lo assessment the structural strength of a 300 lb horizontal beam of lensns manu

Question

lo assessment the structural strength of a 300 lb horizontal beam of lensns manually usk to his th 10 feet, a standing on the beam shown in the figure below, applies a force ot a tly hands to transmit a force to the cable that connects the beam hand. trough three pulleys back to his. and vertical forces a) If the beam is pinned at O and has a fulcrum at A at pin support O and the magnitude and angle of the resultant torce a b) Determine also the roller support reaction at point A. magnitud 4' 2 6 2 Answer:

Explanation / Answer

mass of beam, m = 300 lb

length of beam, l = 10 ft

force applied, F = 150 lbs

a. let horizontal and vertical forces at the pin joint be H and V

let the normal reaction at the rolling supprt be R

the mass of the man is not to be considered

let teh roper make an angle theta with the horizontal

hence from force balance

F*cos(theta) = H

F(1 - sin(theta)) + F + 300 = V + R

from moment balance about the point O

F(1 - sin(theta))10 + F*8 + 300*5 = R*2

R = 150(9 - 5sin(theta)) + 150*5 = 2100 - 750sin(theta) lb

V = 2*150 - 150sin(theta) + 300 - 2100 + 750sin(theta) = -1500 + 500 sin(theta) lb

H = 150cos(theta)

hence H = 150cos(theta) lbs

V = 500sin(theta) - 1500 lbs

b. R = 2100 - 750*sin(theta) lbs

here theta is the angle the rope makes with the horizontal

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