hamrock

Chapter 1: IntroductionTh’ invention all admir’d, and each, how he
To be th’ inventor miss’d; so easy it seem’d,
Once found, which yet unfound most would have thought
Impossible.
John Milton
Image: A modern printing press. Gutenberg described the idea of a printing press as “Coming like a ray of light.”
Hamrock, Jacobson and Schmid
(b) Concurrent Engineering Approach (adapted from Pugh [1996]).
Text Reference: Figure 1.1, page 5
Design for Manufacture
Effect of manufacturing and assembly on design of reciprocating power saw.
(a) Original design, with 41 parts and 6.37 min assembly time. (b) modified design, with 29 parts and 2.58 min assembly time. [From Boothroyd (1992)].
ns,y from Table 1.2
Table 1.2: Safety Factor Characteristics D and E
Text Reference: Tables 1.1 and 1.2, page 9
Characteristica
D=
D=danger to personnel
avg=very good, g=good, f=fair and p=poor
A=quality of materials, workmanship, maintenance and inspection
B=control over load applied to part
C=accuracy of stress analysis, experimental data, or experience with similar parts
(a) SI units
1 000 000 000 = 109
1 000 000 = 106
tera
giga
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
pico
T
G
M
k
h
da
d
c
m
µ
n
p
(a) Fundamental conversion factors
1g=9.8066 m/s2 (32.174 ft/s2)
Btu (British thermal unit)∫amount of energy required to raise 1 lbm of water 1 deg F (1 Btu = 778.2 ft-lbf)

degree Fahrenheit tF=9/5tC+32 (where tC is degrees) (Celsius)
degree Rankine tR=tF+459.67
Kelvin tK=TC+275.15 (exact)

1 kW = 3413 Btu/hr
1 kcal = 3.968 Btu
Wheelchair, courtesy of Sunrise Medical Equipment Co.
When I am working on a problem, I never think
about beauty. I only think of how to solve the
problem. But when I have finished, if the solution
is not beautiful, I know it is wrong.
Richard Buckminster Fuller
Image: A dragline lifts a large load in a mining operation.
A Simple Crane
Figure 2.1 A simple crane and forces acting on it. (a) Assembly drawing; (b) free-body diagram of forces acting on the beam.
text reference: Figure 2.1, page 30
Figure 2.2 Load classified as to location and method of application. (a) Normal, tensile (b) normal, compressive; (c) shear; (d) bending; (e) torsion; (f) combined
©1998 McGraw-Hill
Sign Convention
Figure 2.3 Sign convention used in bending. (a) y coordinate upward; (b) y coordinate downward.
©1998 McGraw-Hill
Lever Assembly
Figure 2.4 Lever assembly and results. (a) Lever assembly; (b) results showning (1) normal, tensile, (2) shear, (3) bending, (4) torsion on section B of lever assembly.
Table 2.1: Four types of support with their corresponding reactions.
text reference: Table 2.1, page 35
Ladder Free Body Diagram
Figure 2.5: Ladder having contact with the house and the ground while having a painter on the ladder. Used in Example 2.4. The ladder length is l.
External Rim Brake and Forces
Figure 2.6 External rim brake and forces acting on it. (a) External rim brake; (b) external rim brake with forces acting on each part. (Linear dimensions are in millimeters.)
Sphere and Forces
Figure 2.7 Sphere and forces acting on it. (a) Sphere supported with wires from top and a spring at the bottom; (b) free-body diagram of forces acting on the sphere. Figure used in Example 2.6.
©1998 McGraw-Hill
Beam Supports
Figure 2.8 Three types of beam support. (a) Simply supported; (b) cantilevered; (c) overhanging.
Simply Supported Bar
Figure 2.9 Simply supported bar with (a) midlength load and reactions; (b) free-body diagram for 0<x<l/2; (c) free body diagram for l/2<x<l; (d) shear and bending moment diagrams.
Singularity Functions (Part 1)
Table 2.2 Six singularity and load intensity functions with corresponding graphs and expressions.
Singularity Functions (Part 2)
Table 2.2 Six singularity and load intensity functions with corresponding graphs and expressions.
Shear and Moment Diagrams
Figure 2.10 (a) Shear and (b) moment diagrams for Example 2.8.
Simply Supported Beam
Figure 2.11 Simply supported beam. (a) Forces acting on beam when P1=8kN, P2=5kN; w0=4kN/m; l=12m; (b) free-body diagram showing resulting forces; (c) shear and (d) moment diagrams of Example 2.9.
©1998 McGraw-Hill
Example 2.10
Figure 2.12 Figures used in Example 2.10. (a) Load assembly drawing; (b) free-body diagram.
Figure 2.13 Stress element showing general state of three-dimensional stress with origin placed in center of element.
2-D State of Stress
Figure 2.14 Stress element showing two-dimensional state of stress. (a) Three dimensional view; (b) plane view.
©1998 McGraw-Hill
Equivalent Stresses
Figure 2.15 Illustration of equivalent stresss states; (a) Stress element oriented in the direction of applied stress. (b) stress element oriented in different (arbitrary) direction.
Mohr’s Circle
Figure 2.17 Mohr’s circle diagram of Eqs. (2.13) and (2.14).
Results from Example 2.13
Figure 2.18 Results from Example 2.13 (a) Mohr’s circle diagram;
(b) stress element for principal normal stresses shown in x-y coordinates;
(c) stress element for principal stresses shown in x-y coordinates.
Mohr’s Circle for Triaxial Stress State
Figure 2.19 Mohr’s circle for triaxial stress state. (a) Mohr’s circle representation; (b) principal stresses on two planes.
©1998 McGraw-Hill
Example 3.5
Figure 2.20 Mohr’s circle diagram for Example 3.5. (a) Triaxial stress state when 1=23.43 ksi, 2=4.57 ksi, and 3=0; (b) biaxial stress state when 1=30.76 ksi and 2=-2.760 ksi; (c) triaxial stress state when 1=30.76 ksi, 2=0, and 3=-2.76 ksi.
Stresses on Octahedral Planes
Figure 2.21 Stresses acting on octahedral planes. (a) General state of stress. (b) normal stress; (c) octahedral shear stress.
©1998 McGraw-Hill
Normal Strain
Figure 2.22 Normal strain of cubic element subjected to uniform tension in x direction. (a) Three dimensional view; (b) two-dimensional (or plane) view.
©1998 McGraw-Hill
Shear Strain
Figure 2.23 Shear strain of cubic element subjected to shear stress. (a) Three dimensional view; (b) two-dimensional (or plane) view.
©1998 McGraw-Hill
Plain Strain
Figure 2.24 Graphical depiction of plane strain element. (a) Normal strain x; (b) normal strain y; and (c) shear strain xy.
Figure 2.26 Expansion process used in honeycomb materials. [From Kalpakjian (1991)]
Glue Spreader Case Study
Figure 2.27 Glue spreader case study. (a) Machine; (b) free body diagram; (c) shear diagram; (d) moment diagram.
Snowmobile with Drive Guard
Figure 2.28 Illustration used in case study. (a) Snowmobile; (b) guard with instrumentation.
Chapter 3: Solid Materials
Iron is taken from the earth and copper is smelted from ore.
Man puts an end to the darkness;
he searches the farthest recesses for ore in the darkness.
The Bible (Job 28:2-3)
Image: Iron flows from a blast furnace. Source: American Iron and Steel Institute.
Ductile Tension Test Specimens
Figure 3.1 Ductile material from a standard tensile test apparatus. (a) Necking; (b) failure.
Brittle Tension Test Specimen
Figure 3.2 Failure of a brittle material from a standard tesile test apparatus.
text reference: Figure 3.5, , page 96
Yield Strength Definition
Figure 3.6 Typical stress-strain behavior for ductile metal showing elastic and plastic deformations and yield strength Sy.
Brittle and Ductile Metal Comparison
Figure 3.7 Typical tensile stress-strain diagrams for brittle and ductile metals loaded to fracture.
Stress-Strain Diagram for a Ceramic
Figure 3.8 Stress-strain diagram for a ceramic in tension and in compression.
Figure 3.9 Bending strength of bar used in Example 3.6.
Stress-Strain Diagram for Polymers
Figure 3.10 Stress-strain diagram for polymer below, at, and above its glass transition temperature Tg.
Density of Various Materials
Figure 3.11 Density for various metals, polymers and ceramics at room temperature (20°C, 68°F) [From ESDU (1984)].
Density for Various Materials
Table 3.1 Density for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
Material
cExcluding “refractory” steels
d“Mechanical” rubber
Elastic Modulus for Various Materials
Figure 3.12 Modulus of elasticity for various metals, polymers, and ceramics at room temperature (20°C, 68°F) [From ESDU (1984)].
Elastic Modulus for Various Materials
Figure 3.12 Modulus of elasticity for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
Material
Steel, stainlessc
eFilled
Poisson’s Ratio for Various Materials
Table 3.3 Poisson’s ratio for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
Material
Thermal Condictivity for Various Materials
Figure 3.13 Thermal conductivity for various metals, polymers, and ceramics at room temperature (20°C, 68°F). [From ESDU (1984)].
Thermal Conductivity for Various Materials
Table 3.4 Thermal conductivity for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU(1984)]
Material
c20 to 100°C
e20 to 200°C
Thermal Expansion Coefficient for Various Materials
Figure 3.14 Linear thermal expansion coefficient for various metals, polymers, and ceramics applied over temperature range 20 to 200°C (68 to 392°F) [From ESDU (1984)].
Linear Thermal Expansion Coefficient for Various Materials
Table 3.5 Linear thermal expansion coefficient for various metals, polymers and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
Material

bCast alloys can be up to 15 x 10-6/(°C)
cTypical bearing materials
d25 x 10-6(°C)-1 to 80 x 10-6(°C)-1 when reinforced
eMineral filled
Specfic Heat Capacity for Various Materials
Figure 3.15 Specific heat capacity for various metals, polymers, and ceramics at room temperature (20°C; 68°F) [From ESDU (1984)].
Specific Heat Capacity for Various Materials
Table 3.6 Specific heat capacity for various metals, polymer, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
Material
aAluminum bronze up to 0.48 kJ/kg-°C (0.12 Btu/lbm-°F)
bRising to 0.55 kJ/kg-°C (0.13 Btu/lbm-°F) at 200°C (392 °F)
©1998 McGraw-Hill
Figure 3.17 Modulus of Elasticity plotted against density. The heavy envelopes enclose data for a given class of material. The diagonal contours show the longitudinal wave velocity. The guidelines of constant E/, E1/2/ , and E1/3/ allow selection of materials for minimum weight, deflection-limited design. [From Ashby (1992)].
Elastic Modulus vs. Density
©1998 McGraw-Hill
Material Classes
Table 3.7 Material classes and members and short names of each member. [From Ashby (1992)].
Class
Members
Aluminum alloys
Copper alloys
Lead alloys
Magnesium alloys
Molybdenum alloys
Nickel alloys
Epoxies
Melamines
Polycarbonate
Polyester
Alumina
Diamond
Sialons
Material Classes (cont.)
Table 3.7 Material classes and members and short names of each member. [From Ashby (1992)].
Class
Members
Engineering composites
(the composites of engineering practice) A distinction is drawn between the properties of a ply (uniply) and a laminate (laminates)
Carbon-fiber reinforced polymer
Glass-fiber reinforced polymer
Kevlar-fiber reinforced polymer
Brick
Cement
Woods
Separate clusters describe properties parallel to the grain and normal to it and wood products
Ash
Balsa
Fir
Oak
Pine
Strength vs. Density
Figure 3.18 Strength plotted against density (yield strength for metals and polymers, compressive strength for ceramics, tear strength for elastomers, and tensile strength for composites). The guidelines of S/, S2/3/, and S1/2/ allow selection of materials for minimum-weight, yield-limited design. [From Ashby (1992)].
Elastic Modulus vs. Strength
Figure 3.19 Modulus of elasticity plotted against strength. The design guidelines help with the selection of materials for such machine elements as springs, knife-edges, diaphragms, and hinges. [From Ashby (1992)].
Wear Constant vs. Limiting Pressure
Figure 3.20 Archard wear constant plotted against limiting pressure. [From Ashby (1992)].
Elastic Modulus vs. Cost x Density
Figure 3.21 Modulus of elasticity plotted against cost times density. The reference lines help with selection of materials for machine elements. [From Ashby (1992)].
Chapter 4: Normal, Bending, and Transverse Shear Stresses and Strains
I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand; otherwise, I do not.
William Thompson (Lord Kelvin)
Image: A portion of the collapsed Hyatt Regency Walkway which claimed over 100 lives.
©1998 McGraw-Hill
Example 4.1
Figure 4.2 Rectangular hole within a rectangular section used in Example 4.1.
Area Moment of Inertia
Figure 4.3 Area with coordinates used in describing area moment of inertia.
Figure 4.5 Coordinates and distance used in describing parallel-axis theorem.
Figure 4.6 Triangular cross section with circular hole within it.
©1998 McGraw-Hill
Example 4.4
Figure 4.7 Circular cross-sectional area relative to x’-y’ coordinates, used in Example 4.4.
Centroid, Area Moment of Inertia and Area
Table 4.1 Centroid, area moment of inertia, and area for seven cross sections.
Centroid, Area Moment of Inertia and Area (cont.)
Table 4.1 Centroid, area moment of inertia, and area for seven cross sections (part 2 of 2).
©1998 McGraw-Hill
Mass Element
Figure 4.8 Mass element in three-dimensional coordinates and distance from the three axes.
2D Mass Element
Figure 4.9 Mass element in two dimensional coordinates and distance from the two axes.
Mass and Mass Moment of Inertia
Table 4.2 Mass and mass moment of inertia for six solids.
Mass and Mass Moment of Inertia (cont.)
Table 4.2 Mass and mass moment of inertia for six solids.
Figure 4.10 Circular bar with tensile load applied.
Figure 4.11 Twisting of member due to applied torque.
Bending of a Bar
Figure 4.12 Bar made of elastomeric material to illustrate effect of bending. (a) Undeformed bar; (b) deformed bar.
Figure 4.13 Bending occurring in cantilevered bar, showing neutral surface.
Elements in Bending
©1998 McGraw-Hill
Example 4.10
Figure 4.16 U-shaped cross section experiencing bending moment, used in Example 4.10.
Figure 4.17 Curved member in bending. (a) Circumferential view; (b) cross-sectional view.
Figure 4.18 Rectangular cross section of curved member.
Deformation due to Transverse Shear
Figure 4.20 Cantilevered bar made of highly deformable material and marked with horizontal and vertical grid lines to show deformation due to transverse shear. (a) Undeformed; (b) deformed.
Moments and Stresses on Elements
Figure 4.21 Three-dimensional and profile views of moments and stresses associated with shaded top segment of element that has been sectioned at y’ about neutral axis. (a) Three-dimensional view; (b) profile view.
Table 4.3 Maximum shear stress for different beam cross sections.
Design of Shaft for Coil Slitter
Figure 4.22 Design of shaft for coil slitting line. (a) Illustration of coil slitting line. From Tool and Manufacturing Engineers Handbook.
Design of Shaft for Coil Slitter (cont.)
Figure 4.22 Design of shaft for coil slitting line. (b) knife and shaft detail; (c) free-body diagram of simplified shaft for case study. Illustration (b) is from Tool and Manufacturing Engineers Handbook.
Shear and Moment Diagrams
Figure 4.23 Shear diagram (a) and moment diagram (b) for idealized coil slitter shaft.
Mohr’s Circle
Figure 4.24 Mohr’s circle for location of maximum bending stress.
Chapter 5: Deformation
Let me tell you the secret that has led me to my goal. My strength lies in my tenacity.
Louis Pateur
Image: High speed photographs of a club striking a golf ball. Note the large deformations in the golf ball.
©1998 McGraw-Hill
Example 5.1
Figure 5.1 Cantilevered beam with concentrated force applied at free end. Used in Example 5.1.
text reference: Figure…

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