Problem 8.24
Determine the internal forces acting on:
The cross section at Ain Example 4.3 on p. 212.
Problem 8.25
One of the cranks of a child’s bicycle is shown. The entire crank lies in the
xy
plane. Determine the internal forces acting on: Cross section A.
Problem 8.26
One of the cranks of a child’s bicycle is shown. The entire crank lies in the
xy
plane. Determine the internal forces acting on: Cross section B.
Problem 8.27
One of the cranks of a child’s bicycle is shown. The entire crank lies in the
xy
plane. Determine the internal forces acting on: Cross section C.
Problem 8.28
One of the cranks of a child’s bicycle is shown. The entire crank lies in the
xy
plane. Determine the internal forces acting on: Cross section
D
, which is
located immediately next to the sprocket.
Problem 8.29
For the simply supported beam shown, let
aD6ft
,
bD4ft
, and
PD1000 lb
.
Determine the shear and moment as functions of position, and draw the shear and
moment diagrams.
Problem 8.30
Repeat Prob. 8.29, using
aD3
m,
bD1
m, and
PD10 kN
. Determine the shear
and moment as functions of position, and draw the shear and moment diagrams.
(10)
Summary:
Problem 8.31
Determine the shear and moment as functions of position. Express your answers
in terms of parameters such as
P
,
a
,
b
, etc. Draw the shear and moment diagrams.
Hint: The answers to this problem are given in the statement of Prob. 8.54.
aCb;(3)
XMcut D0W P b
aCbxCMD0; (4)
)MDP b
aCb;(8)
XMcut D0W MCP a
aCb.a Cbx/ D0; (9)
Problem 8.32
A simply supported beam with two equal forces applied equidistant from the
supports is called four-point bending. This loading arrangement is commonly
used for testing beams in a laboratory.
(a)
Determine the shear and moment as functions of position. Express your
answers in terms of parameters such as
P
,
L
, etc. Draw the shear and
moment diagrams.
(b)
Comment on any interesting features the shear and moment display in the
region between points Band C.
Solution
Part (a) By inspection (or by using PMD0,PFxD0, and PFyD0), the reactions are
We take a cut at an arbitrary position between points
A
and
B
and draw the FBD to the
left of the cut to determine the shear and moment as functions of position for 0xL
3.
XFyD0WPVD0; (2)
)MDPL
3:(10)
Problem 8.33
A simply supported beam with a 2000
ftlb
moment is shown. Determine the
shear and moment as functions of position, and draw the shear and moment
diagrams.
Problem 8.34
A simply supported beam with a 2000
ftlb
moment is shown. Determine the shear
and moment as functions of position, and draw the shear and moment diagrams.
Problem 8.35
A diver stands on the end of a diving board. If the diver’s mass is
70 kg
,
determine the shear and moment as functions of position, and draw the shear
and moment diagrams.
Problem 8.36
For the cantilever beam shown, determine the shear and moment as functions of
position, and draw the shear and moment diagrams.
Problem 8.37
For the cantilever beam shown, determine the shear and moment as functions of
position, and draw the shear and moment diagrams.