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Problem 8.49
In Example 4.11 on p. 252, numerous equivalent force systems for a cantilever beam were developed. For
each of the following force systems, determine the shear and moment as functions of position, and draw
the shear and moment diagrams: Figure 4 on p. 252 with dD2:67 mm.
Solution
Figure 4 on p. 252 is:
Summary:
VD3N; M D 8Nmm C.3 N/x; for 0x2:667 mm:(5)
Problem 8.50
Without solving Probs. 8.46 through 8.49, comment on the agreement you expect between the shear and
moment distributions for each of these load cases. Are there particular points in the beam where you know
the shear and moment must be the same for all of these loadings?
Note:
Concept problems are about
explanations, not computations.
Problem 8.51
Consider the simply supported beam shown with a uniformly distributed load and
a force at midspan. Use superposition of the results from Example 8.5 on p. 506 to
determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
1230 Solutions Manual
Superposition: The total shear and moment are the sums of those for each load case. Thus,
9
>
Problem 8.52
Consider the simply supported beam shown with a uniformly distributed load and a
force at midspan. Use superposition of the results from Example 8.5 on p. 506 to
determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
1232 Solutions Manual
Superposition: The total shear and moment are the sums of those for each load case. Thus,
9
>
Problem 8.53
A wing of a jet is crudely modeled as a beam with the loadings shown. Use
superposition of the results from Example 8.6 on p. 508 to determine the shear
and moment in the wing as functions of position, and draw the shear and moment
diagrams.
Problem 8.54
A simply supported beam is subjected to the 900 and
1200
N forces shown. Use
superposition to determine the shear and moment as functions of position, and
draw the shear and moment diagrams. Hint: The answers to Prob. 8.31 on p. 510,
given below, are helpful for this problem.
VDP b
aCb; M DP b
aCbx; for 0xa;
VD P a
aCb; M DP a1x
aCb;for axaCb:
Problem 8.55
A person uses a wrench to apply a force
FA
and a moment
MA
to the end
of a cantilever beam. The weight of the beam is represented by the uniform
distributed load w0.
(a)
For
FA¤0
,
MAD0
, and
w0D0
, determine the shear and moment as
functions of position. Express your answers in terms of FA.
(b)
For
FAD0
,
MA¤0
, and
w0D0
, determine the shear and moment as
functions of position. Express your answers in terms of MA.
(c)
For
FAD0
,
MAD0
, and
w0¤0
, determine the shear and moment as
functions of position. Express your answers in terms of w0.
(d)
If
FAD20 lb
,
MAD200 in:lb
,
w0D0:5 lb=in:
, and
LD30 in:
, use
superposition of the results of Parts (a) through (c) to determine the shear
and moment as functions of position, and draw the shear and moment
diagrams.
Problem 8.56
A cross section through a railroad bed is shown. The rails are supported by ties
that are made of wood or sometimes concrete, and the ties rest on ballast, which
is usually crushed stone. Assuming the ballast applies a uniformly distributed
load to the ties, determine the shear and moment in a tie due to the
10 kip
forces
and the distributed load from the ballast as functions of position. Draw the
shear and moment diagrams.
2.99 in:x/2:(16)
2.99 in:x/2;for 79 in:x99 in:(17)
Problem 8.57
One of the beams of a staircase is to support a
200 lb=ft
uniformly distributed
vertical force. Determine the axial force, shear, and moment as functions of
position and draw the normal force, shear, and moment diagrams.
Problem 8.58
Determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
Problem 8.59
Determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
