Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Problem 7.80
(a)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the appropriate expression(s) for the dis-
tributed load
w
to determine the
x
position of the line of action for the resultant force produced by
the distributed load.
(b) Determine the support reactions using the results of Part (a).
(c) Determine the support reactions using composite shapes to represent the distributed load.
Loading (b) in Prob. 7.74 on p. 479.
Solution
Part (a) From the solution to Problem 7.74
Equation (7.41) may be applied by inspection to obtain the total force applied to the
beam as
Problem 7.81
(a)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the appropriate expression(s) for the dis-
tributed load
w
to determine the
x
position of the line of action for the resultant force produced by
the distributed load.
(b) Determine the support reactions using the results of Part (a).
(c) Determine the support reactions using composite shapes to represent the distributed load.
Loading (c) in Prob. 7.74 on p. 479.
Part (a) From the solution to Problem 7.74
Problem 7.82
(a)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the appropriate expression(s) for the dis-
tributed load
w
to determine the
x
position of the line of action for the resultant force produced by
the distributed load.
(b) Determine the support reactions using the results of Part (a).
(c) Determine the support reactions using composite shapes to represent the distributed load.
Loading (b) in Prob. 7.75 on p. 479.
Solution
Applying Eq. (7.43), the line of action of Fis positioned at
Problem 7.83
(a)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the appropriate expression(s) for the dis-
tributed load
w
to determine the
x
position of the line of action for the resultant force produced by
the distributed load.
(b) Determine the support reactions using the results of Part (a).
(c) Determine the support reactions using composite shapes to represent the distributed load.
Loading (c) in Prob. 7.75 on p. 479.
Solution
Part (a) From the solution to Problem 7.75
Statics 2e 1073
Part (c)
The FBD is shown at the right, where the distributed loading is repre-
sented using composite shapes. From the solution to Problem 7.75 (or by noting
Problem 7.84
Consider modeling the weights from books 8–11 from Example 7.11 on p. 475,
using the linear force distribution
wDaCbx
, as shown here. The constants
a
and
b
can be determined by requiring the two force systems shown to be
equivalent. That is,
4in:
Z
0
w dx D
11
X
iD8
Wiand
4in:
Z
0
xw dx D
11
X
iD8
MBi ;
where MBi is the moment about point B(the origin) of weight Wi.
(a)
Using the weights and geometry of books 8–11 given in Table 1 of
Example 7.11, evaluate the above expressions and solve for
a
and
b
to
show that wD35
8
lb
in. 15
16
lb
in.2x.
(b)
Evaluate the distributed force from Part (a) at
xD0
and
xD4in:
, and
compare these to the values used in Example 7.11, namely,
4lb=in:
and
1lb=in:, respectively.
(c)
Discuss why the distributed force from Part (a) is better than that used in
Example 7.11.
(d)
Using the distributed force from Part (a), determine the support reactions
for the bookshelf and compare to those found in Example 7.11.
0 4.375 lb=in. 4 lb=in.
4in:0.6250 lb=in. 1 lb=in.
Part (c)
The distributed force given by Eq. (7) and the distributed force used in Example 7.11 both satisfy
Eq. (1). However, the distributed force used in Example 7.11 does not satisfy Eq. (4), thus it is not an
2.4:375 lb=in. 0:625 lb=in./ .4in:/D7:50 lb;(11)
Using the right-hand FBD, the equilibrium equations are
Problem 7.84 Example 7.11
A 17:96 lb 17:9 lb
Problem 7.85
(a)
For the distributed loading shown, develop an expression (or multiple
expressions if needed) for the distributed force
w
as a function of position
x.
(b)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the results of
Part (a) to determine the total force produced by the distributed load and
the xposition of its line of action.
(c) Determine the support reactions using the results of Part (b).
(d)
Determine the support reactions using composite shapes for the dis-
tributed load.
2.6 ft/.4 kip=ft/D12 kip:(11)
The equilibrium equations are
Problem 7.86
A beam is loaded by a distributed force that begins at the left-hand end as an
800 N=m
uniform load with
dw=dx D0
and decreases to zero at the right-hand
end.
(a)
Determine the constants
a
,
b
, and
c
so that the quadratic polynomial
wDaCbx Ccx2describes this loading.
(b)
Determine the constants
d
and
f
so that the trigonometric function
wDdcos.f x/ describes this loading.
Problem 7.87
(a)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the results of
Part (a) of Prob. 7.86 to determine the total force produced by the dis-
tributed load, the
x
position of its line of action, and the support reactions.
(b)
Use integration (Eqs. (7.41) and (7.43) on p. 469) with the results of
Part (b) of Prob. 7.86 to determine the total force produced by the dis-
tributed load, the
x
position of its line of action, and the support reactions.
(c)
Compare the results of Parts (a) and (b), and discuss if these should be
the same or if differences are expected.
Problem 7.88
Determine the support reactions for the loading shown.
2.6 m/.4kN=m/D12:0 kN:(1)
Using the FBD, the equilibrium equations are
Problem 7.89
Determine the support reactions for the loading shown.
Problem 7.90
Determine the support reactions for the loading shown.
Solution
Each of the two distributed loadings have the resultant force
The equilibrium equations are
Problem 7.91
Determine the support reactions for the loading shown.
Problem 7.92
Determine the support reactions for the loading shown.
2.20 ft/ .200 kip=ft/D2:00 kip:(2)
The position for force
F2
is
d2D20 ft C.2=3/.20 ft/D33:33 ft
. Using the FBD, the equilibrium equations
are
