Replace the loading by an equivalent resultant force and cou

Replace the loading by an equivalent resultant force and couple moment acting at point O. Suppose that w_1 = 7.5 kN/m and w_2 = 5 kN/m. (Figure 1) Determine the equivalent resultant force. Express your answer to three significant figures and include the appropriate units. Enter positive value if the force is upward and negative value if the force is downward. Determine the couple moment. Express your answer to three significant figures and include the appropriate units. Enter positive value if the moment is counterclockwise and negative value if the moment is clockwise.

Solution

F_R = 1/2 x 7.5 kN/m x 1.5 m + 1/2 x 5kN/m x 0.75 m + 5 kN/m x 0.75 m = 11.25 kN

M_R = -[1/2 x 7.5 kN/m x 1.5 m x 0.75 m + 1/2 x 5kN/m x 0.75 m x 0.375 m + 5 kN/m x 0.75 m x 0.375 m] = - 6.328 kN-m