ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
Please review the following statement:
I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Signature: ______________________________________
INSTRUCTIONS
Begin each problem in the space provided on the examination sheets. If additional space is required,
use the white lined paper provided to you.
Work on one side of each sheet only, with only one problem on a sheet.
Each problem is worth 20 points.
Please remember that for you to obtain maximum credit for a problem, it must be clearly presented,
i.e.




The coordinate system must be clearly identified.
Where appropriate, free body diagrams must be drawn. These should be drawn separately
from the given figures.
Units must be clearly stated as part of the answer.
You must carefully delineate vector and scalar quantities.
If the solution does not follow a logical thought process, it will be assumed in error.
When handing in the test, please make sure that all sheets are in the correct sequential order
and make sure that your name is at the top of every page that you wish to have graded.
Instructor’s Name and Section:
Sections:
J Jones 9:30-10:20AM
P Sojka 1:30-2:20PM
J Jones Distance Learning
J Silvers 3:30-4:20PM
Problem 1 __________
Problem 2 __________
Problem 3 __________
Total ______________
ME 270 Exam 3
Page 1
ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
PROBLEM 1 (20 points) – Prob. 1 questions are all or nothing.
1A. The frame shown below is made up of links AC and BD.
A lineraly-varying distributed loading is applied to link AC,
where p 0 is the value of the loading at end C. Consider
a perpendicular cut through link AC at location E. For the
cut face on segment AE, determine the shear force V and
the bending moment M. Leave your answer in terms of the
given parameters of the problem, but simplify your final answer
as much as possible.
VE =
(2 pts)
ME =
(3 pts)
1B. A square press that is 2.0 in. x 2.0 in. punches a hole in a ¼ inch thick 31655 stainless steel
metal plate with a shear resistance of τ max = 36 ksi . The plate has the following material properties:
σ yp = 42 kips/in 2 , σu = 84 kips/in2 , E = 28,000 kips/in2 . What is the minimum force required to
ensure the hole can be fully punched?
Fmin =
ME 270 Exam 3
(5 pts)
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
1C. A horizontal bar is attached to a fixed bracket through
two rubber pads onto the upper and lower inner
surfaces of the bracket, as shown in the figure. The
rubber has a shear modulus of G. A horizontal load
P acts on the free end of the bar. Determine the
shear stress in the rubber pads where they meet the
bar. Use the following parameters in your analysis:
P = 450 N , b = 60 mm , w = 100 mm , and G = 0.6 M Pa .
τ=
(Show solution in Pa)
(5 pts)
1D. Determine the maximum shear stress and shear strain on the bolt just below the head for the
following parameters, P = 75 lbs , x = 13 inches , d = 0.375 inches . Sketch the shear stress
distribution over the cross-section of the bolt. Assume the Shear Modulus (G) is 12 x 106 psi.
(1pt)
τmax =
ɣmax =
ME 270 Exam 3
(2 pts)
(2 pts)
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
PROBLEM 2. (20 points)
GIVEN: The truss shown is made of structural steel (σyield =
36 ksi; E = 29 x 103 ksi; ν = 0.29). Beam BH has a
cross-sectional area ABH = 0.5 in2, and beam EF has
a cross-sectional area AEF = 2.0 in2. The truss is
subjected to a 10 kip load at B and a 60 kip load at E.
FIND:
a) Determine the forces in members BH and EF.
Include any free body diagrams used, and identify if the members are in tension or
compression. (5 pts)
b) Determine the normal stress, axial strain, and transverse strain in BH. (6 pts)
c) Determine the normal stress in EF. Has yielding occurred? (3 pts)
d) If the 10 kip load remains constant at point B, determine the maximum allowable load at point
E so that EF will not yield; use a factor of safety of 1.5. Under this loading, will BH yield?
(6 pts)
a) FBH = ___________ T or C
FEF = ___________ T or C
b) Values for BH
Normal stress _______________
Axial strain _________________
Transverse strain ____________
c) Values for EF
Normal stress _______________
Yielding?
Yes
or
No
d) Max load at E ____________
Will BH yield?
ME 270 Exam 3
Yes
or
No
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ME 270 – Spring 2014 Exam 3
ME 270 Exam 3
NAME (Last, First): ________________________________
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
2 kN/m
PROBLEM 3. (20 points)
8 kN-m
GIVEN: Beam ABCD is held in static equilibrium by a
pin support at A and a roller support at C. The beam
is loaded with a concentrated force and couple at B
and uniformly a distributed load between C and D as
shown. The beam cross-section is rectangular with
a height of 10 cm and a width of 6 cm.
2m
2m
D
2m
6 kN
x
FIND:
C
B
a) Determine the reactions at supports A and C. (4 pts)
b) On the graph provided, sketch the shear-force diagram for the load condition shown. At each
interface along the beam (A, B, C, D), label the magnitude of the shear-force on the diagram.
(6 pts)
c) On the graph provided, sketch the bending-moment diagram for the load condition shown. At
each interface, along the beam (A, B, C, D), label the magnitude of the bending moment on the
diagram. (6 pts)
d) Determine the second area moment of inertia (I) of the rectangular cross-section and the
maximum stress that acts on the beam in the section where pure bending occurs. (4 pts)
a)
A
B
C
D
Ax =
Ay =
Cy =
ME 270 Exam 3
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
2 kN/m
8 kN-m
2m
x
b)
D
C
B
2m
2m
6 kN
A
B
B
C
D
A
B
B
C
D
c)
d)
ME 270 Exam 3
I=
(2 pts)
 σMAX  =
(2 pts)
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ME 270 – Spring 2014 Exam 3
ME 270 Exam 3
NAME (Last, First): ________________________________
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
ME 270 Exam 3 Equations
Normal Stress and Strain
∫
Shear Stress and Strain
(
)
Shear Force and Bending Moment
( )
(
)
ME 270 Exam 3
( )
( )
( )
∫ ( )
∫ ( )
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ME 270 – Spring 2014 Exam 3
NAME (Last, First): ________________________________
ME 270 Exam 3 Equations
MB = 5 poL2 /9
1A.
VB = 2 poL/3
1B.
Fmin = 72 kip
1C.
τ = 37500 Pa
1D.
τmax = 94163 psi
γ max = 0.00785 (
2A.
FBH = 10 kip Tension
FEF = 75 kip Tension
2B.
σ x = 20 ksi
ε x = 6.90 x 10-4 (
2C.
σx = 37.5 ksi
in
)
in
ε y = -2 x 10-4 (
in
)
in
Yielding has occurred.
2D. Max load at E is: 38.4 kip
3A.
in
)
in
A x = 0 kN
BH will not yield.
A y = -6 kN
Cy = 4 kN
3B. Shear-Force Diagram
3C. Bending-moment diagram
3D.
I = 5 x 106 m4 = 500 cm4
ME 270 Exam 3
(σMAX ) = 40 MPa
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