Consider the beam with an overhang shown in the figure 18 ft

Consider the beam with an overhang shown in the figure 18 ft lb I380 -260 10 ft 10 ft (a) Determine the shear force V and bending moment M at a cross section located 18 ft from the left-hand end A. Round your answers to the nearest whole. lb lb-ft (b) Find the required magnitude of load intensity q acting on the right half of member BC that will result in a zero shear force on the cross section 18 ft from A. Round your answer to the nearest whole number lb

Solution

a)Let us determine the reaction forces at supports

let us determine reaction at support B by considering moment equilibrium at A

380*10*5 - 260*6*29 - 20*R_B=0

R_B = 1312 lb(upwards)

Shear force at the section 18 ft from A=(260*6)+1312=2872 lb

Bending moment at the section = 260*6*11 +1312*2 = 19784 lb-ft (sagging)

b) Let the required load intensity be q(vertically upwards)

For the shear force at the section 18 ft away to be zero, q has to be such that reaction at B = 6*q(vertically downwards)

Also, this has to satisfy moment equilibrium at suport A

q*6*29-6*q*20-380*10*5=0

q=351.85 lb/ft (upwards)