Question 5.40: The jib crane is pin connected at A and supported by a smoot...

Equations of Equilibrium:

\hookrightarrow + \Sigma M_A=0 ; \quad N_B(12)-5 x=0 \quad N_B=0.4167 x                  (1)

+↑ \Sigma F_y=0 ; \quad A_y-5=0 \quad A_y=5.00  \mathrm{kip}                (2)

\overset{+}{→} \Sigma F_x=0 ; \quad A_x-0.4167 x=0 \quad A_x=0.4167 x                (3)

By observation, the maximum support reactions occur when

x = 10 ft

With x = 10 ft, from Eqs. (1), (2) and (3), the maximum support reactions are

A_x=N_B=4.17  \mathrm{kip} \quad A_y=5.00  \mathrm{kip}

By observation, the minimum support reactions occur when

x = 4 ft

With x = 4 ft, from Eqs. (1), (2) and (3), the minimum support reactions are

A_x=N_B=1.67  \mathrm{kip} \quad A_y=5.00  \mathrm{kip}