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Problem 8.38
For the cantilever beam shown, determine the shear and moment as functions of
position, and draw the shear and moment diagrams.
Problem 8.39
For the cantilever beam shown, determine the shear and moment as functions of
position, and draw the shear and moment diagrams.
Problem 8.40
A simply supported beam has the linear distributed load shown. Determine the shear
and moment as functions of position, and draw the shear and moment diagrams.
Problem 8.41
A beam with an overhang is subjected to the uniformly distributed load shown.
Determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
Problem 8.42
Replace the distributed load of Prob. 8.41 with a single force so that the two force systems are equivalent.
Determine the shear and moment as functions of position (it should be possible to do this by inspection).
Even though the loadings are equivalent, do you expect the results for this problem to be the same as those
for Prob. 8.41?
Solution
If the distributed loading of the previous problem is replaced by an equivalent point load, then the problem
Problem 8.43
One of the beams that supports a balcony is shown. To design a beam for this
purpose, it is common to use a uniformly distributed load that includes the
dead loads (e.g., weight of materials) and live loads (e.g., weight of a large, but
reasonable number of people distributed over the balcony). If the uniformly
distributed load is
2500 N=m
, determine the shear and moment as functions of
position, and draw the shear and moment diagrams. Idealize the supports at
B
and Cto be a roller and pin, respectively.
Problem 8.44
The wooden beam shown can support an allowable absolute maximum shear of
3000 lb
and an allowable absolute maximum moment of
6000 ftlb
. Determine
the largest value of w0that is allowable.
Solution
The FBD of the beam is shown at the right. The reaction at point Bis
The internal forces are determined as follows. For the region 0x3ft,
Summary:
VD w0x; M D w0
2x2;for 0x3ft. (4)
1218 Solutions Manual
The absolute maximum shear is
Problem 8.45
The wooden beam shown can support an allowable absolute maximum shear of
3000 lb
and an allowable absolute maximum moment of
6000 ftlb
. Determine
the largest value of w0that is allowable.
Cw0.14 ft/.18 ft x/ D0; (11)
1220 Solutions Manual
Problem 8.46
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 1 on p. 252.
(5)
We take a cut at an arbitrary position between points
O
and
B
and draw
the FBD to the left of the cut to determine the shear and moment as functions
of position for 0x2mm.
XFyD0W3NVD0; (6)
)VD 1N;(12)
Problem 8.47
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 2 on p. 252.
Problem 8.48
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 3 on p. 252.
(4)
Summary:
