The large list of topics gives the teacher some choice in the design of the course. Lists of Internet sites relevant to the topics in this book are provided at the end of most chapters to assist readers in accessing additional information or data on commercial products.
The Big Picture, You Are the Designer, and Objec- tives features introduced in earlier editions are main-
Chapter 15, Completing the Design of a Power Transmission, is a guide through detailed design decisions such as the overall layout, detail drawings, tolerances and fits. The representation of the complete single reduction gear drive at the end of Chapter 15 has been significantly upgraded, helping students' understanding of how to translate design analysis, component detailing decision making, and commercially available component. form a complete composition.
MECHANICAL DESIGN SOFTWARE
Several new, full-color drawings for an example of a gear-type speed reducer have been added to aid students' perception and understanding of how individual machine elements are designed, assembled, and operated together. The Big Picture, You Are the Designer, and Objectives features introduced in earlier editions are main.
FEATURES OF THE SIXTH EDITION
In Chapter 1, The Nature of Mechanical Design, the first ten figures showing a variety of mechanical devices and machines have been replaced with new full-color images to improve students' perception of the details of many types of equipment. Two of these new images show production machines designed by one of the new co-authors of this book.
INTRODUCING TWO NEW CO-AUTHORS
He is a fellow of the American Society of Mechanical Engineers and the Society of Manufacturing Engineers. Designers' responsibilities are discussed along with an illustration of the iterative nature of the design process.
PRINCIPLES OF DESIGN AND STRESS ANALYSIS
1 When you finish the first six chapters of this book, you will gain an understanding. Much of this chapter is likely review for you, but it is presented here to emphasize the importance of material selection to the design process and to explain the data for materials presented in the appendices.
THE NATURE OF
MECHANICAL DESIGN
FIGURE 1–3 Closed mailer for the printing industry Created by Edward M. Vavrek for The Lettershop Group, Leeks, UK. a) Picture showing housings over mechanisms (b) Covers removed to show drive systems on the right. FIGURE 1–4 Rake and clamshell for a deep rock tunnel pumping station Created by Edward M. Vavrek for Fairfield Service Company, Michigan City, IN. a) Overview of shaft and rake system (b) Inside of lower shaft showing rake and grapple. Superstructure with.
1–1 OBJECTIVES OF THIS CHAPTER
The customers include the person who has to operate the door in normal service or in emergencies, the people who have to pass through the door during use, the personnel who manufacture the opening machine, the installers, the aircraft structural designers who have to accommodate the loads produced by the opener in flight and during operation, the service technicians who maintain the system, and the interior designers who must shield the opener during use while allowing access for installation and maintenance. The following discussion identifies the salient features of some of the approaches and the listed references and Internet sites provide more details.
1–2 THE DESIGN PROCESS
Axiomatic design methods implement a process where developers first think functionally, followed by the innovative creation of a physical embodiment of the product that meets customer requirements, along with the process required to manufacture the product. Note that this process is a subset of the larger list given earlier for the product realization process.
1–3 SKILLS NEEDED IN MECHANICAL DESIGN
A critical evaluation of the desirable features, advantages and disadvantages of each design concept must be completed. The last block in the design flowchart is the detailed design, and the primary focus of this book is on that part of the overall design process.
1–4 FUNCTIONS, DESIGN REQUIREMENTS, AND
Careful preparation of function statements and design requirements will ensure that the design effort is focused on the desired results. Different design concepts may have different levels of inherent security, in addition to meeting the stated security requirements as noted in the list of design requirements.
Requirements, and Evaluation Criteria
The chain drive must finally be connected to the drive wheels of the tractor. The bearings are held in a housing that must be attached to the frame of the tractor.
1–5 EXAMPLE OF THE
Each of the three shafts is supported by two ball bearings, making them statically deterministic and allowing the analysis of forces and stresses using standard principles of mechanics. Details of how the active elements should be installed, lubricated and adjusted are only suggested at this stage of the design process to demonstrate feasibility.
INTEGRATION OF MACHINE ELEMENTS INTO A
Seals are fitted to the input and output shafts to prevent contaminants from entering the housing. Install the right side housing cover while placing the last two bearings in their seats.
MECHANICAL DESIGN
First, you must determine the magnitude of the loads on each bearing from the shaft analysis and gear design. The bearing chosen to support a certain part of the shaft must therefore have a bore (inner diameter) that is not smaller than the safe diameter of the shaft.
Keys
The rotational speed and reasonable design life of the bearings and their compatibility with the shaft on which they are to be mounted must also be considered. For example, based on the shaft analysis, you can specify the minimum allowable diameter at each bearing seat location to ensure safe stress levels.
Housing
Once a specific bearing is selected, the shaft diameter at the location of the bearing seat and the allowable tolerances must be determined in accordance with the bearing manufacturer's recommendations to achieve proper operation and expected bearing life.
1–6 COMPUTATIONAL AIDS
Gears
Shafts
Bearings
The design assumes that a rectangular shape will be used for the cross section of the beam. The objective is to calculate the required cross-sectional dimensions, taking stress and deflection into account.
1–8 PREFERRED BASIC SIZES, SCREW THREADS, AND
A beam is to be designed to span a well of 60 to support a large gear weighing 2050 pounds (lb).
Preferred Basic Sizes
American Standard Screw Threads
1–7 DESIGN CALCULATIONS
For the metric screw threads described below, the pitch is included as part of the thread marking system. DESIGN OF GEAR SUPPORT ROD IN IRRIGATION PIT SHOULD BE 60 AND BETWEEN SUPPORT LENGTH.
REF )
Note that S = I/c, where c is the distance from the neutral axis to the outer part of the section; used for beam analysis and design. Note that Zp = J/c, where c is the outer radius of the pipe or tube; used for torsional analysis and design.
Structural Shapes—Designations
You are encouraged to use this feature for problems and design exercises in this book. I—Moment of inertia, sometimes called the second moment of area; used for beam analysis and design.
Metric Screw Threads
Density = mass/unit volume (kg/m3 or lbm/in3) On Earth, it is typically accurate enough to assume that the U.S. gravity.
Commercially Available Shapes for Load-Carrying Members
Beam Shapes
The term depth is the standard term for the vertical height of the cross section when placed in the orientation shown in Table A15–9. Note from the data in the table that the actual depth is often different from ASTM A572 Grade 50 or A36.
Angles (L-Shapes)
Most of the cross-sectional area is in the flanges furthest from the horizontal centroidal axis (x-axis), making the moment of inertia very high for a given amount of material. These shapes are also best when used in pure bending without twisting as they are quite flexible in torsion.
Channels (C-Shapes)
For most, but not all, of the S-shapes, the actual depth is the same as the nominal depth. The flanges of the S-shapes are tapered with a slope of approx. 2 inches by 12 inches, corresponding to the flanges of the C-forms.
Hollow Tubing (Square and Rectangular)
All sizes listed in Table A15–9, along with many more (see Reference 2), are available in steel. Often, wide flange shapes (W shapes) are preferred over S shapes because of their relatively wide flanges, the constant thickness of the flanges, and the generally higher sectional properties for a given weight and depth.
Pipe and Hollow Circular Tubing
Note that, again, weight per foot of length is included in the designation, such as the S10*35, which weighs 35 lb/ft. Some give the web height, flange width and the thickness for the web or flange.
1–9 UNIT SYSTEMS
1–10 DISTINCTION AMONG
WEIGHT, FORCE, AND MASS
INTERNET SITES FOR GENERAL MECHANICAL DESIGN
The Power Transmission Clearinghouse's home page on the Internet for buyers, users and sellers of power transmission products and services.
INTERNET SITES FOR
INNOVATION AND MANAGING COMPLEX DESIGN PROJECTS
PROBLEMS
Functions and Design Requirements
Units and Conversions
Most of the applications considered in the study of machine element design in this book use metal alloys, plastics and composites. This chapter focuses on material selection and the use of material property data in design decisions, rather than on the metallurgy or chemistry of the materials.
Proportional Limit
The part of the stress-strain diagram where there is a large increase in strain with little or no increase in stress is called the yield stress (sy). The intersection of this line and the stress-strain curve defines the yield stress of the material.
Elastic Limit
If the yield point is quite noticeable, as it is in Figure 2–1, the property is called the yield point rather than the yield strength. Figure 2–2 shows the stress-strain diagram typical of a nonferrous metal such as aluminum or titanium or of certain high-strength steels.
Modulus of Elasticity in Tension, E
In this book, the term yield strength is used for sy, regardless of whether the material exhibits true yield strength or whether the offset method is used. Both yield strength and ultimate shear strength (sys and sus respectively) are important properties of materials.
Poisson’s Ratio, n
Modulus of Elasticity in Shear, G
Non-Destructive Measurement of Elastic Modulus and Poisson’s Ratio
Ductility and Percent Elongation
To find this value, compare the original cross-sectional area to the final area at break for the tensile test specimen.
Flexural Strength and Flexural Modulus
Hardness
The Vickers hardness test, preferred in some European countries and elsewhere, is similar to the Brinell test except for the nature of the indenter (diamond pyramid with a square base) and the applied load, usually 50 kg. Abrasive wear - the mechanical tearing of particles from a material by the action of the mating material resulting in mass loss from one or both materials.
Wear in Mechanical Devices
The impactor contacts the sample at high speed at the bottom of the pendulum arc; therefore, the pendulum has a known amount of kinetic energy. The specimen usually breaks during the test, taking some energy from the pendulum but allowing it to pass through the test area.
Machinability
The standard Izod test uses a square specimen with a V-shaped notch carefully machined 2.0 mm (0.079 in) deep according to specifications in ASTM Standard D 256.5. The sample is clamped in a special vise with the notch aligned with the top edge of the vise. This obviously changes the total amount of energy the specimen will absorb during fracture.
Toughness, Impact Energy
The striker makes contact with the sample at a height of 22 mm above the notch, loading it as a cantilever into flexion. Therefore, the data for impact energy is divided by the actual width of the specimen, and the results are reported in units of N#m/m or ft#lb/in.
Fatigue Strength or Endurance Strength
Creep
Relaxation
Physical Properties
The primary series of numbers within UNS are listed in Table 2–5, along with the organization responsible for assigning numbers within each series.
Recent Developments in Steel Designations
A–10 Properties of cast zinc and magnesium alloys A–11 Properties of nickel-based alloys and titanium alloys A–12 Properties of bronze, brass, and other copper alloys A–13 Properties of selected plastics.
Material Property Data Used in This Book
Appendices
Suppliers of such designs usually offer only selected types of materials under certain conditions as stock items. While it is possible to obtain such products from other materials, it is usually cheaper to specify standard alloys.
Metals Used for Commercially Available Shapes
Table 2–6 lists some of the most commonly used materials and their properties for carbon and alloy steels, stainless steels, and aluminum alloys. Table 2–7 lists some common materials and their designations in Germany, the United Kingdom (UK-England), other parts of the European Union (also known as Euronorm or EN), Japan, and China.
Designation Systems
The main alloying elements present in the various alloy steels are sulphur, phosphorus, silicon, nickel, chromium, molybdenum and vanadium. The first two digits indicate the specific alloy group that identifies the major alloying elements other than carbon in the steel, as shown in Table 2-8.
Alloy Groups
These situations often arise in production operations in the automotive, aerospace, equipment, construction equipment, agricultural equipment, manufacturing equipment, energy production equipment and similar industries. Carbon steel bar and sheet shapes are usually supplied in rolled form; that is, they are rolled at an elevated temperature which facilitates the rolling process.
Heat Treating
The final properties of the steel are dramatically affected by the way the steel is manufactured. Cold drawn bar and wire have the highest strength of the machined forms, along with a very good surface finish.
AHSS—Advanced High-Strength Steels
The microstructure of heat-treated zones in the body or core of the part. The bearing is impregnated with a lubricant that may be sufficient for the life of the part.
Aluminum Casting Alloys
Note that it is available in virtually all forms, has good strength and corrosion resistance, and is heat treatable to obtain a wide variety of properties.
Aluminum Forging Alloys
The most widely used alloy is AZ91, where A refers to aluminum and Z refers to zinc, the two main alloying elements. The AS alloys contain aluminum and silicon, which gives them better performance at high temperatures.
Nickel-Based Alloys
Its density of approximately 1800 kg/m3 (0.065 lbm/in3) is two-thirds aluminum and about one-fifth steel.
Magnesium Alloys
Leaded tin bronze: Copper-tin-lead alloy Nickel tin bronze: Copper-tin-nickel alloy Aluminum bronze: Copper-aluminium alloy. In UNS, copper alloys are designated by the letter C, followed by a five-digit number.
Titanium Alloys
In general, as the degree of cold working increases, the strength is greater, but the ductility is lower indicated by the percentage elongation. Some designers recommend the terms linear and cross-linked instead of the more familiar thermoplastic and thermosetting.
Thermoplastics
In general, the thermoplastic materials can be repeatedly shaped by heating or molding because their basic chemical structure is unchanged from its initial linear form. Used for seals, belts, pump diaphragms, protective boots, tubes, springs and impact absorbing devices.
Thermosets
Special Considerations for Selecting Plastics
When the two materials bond together, much of the composite's load-bearing capacity is produced by the reinforcement. Designers can tailor the properties of composite materials to the specific needs of a particular application by selecting any of several variables that determine the performance of the final product.
Classifications of Composite Materials by Matrix
Graphite fibers: More than 99% carbon and a modulus of elasticity even higher than carbon; the strongest fibers commonly used in composites. Tungsten Fiber Coated Silicon Carbide: Similar hardness and toughness to boron/tungsten, but with higher temperature capabilities.
Processing of Composites
A member of the polyamide family of polymers; greater strength and stiffness with lower density compared to glass; very flexible.
Types of Reinforcement Materials
Advantages of Composites
Selection of Composite Materials
Composite structures can often be made in complex shapes in one piece, reducing the number of parts in a product and the number of necessary fastening operations. Composite structures are typically manufactured in their final form directly or in a near-net form, reducing the number of secondary operations required.
Limitations of Composites
The properties of composite materials are not isotropic: Properties vary dramatically with the direction of the applied loads. The analysis of composite structures requires detailed knowledge of more properties of the materials than would be necessary for metals.
Laminated Composite Construction
If the longitudinal direction of the surface layer is called the 0° layer, this structure is called Sometimes two or more adjacent inserts of the same orientation are used and it is simpler to specify the number of identical inserts.
Predicting Composite Properties
The relationship between density and specific gravity is simply g = rg, where g is the acceleration due to gravity.
Design Guidelines for Members Made from Composites
Brackets, ribs, flanges and the like can be cast together with the basic shape of the part. Adding CNTs to MMC (Metal Matrix Composite) also increases the strength and stiffness of the composite that becomes MMNC.
STRESS AND DEFORMATION ANALYSIS
Could the fault be due to the manufacture of the product rather than its design. You should have learned to prepare such FIGURE 3–3 free-body diagrams of each component of the crane. diagrams in the prerequisite study of strength of materials.
3–2 PHILOSOPHY OF A SAFE DESIGN
Tensile and compressive stresses, called normal stresses, are shown acting at right angles to opposite faces of the tension member. To create equilibrium, a second pair of shear stresses must exist on the other two faces of the member, acting in a direction opposite to the first pair.
3–3 REPRESENTING STRESSES ON A STRESS ELEMENT
In summary, shear stresses on a member will always appear as two pairs of equal stresses acting (parallel to) the four sides of the member. The line of action of the load must pass through the center of the cross section of the beam.
Sign Convention for Shear Stresses
The member must have a uniform cross-section near where the stress is calculated.
3–4 NORMAL STRESSES DUE TO DIRECT AxIAL LOAD
In SI units, power is expressed in units of watts (W) or its equivalent, newton meters per second (N#m/s).
3–5 DEFORMATION UNDER DIRECT AxIAL LOAD
3–6 SHEAR STRESS DUE TO DIRECT SHEAR LOAD
However, in torsional shear, the stress distribution is not uniform across the cross section. The most frequent case of torsional shear in machine design is that of transmitting power on a round circular shaft.
3–8 SHEAR STRESS DUE TO TORSIONAL LOAD
Note that the material near the center of the solid shaft is not heavily loaded. This form of the torsional shear stress equation is useful for design problems because the polar section modulus is the only term related to cross-section geometry.
Torsional Shear Stress Formula
Figure 3–8 graphically shows that this equation is based on the linear variation of the torsional shear stress from zero at the center of the shaft to the maximum value at the outer surface.
3–9 TORSIONAL DEFORMATION
3–10 TORSION IN MEMBERS HAvING NON-CIRCULAR
Calculate the maximum shear stress on the square part of the shaft when a torque of 15,000 lb#in is applied. Also, if the length of the square part is 8.00 in, calculate the angle of rotation about this part.
3–12 TORSION IN OPEN, THIN-wALLED
The shear stress calculated by this approach is the average stress in the tube wall. However, if the wall thickness t is small (a thin wall), the stress is almost uniform throughout the wall, and this approximation will give a close approximation of the maximum stress.
TUBES
3–11 TORSION IN CLOSED, THIN-wALLED TUBES
Then we can compare the strengths of the two forms by calculating the ratio Zp/Q. Then we make the comparison of the strengths of the two forms by calculating the ratio Zp/Q.
3–13 SHEAR STRESS DUE TO BENDING
In particular, if the thickness is not less at a place remote from the central axis, then it is ensured that the maximum vertical shear stress occurs at the central axis. Note that the vertical shear stress is equal to the horizontal shear stress because any material element subjected to a shear stress on one face must have a shear stress of the same magnitude on the adjacent face.
3–14 SHEAR STRESS DUE TO BENDING – SPECIAL
3–15 NORMAL STRESS DUE TO BENDING
Furthermore, the maximum bending stress occurs at the outermost fibers of the beam section, where the shear stress is effectively zero. Calculate the maximum bending moment that occurs at the point of application of the load using the formula shown in part (b) of Figure 3-16.
CONCENTRATED BENDING MOMENTS
Draw the free-body diagram for the horizontal portion of the printhead, along with the shear force and bending moment diagrams. Solution Objective Draw the free-body diagram of the horizontal portion of the printhead in Figure 3–19.
3–18 BEAM DEFLECTIONS
3–16 For the two gears, A and B, in Fig. 3–23, calculate the relative deflection between them in the plane of the paper that is due to the forces shown in Fig. 3–23 (c). It is common to consider the loads on the gears and the reactions on the bearings to be concentrated.
DEFLECTED BEAM SHAPE
The stress distribution within the cross-section of the element is non-linear; rather, it is hyperbolic. However, the neutral axis does not coincide with the centroidal axis of the cross-sectional shape.
General Procedure for Analyzing Curved Beams Carrying a Pure Bending Moment
These goals can be achieved by adjusting the shape and cross-sectional dimensions of the curved beam. R depends on the cross-sectional shape using the surface shape factor, ASF, determined from the relationships shown in Figure 3-25.
Procedure for Analyzing Curved Beams with Composite Cross-sectional Shapes Carrying
FIGURE 3–27 Examples of composite shapes for curved beam cross sections. a) Trapezoid with two semicircular edges. However, many curved beams carry a combination of a moment and a normal load acting perpendicular to the cross section of the beam.
3–21 SUPERPOSITION PRINCIPLE
Eccentricity of the load = e = 6.0 and from the neutral axis of the beam to the line of action of the horizontal component of the applied load. Transfer the horizontal component to the equivalent load on the neutral axis by the direct tensile force and the moment due to the eccentric placement of the force.
3–22 STRESS
CONCENTRATIONS
The nominal stress is based on the applied bending moment, M, divided by the section modulus of the smaller cross-section as shown in the figure. The primary reason is the complexity of the calculation of the polar section modulus around the hole.
Stress Concentration Factors for Lug Joints
The clearances between the faces of the cam and the side plates of the gaff. The clearance between the faces of the cam and the side plates of the fork should be small to reduce bending of the pin.
INTERNET SITES RELATED TO STRESS AND DEFORMATION
The bearing stress between the surface of the plug and the inside of the plug hole should be acceptable, usually less than 0.9sy. The amount by which a supporting member is weakened by the presence of a stress concentration (notch), taking into account the material and the sharpness of the notch, is defined as
Direct Tension and Compression
The distance, h, from the centerline of the hole to the top of the protrusion should be nominally equal to the width of the plate, w, and as large as practicable to minimize bending stresses in the upper part of the protrusion and to prevent the ridge from tearing out. Calculate the stresses in all members of the truss near their centers away from the joints.
Direct Shear Stress
Calculate the compressive stress if the cross section has the shape shown and the applied force is F= 52,000 lb. Calculate the compressive stress if the cross section has the shape shown and the applied load is 640 kN.
Noncircular Members in Torsion
Calculate the shear stress in the aluminum when a force of 52,000 lb is applied by the punch. Calculate the torsional shear stress on a solid circular shaft having a diameter of 1.25 in that transmits 110 hp at a speed of 560 rpm.
Torsion
Calculate the torsional shear stress in a hollow shaft with an outside diameter of 40 mm and an inside diameter of 30 mm when transmitting 28 kilowatts (kW) of power at a speed of 45 rad/s. Calculate the angle of twist for the hollow shaft in problem 26 over a length of 400 mm.
Beams
Beams with Concentrated Bending Moments
Include any unbalanced torque on the shaft that tends to rotate it about the z-axis. In each case, the reaction to the unbalanced torque is taken at the right end of the shaft labeled C.
Combined Normal Stresses
Calculate the maximum stress in the horizontal part of the bar and state where it occurs on the cross section. Calculate the maximum stress in the horizontal part of the bar and indicate where it occurs on the cross section.
Stress Concentrations
Specify a suitable diameter of a solid circular bar to be used for the upper horizontal part, which is supported in the bearings.
Problems of a General Nature
Lug Joints
Curved Beams
How the shape and size of the critical parts of the object relate to the expected stresses. Consider an element on the top surface of the bar, labeled element A in Figure 4-2.
Sign Convention
Shear stress can be due to direct shear, torsional shear or vertical shear. For example, txy denotes the shear stress acting on a face of the element that is perpendicular to the x-axis and the direction of the shear stress is parallel to the y-axis.
Maximum and Minimum Principal Stresses
Angle for Principal Stress Element
The angle fs is measured from the positive x-axis of the original stress element to the maximum principal stress s1. When the stress element is oriented as discussed so that the principal stresses act on it, the shear stress is zero (tx′y′ = t12 = 0).
Maximum Shear Stress
Three-Dimensional Stress Transformation
Summary and General Procedure for Analyzing Combined Stresses
Calculate the maximum shear stress on the element and the orientation of the plane on which it acts. In Figure 4–18(c), we draw the maximum shear stress element to the right of the principal stress element.
Mohr’s Circles for Three-Dimensional Stresses
These are identical to those shown in Figure 4–11 from the hand calculations performed in Example Problem 4–1. FIGURE 4-19 General example of Mohr's circles for three-dimensional state of stress where all three principal stresses are nonzero.
Tresca Stress
To a person seeing the construction of Mohr's circle for the first time, it may seem long and involved. Mohr's circle is used here to demonstrate the relationship between applied stresses, principal stresses, and maximum shear stress for the following special cases:
Uniaxial Tension
Uniaxial Compression
Biaxial Tension
Biaxial Tension and Compression
Pure Shear
Combined Tension and Shear
Now the torsional moment induces a torsional shear stress in the x–y plane at point A of magnitude . It is convenient to define the quantity in the numerator of this equation as the equivalent torque, Te.
Stresses in a Cylinder with Internal Pressure
For shaft ABC, create a stress element on the underside of the shaft, just to the right of section B. Draw a stress element on the surface of the bar, then draw the Mohr circle for the element.
DESIGN FOR DIFFERENT TYPES OF LOADING
Discuss how the load is applied and which parts of the load-bearing part are exposed to the higher load levels. Some of the examples you discovered during the discussion of The Big Picture for Chapter 3 could be used again here.
5–1 OBJECTIVES OF THIS CHAPTER
5–2 TYPES OF LOADING AND STRESS RATIO
Static Stress
Repeated and Reversed Stress—
Pure Oscillation
The shaft is rotated by an electric motor while the system counts the number of revolutions. It also has a device to sense when the specimen breaks so that there is a known relationship between the stress level and the number of cycles to failure.
Fluctuating Stress—Pulsating Stress
Point A at the base of the spring on the convex side experiences the varying tensile stresses of the type shown in Figure 5–4(a). The plot of stress versus time in Figure 5–4(a) illustrates the shape of the varying stress on the spring.
Shock or Impact Loading
Because the force on the spring is proportional to the deflection, the force exerted on the deflection is 8.0 mm. In sections 5–8 you will see how to design parts that will be subjected to these kinds of stresses.
Random Loading
5–3 FAILURE THEORIES
5–4 DESIGN FOR STATIC LOADING
Ductile Materials under Static Loading
By plotting the principal stresses, the stress states that lie within the hexagon are expected to be safe, while those outside would predict failure. As the concept demonstrated in MSST, the stresses that lie within the ellipse are predicted to be safe, while those outside would predict failure.
Brittle Materials under Static Loading
When all the principal stresses are in compression, 0 7 s1 7 s2 7 s3, the stress element is safe when. For design, due to the many different shapes and dimensions of safe-stress zones, it is suggested that a rough plot be made of the pertinent part of the modified Mohr diagram from actual material strength data as shown in Figure 5-9. Then the actual values of s1 and s2 can be plotted to ensure that they lie within the safe zone of the diagram as shown in Figure 5–9.
Summary of Static Loading Failure Theories
The rotary bending test, as shown in Figure 5–3, has been used for many years to obtain endurance limit data and much of the reported data is based on it. Test specimens can be loaded in many different patterns, simulating any of the conditions shown in Figures and others.
Low-cycle Fatigue
Since the entire material is subjected to the maximum load in the axial load test, the reported ultimate strength data are typically about 20% lower than those for the rotational bending test. Endurance limit data should be used wherever available, either from test results or from reliable published data.
Surface Finish
If data for other factors can be determined by additional research, they should be multiplied as additional terms in equation (5-21). Ideally, a statistical analysis of actual data should be obtained for the material to be used in the design.
Size Factor, C s —Circular Sections in Rotating Bending
A factor can be used to estimate a lower endurance limit, which can be used in design to produce the higher confidence values. By making certain assumptions about the shape of the strength data distribution, Reference 8 reports the values in Table 5–3 as estimated confidence factors, CR.
Size Factor, C s —Other Conditions
Only the top and bottom segments beyond the 0.475D radius experience 95% or more of the maximum bending stress, as shown in Figure 5–13(c). In bending and torsion, the maximum tensile stress occurs in the outermost parts of the cross-section, and this is the basis for the data in Figure 5-12.
Other Factors
The A95 region is shown in Figure 5–13(d) as the two strips of thickness 0.025h at the top and bottom of the section. For axial tensile stress, all parts of the cross-section experience the same level of tensile stress and therefore all parts are equally susceptible to the initiation of a fatigue crack.
