Author: admin

1. Determine the stresses in the member with a re-entrant corner as shown in Figure P7–17. At what location are the principal stresses largest? Let E = 30
10
6
psi and n = 0:25. Use plane strain conditions.
2. Determine the stresses in the soil mass subjected to the strip footing load shown in Figure P7–18. Use a width of 2D and depth of D, where D is 3, 4, 6, 8, and 10 ft.
Plot the maximum stress contours on your finite element model for each case. Compare your results. Comment regarding your observations on modeling infinite media. Let E = 30,000 psi and n = 0:30. Use plane strain conditions.

For the tooth implant subjected to loads shown in Figure
P7–19, determine the maximum principal stresses. Let E = 1:6
10
6
psi and n = 0:3 for the dental restorative implant material (cross-hatched),
and let E = 1
10
6
psi and n = 0:35 for
the bony material. Let X
0:05 in., 0.1 in., 0.2
in., 0.3 in., and 0.5 in., where X represents the various depths of the implant
beneath the bony surface. Rectangular elements are used in the finite element
model shown in Figure P7–19. Assume the thickness of each element to be t =
0:25 in.

Determine the middepth deflection at the free end and the
maximum principal stresses and their location for the beam subjected to the
shear load variation shown in Figure P7–20. Do this using 64 rectangular
elements all of size 12 in.
in.; then all of size 6 in.
1
in.; then all of size 3 in.
2 in. Then use 60
rectangular elements all of size 2.4 in.
in.; then all of size 4.8 in.
in. Compare the free-end deflections
and the maximum principal stresses in each case to the exact solution. Let E =
30
10
6
psi, n = 0:3, and t =
1 in. Comment on the accuracy of both displacements and stresses.

1. Determine the stresses in the shear wall shown in Figure P7–21.
At what location are the principal stresses largest? Let E = 21 GPa, n = 0:25,
twall = 0:10 m, and tbeam = 0:20 m. Use 0.1 m radii at the re-entrant corners.
2. Determine the stresses in the plates with the round and
square holes subjected to the tensile stresses shown in Figure P7–22. Compare
the largest principal stresses for each plate. Let E = 210 GPa, n = 0:25, and t
= 5 mm.

1. For the concrete overpass structure shown in Figure
P7–23, determine the maximum principal stresses and their locations. Assume
plane strain conditions. Let E = 3:0
10
6
psi and n = 0:30.
2. For the steel culvert shown in Figure P7–24 on the next
page, determine the maximum principal stresses and their locations and the
largest displacement and its location. Let E
steel
= 210 GPa and let
n = 0:30.

1. For the tensile member shown in Figure P7–25 on the next page with two holes, determine the maximum principal stresses and their locations. Let E = 210 GPa, n = 0:25, and t = 10 mm. Then let E = 70 GPa and n = 0:30. Compare your results. Use 20 kN spread uniformly over the right side.
2. For the plate shown in Figure P7–26 on the next page, determine the maximum principal stresses and their locations. Let E = 210 GPa and v = 0:25.

1. For the concrete dam shown subjected to water pressure in
Figure P7–27, determine the principal stresses. Let E = 3:5
10
6
psi and n = 0:15. Assume plane strain conditions. Perform the analysis for
self-weight and then for hydrostatic (water) pressure against the dam vertical
face as shown.
2. Determine the stresses in the wrench shown in Figure
P7–28 on the next page. Let E = 200 GPa and n = 0:25, and assume uniform
thickness t = 10 mm.

1. Determine the principal stresses in the blade implant and
the bony material shown in Figure P7–29 on page 431. Let E
blade
= 20
GPa, v
blade
= 0:30, E
bone
= 12 GPa, and v
bone
= 0:35. Assume plane stress conditions with t = 5 mm.
2. For the 0.5 in. thick canopy hook shown in Figure P7–31
on page 432, used to hold down an aircraft canopy, determine the maximum von
Mises stress and maximum deflection. The hook is subjected to a concentrated
upward load of 22,400 lb as shown. Assume boundary conditions of fixed supports
over the lower half of the inside hole diameter. The hook is made from AISI
4130 steel, quenched and tempered at 400F. (This problem is compliments of Mr.
Steven Miller.)