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Problem 10.1 In Active Example 10.1, suppose that
the distance from point Ato point Cis increased from
1
4Lto 1
2L. Draw a sketch of the beam with Cin its
new position. Determine the internal forces amd moment
at C.
AB
C
L
y
3
4L
1
4
LF
1
4
Problem 10.2 The magnitude of the triangular distri-
buted load is w0D2 kN/m. Determine the internal
forces and moment at A.
0.4 m
0.6 m
0.6 m
w0
A
y
x
Solution: The free-body diagram of the beam is shown in Fig. a.
From the equilibrium equations
Fx:BxD0,
Problem 10.3 The Cclamp exerts 30-lb forces on
the clamped object. Determine the internal forces and
moment in the clamp at A.
y
2 in
Solving: PAD30 lb,V
AD0,M
AD60 in-lb
VA
Problem 10.4 Determine the internal forces and
moment at A.
y
x
900 ft-lb
A
400 lb
100 lb
790
Problem 10.5 The pipe has a fixed support at the left
end. Determine the internal forces and moment at A.
y
x
0.2 m
2 kN
A
0.2 m
0.2 m
0.2 m
2 kN
20⬚
Solving:
PAD1.88 kN,V
AD2.68 kN,M
AD0.561 kN-m
MA
0.2 m
0.2 m
Problem 10.6 Determine the internal forces and
moment at Afor each loading.
2 kN/m
(a)
2 m
1 m
8 kN
4 m
A
A
from which MAD4 kN-m VAD4kN PAD0
(b) Determine the reaction at B: The sum of the moments about R:
MRD4
2xdxC4BD0,
792
Problem 10.7 Model the ladder rung as a simply
supported (pin supported) beam and assume that the
750-N load exerted by the person’s shoe is uniformly
distributed. Determine the internal forces and moment
at A.A
200 mm 100 mm
375 mm
250 mm
Solution:
FyDBCC750 D0,
750 N
Problem 10.8 In Example 10.2, suppose that the
distance from point Ato point Bis increased from 3 m
to 4 m. Draw a sketch of the beam with Bin its new
position. Determine the internal forces and moment at B.
y
x
60 N/m
3 m 3 m
BC
A
Problem 10.9 If xD3 ft, what are the internal forces
and moment at A?
x
y
600 lb/ft
600 lb/ft
xA
794
Problem 10.10 If xD4 ft, what are the internal forces
and moment at A?
x
y
600 lb/ft
600 lb/ft
xA
Problem 10.11 Determine the internal forces and
moment at Afor the loadings (a) and (b).
AB
4 ft
3 ft 5 ft
6 ft
AB
240 lb 180 lb
60 lb/ft
(a)
(b)
796
Problem 10.12 For the loadings (a) and (b) shown
in Problem 10.11, determine the internal forces and
moment at B.
Solution: The external reactions are the same for either loading
(b) Use the right section with the discrete loads
Problem 10.13 Determine the internal forces and
moment at A.
6 ft
8 ft 4 ft
A
200 lb/ft 300 lb/ft
1200 lb
225 lb
275 lb/ft
200 lb/ft
798
Problem 10.14 Determine the internal forces and
moment at A.A
B
1 m
10 kN
1 m 1 m 1 m 1 m
Solution: The complete structure as a free body: The sum of the
MD3⊲10⊳5RD0,
Solve the simultaneous equations: F1D8 kN, F2D2 kN. Make a
cut at A: Isolate the left end of CA. The sum of the moments about A:
MDMA2F1C10 D0,
from which
MAD10 C16 D6 kN-m
VAD810 D2kN,
PAD0
RY
CY
10 kN
1 m 1 m
Problem 10.15 Determine the internal forces and
moment at point Bin Problem 10.14.
Solution: Use the solutions to Problem 10.14. Make a cut at point
F1 = 8
Problem 10.16 Determine the internal forces and
moment at A.
x
0.2
m
0.2
m0.6 m
0.4 m
0.4 m
0.4 m 0.4 m
600 N
y
Solution: Use the entire structure to find the reactions
Fx:CxC600 N D0)CxD600
MC:⊲600 N⊳⊲1.0m⊳CD⊲0.8m⊳D0)DD750 N
Finally cut at Aand look at the left section
800
Problem 10.17 Determine the internal forces and
moment at point Bof the frame in Problem 10.16.
MB:MBCD⊲0.2m⊳D0
Solving PBD0,V
BD750 N,M
BD150 N-m
D
Problem 10.18 The tension in the rope is 10 kN.
Determine the internal forces and moment at point A.
0.6 m
0.6 m
0.8 m
A
y
3 kN
Solution: Use the whole structure first
Problem 10.19 Determine the internal forces and
moment at point Aof the frame.
0.2 m
0.2 m
0.2 m
0.8 m
A
x
y
3 kN
Solution: Use the whole structure first
Now cut the bar at Aand look at the lower right section
802
Problem 10.20 Determine the internal forces and
moment at A.
1 m
4 kN/m
1 m 1 m
2 m
B
Ax
y
Solution: The free-body diagrams of the horizontal members are
and from free-body diagram (b),
Problem 10.21 Determine the internal forces and
moment at point Bof the frame in Problem 10.20.
Solution: See the solution of Problem 10.20. Cutting member (a)
9 kN
4 kN
MB
PB
0.5 m
VB
Problem 10.22 Determine the shear force and bending
moment as functions of x.
Strategy: Cut the beam at an arbitrary position xand
400 lb
y
Solving we have
VD400 lb
MD⊲400 lb⊳x
V
Problem 10.23 (a) Determine the shear force and
bending moment as functions of x.
(b) Draw the shear force and bending moment diagrams.
6 m
48 kN/ m
y
x
804
Problem 10.24 (a) Determine the shear force and
bending moment as functions of x.
(b) Show that the equations for Vand Mas functions
of xsatisfy the equation VDdM/dx.
Strategy: For part (a), cut the beam at an arbitrary
position xand draw the free-body diagram of the part
of the beam to the right of the plane.
12 ft
x
y
60 lb/ft
the right
RD1
2⊲12 x⊳ 12 x
12 ⊲60⊳D5
2⊲12 x⊳2
Fy:VRD0
Mcut :MR12 x
3D0
(a) Solving VD5
2⊲x 12⊳2lb,MD5
6⊲x 12⊳3ft-lb
(b) dM
dx D5
2⊲x 12⊳2DV
12 − x
V
M
Problem 10.25 Draw the shear force and bending
moment diagrams for the beam in Problem 10.24.
Solution: The diagrams
60 ft/lb
y
Problem 10.26 Determine the shear force and bending
moment as functions of xfor 0 <x<2m.
3600 N-m
x
y
Fy:AVD0
Mcut :Ax CMD0
Solving VD600 N,MD⊲600 N⊳x for 0 <x<2m
A
V
Problem 10.27 In Active Example 10.3, suppose that
the 40 kN/m distributed load extends all the way across
the beam from Ato C. Draw a sketch of the beam
y
x
40 kN/m
60 kN
BC
806
Problem 10.28
(a) Determine the internal forces and moment as func-
tions of x.
(b) Determine the shear force and bending moment
100 lb/ft
x
y
6. The shear diagram over this
interval is
–500
Shear
Problem 10.29 The loads FD200 N and CD
800 Nm.
(a) Determine the internal forces and moment as func-
tions of x.
y
x
F
C
The sum of the forces: FyDRyCBFD0,
MxDM2⊲x⊳ CCRyxD0,
–2000
–1750
–750
–500
0246810121416
X, m
Problem 10.30 The beam in Problem 10.29 will safely
support shear forces and bending moments of magni-
tudes 2 kN and 6.5 kN-m, respectively. On the basis
of this criterion, can it safely be subjected to the loads
FD1 kN, CD1.6 kN-m?
808
