■ Data input

Since the sum of the moments (clockwise +) at points A and B is zero, the following is established.

∑MA = 0 = L1*P1 + (L1+L2+L3)*P2 + (L1+L2+L3+L4)*VC + H2*HC

VC and HC represent the vertical and horizontal reactions at point C, respectively.

From the hinge B to the hinge C,

∑MB = 0 = L3*P2 + (L3+L4)*VC + (H1+H2)*HC

In the second equation,

HC = -(L3*P2 + (L3+L4)*VC)/(H1+H2)

Thus, solving by substituting this into the first equation,

L1*P1 + (L1+L2+L3)*P2 + (L1+L2+L3+L4)*VC - H2*(L3*P2 + (L3+L4)*VC)/(H1+H2) = 0

Let H=H1+2 and L=L1+L2+L3+L4, then,

L*Vc - H2*(L3+L4)*VC)/H = H2*L3*P2/H - L1*P1 - (L1+L2+L3)*P2

(L-H2*(L3+L4)/H)*VC = H2*L3*P2/H - L1*P1 - (L1+L2+L3)*P2

※ Direction of VC ( + : ↓, - :↑ )

※ Direction of HC ( + : ←, - : →)

지점 A 에서의 수직반력과 수평반력을 VA, HA 라 하면, ∑수직력 = 0 이므로,

※ Direction of VA ( + : ↓, - :↑ )

Since ∑(horizontal forces) = 0, then,