The diving board consists of a very strong wall with a suppo

The diving board consists of a very strong wall with a support pipe embedded into it with very strong concrete. The pipe is welded together with a diving board that has a hollow, rectangular cross section. BOTH THE PIPE AND THE BOARD ARE FABRICATED FROM AISI 1020 HR CARBON STEEL. The arrows in the views on the right represent the forces from each of the animal’s feet as she stands at the end of the board, ready to dive in. EACH OF THESE FORCES HAS A MAGNITUDE OF 1.000 kip.

Problem 1) Look at each of these points and think about the stresses that are generated at that point. Then, for each of

the points a-h write down the stress types that you believe are generated. Select the stress types from this list:

normal stress due to bending

normal stress due to axial loading

normal circumferential stress

shear stress due to direct shear

shear stress due to torsion

normal circumferential stress

shear stress due to bending

Problem 2) For each of the points a-h, do the following: (NOTE: Do all of the steps for a particular point in order, then

move on to the next point. Also, please present your work for each point in alphabetical order.)

1         Calculate the values of all of the stresses that you identified at the point in Problem 1 (NOTE: You may assume that the

2         weight of the board and pipe are small compared with that of the animal)

3         Draw a stress cube at the point. Show all non-zero stresses

4         Draw 3-D Mohr’s circle for the point

5         Find the values of the principle stresses and the maximum shear stress

6         Calculate the Von Mises’ stress at the point using this equation:

7         Calculate a factor of safety against static yielding at the point

Problem 3) Suppose a series of progressively heavier animals walks out onto the end of the board and dives off. Each animal stands at the same spot as the first just before diving off. What is the weight of the animal that finally causes static yielding of the board? At which point will the board yield? How do you know?

30.00 NOTE EACH FORCE ARROW I KIP H 32.00 56.00 40.00 4.00 30.00 ALL DIMENSIONS IN INCHES

Solution

3. Given

the weight is dependent on the mass of the animal.

at the end point

as the animal are driven off when they are at the end.