Category: Writing

1. Evaluate the nodal forces used to replace the linearly
varying surface traction shown in Figure P9–2. Hint: Use Eq. (9.1.34).
2. For an element of an axisymmetric body rotating with a
constant angular velocity o = 20 rpm as shown in Figure P9–3, evaluate the
body-force matrix. The coordinates of the element are shown in the figure. Let
the weight density p
w
be 0.283 lb/in
3
.

For the linear-strain elements shown in Figure P8–5,
determine the strains e
x
;e
y
, and g
xy
. Evaluate
the stresses s
x
; s
y
, and t
xy
at the centroids.
The coordinates of the nodes are shown in units of inches. Let E = 30 10
6
psi, n = 0:25, and t = 0:25 in. for both elements. Assume plane stress
conditions apply. The nodal displacements are given as

1. For the element of Figure 8–3 (shown again as Figure
P8–3) subjected to the uniform pressure shown acting over the vertical side,
determine the nodal force replacement system using Eq. (6.3.7). Assume an
element thickness of t.
2. For the element of Figure 8–3 (shown as Figure P8–4)
subjected to the linearly varying line load shown acting over the vertical
side, determine the nodal force replacement system using Eq. (6.3.7). Compare
this result to that of Problem 6.11. Are these results expected? Explain.

1. Evaluate the shape functions given by Eq. (8.2.6). Sketch
the variation of each function over the surface of the triangular element shown
in Figure 8–3.
2. Express the strains e
x
;e
y
, and g
xy
for the element of Figure 8–3 by using the results given in Section 8.2.
Evaluate these strains at the centroid of the element; then evaluate the
stresses at the centroid in terms of E and n. Assume plane stress conditions
apply

For the tapered solid circular shaft shown in Figure P9–24,
a semicircular groove has been machined into the side. The shaft is made of a
hot rolled 1040 steel alloy with yield strength of 71,000 psi. The shaft is
subjected to a uniform axial pressure of 4000 psi. Determine the maximum
principal stresses and von Mises stresses at the fillet and at the semicircular
groove. Is the shaft safe from failure based on the maximum distortion energy theory?

For the various parts shown in Figure P7–39 on the next page
determine the best one to relieve stress. Make the original part have a small
radius of 0.1 in. at the inside reentrant corners. Place a uniform pressure
load of 1000 psi on the right end of each part and fix the left end. All units
shown are taken in inches. Let the material be A36 steel.

The syringe with plunger is shown in Figure P9–23. The
material of the syringe is glass with E = 69 GPa, n = 0:15, and tensile
strength of 5 MPa. The bottom hole is assumed to be closed under test
conditions. Determine the deformation and stresses in the glass. Compare the
maximum principal stress in the glass to the ultimate tensile strength. Do you
think the syringe is safe? Why?

Design the bicycle wrench with the approximate dimensions
shown in Figure P7–38. If you need to change dimensions explain why. The wrench
should be made of steel or aluminum alloy. Determine the thickness needed based
on the maximum distortion energy theory. Plot the deformed shape of the wrench
and the principal stress and von Mises stress. The boundary conditions are
shown in the figure, and the loading is shown as a distributed load acting over
the right part of the wrench. Use a factor of safety of 1.5 against yielding.
Round each corner with a 0.1 cm radius.