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A tractor bucket with dimensions is shown in Figure P12–16.
The load on the bucket is 600 lb spread uniformly over the inside surface.
Three split surfaces are fully constrained. The bucket material is A36
structural steel. Determine the von Mises stress throughout the bucket. (This
problem was done in Cosmos Works and created by John Mirth and Brian
Niggemann.)
Draw the typical bucket using your own dimensions or use the
scaled drawing with dimensions shown in Figure P12–16.

For the one-dimensional composite bar shown in Figure P13–1,
determine the interface temperatures. For element 1, let K
xx
= 200
W/(m C); for element 2, let K
xx
= 100 W/(m C); and for element 3, let
K
xx
= 50 W/(m C). Let A = 0:1 m
2
. The left end has a
constant temperature of 100 C, and the right end has a constant temperature of
300 C.

1. For the one-dimensional rod shown in Figure P13–2
(insulated except at the ends), determine the temperatures at L/3, 2L/3, and L.
Let K
xx
= 3 Btu/(h.-in.-F), h = 1:0 Btu/(h-in
2
– F), and
Ty = 0 F. The temperature at the left end is 200 F.
2. A rod with uniform cross-sectional area of 2 in
2
and thermal conductivity of 3 Btu/ (h-in.-F) has heat flow in the x direction
only (Figure P13–3). The right end is insulated. The left end is maintained at
50 F, and the system has the linearly distributed heat flux shown.
Use a two-element model and estimate the temperature at the
node points and the heat flow at the left boundary.

The rod of 1-in. radius shown in Figure P13–4 generates heat
internally at the rate of uniform Q = 10;000 Btu/(h-ft
3
) throughout
the rod. The left edge and perimeter of the rod are insulated, and the right
edge is exposed to an environment of Ty = 100 F. The convection heat-transfer
coefficient between the wall and the environment is h = 100 Btu/(h-ft
2
–
F). The thermal conductivity of the rod is K
xx
= 12 Btu/(h-ft-F). The
length of the rod is 3 in. Calculate the temperature distribution in the rod.
Use at least three elements in your finite element model.

The fin shown in Figure P13–5 is insulated on the perimeter.
The left end has a constant temperature of 100 C. A positive heat flux of q
x
= 1000 W/m
2
acts on the right end. Let K
xx
= 6 W/(m C)
and cross-sectional area A = 0:1 m
2
. Determine the temperatures at
L/4, L/2, 3L/4, and L, where L = 0:4 m.

1. For the composite wall shown in Figure P13–6, determine
the interface temperatures. What is the heat flux through the 8-cm portion? Use
the finite element method. Use three elements with the nodes shown. 1 cm = 0:01
m.
2. For the composite wall idealized by the one-dimensional
model shown in Figure P13–7, determine the interface temperatures. For element
1, let K
xx
= 5 W/(m C); for element 2, K
xx
= 10 W/(m C);
and for element 3, K
xx
= 15 W/(m C). The left end has a constant
temperature of 200 C and the right end has a constant temperature of 600 C.

A composite wall is shown in Figure P13–8. For element 1,
let K
xx
= 5 W/(m-C), for element 2 let K
xx
= 10 W/(m-C),
for element 3 let K
xx
= 15 W/(m-C). The left end has a heat source
of 600 W applied to it. The right end is held at 10C. Determine the left end
temperature and the interface temperatures and the heat flux through element 3.