☆Stars denote specialized and advanced topics. vii . Mechanics of materials is a basic engineering subject that must be understood by. Arthur p. borlsi Richard J. Schmidt Advanced Mechanics of Materials? . Send your remarks to Dr. Arthur P. Boresi, Department of Civil and Archi- tectural. eBook free PDF download on Advanced Mechanics of Materials by Arthur P. Boresi, Richard J Schmidt. Book download link provided by soundofheaven.info
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Library of Congress Cataloging in Publication Data: Boresi, Arthur P. (Arthur Peter), Advanced mechanics of materials /Arthur P. Boresi, Richard J. Arthur P. Boresi and Richard J. Schmidt, “Advanced Mechanics of Materials”. Sixth Edition, John soundofheaven.info∼willam/matlpdf. Software. SIXTH EDITION ADVANCED MECHANICS OF MATERIALS ARTHUR P. BORES1 How can I get a pdf file of this book. Thanks . Send your remarks to Dr. Arthur P. Boresi, Department of Civil and Archi- tectural Engineering.
Before point C is reached, the strain-hardeningeffect is greater than the loss resulting from area reduction. Solution manual to Applied Quantum Mechanics. What is a load factor? Classical Mechanics solution manual. A permanent strain ep remains. This is because the transitionsfrom elastic to inelastic behavior and from linear to nonlinear behavior are so gradual that these limits are very difficult to determinefrom the stress-strain diagram part OAB of the curves in Figures 1.
Yield Strength The value of stress associated with point L Figure 1.
The yield strength is determined as the stress associated with the intersectionof the curve OAB and the straightlineLM drawn from the offset strain value, with a slope equal to that of line OA Figure 1. The value of the offset strain is arbitrary. However, a commonly agreed upon value of offset is 0. Typical values of yield strength for several structural materials are listed inAppendixA, for an offsetof 0.
For materialswith stress-strain curveslike that of alloy steels Figures 1. Ultimate Tensile Strength Another importantproperty determinedfrom the stress-strain diagram is the ultimate ten- sile strength or ultimate tensile stress 0,.
It is defined as the maximum stress attained in the engineering stress-strain diagram, and in Figure 1. As seen from Figure 1. As the material is loaded beyond its yield stress, it maintains an ability to resist additional strain with an increase in stress. This response is called strain hardening. At the same time the material loses cross-sectionalarea owing to its elongation. This areareductionhas a softening strengthloss effect,measuredin terms of initial areaAo.
Before point C is reached, the strain-hardeningeffect is greater than the loss resulting from area reduction. At point C, the strain-hardeningeffect is balanced by the effect of the area reduction. The constant of proportionalityE is called the modulus of elasticity. Geometrically,it is equal in magnitude to the slope of the stress-strain relation in the region OA Figure 1. The percent elongation is a measure of the ductility of the material.
From Figure 1. An importantmetal for structuralapplications,mild or structuralsteel, has a distinct stress-strain curve as shownin Figure 1. The portion OAB of the stress-strain diagram is shown expanded in Figure 1. The stress-strain diagram for structural steel usually exhibits a so-calledupper yield point, with stress bYu,and a loweryield point, with stress oyLThis is because the stress required to initiate yield in structuralsteel is largerthan the stress required to continue the yielding process.
At the lower yield the stress remains essentially constant for increasing strain until strain hardening causes the curve to rise Figure 1. The constant or flat portion of the stress-strain diagram may extend over a strain range of 10 to 40 times the strain at the yield point. Actual test data indicatethat the curve fromA to B bounces up and down.
However,for simplicity,the data arerepresented by a horizontal straightline. Yield Point for Structural Steel The upper yield point is usually ignored in design, and it is assumed that the stress initiat- ing yield is the lower yield point stress, on.
Consequently, for simplicity, the stress- strain diagram for the region OAB is idealized as shown in Figure 1. Also for simpiic- ity, we shall refer to the yield point stress as the yield point and denote it by the symbol I: Recall that the yield strength or yield stress for alloy steel, and for materials such as alu- minum alloys that have similar stress-strain diagrams,was also denotedby Y Figure 1.
Modulus of Resilience The modulus of resilience is a measure of energy per unit volume energy density absorbed by a material up to the time it yields under load and is represented by the area under the stress-strain diagram to the yield point the shaded area OAH in Figure 1. In Figure l. Modulus of Toughness The modulus of toughness U, is a measure of the ability of a material to absorb energy prior to fracture.
It represents the strain energy per unit volume strain-energydensity in the material at fracture. The larger the modulus of toughnessis, the greater is the ability of a material to absorb energy with- out fracturing. A large modulus of toughness is important if a material is not to fail under impact or seismic loads. Modulus of Rupture The modulus of rupture is the maximum tensile or compressivestress in the extreme fiber of a beam loaded to failure in bending.
Hence, modulus of rupture is measured in a bend- ing test, rather than in a tension test. Consequently, modulus of rupture normally overpredicts the actual maximum bending stress at failure in bending.
Modulus of rupture is used for materials that do not exhibit large plastic deformation,such as wood or concrete. It is found by measuringboth the axial strain E , and the lateral strain in a uniaxial tension test and is given by the value 1.
Necking of a Mild Steel Tension Specimen As noted previously,the stress-strain curve for a mild steel tension specimen first reaches a local maximum called the upper yield or plastic limit byu,after which it drops to a local minimum the lower yield point Y and runs approximately in a wavy fashion parallel to the strain axis for some range of strain. For mild steel, the lower yield point stress Y is assumed to be the stress at which yield is initiated. After some additional strain, the stress rises gradually; a relatively small change in load causes a significantchange in strain.
In this region BC in Figure 1. With area A,, the curve first rises rapidly and then slowly,turning with its concaveside down and attaining a maximum value o,, the ultimatestrength,before turning down rapidly to fracture pointF, Figure 1.
Physically, after O, is reached,necking of the bar occurs Figure 1. This necking is a drastic reduction of the cross-sectionalarea of the bar in the region where the fracture ultimatelyoccurs. In addition, the engineering stress-strain curves for However,as can be seen from Figure 1. Once necking beings, the engineering strain E is no longer constant in the gage length see Fig- ures 1.
However, a good approximation of the true strain may be obtained from the fact that the volume of the specimen remains nearly constant as necking occurs. I2 Comparison of tension and compression engineering stress-strain diagrams with the true stress-strain diagram for structural steel. Substitutionof Eq. Other Materials There are many materials whose tensile specimens do not undergo substantial plastic strain before fracture.
These materials are called brittle materials. A stress-strain diagram typical of brittle materials is shown in Figure 1. It exhibits little plastic range, and frac- ture occurs almost immediatelyat the end of the elastic range. In contrast, there are mate- rials that undergo extensive plastic deformation and little elastic deformation. Lead and clay are such materials. The idealized stress-strain diagram for clay is typical of such materials Figure 1. This response is referred to as rigid-perfectlyplastic.
Assume that elastic unloading occurs. The designer must determine the possible modes of failure of the system and then establish suitablefailure criteriathat accuratelypredict the failure modes. In particular, it requires a comprehensive stress analysisof the system. Sincethe responseof a structuralsystemdependsstronglyon the materialused, so does the mode of failure. In turn, the mode of failure of a given mate- rial also dependson the manner or history of loading,such as the number of cycles of load applied at a particular temperature.
Accordingly, suitable failure criteria must account for differentmaterials,differentloadinghistories, and factors that influencethe stress distribu- tion in the member. A major part of this book is concerned with 1. The critical parameter that signals the onset of failure might be stress, strain, displacement, load, and number of load cycles or a combination of these.
The discussionin this book is restrictedto situationsin which failure of a system is related to only a single critical parameter. In addition, we will examine the accuracy of the theo- ries presented in the text with regard to their ability to predict system behavior. In particu- lar, limits on design will be introduced utilizing factors of safety or reliability-based concepts that provide a measure of safety againstfailure. Historically,limits on the design of a system have been establishedusing afactor of safety.
The letterR is used to represent the resistance of the system to failure. Generally,the magnitude of R, is based on theory or experimental observation. The factor of safety is chosen on the basis of experiments or experience with similar systems made of the same material under similar loading condi- tions.
Then the safe working parameter R, is determined from Eq. The factor of safety must account for unknowns, including variability of the loads, differences in mate- rial properties, deviationsfrom the intended geometry, and our ability to predict the criti- cal parameter.
In industrial applications,the magnitude of the factor of safety SF may range from just above 1.
For example, in aircraft and space vehicledesign, where it is critical to reduce the weight of the vehicle as much as possible, the SF may be nearly 1. In the nuclear reactor industry, where safety is of prime importance in the face of many unpredictableeffects,SF may be as high as 5. Generally, a design inequality is employed to relate load effects to resistance.
Design philosophies based on reliability concepts Harr,; Cruse, have been developed. It has been recognized that a single factor of safety is inadequate to account for all the unknowns mentioned above. Furthermore, each of the particular load types will exhibit its own statistical variability.
Consequently, appropriate load and So modified, the design inequalityof Eq. The statisticalvariationof the individualloads is accountedfor in x, whereas the variability in resistance associated with material properties, geometry, and analysis procedures is represented by Cp. The use of this approach, known as limit-states design, is more rational than the factor-of-safety approach and produces a more uniform reliabilitythroughout the system.
A limit state is a condition in which a system, or component, ceases to fulfill its intended function.
This definition is essentially the same as the definition offailure used earlier in this text. However,someprefer the term limit state becausethe term failure tends to imply only some catastrophicevent brittlefracture ,rather than an inability to function properly excessive elastic deflections or brittle fracture. Nevertheless, the term failure will continueto be used in this book in the more general context. Select a circular rod of appropriate size to carry these loads safely. Use steel with a yield strength of MPa.
Make the selection using a factor-of-safety design and b limit-states design. For simplicity in this example, the only limit state that will be considered is yielding of the cross sec- tion. Other limit states, including fracture and excessive elongation, are ignored. In the design of tension members for steel structures, a factor of safety of is used AISC, These equations represent the condition in which a single load quantity is at its maximum lifetime value, whereas the other quantities are taken at an arbitrary point in time.
The relevant load combinations for this situation are specified ASCE, as 1. The total load effect is Hence, the limit-states design inequality is , I0. A rod 28 mm in diameter, with a cross-sectional area of mm2, is adequate.
Discussion The objectiveof this example has been to demonstrate the use of different design philosophies through their respective design inequalities, Eqs. For the conditions posed, the limit-states approachproduces a more economical design than the factor-of-safety approach. This can be attributed to the recognition in the load factor equations d-f that it is highly unlikely both live load and wind load would reach their maximum lifetime values at the same time.
Differentcombinations of dead load, live load, and wind load, which still give a total service-levelload of IcN,could produce different factored loads and thus differentarea requirements for the rod under limit-statesdesign. Depending on how the member is loaded, it may fail by excessive dejection, which results in the member being unable to perform its design function; it may fail by plastic deformation general yielding ,which may cause a permanent,undesirablechange in shape; it may fail because of afracture break , which depending on the material and the nature of loadingmay be of a ductile type preceded by appreciableplastic deformation or of a brittle type with little or no prior plastic deformation.
Fatiguefailure, which is the progressive growth of one or more cracks in a member subjectedto repeated loads, often culminatesin a brittle fracture type of failure.
Another manner in which a structuralmember may fail is by elastic or plastic insta- bility. In this failure mode, the structural member may undergo large displacements from its design configurationwhen the applied load reaches a critical value, the buckling load or instability load.
This type of failure may result in excessive displacement or loss of ability because of yielding or fracture to carry the design load.
In addition to the failure modes already mentioned, a structuralmember may fail because of environmentalcorro- sion chemicalaction. To elaborate on the modes of failure of structural members, we discuss more fully the following categoriesof failure modes: Failureby excessive deflection a. Elastic deflection b. Deflection caused by creep 2. Failureby general yielding 3. Failureby fracture a. Suddenfracture of brittle materials b.
Fracture of cracked or flawed members c. Progressive fracture fatigue 4. Failure by instability For more complicated two- and three-dimensionalproblems, the significance of such simplefailure modes is open to question.
Many of these modes of failurefor simple structuralmembersarewell known to engi- neers. However,under unusualconditionsof load or environment,other types of failuremay occur. For example, in nuclear reactor systems,cracks in pipe loops have been attributedto stress-assistedcorrosioncracking, with possible side effects attributableto residual welding stresses Clarkeand Gordon, ;Hakalaet al.
The physical action in a structural member leading to failure is usually a compli- cated phenomenon, and in the following discussion the phenomena are necessarily over- simplified, but they nevertheless retain the essential features of the failures. Failure by Excessive Elastic Deflection The maximum load that may be applied to a member without causing it to cease to func- tion properly may be limitedby the permissibleelastic strain or deflection of the member.
Elastic deflection that may cause damage to a member can occur under these different conditions: Deflection under conditions of stable equilibrium, such as the stretch of a tension member, the angle of twist of a shaft, and the deflection of an end-loaded cantilever beam.
Elasticdeflections,under conditionsof equilibrium,are computedin Chapter5. Buckling, or the rather sudden deflection associated with unstable equilibrium and often resulting in total collapse of the member. This occurs, for example, when an axial load, applied gradually to a slendercolumn,exceeds the Euler load. See Chap- ter Elastic deflectionsthat are the amplitudes of the vibration of a member sometimes associated with failure of the member resulting from objectionable noise, shaking forces, collision of moving parts with stationary parts, etc.
When a memberfails by elastic deformation,the significantequationsfor design are those that relate loads and elastic deflection. The stressescausedby the loads arenot the significantquantities;that is, the stresses do not limit the loads that can be applied to the member.
In other words, if a member of given dimensions fails to perform its load-resistingfunction because of excessive elastic deflection,its load-carrying capacity is not increased by making the member of stronger material. As a rule, the most effective method of decreasingthe deflection of a member is by changing the shape or increasing the dimensions of its cross section, rather than by making the memberof a stiffermaterial.
Failure by General Yielding Another conditionthat may cause a memberto fail is general yielding. Generalyielding is inelastic deformation of a considerable portion of the member, distinguishing it from localizedyieldingof a relatively smallportion of the member.
The followingdiscussionof Yielding at elevated temperatures creep is discussed in Chapter Polycrystallinemetals are composedof extremelylarge numbers of very small units called crystals or grains.
The crystals have slip planes on which the resistance to shear stress is relatively small. Under elastic loading, before slip occurs, the crystal itself is dis- torted owing to stretching or compressing of the atomic bonds from their equilibrium state. If the load is removed,the crystal returns to its undistorted shape and no permanent deformationexists. When a load is applied that causes the yield strength to be reached, the crystals are again distorted but, in addition, defects in the crystal, known as dislocations Eisenstadt, ,move in the slip planes by breaking and reforming atomic bonds.
After removal of the load, only the distortion of the crystal resulting from bond stretching is recovered. The movement of the dislocationsremains as permanent deformation. After sufficient yieldinghas occurred in some crystals at a given load, these crystals will not yield further without an increase in load.
This is due to the formation of disloca- tion entanglementsthat make motion of the dislocationsmore and more difficult. A higher and higher stress will be needed to push new dislocations through these entanglements. This increasedresistancethat developsafter yielding is known as strain hardening or work hardening. Strain hardening is permanent.
Hence, for strain-hardeningmetals, the plastic deformationand increase in yield strengthare both retained after the load is removed. When failureoccursby generalyielding, stressconcentrationsusually arenot signif- icant because of the interaction and adjustments that take place between crystals in the regions of the stressconcentrations.
Slip in a few highly stressedcrystalsdoes not limit the general load-carryingcapacity of the member but merely causes readjustment of stresses that permit the more lightly stressedcrystals to take higher stresses.
The stress distribution approaches that which occurs in a member free from stress concentrations. Thus, the member as a whole acts substantiallyas an ideal homogeneousmember, free from abrupt changes of section. It is important to observe that, if a member that fails by yielding is replaced by one with a material of a higher yield stress, the mode of failure may change to that of elastic deflection,buckling, or excessivemechanical vibrations.
Hence, the entire basis of design may be changed when conditionsare altered to prevent a given mode of failure. Failure by Fracture Some members cease to function satisfactorilybecause they break fracture before either excessive elastic deflection or general yielding occurs. Three rather different modes or mechanismsof fracture that occur especiallyin metals are now discussed briefly. Sudden Fracture of Brittle Material. Some materials-so-called brittle materi- als-function satisfactorilyin resisting loads under static conditions until the material breaks rather suddenlywith little or no evidenceof plastic deformation.
Ordinarily,the tensile stress in members made of such materials is considered to be the significant quantity associated with the failure, and the ultimate strength 0,is taken as the mea- sure of the maximumutilizable strengthof the material Figure l.
Fracture of Flawed Members. A member made of a ductile metal and subjected to static tensile loads will not fracture in a brittle manner as long as the member is free of flaws cracks, notches, or other stress concentrations and the temperature is not unusually low. However, in the presence of flaws, ductile materials may experi- ence brittle fracture at normal temperatures.
Plastic deformation may be small or nonexistenteven though fractureis impending. Thus, yield strength is not the critical Instead, notch toughness, the ability of a material to absorb energy in the presence of a notch or sharp crack , is the parameter that governs the failure mode.
Dynamic loading and low tempera- tures also increase the tendency of a material to fracture in a brittle manner. Failure by brittle fracture is discussed in Chapter Progressive Fracture Fatigue. If a metal that ordinarily fails by general yield- ing under a static load is subjected to repeated cycles of stress, it may fail by fracture without visual evidence of yielding, provided that the repeated stress is greater than a value called thefatigue strength.
Under such conditions, minute cracks start at one or more points in the member, usually at points of high localized stress such as at abrupt changes in section, and gradually spread by fracture of the material at the edges of the cracks where the stress is highly concentrated. Theprogressivefracture continues until the member finally breaks. This mode of failure is usually called a fatiguefailure, but it is better designated asfailure by progressivefracture resulting from repeated loads.
See Chapter Failure by Instability Buckling Some members may fail by a sudden, catastrophic, lateral deflection instability or buck- ling , rather than by yielding or crushing Chapter Consider an ideal pin-ended slen- der column or strut subjected to an axial compressive load P.
What requirements control the derivation of load-stress relations? Describe the method of mechanics of materials. How are stress-strain-temperature relations for a material established? Explain the differences between elastic response and inelastic response of a solid.
What is a stress-strain diagram? Explain the difference between elastic limit and propor- tional limit. Explain the difference between the concepts of yield point and yield stress.
What is offset strain? How does the engineeringstress-strain diagram differfrom the true stress-strain diagram? What are modes of failure? What are failure criteria? How are they related to modes of failure?
What is meant by the term factor of safety? How are fac- tors of safety used in design?
What is a design inequality? How is the usual design inequality modified to account for statistical variability? What is a load factor? A load effect? A resistance factor? What is a limit-states design? Discuss the various ways that a structural member may fail. Discuss the failure modes, critical parameters, and failure criteria that may apply to the design of a downhill snow ski. For the steels whose stress-strain diagrams are repre- sented by Figures 1.
Use the mechanics of materials method to derive the load-stress and load-displacementrelations for a solid circular rod of constant radius r and length L subjected to a torsional moment T as shown in Figure P1. Use the mechanics of materials method to derive the load-stress and load-displacement relations for a bar of con- stant width b, linearly varying depth d, and length L subjected to an axial tensile force P as shown in Figure P1.
A Longitudinalsection rods not shown End plate Pipe: A pressure vessel consists of two flat plates clamped to the ends of a pipe using four rods, each 15 mm in diameter, to form a cylinder that is to be subjected to internal pressure p Figure P1. The pipe has an outside diameter of mm and an inside diameter of 90 mm. During assembly of the cylinder before pressuriza- tion , the joints between the plates and ends of the pipe are sealed with a thin mastic and the rods are each pretensioned to 65 IcN.
Using the mechanics of materials method, determine the internal pressure that will cause leaking. Leaking is defined as a state of zero bearing pressure between the pipe ends and the plates. Also determine the change in stress in the rods. Ignore bending in the plates and radial deformation of the pipe. A steel bar and an aluminum bar arejoined end to end and fixed between two rigid walls as shown in Figure P1.
The cross-sectional area of the steel bar isA, and that of the alumi- num bar is A,. Initially, the two bars are stress free. Derive gen- eral expressions for the deflection of point A, the stress in the steel bar, and the stress in the aluminum bar for the following conditions: A load P is applied at point A.
The left wall is displaced an amount 6to the right. In South African gold mines, cables are used to lower worker cages down mine shafts. Ordinarily, the cables are made of steel. To save weight, an engineer decides to use cables made of aluminum. A design requirement is that the stress in the cable resulting from self-weightmust not exceed one-tenth of the ulti- mate strength o,of the cable. Determine the lengths of two cables, one of steel and the other of aluminum, for which the stress resulting from the self- weight of each cable equals one-tenth of the ultimate strength of the material.
Assume that the cross-sectional area A of a cable is constant over the length of the cable. Assuming that A is constant, determine the elongation of each cable when the maximum stress in the cable is 0.
The cables are used to lower a cage to a mine depth of 1 km. Determine the maximum allowable weight of the cage includ- ing workers and equipment , if the stress in a cable is not to exceed 0.
A steel shaft of circular cross section is subjected to a twisting moment T. The maximum allowable twist is 0. Determine the diameter at which the maximum allowable twist, and not the maximum shear stress, is the controlling factor. An elastic T-beam is loaded and supported as shown in Figure P1. The cross section of the beam is shown in Fig- ure P1.
Determine the location j of the neutral axis the horizontal centroidal axis of the cross section. Draw shear and moment diagramsfor the beam. Determine the maximum tensile stress and the maximum compressivestress in the beam and their locations.
Determine the maximum and minimum shear stresses in the web of the beam of Problem 1. Hence, Eq. A steel tensile test specimenhas a diameterof 10mm and a gage length of 50 mm. Test data for axial load and corre- spondingdata for the gage-lengthelongationare listed in Table P1.
Convert these data to engineering stress-strain data and determinethe magnitudesof the toughness U, and the ultimate strength 0,.
Chicago, IL: American Institute of Steel Construction. AISC June 1. New York. Elasticity in Engineering Mechanics, 2nd ed. New York: Corrosion, 29 1: Reliability-Based Mechanical Design.
Mechanics of Materials, 5th ed. Pacific Grove, CA: Reliability-Based Design in Civil Engineering. SCo'lT, P. New York Macmillan. Design, 2,3: In this chapter,we developtheories of stress and strainthat are essentialfor the analysisof a structuralor mechanicalsystem sub- jected to loads. The relations developed are used throughoutthe remainder of the book. Pass a ficti- tious plane Q through the body, cutting the body along surfaceA Figure 2. Designate one side of plane Q as positive and the other side as negative.
The portion of the body on the positive side of Q exerts a force on the portion of the body on the negative side. This force is transmitted through the plane Q by direct contact of the parts of the body on the two sidesof Q. Let the force that is transmittedthrough an incrementalarea AA ofA by the part on the positive side of Q be denoted by AF. Theseratios arecalledthe average stress, average normal stress, and average shear stress, respectively, acting on area AA.
The concept of stress at a point is obtained by letting AA become an infinitesimal. For simplicity, we show the volume element with one corner at point 0 and assume that the stress components are uniform constant throughout the volume element.
Advanced Mechanics of Materials by Arthur P. The text treats each type of structural member in sufficient detail so that the resulting solutions are directly applicable to real-world problems. New examples for various types of member and a large number of new problems are included.
To facilitate the transition from elementary mechanics of materials to advanced topics, a review of the elements of mechanics of materials is presented along with appropriate examples and problems. Page Number 53 t0 78 is missing here and which is the most impotent part that contains theory of strain. Your email address will not be published. Notify me of follow-up comments by email.
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