Examples on Equilibrium Problem1 Calculate the tension T

Examples on Equilibrium

Problem-1 Calculate the tension T in the cable which supports the 500 -kg mass with the pulley arrangement shown. Each pulley is free to rotate about its bearing, and the weights of all parts are small compared with the load. Find the magnitude of the total force on the bearing of pulley C. 11/9/2020 2

Solution 11/9/2020 3

Problem-2 A cantilever beam OABC is subjected to the forces and moment as shown. (i) Draw free body diagram of the cantilever beam OABC. (ii) Compute the reactions at the fixed support point O. Assume beam is weightless and its thickness is negligible compared to other dimensions. Note the two pulleys, shown in the figure, are smooth. 11/9/2020 4

Solution (i) Free body diagram of the cantilever beam (ii) Reactions at the fixed support O November 9, 2020 5

Problem-3 Determine the force P required to maintain the 200 kg weight in the position. The diameter of the pulley at B is negligible. Given, θ = 300 11/9/2020 . 6

Solution T 150 P 600 200× 9. 81 Free Body Diagram 11/9/2020 7

Problem-4 The uniform concrete slab shown in edge view has a mass of 25000 kg and is being hoisted slowly into a vertical position by the tension P in the hoisting cable. For the position where θ = 600 calculate the force T in the horizontal anchor cable. Assume support A is a roller. 11/9/2020 8

Solution Free Body Diagram of Slab 11/9/2020 9

Sample Problem 5 A fixed crane has a mass of 1000 kg and is used to lift a 2400 kg crate. It is held in place by a pin at A and a rocker at B. The center of gravity of the crane is located at G. Determine the components of the reactions at A and B.

Sample Problem 5 -Continued y • Determine the reaction at B by solving the equation for the sum of the moments of all forces about A. x • Draw the free-body diagram • Determine the reactions at A by solving the equations for the sum of all horizontal forces and all vertical forces.

Sample Problem 6 The frame supports part of the roof of a small building. The tension in the cable is 150 k. N. Determine the reaction forces at the fixed end E.

Sample Problem 6 -Continued • Solve 3 equilibrium equations for the reaction force components and couple. • Draw a free-body diagram for the frame and the cable.

Sample Problem 4

Sample Problem 4 -Continued