣF_{x} = 0, gives
F cos30 = 4.909 cosθ
F = 5.669 cosθ
Summing all forces in y direction, ΣF_{y} = 0, gives
T = 4.909 sinθ - F sin30
T = 4.909 sinθ - 0.5 F
Summing all moments about B, ΣM_{B} = 0, gives
(T)(12) = (Fsin30)(8)
T = 0.3333 F
Combining last two equations,
0.3333 F = 4,909 sinθ - 0.5 F
F = 5.891 sinθ
Replacing F in the first equation,
5.669 cosθ = 5.891 sinθ
θ = tan^{-1}(5.669 / 5.891)
= 43.90°
Calculating for axial force,
F = 5,891 sin43.90
= 4085 lb > F_{max}
Hence, the assumption for failure is not correct and it is obvious that the failure will occur due to axial stress. |