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Two parts are connected with a bolt which is preloaded to an initial tension of 1200lb. The stiffness of the clamped joint is 7.6 times as big as the bolt stiffness. An external force acting to separate the joint varies from 0 to 7600lb. Draw a graph (plotting bolt force and joint force vs, time) for 3 or 4 fluctuations of the external load.

User Srgerg
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Given:Initial tension of bolt=1200 lbStiffness of clamped joint= 7.6 times the bolt stiffnessExternal force acting on joint = 0 to 7600lbTo draw a graph of bolt force and joint force vs time for 3 or 4 fluctuations of the external load.For a bolt which is preloaded, the bolt force Fb is given by:Fb = Ks x δbwhere Ks is the bolt stiffness and δb is the displacement of the bolt.The stiffness of the clamped joint is given as:Kj = 7.6 KsThe force in the joint is given as:Fj = Kj x δjwhere Kj is the joint stiffness and δj is the joint displacement.δj = δb / (1 + α)Where α is the ratio of the joint stiffness to the bolt stiffness.α = Kj / Ks = 7.6From the above equations, we can say that the bolt force Fb and the joint force Fj are related as:Fb = (Ks / Kj) x Fj = (1 / 7.6) Fj = 0.131 FjThe external load on the joint varies from 0 to 7600lb. Let's plot the graphs for Fb and Fj vs time for 3 or 4 fluctuations of external load.For the maximum external load of 7600 lb,Fj = 7600 lbFb = 0.131 Fj = 994.6 lbAt minimum external load, Fj = 0lbFb = 0.131 Fj = 0lbLet's assume that the external load changes linearly with time. Then the variation of external load with time is given by:Fext = mtwhere m is the rate of change of external load.For 3 or 4 fluctuations, we can assume the external load varies from 0 to 7600lb and back to 0 in 2 seconds. So we have m = 7600 / 2 = 3800 lb/sec.On substituting the values of Fj and Fb in the above equations, we get:Fj = 3800t lbFb = 0.131 Fj = 497.8t lbThe graph of Fj and Fb vs time is as shown below:Graph of Fj vs time:Graph of Fb vs time:
User Dineshkumar
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