Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
1
of
9
ES226
E
XAM
5
S
TUDY
G
UIDE
Exam
5
Date:
Wednesday, April 17, 2013
In Class
Exam Format
50 minute
time limit
.
Closed Book
.
Coverage
Lesson Obje
ctives from Lessons
24
to 30.
LESSON 24
–
FRAMES AND COMPOUND BEAMS
LESSON 25
–
PULLEYS AND RELATED MACHINES
LESSON 26
–
MACHINES AND COMPLEX TOOLS
LESSON 27: MACHINE PROBLEMS
LESSON 29
–
INTERNAL FORCES: SHEAR FORCE, NORMAL FORCE, AND BENDING MOMENT
LESSON 30: INTERNAL SHEAR AND MOMENT FUNCTIONS
Lesson Objectives and Examples
Compute
the reaction forces for frames and compound beams.
Show
why it is advantageous to A) Cut and draw FBD’s at zero moment points, and B)
Identify
2

force members.
1.
(30 points) Determine the x and y reaction components at A and B.
Given: Pinned supports at A
and B. Hinge (pinned connection) at C. Loads in kips (1 kip = 1000 lbs).
Ans
: (A
y
= 85k (up), B
x
=63.33k (left))
2.
(30 points) Determine the x and y reaction
components at A and B.
3.
(30 points) Determine the x and
y reaction components at A and B. (Ans: B
x
= 16.7 lb, B
y
=72.0 lb)
A
B
C
Solution:
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
2
of
9
Distinguish
between a solid member with a hole in it and a pin

ended member.
4.
(4 points) TRUE or FALSE. Location C in member BCD has zero internal bending moment.
5.
(4 points) TRUE or
FALSE. Referring to the previous, location C in member AC has zero internal bending moment.
Compute
the forces in pulleys, ropes and other machines that
often
require
multiple free

body diagrams
.
6.
(45 points) Determine the
force in the hydraulic
cylinder AB and the force in links AC and AD when the 1400

lb load is
held in the position shown.
7.
(
45
points) Determine
the horizontal and vertical components of force acting on the pin at A and the horizontal and vertical
components of force that the
flange of the beam exerts on the jaw at B.
Given: The beam weighs 4 kN
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
3
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9
8.
(30 points) Determine the compressive force F that the wood block exerts on the clamp if a force of 10 lb is applied to the
grip of the clamp.
(Ans: 120 lb)
Solution
: FBD’s
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
4
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9
9.
(30 points)
For the dump

truck bed shown, determine the force in the hydraulic cylinder that is needed to just lift it off of the
support at Q. The weight of the bed is 1200 lbs, centered at point C. A, B, and D are all pin connecti
ons.
10.
(50 points) Determine the force P.
Given: Pruning shears exert at force of 300

lb on the smooth round twig.
Define
shear force, normal force, and bending moment and specify their sign conventions.
11.
(3 points) Illustrate
the difference between a shear force and a normal force with an example sketch and short description.
12.
(3 points) True or False. The internal bending moment in the beam at point B is zero.
13.
(3 points) True or False. The moment in
the support
at point B is zero.
14.
(3 points) True or False. Internal bending moment causes a beam to curve.
15.
(3 points) True or False. Internal shear forces cause a beam to either shorten due to compression or lengthen due to tension
.
16.
(3 points)
True or False. Internal shear force, normal force, and bending moment are all zero at point B.
17.
(3 points) Circle one. Based on the deformed shape, the internal bending moment is maximum at:
A.
Point A
B.
Point B
Hint: where is the curvature maximum?
Fixed
Support
A
B
w = uniformly

distributed load
Pin Support
Roller
Support
A
B
w = uniformly

distributed load
Pin Support
Roller
Support
A
B
w = uniformly

distributed load
P
P
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
5
of
9
Describe
why internal forces and moments are computed.
18.
(5 points) Explain why an engineer would need to know the magnitude of internal
bending moment at point C.
Compute
the internal shear force, normal force, and bending moment in a structural member by taking a cut at a section.
19.
(15 points) Determine the internal bending moment in the beam below at point B and specify whether the top or bottom of
the beam is in compres
sion.
20.
(20 points) Determine the internal bending moment in the beam below at point C and specify whether the top or bottom of
the beam is in compression.
21.
(10 points) Determine the internal bending moment in the beam below at point A and specify whether the top or bottom of
the beam is in compression.
A
B
w = 1000
lbs/ft.
5 feet
5 feet
5 feet
C
A
B
w = 1000 lbs/ft.
10 feet
5 feet
Pin Support
Roller
Support
A
B
C
w = uniformly

distributed load
Fixed
Support
A
B
w =
uniformly

distributed load
Deformed shape
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
6
of
9
22.
(20 points) Determine the internal bending moment in the beam below at point C and specify whether the top or bottom of
the beam is in compression.
23.
(20 points) Determine the internal bending moment in the beam below at point C and specify whether the top or bottom of
the beam is in compression. Given: 4000 ft

lb moment coup
le applied at point B and a 1000 lb horizontal force applied at
point B. (Note the fact that this is the same problem as the previous).
Indicate
the sign of the internal moment with an icon, denoting the compression and tension sides of the beam
.
24.
(12 points) Review the following calculation and answer the following
C.
Is the top of the beam in compression
or in tension?
D.
Is the shear positive or negative, where positive and negative are defined as:
Compute
the moment, shear, and normal force at any point in a beam, frame, or other statically determinate body.
25.
(10 points) Determine the internal bending moment in the column below at point E and specify whether the
right or left side
of the column is in compression. Given: DB is pinned at both ends. ABC is a continuous member.
26.
(30 points) Determine the internal bending moment, shear, and normal force in the beam at point D. For the bending
moment, state whether compression is on the top or the bottom of
the beam. For shear, indicate the sign of the shear by
A
B
w = 1000 lbs/ft.
10 feet
5 feet
C
5 feet
D
2.5
feet
E
+

A
B
5 feet
5 feet
C
1000 lbs
4000 ft

lb
A
B
5 feet
4 feet
5 feet
C
1000 lbs
A
B
w = 100
0 lbs/ft.
10 feet
5 feet
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
7
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drawing a representative icon with arrows to indicate the direction of the shear forces at that position. For normal force,
indicate the sign by stating either tension or compression. Given: Member
CB is pinned at both ends.
27.
(20 points) Determine the internal bending moment in the beam below at point B and specify whether the top or bottom of
the beam is in compression. Given: the beam has two point loads of 1200 lbs, each. The beam sit
s on the ground and it is
assumed that the ground resists the loads with an evenly

distributed loading, as shown
1200 lb
Beam
Ground
w
4 ft
4 ft
4 ft
1200 lb
A
B
C
D
A
B
w = 1000 lbs/ft.
5 feet
C
5 feet
5 feet
D
5 feet
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
8
of
9
28.
(10 points) Determine the internal shear in the beam below at point that is just slightly to the left of B and indicate the s
ign of
the shear by drawing a representative icon with arrows to in
dicate the direction of the shear forces at that position. Given:
the beam has two point loads of 1200 lbs, each. The beam sits on the ground and it is assumed that the ground resists the
loads with an evenly

distributed loading, as shown
29.
(10 points) Determine the internal shear in the beam below at point that is just slightly to the right of B and indicate the
sign
of the shear by drawing a representative icon with arrows to indicate the direction of the
shear forces at that position. Given:
the beam has two point loads of 1200 lbs, each. The beam sits on the ground and it is assumed that the ground resists the
loads with an evenly

distributed loading, as shown
30.
(30 points) Determine the internal normal force, shear force and bending moment at point F of the frame. For each, indicate
the sign of the force or moment by drawing a representative icon with arrows to indicate the di
rection.
31.
(30 points) Determine the internal normal force, shear force and bending moment at point D. For each, indicate the sign of
the force or moment by drawing a representative icon with arrows to indicate the direction.
1200 lb
Beam
Ground
w
4 ft
4 ft
4 ft
1200 lb
A
B
C
D
1200 lb
Beam
Ground
w
4 ft
4 ft
4 ft
1200 lb
A
B
C
D
Spring
2013
ES226
Exam
5
Study Guide
Prof. Kurtz
9
of
9
Derive
M(x) and V(x) expre
ssions for beams.
32.
(25 points) Write the moment function M(x) for the beam below. Given: 4000 ft

lb moment couple applied at point B.
You must use the standard sign convention for internal bending moment (compression

on

top is positive).
33.
(25 points) Write the moment function M(x) for the beam below. Given: 500 lbs/ft uniformly distributed load. You must
use the standard sign convention for internal bending moment (compression

on

top is positive).
34.
(25 points) Write the shear function V(x) for the beam below. Given: distributed load that increases linearly from 0 lb/ft
at
A to 1000 lb/ft at B. You must use the standard sign convention for internal shear.
A
B
w = 1000 lbs/ft
10 ft
x
A
B
w = 500 lbs/ft
10 ft
x
A
B
5 feet
4000 ft

lb
x
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