7 2 + 2 4 + 2 + 3 5

Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. For the shape below, assume the following dimensions: a = 175 mm b = 220 mm d = 300 mm t = 23 mm The centroid of this shape is located 71.762 mm to the right of point H shown in the figure. What is the moment of inertia ly about the y centroidal axis for this shape? H Answer: ly M b 2t mm4

This is an exercise to illustrate the effects of mesh refinement on a 1-d rod. To estimate the self-weight elongation (8) of the tapered conical rod shown in the figure. The diameter varies linearly from Do at the bottom to aDo at the top, where 0.1 < E Young's Modulus y Unit weight (Diameter at top) 8 clongation D (Diameter at bottom) a<0.5. Solve for L= 5m, y= unit weight of steel, E= young's modulus of steel, Do=3m and a=0.3. Solve the problem at least four times using an increasing number of rod elements (nels=2, 4, 6, 8). Make appropriate assumptions about how to deal with the changing cross-sectional area and self-weight loading along the length of the rod. A plot of the dimensionless tip deflection SE/yL? vs. number of elements (nels) used in the discretization to show convergence on the exact solu- tions of

Page 6 Question 6 A cantilever beam AB of length L is subjected to a uniformly distributed load w and simply supported at the end A with a spring. Assume that El is constant and stiffness of the spring is k. (a) Determine the reaction forces at the end B of the beam shown in Figure Q6 by using the virtual-work method. (b) Describe the procedure to determine the deflection at the middle of the beam in 100 words (without actually solving the problem). O DEN5102 (2022) W L Figure Q6 B