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A square steel plate (Figure P12–1) of dimensions 20 in.
20
in. with thickness of 0.1 is clamped all around. The plate is subjected to a
uniformly distributed loading
of 1 lb/in
2
. Using a 2
2
mesh and then a 4
4 mesh, determine the maximum
deflection and maximum stress in the plate. Compare the finite element solution
to the classical one in [1].

An L-shaped plate (Figure P12–2) with thickness 0.1 in. is
made of ASTM A-36 steel. Determine the deflection under the load and the
maximum principal stress and its location using the plate element. Then model
the plate as a grid with two beam elements with each beam having the sti¤ness
of each L-portion of the plate and compare your answer.

1. A square (Figure P12–3) simply supported 20 in.
20
in. steel plate with thickness 0.15 in. has a round hole of 4 in. diameter
drilled through its center. The plate is uniformly loaded with a load of 2
lb/in2. Determine the maximum principal stress in the plate.
2. For the structural steel plate structure shown in Figure
P12–6, determine the maximum principal stress and its location. If the stresses
are unacceptably high, recommend any
design changes. The initial thickness of each plate is 0.25
in. The left and right edges are simply supported. The load is a uniformly
applied pressure of 10 lb/in.
2
over the top plate.

A C-channel section (Figure P12–4) structural steel beam of 2-in. wide flanges, 3 in. depth and thickness of both flanges and web of 0.25 in. is loaded as shown with 100 lb acting in the y direction on the free end. Determine the free end deflection and angle of twist. Now move the load in the z direction until the rotation (angle of twist) becomes zero.
This distance is called the shear center (the location where the force can be placed so that the cross section will bend but not twist). You will need to add a beam or plate element to the center of the web extended into the negative z direction and place the load at the end of this proper length beam. (See Table 5–1 for the equation for the shear center location.)

For the simply supported structural steel W 14
61 wide flange beam shown in Figure P12–5, compare the plate element model
results with the classical beam bending results for deflection and bending
stress. The beam is subjected to a central vertical load of 22 kip. The
cross-sectional area is 17.9 in.
2
, depth is 13.89 in., flange width
is 9.995 in., flange thickness is 0.645 in., web thickness is 0.375 in., and
moment of inertia about the strong axis is 640 in.4

Design a steel box structure (Figure P12–7) 4 ft wide
8
ft long made of plates to be used to protect construction workers while working
in a trench. That is, determine a recommended thickness of each plate. The
depth of the structure must be 8 ft. Assume the loading is from a side load
acting along the long sides due to a wet soil (density of 62.4 lb/ft
3
)
and varies linearly with the depth. The allowable deflection of the plate type
structure is 1 in. and the allowable stress is 20 ksi.

1. Determine the maximum deflection and maximum principal
stress of the circular plate shown in Figure P12–8. The plate is subjected to a
uniform pressure p = 700 kPa and fixed along its outer edge. Let E = 200 GPa, n
= 0:3, radius r = 500 mm, and thickness t = 12 mm.
2. Determine the maximum deflection and maximum principal
stress for the plate shown in Figure P12–9. The plate is fixed along all three
sides. A uniform pressure of 70 MPa is applied to the surface. The plate is
made of steel with E = 200 GPa, n = 0:3, and thickness t = 6 mm, a = 0:75 m and
b = 1 m.

An aircraft cabin window of circular cross section and
simple supports all around as shown in Figure P12–10 is made of polycarbonate
with E = 0:345
106 psi, n = 0:36, radius = 20 in.,
and thickness t = 0:75 in. The safety of the material is tested at a uniform
pressure of 10 psi. Determine the maximum deflection and maximum principal
stress in the material. The yield strength of the material is 9 ksi. Comment on
the potential use of this material in regard to strength and deflection.

A square steel plate 2 m
2 m and 10 mm thick at the bottom of
a tank must support salt water at a height of 3 m, as shown in Figure P12–11.
Assume the plate to be built in (fixed all around). The plate allowable stress
is 100 MPa. Let E = 200 GPa, n = 0:3 for the steel properties. The weight
density of salt water is 10.054 kN/m
3
. Determine the maximum
principal stress in the plate and compare to the yield strength.