Category: Writing

Design the rigid highway bridge frame structure shown in Figure P5–71 for a moving truck load (shown below) simulating a truck moving across the bridge. Use the load shown and place it along the top girder at various locations. Use the allowable stresses in bending and compression and allowable deflection given in the Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C. or use some other reasonable values.

1. Design the gabled frame shown for a balanced snow load
shown in Figure P5–69 (typical of the Midwest) for an apartment building.
Select a wide flange section for the frame. Assume the allowable bending stress
not to exceed 140 MPa. Use ASTM A36 steel.
2.
Design a gantry crane that must be able to lift 10
tons as it must lift compressors, motors, heat exchangers, and controls. This
load should be placed at the center of one of the main 12-foot-long beams as
shown in Figure P5–70, by the hoisting device location. Note that this beam is
on one side of the crane. Assume you are using
ASTM A36 structural steel. The crane must be 12 feet long, 8
feet wide, and 15 feet high. The beams should all be the same size, the columns
all the same size, and the bracing all the same size. The corner bracing can be
wide flange sections or some other common shape. You must verify that the
structure is safe by checking the beam’s bending strength and allowable
deflection, the column’s buckling strength, and the bracing’s buckling
strength. Use a factor of safety against material yielding of the beams of 5.
Verify that the beam deflection is less than L/360, where L is the span of the
beam. Check Euler buckling of the long columns and the bracing. Use a factor of
safety against buckling of 5. Assume the column-to-beam joints to be rigid
while the bracing (a total of eight braces) is pinned to the column and beam at
each of the four corners. Also assume the gantry crane is on rollers with one
roller locked down to behave as a pin support as shown.

Design the gabled frame subjected to the external wind load
shown in Figure P5–68 (comparable to an 80 mph wind speed) for an industrial
building. Assume this is one of a typical frame spaced every 20 feet. Select a
wide flange section based on allowable bending stress of 20 ksi and an
allowable compressive stress of 10 ksi in any member. Neglect the possibility
of buckling in any members. Use ASTM A36 steel.

For the plane structures modeled by triangular elements
shown in Figure P6–20, show that numbering in the direction that has fewer
nodes, as in Figure P6–20(a) (as opposed to numbering in the direction that has
more nodes), results in a reduced bandwidth. Illustrate this fact by filling
in, with X’s, the occupied elements in ½K for each mesh, as was done in
Appendix B.4. Compare the bandwidths for each case.

The shaft in Figure P5–67 supports a winch load of 780 lb
and a torsional moment of 7800 lb-in. at F (26 inches from the center of the
bearing at A). In addition, a radial load of 500 lb and an axial load of 400 lb
act at point E from a worm gearset. Assume the maximum stress in the shaft
cannot be larger than that obtained from the maximum distortional energy theory
with a factor of safety of 2.5. Also make sure the angle of twist is less than
1.5 deg between A and D. In your model, assume the bearing at A to be frozen
when calculating the angle of twist. Bearings at B; C, and D can be assumed as
simple supports. Determine the required shaft diameter.

1. The plane stress element only allows for in-plane
displacements, while the frame or beam element resists displacements and
rotations. How can we combine the plane stress and beam elements and still
ensure compatibility?
2. Compute the stiffness matrix of element 1 of the two-triangle
element model of the rectangular plate in plane stress shown in Figure P6–23.
Then use it to compute the stiffness matrix of element 2.

Determine the size of a solid round shaft such that the
maximum angle of twist between C and B is 0.26 degrees per meter of length and
the deflection of the beam is less than 0.005 inches under the pulley C for the
loads, as shown in Figure P5–66. Assume simple supports at bearings A and B.
Assume the shaft is made from cold-rolled AISI 1020 steel. (Recommended angles
of twist in driven shafts can be found in Machinery’s Handbook, Oberg, E., et.
al., 26th ed., Industrial Press, N.Y., 2000.)

Can you use the plane stress or plane strain element to
model the following:
a. a flat slab floor of a building with vertical loading
perpendicular to the slab
b. a wall subjected to wind loading (the wall acts as a
shear wall with loads in the plane of the wall)
c. a tensile plate with a hole drilled transversely through
it
d. an eyebar with loads in the plane of the eyebar
e. a soil mass subjected to a strip footing loading
f. a wrench subjected to a force in the plane of the wrench
g. a wrench subjected to twisting forces (the twisting
forces act out of the plane of the wrench)
h. a triangular plate connection with loads in the plane of
the triangle
i. a triangular plate connection with out-of-plane loads

A small hydraulic floor crane as shown in Figure P5–65
carries a 5000-lb load. Determine the size of the beam and column needed.
Select either a standard box section or a wide-flange section. Assume a rigid
connection between the beam and column. The column is rigidly connected to the
floor. The allowable bending stress in the beam is 0:60Sy. The allowable
deflection is 1=360 of the beam length. Check the column for buckling.

Determine the nodal displacements and the element stresses,
including principal stresses, due to the loads shown for the thin plates in
Figure P6–14 on the next page. Use E = 210 GPa, n = 0:30, and t = 5 mm. Assume
plane stress conditions apply. The recommended discretized plates are shown in
the figures.