Calculate: Vertical reaction at A. Vertical Reaction at B. The shear and moment
ID: 1713813 • Letter: C
Question
Calculate:
Vertical reaction at A.
Vertical Reaction at B.
The shear and moment equations at each section across the beam.
The magnitude of the maximum shear force.
The maximum shear stress.
The location of the maximum bending moment.
The magnitude of the maximum bending moment.
The maximum tensile stress.
The 1.5L feet long, 0.5 feet high, and 0.25 feet wide beam is subjected to two concentrated loads and two distributed loads. Calculate q lb/ft Qlb 0.5q lb/ qIb/ft 0.5Q lb ME ft.lb 8 Lft 0.5L ft COLLAPSE IMAGES -25 ft q = 190 lbft Q-840 lb ME = 870 lb.ftExplanation / Answer
The reactions forces can be calculated by considering equilibrium equations:
Vertical reaction force at B can be determined by considering moment equilibrium at support A
0.5*0.5L*q*(2/3)*(0.5L) + (0.5q*0.5L*0.75L)+[0.5*0.5L*0.5q*[0.5L+(2/3)*0.5L]]+(Q*0.75L)+(0.5Q*1.25L)-ME-RBL=0
Substituting values of q,Q,L and ME,we get
0.5*0.5*25*190*(2/3)*(0.5*25) + (0.5*190*0.5*25*0.75*25)+[0.5*0.5*25*0.5*190*[0.5*25+(2/3)*0.5*25]]+(840*0.75*25)+(0.5*840*1.25*25)-870-RB*25=0
RB=2901.45 lb(vertically upwards)
RA =(0.5*0.5*25*190)+[0.5*0.5*25*(0.5*190+190)]+840+0.5*840-2901.45=1327.3 lb(vertically upwards)
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