Category: Writing

1. For the rigid frame shown in Figure P5–20, determine (1)
the nodal displacement components and (2) the support reactions. (3) Draw the
shear force and bending moment diagrams. Let E = 30
10
6
psi, I = 200 in.
4
, and A = 10 in.
2
for all elements,
except as noted in the figure.
2. For the slant-legged rigid frame shown in Figure P5–21,
size the structure for minimum weight based on a maximum bending stress of 20
ksi in the horizontal beam elements and a maximum compressive stress (due to
bending and direct axial load) of 15 ksi in the slant-legged elements. Use the
same element size for the two slant-legged elements and the same element size
for the two 10-foot sections of the horizontal element. Assume A36 steel is
used.

1. Solve the structures in Figures P5–16 through P5–18 by
using substructuring.
2. For the rigid frame shown in Figure P5–19, determine (1)
the nodal displacement components and (2) the support reactions. (3) Draw the
shear force and bending moment diagrams. For all elements, let E = 30
10
6
psi, I = 200 in.
4
, and A = 10 in
2
.

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.

For the rigid frames shown in Figures P5–5 through P5–15, determine the displacements and rotations of the nodes, the element forces, and the reactions. The values of E; A, and I to be used are listed next to each figure.

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.

For the rigid stairway frame shown in Figure P5–3, determine
(1) the displacements at node 2, (2) the support reactions, and (3) the local
nodal forces acting on each element. Draw the bending moment diagram for the
whole frame. Remember that the angle between elements 1 and 2 is preserved as
deformation takes place; similarly for the angle between elements 2 and 3.
Furthermore, owing to symmetry, u
2
= u
3
, v
2
=
v
3
, and
2
=
3
.
What size A36 steel channel section would be needed to keep the allowable
bending stress less than two-thirds of the yield stress? (For A36 steel, the
yield stress is 36,000 psi.)

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.

1. For the rigid frame shown in Figure P5–2, determine (1)
the nodal displacement components and rotations, (2) the support reactions, and
(3) the forces in each element. Let E = 30
10
6
psi, A = 10 in
2
,
and I = 200 in
4
for all elements.
2. For the rigid frame shown in Figure P5–4, determine (1)
the nodal displacements and rotation at node 4, (2) the reactions, and (3) the
forces in each element. Then check equilibrium at node 4. Finally, draw the
shear force and bending moment diagrams for each element. Let E = 30
10
3
ksi, A = 8 in.
2
, and I = 800 in.
4
for all elements.

1. Determine the displacements and reactions for the space
frames shown in Figures P5–58 and P5–59. Let I
x
= 100 in.
4
,
I
y
= 200 in.
4
, I
z
= 1000 in.
4
, E =
30,000 ksi, G = 10,000 ksi, and A = 100 in.
2
for both frames.
2.
Design a jib crane as shown in Figure P5–60 that
will support a downward load of 6000 lb. Choose a common structural steel shape
for all members. Use allowable stresses of 0:66Sy (S
y
is the yield
strength of the material) in bending, and 0:60S
y
in
tension on gross areas. The maximum deflection should not
exceed 1=360 of the length of the horizontal beam. Buckling should be checked
using Euler’s or Johnson’s method as applicable.

Solve the grid structures shown in Figures P5–52 through
P5–57 using a computer program. For grids P5–52—P5–54, let E = 30
10
6
psi, G = 12
10
6
psi, I = 200 in.
4
,
and J = 100 in.
4
, except as noted in the figures. In Figure P5–54,
let the cross elements
have I = 50 in.
4
and J = 20 in.
4
, with
dimensions and loads as in Figure P5–53. For grids P5–55 through P5–57, let E =
210 GPa, G = 84 GPa, I = 2
104 m
4
, J =1
10
4
m
4
, and A = 1
10
-2
m
2
.