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1. Solve Problems 4.5 through 4.11, 4.19 through 4.30, and
4.40 through 4.42 using a suitable computer program.
2. For the beam shown in Figure P4–77, use a longhand
solution to solve the problem. Compare answers using the beam stiffness matrix,
Eq. (4.1.14), without transverse shear deformation effects and then Eq.
(4.1.15o), which includes the transverse shear effects.

For the beam shown in Figure P4–77, use a computer program
to determine the deflection at the mid-span using four beam elements, making
the shear area zero and then making the shear area equal 5/6 times the cross-sectional
area (b times h). Then make the beam have decreasing spans of 200 mm, 100 mm,
and 50 mm with zero shear area and then 5/6 times the cross-sectional area.
Compare the answers. Based on your program answers, can you conclude whether
your program includes the effects of transverse shear deformation?

For the rigid frame shown in Figure P5–1, determine (1) the
displacement components and the rotation at node 2, (2) the support reactions,
and (3) the forces in each element. Then check equilibrium at node 2. Let E =
30
10
6
psi, A = 10 in
2
,
and I = 500 in4 for both elements.

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.

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.)

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.

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
.

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.

For the rigid building frame shown in Figure P5–22,
determine the forces in each element and calculate the bending stresses. Assume
all the vertical elements have A =- 10 in.
2
and I = 100 in.
4
and all horizontal elements have A = 15 in.
2
and I = 150 in.
4
Let E = 29
10
6
psi for all elements.
Let c = 5 in. for the vertical elements and c = 6 in. for the horizontal
elements, where c denotes the distance from the neutral axis to the top or
bottom of the beam cross section, as used in the bending stress formula s =
(Mc=I).

1. For the rigid frames or beams shown in Figures P5–23
through P5–38, determine the displacements and rotations at the nodes, the
element forces, and the reactions.
2. Consider the plane structure shown in Figure P5–39. First
assume the structure to be a plane frame with rigid joints, and analyze using a
frame element. Then assume the structure to be pin-jointed and analyze as a
plane truss, using a truss element. If the structure is actually a truss, is it
appropriate to model it as a rigid frame?
How can you model the truss using the frame (or beam)
element? In other words, what idealization could you make in your model to use
the beam element to approximate a truss?