HW 11 Solutions Virtual Work Method 2023
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3210
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Mechanical Engineering
Date
Jan 9, 2024
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7
Uploaded by BarristerRabbit3362
CvEEN-3210
Fall 2023
Homework # 11
HW 11-1
VIRTUAL WORK METHOD
Due date: Monday December 4, 2023 at 9 pm (100 points)
1.
Find the vertical deflection at point C. E = 29,000 ksi.
CvEEN-3210
Fall 2023
Homework # 11
HW 11-2
CvEEN-3210
Fall 2023
Homework # 11
HW 11-3
2.
Use the two virtual work method approaches (direct integration and computation of areas) to
find the vertical deflection at B, and the slope at A of the following steel beam. Assume A is
pinned, B is a roller, and C is a free end. E = 29,000 ksi, and I = 300 in
4
.
Courtesy of Nicholas Anewalt:
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CvEEN-3210
Fall 2023
Homework # 11
HW 11-4
CvEEN-3210
Fall 2023
Homework # 11
HW 11-5
3.
Use the two virtual work method approaches (direct integration and computation of areas) to
find the horizontal displacement at point A, and the vertical displacement at B of the following
frame. Assume C is a fixed connection, B is a rigid joint and A is a free end.
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CvEEN-3210
Fall 2023
Homework # 11
HW 11-6
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CvEEN-3210
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Homework # 11
HW 11-7
4.
Use the virtual work method (only direct integration) to find the horizontal deflection at C.
Assume EI is constant, A is a pin, C is a roller and B is a rigid joint.
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12.
Figure Q12 shows a prospective design for a conveyor roller system, for transferring
crates, one at a time. The system is made up of two parallel rectangular steel
beams, built-in at one end and simply supported at the other, with closely spaced
rollers mounted in-between, for the crate to pass over.
a) Using Macaulay notation, carry out an analysis of the problem and calculate
the deflection of the mid-length point of the beams when the crate is
centrally located, midway between A and B. State any important
assumptions used in your analysis.
[20 marks]
b) Comment briefly whether this would be the maximum deflection of the beams
when the crate is centrally located.
2 m
8 m
A
Direction of travel
Figure Q12 (side view, only one beam visible)
Useful information
I for each separate beam = 12 ×10 m²
E for both beams = 210 GPa
Weight of one crate = 800 N
[5 marks]
B
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Question No 3 Use both IC method and regular (vector/scalar) method
Given: ASF. Angular velocity of link AB = 10 rad/s.
Required: (1) Angular velocity of link BC, (2) Angular velocity of link CD,
(3) Vc at shown instant and (4) show directions on the sketch
(5) Draw deflection line (on ONE separate sketch for angles 30, 45 and 60
degrees
0.2 m
0.4 m
0.2 m
B
300
A
@=10 rad/s
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Homework #6
P (MAE 271-03) (FA24) STAT...
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The built-up beam is subjected to a moment of M = 80 kNm.
d₁
d₂
d3
d₁
d5
d3
do
wamap.org
Value
d₂
Values for the figure are given in the following table. Note
the figure may not be to scale.
Variable
128 mm
22 mm
276 mm
11 mm
138 mm
d4
12 mm
M₁
de
d5
a. Determine the distance from the Neutral Axis to the
top of the beam, NA.
b. Determine the mass moment of inertia of the beam, I.
Determine the max compressive stress acting on the
c.
beam, compression.
d. Determine the max tensile stress acting on the beam,
Tin
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FEA
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For the simply supported beam shown
below:
O
4klf
98 downward
116 upward
70 downward
15'
104 downward
0
The vertical reaction in kips at A (Ay) is
mostly near____
70 upward
116 downward
98 upward
104 upward
150k
B
30k
с
151
-3xlf
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Part 1
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b-9.0 ft,
c-5.0 ft.d-4.0 ft. w- 10.5 kips/ft and P-117 kips. Construct the shear-force and bending-moment diagrams on paper and use the
results to answer the questions in the subsequent parts of this GO exercise.
A
D
For this loading, calculate the reaction forces A, and Ey acting on the beam. Positive values for the reactions are indicated by the
directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body
diagram.)
Answers: Ay=
D
d
2
kips, Ey
E
kips
Part 2
Determine the shear force acting at each of the following locations:
(a)x=0+ ft (l.e., just to the right of support.A)
(b)x=4,0 ft
(c) x-13.0 ft
(d) x-18.0-ft (le, just to the left of D)
(e)x= 18.0+ ft (l.e., just to the right of D)
(f)x=22.0-ft (ie, just to the left of support E)
When entering your answers, use the shear force sign convention.…
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Find the diameter of a steel line shaft to transmit 10 horsepower at 150 revolutions per minute with a torsional
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Question 01 Calculate the number of convolutions (n) to get a deflection of 310 degrees in a
bellow:
P.R2
8 = 2.n.Ae.
E.t3
8 = deflection of the bellows
n=?
(mumber of convolutions)
Ae = u and r= 2 m
P = 50 Pa
R= 0.6 m
E = 2 Pa (Young's modulus)
t=2 m
(wall thickness)
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Refer to the table of equations when answering.
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TOPIC: Machine Design
Multiple choice
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Please Provide correct solution, correct Method.
No Missing steps / calculations.
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Show detailed solution refer to the table of equations.
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Considering Figure 20-8 (textbook), the torsion geometry parameter, Jw, for case 8 when b=6 and d=9 is most likely:
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386.0
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