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Nov 15, 2013 (3 years and 11 months ago)

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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

of
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

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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






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9

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