Determine the resultant of the loads:
A system of loads acting on beam is shown in the figure given below. Determine the resultant of the loads. Sol.: Let R be resultant of given system. And ∑H and ∑V be the horizontal and vertical component of resultant. And resultant makes an angle of θ with the horizontal.
Resolving all the forces horizontally
∑H = 20 cos 60º
∑H = 10KN ...(i)
By resolving all the forces vertically
∑V = 20 + 30 + 20 sin 60º
∑V = 67.32KN ...(ii)
Since, ∑R = √(∑H)^{2} + (∑V)^{2 }√(10)^{2 }+ (67.32)^{2}
R = 68.05KN .......ANS
Let θ= Angle makes by the resultant
tanθ= ∑V/∑H = 67.32/10 = 81.55º For position of the resultant
Let, d = Distance between Point A and the line of action of the resultant force. Now apply varignon's theorem
R.d = 20 × 2 + 30 × 4 + 20 sin 30º × 7
68.05.d = 281.2
d = 4.132 m .......ANS