2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Introduction
Suggested Review Materials
- Schaum’s Outline Series, Theory & Problems of:
· Engineering Mechanics
· Strength of Materials
· Machine Design
Published by McGraw-Hill
- The following by Michael R. Lindeburg, Professional Publications, Inc. Belmont CA (www.ppi2pass.com)
· Mechanical Engineering Reference Manual
· Practice Problems for the Mechanical Engineering PE Exam
- ABS Rules for Building and Classing Steel Vessels 2001, Part 4, Vessel Systems and Machinery, American Bureau of Shipping, Houston, TX.
- Mechanical Engineering Design by J. Shigley & C. Mischke, McGraw-Hill.
- ANSI/ASME B106.1M, Design of Transmission Shafting, ASME, New York, NY
- Formulas for Natural Frequency and Mode Shape by R.D. Blevins, Ph.D, Kreiger
- Methods of Analytical Dynamics by L. Meirovitch, McGraw-Hill
- Fundamentals of Vibrations by L. Meirovitch, McGraw-Hill
- Marks Standard Handbook for Mechanical Engineers, Knovel
- Fundamentals of Acoustics by Kinsler & Coppens, Wiley
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Introduction (con’t)
LOADS RESULTING FROM PITCH & ROLL
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Introduction (con’t)
LEGEND
W = weight, lbf
q (t) = pitch or roll angle as a function of time, rad
qmax = maximum pitch or roll angle, rad or deg
w(t) = angular velocity due to pitch or roll as a function of time, rad/s
a(t) = angular acceleration due to pitch or roll as a function of time, rad/s2
T = pitch or roll period, s
R = pitch or roll radius, ft
t = time, s
x = horizontal distance athwartships from component cg to vessel’s roll axis, ft
y = vertical distance from component cg to vessel’s pitch or roll axis, ft
z = horizontal distance fore & aft from component cg to vessel’s pitch axis, ft
y = orientation angle of pitch or roll radius with vertical, rad or deg
FW = static load due to weight
FN = force due to centripetal acceleration, lbf
FT = force due to tangential acceleration, lbf
Subscript P = pitch
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Introduction (con’t)
Subscript R = roll
Subscript = component parallel to deck
Subscript ^ = component perpendicular to deck
Mg(t) = gyroscopic moment as a function of time, ft-lbf
IP = mass polar moment of inertia, lbf-ft-s2
N = operating speed, rpm
W = angular velocity of rotor due to operating speed, rad/sec
X = cross product
ASME B106.1M Shafting Criteria
Per ASME B106.1M,
d0 =
d0 = outside diameter
di = inside diameter
K =
FS = factor of safety
Sf = fatigue strength (endurance limit)
Sy = yield strength
T = torque
M = bending moment
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment
1. Mohr’s Circle:
The rigid body shown below is acted on by forces that result in σx = 10,000 psi, σy = -15,000 psi, and xy = 5000 psi cw.
a) Find principal normal stresses σ1, σ2, and σ3.
b) Find the maximum shear stress
2. Combined Stress
A rigid body is acted on by forces that result in σx = 10,000 psi, σy = -15,000 psi, σz = 25,000 and xy = 5000 psi, xz = 2500 psi, and yz = 20000 psi. The yield stress of the material is 15,000 psi. Is yielding predicted based on the maximum distortion energy theory (vonMises)?
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
3. Critical Speed
What is the critical speed (first lateral natural frequency) of the constant diameter round shaft assembly shown below? Give the answer in rpm.
Assume that the bearings are rigid simple supports. Also, ignore shaft and bearing weights.
The following applies:
Shaft material = steel (E = 30E6 psi)
L1 = 3 ft
L2 = 10 ft
L3 = 8 ft
d = 1.500 inch
Disk 1 Weight = 1000 lbf
Disk 2 Weight = 200 lbf
NOT DRAWN TO SCALE
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
4. Lateral Deflection
The following applies to the cantilever shown below:
A = 6”
B = 24”
F = 100 lbf
w = 10 lbf/in
L = 36”
h = 2”
b = 4”
Shaft material = steel (E=30E6 psi)
Find the deflection at the free end of the beam.
NOT DRAWN TO SCALE
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
5. Torsional Deflection
The left end of the shaft shown below is fixed. A torque of 1000 ft-lbf is applied to the disk. Also, the diameter and length of the large diameter shaft section are 3 inches and 2 feet, respectively. Similarly, the diameter and length of the small diameter shaft section are 1 inch and 4 feet, respectively. The shaft is in one piece and is made from a material with a shear modulus of 15000000 psi.
Find the torsional (angular) deflection (in deg) of the disk shown below with respect to the fixed end.
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
6. Shaft Diameter
A constant-diameter horizontally mounted shaft is shown below. The following applies:
· Ignore bearing weights.
· Assume that the disk weight acts as a concentrated load.
· The shaft is hollow with an od of 4 inches and an id of 2 inches.
· The shaft will be used to transmit 500 hp at 1760 rpm.
· Assume that the bearings act as simple supports with the reaction at the center of each bearing.
· The shaft material is alloy steel with a yield strength of 100,000 psi, a fatigue strength of 60,000 psi, and a modulus of elasticity is 30E6 psi, and a specific weight of 0.3 lbf/in3.
· Ignore fatigue strength adjustment or stress concentration factors
Find the safety factor for the shaft at x = 120 inches (the center of the disk) using ASME B106.1M (Design of Transmission Shafting) criteria.
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
6. (con’t)
7. Pipe Stress
A plain-end NPS 6 pipe is used to convey steam at a maximum allowable working pressure of 850 psig and a temperature of 900F. The pipe is made from seamless ½ Cr-½ Mo Steel (ASTM A335, Gr P2). The mill tolerance for the pipe is +/- 12.5%.
What is the minimum schedule required based on hoop stress. (Ignore expansion or longitudinal stress).
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
8. Reaction Loads
For the cantilever shown below, find the resultant reaction force and moment.
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
8. (con’t)
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
9. Unbalance
The rotating assembly shown below turns at 1800 rpm. The disk has a net unbalance of 1.5 oz-in. What is the radial force that results from this unbalance?
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
10. Natural Frequency
The object shown below has a mass of 100 kg and is supported by three equal springs. A force of 1000 N is applied to the mass shown below and results in a vertical deflection of 25 mm. At what frequency (in hz) will the mass vibrate when the force is removed? Also, what will be the maximum velocity? (Assume that damping and the spring mass are negligible).
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
11. Friction
The static coefficient of friction between the block and the ramp shown below is 0.20. Also, the kinetic coefficient of friction between the block and the ramp is 0.15. Ignore the mass of the pulleys and the cable.
a) Assuming that both pulleys and the cable are weightless and frictionless, what is the minimum vertical force that must be applied to the pulley 2 to hold the block in place?
b) If the vertical force found in part a is set equal to ½ of the value found in part a, what will the velocity of the block be after it has moved 10 m along the ramp.
c) Repeat part a with a coefficient of friction between the cable and the pulley 1 of 0.30. Pulley 2 remains frictionless.
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
12. Pitch and Roll
A 2000 lbf component is mounted on the deck of a ship. The following applies:
Max roll angle = +/- 30 deg
Roll period = 15s
Athwartships distance from component center of gravity to vessel roll center: 12.5 ft
Vertical distance from component center of gravity to vessel roll center:
-10 ft
Find the loads that are perpendicular to the deck when the roll angle is 15 deg.
13. Gyroscopic Moment
A shipboard horizontal pump mounted with its shaft axis in the fore-aft direction operates at a speed of 3560 rpm. The rotor resembles a hollow cylinder with an outside diameter of 12 inches and an inside diameter of 2 inches. The rotor length is 6 in. The density of the rotor material is 0.3 lbm/in3.
What is the maximum gyroscopic moment that will be applied to the rotor when the vessel pitches at an angle of +/- 10 deg with a period of 15 seconds?
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
14. Propulsion Shaft Diameter
Following the ABS Rules, determine the minimum outside diameter of solid lineshafting and the tailshaft for a vessel.
Assume that:
· Shrink-fit couplings are used to join adjacent shaft sections.
· The stern-tube bearing is seawater lubricated with a continuous liner
· The vessel is propelled by a single 30,000 hp slow-speed diesel engine.
· The shaft material is Alloy 4 Steel with a tensile strength of 120,000 psi.
· The propeller is attached by a shrink fit.
· The rated propeller speed is 100 rpm.
15. Buckling
a) Solve for the minimum force that will result in buckling with a safety factor of 1.00
Column cross-section = 6” x 12”
Column length = 200 “
Yield strength = 100,000 psi
F = 1000 lbf
E = 30E6 psi
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
16. Continuous System
What is the first natural frequency of a steel wire with a total mass of 0.2 kg and a length of 30 m that is fixed at both ends and is stretched with a tension of 20 N?
17. Forces and Moments
Find the resultant reaction force and moment acting at the fixed end of the handle shown below
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
18. Force Distribution
At what angle θ will the load on each runner of the married fall system shown below be equal to the load W being hoisted?
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
19. Thermal Expansion
A bronze bearing is inserted into a steel shell, as shown below. At room temperature (70 F), the outside diameter of the bearing is just equal to the inside diameter of the outer shell.
What will the interference be between the two cylinders during operation if their temperature increases to 150F? Assume that both the bearing and the shell are free to expand axially and that the outside diameter of the shell is free to expand radially.
The following applies (dimensions are at 70 F):
Bearing id, 6.000 “
Bearing od = Shell id = 6.500”
Shell od = 7.000”
Ebrg = 15E6 psi αbrg = 9.3E-6 in/in-F
Eshell = 30E6 psi αshell = 6.5E-6 in/in-F
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
19. (con’t)
2004 Professional Engineer Review Course
Unit I – Fundamentals: Instructor: M. Ales
Introduction and Assignment
Assignment (con’t)
20. Speed of Sound
a) What is the speed of sound through air that is at atmospheric pressure and a temperature of 0 C?
b) What is the speed of sound through fresh water that is at atmospheric pressure and a temperature of 20 C?
21. A reciprocating air compressor discharges air at a pressure of 6 bar and a temperature of 90C into a constant diameter piping system that has a length of 20 m. The compressor operates at a low enough speed to generate only plane waves through the air. What is the first natural frequency of a piping system when a valve at the end of the system (the end not connected to the compressor) is closed?