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Question

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The 500-lb beam is supported at A and B when it is subjected to

a force of 1000 lb as shown. If the pin support at A suddenly

fails, determine the beam’s initial angular acceleration and the

force of the roller support on the beam. For the calculation,

assume that the beam is a slender rod so that its thickness can be

neglected. (Ans: 23.4 rad/s2, 9.62 lb)

Explanation / Answer

1 lb = 4.448 N , 1 ft = 0.3048 m mass of beam = 500*4.448/9.8 = 226.939 kg torque(about the roller end) = I(about the roller end) * angular acceleration => (1000*4.448)*(3/5)*8 *0.3048 + (500*4.448)*3* 0.3048= [{226.939*(10*0.3048)^2/12} +226.939*(3*0.3048)^2]*angular acceleration => 8541.226 = (175.69 +189.75)*angular acceleration => angular acceleration = 23.37 rad/s^2

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