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Design the support members AB and CD for the platform lift
shown in Figure P5–61. Select a mild steel and choose suitable cross-sectional
shapes with no more than a 4 : 1 ratio of moments of inertia between the two
principal directions of the cross section. You may choose two different cross
sections to make up each arm to reduce weight. The actual structure has four
support arms, but the loads shown are for one side of the platform with the two
arms shown. The loads shown are under operating conditions. Use a factor of
safety of 2 for human safety. In developing the finite element model, remove
the platform and replace it with statically equivalent loads at the joints at B
and D. Use truss elements or beam elements with low bending stiffness to model
the arms from B to D, the intermediate connection E to F, and the hydraulic
actuator. The allowable stresses are 0:66S
y
in bending and 0:60S
y
in tension. Check buckling using either Euler’s method or Johnson’s method as
appropriate. Also check maximum deflections. Any deflection greater than 1=360
of the length of member AB is considered too large.

A two-story building frame is to be designed as shown in
Figure P5–62. The members are all to be I-beams with rigid connections. We
would like the floor joists beams to have a 15-in. depth and the columns to
have a 10 in. width. The material is to be A36 structural steel. Two horizontal
loads and vertical loads are shown. Select members such that the allowable
bending in the beams is 24,000 psi. Check buckling in the columns using Euler’s
or Johnson’s method as appropriate. The allowable deflection in the beams
should not exceed 1=360 of each beam span. The overall sway of the frame should
not exceed 0.5 in.

A pulpwood loader as shown in Figure P5–63 is to be designed
to lift 2.5 kip. Select a steel and determine a suitable tubular cross section
for the main upright member BF that has attachments for the hydraulic cylinder
actuators AE and DG. Select a steel and determine a suitable box section for
the horizontal load arm AC. The horizontal load arm may have two different
cross sections AB and BC to reduce weight. The finite element model should use
beam elements for all members except the hydraulic cylinders, which should be
truss elements. The pinned joint at B between the upright and the horizontal
beam is best modeled with end release of the end node of the top element on the
upright member. The allowable bending stress is 0:66Sy in members AB and BC.
Member BF should be checked for buckling. The allowable deflection at C should
be less than 1=360 of the length of BC. As a bonus, the client would like you
to select the size of the hydraulic cylinders AE and DG.

A piston ring (with a split as shown in Figure P5–64) is to
be expanded by a tool to facilitate its installation. The ring is sufficiently
thin (0.2 in. depth) to justify using conventional straight-beam bending
formulas. The ring requires a displacement of 0.1 in. at its separation for
installation. Determine the force required to produce this separation. In
addition, determine the largest stress in the ring. Let E = 18
10
6
psi, G = 7
106 psi, cross-sectional area A =
0:06 in.
2
, and principal moment of inertia I = 4:5
10
-4
in.
4
. The inner radius is 1.85 in., and the outer radius is 2.15 in.
Use models with 4, 6, 8, 10, and 20 elements in a symmetric model until
convergence to the same results occurs. Plot the displacement versus the number
of elements for a constant force F predicted by the conventional beam theory
equation of Reference [8].

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 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.)

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.

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.

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 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.