PROBLEM 7.68
Using the method of Section 7.6, solve Problem 7.34.
PROBLEM 7.34 For the beam and loading shown, (a) draw the shear
and bending-moment diagrams, (b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Free body: Entire beam
0: 0
y
F BPΣ = −=
PROBLEM 7.69
For the beam and loading shown, (a) draw the shear and
bending-moment diagrams, (b) determine the maximum
absolute values of the shear and bending moment.
SOLUTION
Reactions:
( )( ) ( )( )
0: 24 kN m (8 kN)(3 m) 10 kN 6 m 8 kN 9 m (12 m) 0
A
MEΣ = ⋅− − − + =
11 kNE=
PROBLEM 7.70
For the beam and loading shown, (a) draw the shear and
bending-moment diagrams, (b) determine the maximum
absolute values of the shear and bending moment.
SOLUTION
Reactions
0: 12 kN m (9 kN)(3.5 m) (18 kN)(2 m) 3 kN m (4.5 m) 0
Dy
MAΣ = + ⋅+ + − ⋅− =
PROBLEM 7.71
Using the method of Section 7.6, solve Problem 7.39.
PROBLEM 7.39 For the beam and loading shown, (a) draw the shear
and bending-moment diagrams, (b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Free body: Beam
0: 0
xx
FAΣ= =
0: (60 kN)(3 m) (50 kN)(1 m) (5 m) 0
By
MAΣ= + − =
PROBLEM 7.72
Using the method of Section 7.6, solve Problem 7.40.
PROBLEM 7.40 For the beam and loading shown, (a) draw the shear
and bending-moment diagrams, (b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Free body: Beam
0: 0
xx
FAΣ= =
0: (50 kN)(2 m) (40 kN)(1 m) (4 m) 0
Dy
MAΣ= − − =
15.00 kN
y
A= +
PROBLEM 7.73
Using the method of Section 7.6, solve Problem 7.41.
PROBLEM 7.41 For the beam and loading shown, (a) draw the shear
and bending-moment diagrams, (b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Reactions at supports.
Because of the symmetry:
1(8 8 4 5) kips
2
= = ++×AB
PROBLEM 7.74
Using the method of Section 7.6, solve Problem 7.42.
PROBLEM 7.42 For the beam and loading shown, (a) draw the shear
and bending-moment diagrams, (b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Free body: Beam
0: 0
xx
FAΣ= =
0: (12 kips)(4ft) (15 kips)(7 ft) (10 ft) 0
By
MAΣ= + − =
PROBLEM 7.75
For the beam and loading shown, (a) draw the shear and bending-
moment diagrams, (b) determine the maximum absolute values of
the shear and bending moment.
SOLUTION
PROBLEM 7.76
For the beam and loading shown, (a) draw the shear and
bending-moment diagrams, (b) determine the maximum
absolute values of the shear and bending moment.
SOLUTION
Reactions
From symmetry, CG=
0: 2(16 lb/in.)(10 in.) 100 lb 150 lb 100 lb 2 0
y
FCΣ=− −−−+=
PROBLEM 7.77
For the beam and loading shown, (a) draw the shear and bending–
moment diagrams, (b) determine the magnitude and location of the
maximum absolute value of the bending moment.
SOLUTION
Reactions
PROBLEM 7.78
For the beam and loading shown, (a) draw the shear and bending–
moment diagrams, (b) determine the magnitude and location of the
maximum absolute value of the bending moment.
SOLUTION
PROBLEM 7.79
For the beam and loading shown, (a) draw the shear and bending-moment
diagrams, (b) determine the magnitude and location of the maximum
bending moment.
SOLUTION
Free body: Beam
0: 0
xx
FAΣ= =
0: (40 kN)(1.5 m) (3.75 m) 0
By
MAΣ= − =
16.00 kN
y
A= +
PROBLEM 7.80
For the beam and loading shown, (a) draw the shear and bending-
moment diagrams, (b) determine the magnitude and location of the
maximum bending moment.
SOLUTION
0: (8)(2) (4)(3.2) 4 0
A
MCΣ= + −=
7.2 kN=C
0: 4.8 kN
y
FΣ= =A
PROBLEM 7.81
For the beam and loading shown, (a) draw the shear and bending-
moment diagrams, (b) determine the magnitude and location of the
maximum absolute value of the bending moment.
SOLUTION
Reactions
0: 0
xx
FAΣ= =
0: (800 lb/ft)(9 ft)(4.5 ft) (600 lb)(9 ft) (15 ft) 0
A
MCΣ=− + + =
1800 lbC= +
1.800 kips=C
PROBLEM 7.82
For the beam and loading shown, (a) draw the shear and bending-
moment diagrams, (b) determine the magnitude and location of the
maximum absolute value of the bending moment.
SOLUTION
Reactions
0: 0
xx
FBΣ= =
0: (400 lb/ft)(20 ft)(10 ft) (3200 lb)(22.5 ft) (20 ft) 0
C
MBΣ= + − =
7600 lbB= +
7.60 kips=B
3.60 kips=C
PROBLEM 7.83
(a) Draw the shear and bending-moment diagrams for beam AB,
(b) determine the magnitude and location of the maximum absolute value
of the bending moment.
SOLUTION
Reactions at supports
Because of symmetry of load
1(300 8 300)
2
AB= = ×+
1350 lb= =AB
PROBLEM 7.84
Solve Problem 7.83 assuming that the 300-lb force applied at D is
directed upward.
PROBLEM 7.83 (a) Draw the shear and bending–moment diagrams for
beam AB, (b) determine the magnitude and location of the maximum
absolute value of the bending moment.
SOLUTION
Reactions at supports
Because of symmetry of load:
1(300 8 300)
2
AB= = ×−
PROBLEM 7.85
For the beam and loading shown, (a) write the equations of the shear
and bending-moment curves, (b) determine the magnitude and location
of the maximum bending moment.
SOLUTION
PROBLEM 7.86
For the beam and loading shown, (a) write the equations of the
shear and bending-moment curves, (b) determine the magnitude
and location of the maximum bending moment.
Solution
PROBLEM 7.86 (Continued)
3
2
max 0
1 11
633
M wL



= − 



2
max 0
0.0642M wL=