Calculate the Tension Force in Sling

The rigging configuration shown below will be used to lift a bridge girder using a 200-ton capacity luffing jib crane onto the foundation abutment.  The tension force (lb.) in Sling A is most nearly:

Solution:

By inspection, the center of gravity of the load is offset causing an eccentric load condition.  The reaction load is heavier on the left side (R_L).  The distribution of the 40,000-lbs load at RL is:   (40-ft ÷ 60-ft) (40,000-lbs) = 26,667-lbs.  The reaction force R_L must be adjusted for the slope of the slings.  The vector force length of Sling A is √ 60² + 20² = 63.25-ft.  The force in Sling A is (63.25-ft ÷ 60-ft) (26,667-lbs) = 28,111-lbs