HW11 - Homework 11 PDF

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Homework 11...

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530.215 Mechanical Based Design HW#11 Assigned 4/26/2018 Due 5/3/2018 1. Consider a beam with length of 2d and depth of d shown in the figure below. We can use 2 CST (constant strain triangle) elements to discretize the beam, with the lower element 123 and the upper element 341. The nodes 1 and 4 are both fixed at the wall. Now a force F is acting on the node 3 and pushes to the right. Assume that Young’s Modulus and the Poisson’s ratio of the beam are E and ν and the beam thickness is t (thickness orthogonal to the paper sheet direction). 4

3

F

d

1

2d

2

a. Form the element stiffness matrix for element 123 in terms of d, E and ν. Now use the material constants E and ν for 4340 steel, the beam depth d = 100 mm, the thickness of the beam t = 10 mm, and the force F = 120 kN. b. Compute the element stiffness matrices [Ke] for both elements 123 and 341. c. Using global assembly, form the global stiffness matrix and apply the boundary conditions to the global stiffness matrix [K]. d. Calculate the approximate FEM displacements (u, v) for every node.

e. Compare your results with what you would expect to find from an analytical solution. (State the assumptions you have made for your analytical solution.) f. What if the load F is acting on both nodes 2 and 3 toward to the right? Calculate the nodal displacements based on the same beam and element configurations and compare your results with your analytical solution. (Again, state the assumptions that you have made for this solution.)

2. The figure shows a pair of shaft-mounted spur gears having a diametral pitch of 5 teeth/in with an18-tooth 20◦ pinion driving a 45-tooth gear. The horsepower input is 32 maximum at 1800 rev/min. Find the direction and magnitude of the maximum forces acting on bearings A, B, C, and D....