ME 270 Fall 2013 Final Exam NAME (Last, First): Please · PDF file · 2016-05-02......
Transcript of ME 270 Fall 2013 Final Exam NAME (Last, First): Please · PDF file · 2016-05-02......
ME 270 – Fall 2013 Final Exam 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. Silvers 8:30-9:30am B. Hylton 2:30-3:20pm J. Jones 11:30am-12:20pm J. Seipel 12:30-1:20pm M. Murphy 9:00-10:15am E. Nauman 9:30-10:20 am K. Li 1:30-2:20pm J. Jones Distance Learning
Problem 1 __________
Problem 2 __________
Problem 3 __________
Problem 4 __________
Problem 5 __________
Total ______________
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ PROBLEM 1 (20 points) – Prob. 1 questions are all or nothing.
1(a) An overhead lamp is held in static equilibrium by cable AC and horizontal spring AB. Given the spring constant is k=300 N/m and the net deformation of the spring is 0.453m, determine the magnitude of the tension in cable AC and the weight of the lamp. (4pts)
1(b) Bar ABC is loaded at C with one force and one couple as shown. Determine the equivalent force-couple system at A. Express your solution in vector form. (Hint –
This is not a static equilibrium problem.) (4pts)
AC
Lamp
(2 pts)T =
W = (2 pts)
eq A
eq A
(F ) = (2 pts)
(M ) = (2 pts)
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ 1(c) Bar OA is loaded with a single force as shown and is held in static equilibrium by a built-in support at O. Determine the reactions at O due to this loading. (4pts)
1(d) The fink truss is loaded as shown. Identify all zero-force members by placing a zero over that member. (4pts)
A
O
O
F = (2 pts)
M = (2 pts)
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ 1(e) The 15° wedge shown is being removed by force P. On the figures provided, complete the free body diagram of the crate and wedge. Write the x and y-equilibrium equations for the wedge. Assume friction exists on all interfaces (A, B and C). Leave the friction forces generic (i.e., fA, fB, fC) DO NOT SOLVE THE EQUATIONS. (4pts)
1 pt
1 pt
x
y
F = 0 = (1 pt)
F = 0 =
(1 pt)
C
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ PROBLEM 2 (20 points)
Given: Rod AB is loaded at its midpoint with a vertical
force CP 72 lb . The weight of the rod is negligible. It
is held in place at A by a ball and socket joint. At B, the rod rests against a smooth wall in the x-z plane, and is held in place by a cable (BD) which is parallel to the x-axis. Find:
a) On the figure provided, draw a complete free body diagram. (5 pts)
b) Write the position vector from A to B, and the position vector from A to C. (3 pts)
c) Determine the tension in cable BD, and the force from the smooth wall at B. Give your answers in vector form. (8 pts)
d) Determine the reactions from the ball and socket joint at A. Give your answer(s) in vector form. (4 pts)
Free Body Diagram
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________
Name (last, first)
Problem #3 Fall 2013 Final
a.
b. Ax=
Ay= Fy= .
c. |VA|= τA= .
d. γA=
e. Load BD tension or compression (circle one)
f. σBD
g. εx in member BD
12 ft
6 ft
3 ft
4 ft
80 kip
A
B
C
D
F
80 kip
Ax
B
C
D
F
80 kip
A
B
C
D
F
B D
C
The structure is subjected to a 80kip (80,000 lb) load as shown. The
mass of the members is negligible when compared to applied load.
BD is a two-force member. A support pin at Joint A makes contact
with the joint on two sides (double shear pin).
The modulus of elasticity (E) is 10x106 psi (10x10
3ksi) for all
members, including the pin at A.
Poisson’s Ratio for all members, including the pin at A.
The cross-sectional area of member BD is 0.5 in2.
The joint at A is supported on two sides by a pin with a cross-
sectional area of 0.5 in2.
Please place your answers in the box provided. Remember units! Coordinate axis is provided for this problem.
ALL steps of your work must be shown to earn credit.
a. The free-body diagrams for the entire structure is provided,
please complete the free-body diagram for the exploded
structure (3 points) on the figure provided.
b. Determine the reactions at A and F (3 points)
c. Determine the magnitude of the shear force |VA| and the shear
stress τA on the support pin at A (3 points).
d. Determine the shear strain on the Pin at A (3 Points)
e. Determine the load carried by member BD and circle
whether it is in tension or compression (3 points)
f. Determine the axial stress σBD in member BD (3 points)
g. Determine the axial strain εx in BD (2 points)
Ay Fy
Ax Ay
A
Fy
y
x
Joint A
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ PROBLEM 4 (20 points)
4(a) A cantilevered structure is loaded as shown, with F = 100 N. Calculate the internal forces and moments, in vector form, at cut A. A coordinate system is provided on the figure. (4 pts)
4(b) A leather worker is punching a square hole in a leather strap. The punch cross-section is 5mm by 5mm. The leather strap is 2 mm thick. If the leather worker applies a 5 N force to the punch, calculate the average shear stress in the leather. (3 pts)
FBD
�⃑⃑� _____________________________ �⃑⃑⃑� _____________________________
𝝉𝒂𝒗𝒈 _____________________________
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ 4(c) A cantilevered shaft is loaded as shown. Section AB is a solid aluminum shaft with diameter d. Section BC is a hollow steel shaft with an outer diameter d and wall thickness 0.1*d. Let d = 6 inches and T = 10 ft-kips. Calculate the polar moment of area and maximum torsional stress in the hollow region of the shaft (BC). Then, using the provided values, calculate the maximum torsional strain in the shaft. (6 pts)
AB BC
Polar Moment of Area (J) 127.23 in4 _________________
Maximum Torsional Stress (𝝉𝒎𝒂𝒙) 2.83 ksi _________________
Modulus of Rigidity (G) 3.8 x 103 ksi 11.2 x 103 ksi
Torsional Strain (𝜸) __________________ _________________
𝜸𝒎𝒂𝒙 _____________________________
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ 4(d) Setup but do not integrate the equation for the 2nd moment of area of the cross-section shown below, rotating about the given axis, x. (3 pts)
4(e) Using the method of composite parts, calculate the 2nd moment of area of the cross section shown below, rotating about the given axis, x. Both cross-bars have the same length and thickness. (4 pts)
𝑰𝒙 ______________________________________________________
𝑰𝒙 _____________________________
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ ME 270 –Fall 2013
Problem 5. (20 pts).
5a. The beam given below is supported by a pin and roller. Determine the reactions at points A and D and write them in the space provided below. Note that the beam cross section is rectangular, with a base of 200 mm and a height of 400 mm.
(Draw Free Body Diagrams used for part 5a here):
(2 pts) Reaction at point A (WRITE ANSWER HERE): _______________________________
(2 pts) Reaction at point D (WRITE ANSWER HERE): ________________________________
4 kN
1m
2m
1m
5 kN/m
4 kN-m
A B
C D
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ ME 270 –Fall 2013
Problem 5 Continued
5b. For the beam given in part a above, draw the shear force and bending moment diagram in the space provided. (9 pts).
4 kN
Shear
Force
V(x)
Bending
Moment
M(x)
1m 2m 1m
5 kN/m
4 kN-m
A B
C
D
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________ ME 270 –Fall 2013
Problem 5 Continued
5c. Locate the point where pure bending occurs as the distance from pt A. (2 pts)
Location of pure bending measured from A (WRITE ANSWER HERE):______________________
5d. What is the maximum magnitude of bending moment that occurs in the beam. (2 pts).
Maximum bending moment (WRITE ANSWER HERE) : _______________________________
5e. For the location found in part c, determine the maximum axial stress due to bending. (3 pts).
Maximum axial stress (WRITE ANSWER HERE): _________________________________
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________
ME 270 Final Exam Equations Fall 2013
Normal Stress and Strain
σx =Fn
A
σx(y) =−My
I
εx =σx
E=∆L
L
εy = εz = − ϑεx
εx(y) =−y
ρ
FS =σfail
σallow
Shear Stress and Strain
τ =V
A
τ(ρ) =Tρ
J
τ = Gγ
G =E
2�1 + ϑ
γ =δs
Ls=π
2− θ
For a rectangular cross-
section,
τ(y) =6V
Ah2
h2
4− y2
τmax =3V
2A
Second Area Moment
I = y2dA
A
I =1
12bh3 Rectangle
I =π
4r4 Circle
IB = IO + AdOB2
Polar Area Moment
J =π
2�ro
4 − ri4 Tube
Shear Force and Bending
Moment
V�x = V�0 + p�ϵ dϵx
0
M�x = M�0 + V�ϵ dϵx
0
Buoyancy
BF gV
Fluid Statics
p gh
eq avgF p Lw
Belt Friction
L
S
Te
T
Distributed Loads
L
eq 0F w x dx
L
eq 0xF x w x dx
Centroids
cx dAx
dA
cy dAy
dA
ci ii
ii
x A
xA
ci ii
ii
y A
yA
In 3D,
ci ii
ii
x V
xV
Centers of Mass
cmx dAx
dA
cmy dAy
dA
cmi i ii
i ii
x A
xA
cmi i ii
i ii
y A
yA
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________
Fall 2013 ME 270 Final Answers
1A. ACT = 157 N LampW = 78.5 N
1B. eq A(F ) = 25 i + 43.3j lb eq A(M ) = 520 lb-ft
1C. OF = -80 i + 60j N OM = 460k N-m
1D. Zero Force Members: BP, CP, CO, CN, DN, EM, ON, & NE.
1E. o o
A B BXF = 0 = -P + f + f cos 15 - N sin 15
o o
A B ByF = 0 = -N + N cos 15 + f sin 15
2A. Free Body Diagram
2B. ABr = 4 i - 7j + 9k ft ACr = 2 i - 3.5j + 4.5k ft
2C. N = 28 lb j T = -16 lb i
2D. AF = 16 i - 28j + 72k lb
3A. Free Body Diagram
3B. xA = -80 kip yA = -60 kip yF = 60 kip
3C. AV = 100 kip A = 100 ksi
3D. Aγ = 0.026 in/in
3E. Load BD 120 kip Tension
3F. BD = 240 ksi
3G. x in member BD is 0.024 in/in
4A. F = (-160 i + 120j) N M = (360k) N-m
4B. AVG = 0.125 MPa
4C. maxγ = 0.000745
ME 270 – Fall 2013 Final Exam NAME (Last, First): ________________________________
4D.
3 43 - x 4 - y
4 2 3 24 3x 0 0
0 0
3I = y dydx or (3 - x) dxdy
4
4E. 4
xI = 1365.6 in
5A. FBD Reaction at point A: 9j kN Reaction at point D: 5j kN
5B. Shear force bending moment diagram
5C. Location of pure bending measured from A: x = 2m or 2m from pt A
5D. Maximum bending moment: 11.5 kN-m
5E. Maximum axial stress: 2.156 MPa