688:
yield point. Such failures are called fatigue failure. The failure is by a fracture that appears to be brittle with little or no visible evidence of yielding. However, when the stress is kept below "fatigue stress" or "endurance limit stress", the part will endure indefinitely. A purely reversing or cyclic stress is one that alternates between equal positive and negative peak stresses during each cycle of operation. In a purely cyclic stress, the average stress is zero. When a part is subjected to a cyclic stress, also known as stress range (Sr), it has been observed that the failure of the part occurs after a number of stress reversals (N) even if the magnitude of the stress range is below the material's yield strength. Generally, higher the range stress, the fewer the number of reversals needed for failure.
87:
member is composed. The applied loads may be axial (tensile or compressive), or rotational (strength shear). With a complete description of the loading and the geometry of the member, the state of stress and state of strain at any point within the member can be calculated. Once the state of stress and strain within the member is known, the strength (load carrying capacity) of that member, its deformations (stiffness qualities), and its stability (ability to maintain its original configuration) can be calculated.
131:
83:. The field of strength of materials deals with forces and deformations that result from their acting on a material. A load applied to a mechanical member will induce internal forces within the member called stresses when those forces are expressed on a unit basis. The stresses acting on the material cause deformation of the material in various manners including breaking them completely. Deformation of the material is called strain when those deformations too are placed on a unit basis.
721:– This theory postulates that failure will occur if the maximum normal stress in the part exceeds the ultimate tensile stress of the material as determined from uniaxial testing. This theory deals with brittle materials only. The maximum tensile stress should be less than or equal to ultimate tensile stress divided by factor of safety. The magnitude of the maximum compressive stress should be less than ultimate compressive stress divided by factor of safety.
527:, or the "modulus of elasticity". The modulus of elasticity can be used to determine the stress–strain relationship in the linear-elastic portion of the stress–strain curve. The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress–strain plot it is defined to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.
737:. This theory postulates that failure will occur when the distortion energy per unit volume due to the applied stresses in a part equals the distortion energy per unit volume at the yield point in uniaxial testing. The total elastic energy due to strain can be divided into two parts: one part causes change in volume, and the other part causes a change in shape. Distortion energy is the amount of energy that is needed to change the shape.
206:) along the axis of the applied load, it is, in other words, a stress state that causes a squeezing of the material. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than their tensile strength. However, structures loaded in compression are subject to additional failure modes, such as
505:
98:(yield stress) beyond which the material experiences deformations that will not be completely reversed upon removal of the loading and as a result, the member will have a permanent deflection. The ultimate strength of the material refers to the maximum value of stress reached. The fracture strength is the stress value at fracture (the last stress value recorded).
448:, distribution of forces, and yield strength affect the impact strength of a material. In order for a material or object to have a high impact strength, the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength.
781:
is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts
687:
Design stresses that have been determined from the ultimate or yield point values of the materials give safe and reliable results only for the case of static loading. Many machine parts fail when subjected to a non-steady and continuously varying loads even though the developed stresses are below the
536:
or plastic deformation is the opposite of elastic deformation and is defined as unrecoverable strain. Plastic deformation is retained after the release of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do
90:
The calculated stresses may then be compared to some measure of the strength of the member such as its material yield or ultimate strength. The calculated deflection of the member may be compared to deflection criteria that are based on the member's use. The calculated buckling load of the member may
86:
The stresses and strains that develop within a mechanical member must be calculated in order to assess the load capacity of that member. This requires a complete description of the geometry of the member, its constraints, the loads applied to the member and the properties of the material of which the
66:
The theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An
550:
Ultimate strength is an attribute related to a material, rather than just a specific specimen made of the material, and as such it is quoted as the force per unit of cross section area (N/m). The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. For
476:
is a mathematical term that expresses the trend of the deformation change among the material field. Strain is the deformation per unit length. In the case of uniaxial loading the displacement of a specimen (for example a bar element) lead to a calculation of strain expressed as the quotient of the
339:
that leads to tensile failure in the manner of ductile failure (yield as the first stage of that failure, some hardening in the second stage and breakage after a possible "neck" formation) or brittle failure (sudden breaking in two or more pieces at a low-stress state). The tensile strength can be
110:
loadings – Forces applied perpendicular to the longitudinal axis of a member. Transverse loading causes the member to bend and deflect from its original position, with internal tensile and compressive strains accompanying the change in curvature of the member. Transverse loading also induces shear
702:
There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy theory, and maximum distortion energy theory (Von Mises
Criterion of Failre). Out of these four theories of failure, the maximum normal stress theory is only applicable for brittle
776:
and can be quantitatively and qualitatively explained. Strengthening mechanisms are accompanied by the caveat that some other mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although
518:
is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress is directly proportional to the resulting strain (up to a certain limit), and a graph representing those two quantities is a straight
226:
such as material defects or abrupt changes in geometry. However, materials exhibiting ductile behaviour (many metals for example) can tolerate some defects while brittle materials (such as ceramics and some steels) can fail well below their ultimate material
703:
materials, and the remaining three theories are applicable for ductile materials. Of the latter three, the distortion energy theory provides the most accurate results in a majority of the stress conditions. The strain energy theory needs the value of
348:
is a more complex measure of the strength of a material that considers several loading episodes in the service period of an object, and is usually more difficult to assess than the static strength measures. Fatigue strength is quoted here as a simple
46:
in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its
707:
of the part material, which is often not readily available. The maximum shear stress theory is conservative. For simple unidirectional normal stresses all theories are equivalent, which means all theories will give the same result.
786:
in the material, one can make informed decisions on how to increase the strength of a material depending on its microstructural properties and the desired end effect. Strength is expressed in terms of the limiting values of the
463:
of the material is the change in geometry created when stress is applied ( as a result of applied forces, gravitational fields, accelerations, thermal expansion, etc.). Deformation is expressed by the displacement field of the
416:
91:
be compared to the applied load. The calculated stiffness and mass distribution of the member may be used to calculate the member's dynamic response and then compared to the acoustic environment in which it will be used.
541:
Consider the difference between a carrot and chewed bubble gum. The carrot will stretch very little before breaking. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.
120:
loading – Twisting action caused by a pair of externally applied equal and oppositely directed force couples acting on parallel planes or by a single external couple applied to a member that has one end fixed against
537:
not experience any plastic deformation and will fracture under relatively low strain, while ductile materials such as metallics, lead, or polymers will plastically deform much more before a fracture initiation.
727:– This theory postulates that failure will occur when the strain energy per unit volume due to the applied stresses in a part equals the strain energy per unit volume at the yield point in uniaxial testing.
63:. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
319:
that leads to failure in a material in the manner of ductile failure (infinite theoretical yield) or brittle failure (rupture as the result of crack propagation, or sliding along a weak plane – see
235:
is the stress state caused by the combined energy of a pair of opposing forces acting along parallel lines of action through the material, in other words, the stress caused by faces of the material
807:
especially changes in cross-section of the product or defects in manufacturing, near holes and corners at nominal stress levels far lower than those quoted for the strength of the material.
1405:, A.N. Gent, W.V. Mars, In: James E. Mark, Burak Erman and Mike Roland, Editor(s), The Science and Technology of Rubber (Fourth Edition), Academic Press, Boston, 2013, Pages 473–516,
715:– This theory postulates that failure will occur if the magnitude of the maximum shear stress in the part exceeds the shear strength of the material determined from uniaxial testing.
222:
the material. The strength of structures of equal cross-sectional area loaded in tension is independent of shape of the cross-section. Materials loaded in tension are susceptible to
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that would cause failure. The effects of dynamic loading are probably the most important practical consideration of the theory of elasticity, especially the problem of
662:
1498:
Green, D., An
Introduction to the Mechanical Properties of Ceramics, Cambridge Solid State Science Series, Eds. Clarke, D.R., Suresh, S., Ward, I.M.Babu Tom.K (1998)
609:
477:
displacement and the original length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order
305:, the point of yielding is difficult to identify, thus it is usually defined as the stress required to cause 0.2% plastic strain. This is called a 0.2% proof stress.
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803:. Repeated loading often initiates cracks, which grow until failure occurs at the corresponding residual strength of the structure. Cracks always start at a
218:
is the stress state caused by an applied load that tends to elongate the material along the axis of the applied load, in other words, the stress caused by
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Axial loading – The applied forces are collinear with the longitudinal axis of the member. The forces cause the member to either stretch or shorten.
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For example, to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be calculated to be
292:. Strength parameters include: yield strength, tensile strength, fatigue strength, crack resistance, and other parameters.
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In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or
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is a term to describe the magnitude to which a structural element is displaced when subject to an applied load.
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756:. The engineering processes to which a material is subjected can alter this microstructure. The variety of
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forces that cause shear deformation of the material and increase the transverse deflection of the member.
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611:, where FS: the factor of safety, Rf The applied stress, and F: ultimate allowable stress (psi or MPa)
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is the lowest stress that produces a permanent deformation in a material. In some materials, like
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684:= 110Ă—10 N/m. Such allowable stresses are also known as "design stresses" or "working stresses".
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Lawn, B.R., Fracture of
Brittle Solids, Cambridge Solid State Science Series, 2nd Edn. (1993)
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Davidge, R.W., Mechanical
Behavior of Ceramics, Cambridge Solid State Science Series, (1979)
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891: – Branch of mechanics concerned with balance of forces in nonmoving systems
185:. The area can be the undeformed area or the deformed area, depending on whether
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844: – Initiation and propagation of cracks in a material due to cyclic loading
411:{\displaystyle \Delta \sigma =\sigma _{\mathrm {max} }-\sigma _{\mathrm {min} }}
1389:
Approximating
Perfection: A Mathematician's Journey into the World of Mechanics
614:
Margin of Safety is the common method for design criteria. It is defined MS = P
733:– This theory is also known as maximum distortion energy theory of failure or
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277:
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is a design criteria that an engineered component or structure must achieve.
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423:
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1016:
Beer, Ferdinand Pierre; Johnston, Elwood
Russell; Dewolf, John T (2009).
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Fa-Hwa Cheng, Initials. (1997). Strength of material. Ohio: McGraw-Hill
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example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440
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850: – Investigation of failures associated with legal intervention
129:
134:
A material being loaded in a) compression, b) tension, c) shear.
555:. In Imperial units, the unit of stress is given as lbf/in or
276:. The traditional measure unit for strength are therefore
239:
relative to one another. An example is cutting paper with
873: – Step in the process of designing physical objects
94:
Material strength refers to the point on the engineering
67:
important founding pioneer in mechanics of materials was
38:) typically refers to various methods of calculating the
27:
Behavior of solid objects subject to stresses and strains
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Pages displaying short descriptions of redirect targets
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Pages displaying short descriptions of redirect targets
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List of materials properties § Mechanical properties
856: – Study of propagation of cracks in materials
1346:, 2nd edition. John Wiley & Sons, Inc., 2002.
1145:(7 ed.). Pearson Prentice Hall. p. 305.
676:
656:
603:
410:
166:
1474:, 3rd edition. Krieger Publishing Company, 1976,
508:Basic static response of a specimen under tension
1435:. Prentice Hall, Englewood Cliffs, N. J., 1990.
1359:Foundations of Materials Science and Engineering
885: – Ratio of strength to mass for a material
252:Material resistance can be expressed in several
1070:(5th ed.). McGraw Hill. pp. 693–696.
760:that alter the strength of a material includes
1328:Introduction to Mechanics of Deformable Solids
1195:(5thv ed.). McGraw Hill. pp. 27–28.
210:, that are dependent on the member's geometry.
1170:(5th ed.). McGraw Hill. pp. 53–56.
835: – Description of large objects' physics
8:
995:(5th ed.). McGraw Hill. pp. 9–10.
920:(5th ed.). McGraw Hill. p. 210.
752:A material's strength is dependent on its
1387:Lebedev, Leonid P. and Michael J. Cloud.
1220:(5th ed.). McGraw Hill. p. 28.
1120:(5th ed.). McGraw Hill. p. 49.
1095:(5th ed.). McGraw Hill. p. 47.
1045:(5th ed.). McGraw Hill. p. 60.
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970:(5th ed.). McGraw Hill. p. 5.
945:(5th ed.). McGraw Hill. p. 7.
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422:it can be appropriately expressed as an
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740:Fracture mechanics was established by
167:{\displaystyle \sigma ={\frac {P}{A}}}
1455:Elastic and inelastic stress analysis
1357:Hashemi, Javad and William F. Smith.
243:or stresses due to torsional loading.
7:
1420:, 4th edition. Prentice-Hall, 2002.
1413:, 10.1016/B978-0-12-394584-6.00010-8
1391:. Princeton University Press, 2004.
1344:Fundamentals of Modern Manufacturing
559:. This unit is often abbreviated as
1403:Chapter 10 – Strength of Elastomers
1376:, SI Edition. Prentice-Hall, 2004.
1337:The New Science of Strong Materials
523:The slope of this line is known as
1515:Case studies in structural failure
1453:Shames, I.H. and F.A. Cozzarelli.
1374:Statics and Mechanics of Materials
1361:, 4th edition. McGraw-Hill, 2006.
1315:. Dover Publications, Inc., 1961,
1294:, 3rd edition. McGraw-Hill, 2001.
1290:Beer, F.P., E.R. Johnston, et al.
1248:Mechanics of Materials, E.J. Hearn
563:. One thousand psi is abbreviated
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1487:Elements of Strength of Materials
1485:Timoshenko, S.P. and D.H. Young.
731:Maximum Distortion Energy Theory
453:Strain parameters for resistance
248:Stress parameters for resistance
181:is the force acting on an area
138:Uniaxial stress is expressed by
1433:Engineering Mechanics of Solids
1306:Mechanical Properties of Matter
189:or true stress is of interest.
481:(with 6 independent elements).
268:with dimension homogeneous to
1:
1418:Applied Strength of Materials
1285:Materials Selection in Design
290:United States customary units
282:International System of Units
1216:Beer & Johnston (2006).
1191:Beer & Johnston (2006).
1166:Beer & Johnston (2006).
1116:Beer & Johnston (2006).
1091:Beer & Johnston (2006).
1066:Beer & Johnston (2006).
1041:Beer & Johnston (2006).
1020:(5th ed.). p. 52.
991:Beer & Johnston (2006).
966:Beer & Johnston (2006).
941:Beer & Johnston (2006).
916:Beer & Johnston (2006).
774:grain boundary strengthening
766:solid solution strengthening
725:Maximum Strain Energy Theory
719:Maximum Normal Stress Theory
557:pounds-force per square inch
1489:, 5th edition. (MKS System)
713:Maximum Shear Stress Theory
1566:
695:
497:
260:is used when referring to
1270:. TehniÄŤka knjiga, 1999.
1255:. TehniÄŤka knjiga, 1995.
895:Universal testing machine
824:Deformation mechanism map
438:Izod impact strength test
333:ultimate tensile strength
1550:Condensed matter physics
1308:. Wiley, New York, 1964.
1268:Strength of Materials II
758:strengthening mechanisms
657:{\displaystyle F=UTS/FS}
1545:Deformation (mechanics)
1457:. Prentice-Hall, 1991.
1253:Strength of Materials I
1141:R. C. Hibbeler (2009).
770:precipitation hardening
735:von Mises-Hencky theory
698:Material failure theory
494:Stress–strain relations
1292:Mechanics of Materials
1218:Mechanics of Materials
1193:Mechanics of Materials
1168:Mechanics of Materials
1118:Mechanics of Materials
1093:Mechanics of Materials
1068:Mechanics of Materials
1043:Mechanics of Materials
1018:Mechanics of Materials
993:Mechanics of Materials
968:Mechanics of Materials
943:Mechanics of Materials
918:Mechanics of Materials
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664:= 440/4 = 110 MPa, or
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604:{\displaystyle FS=F/f}
509:
412:
274:force per unit surface
264:parameters. These are
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36:mechanics of materials
18:Mechanics of materials
1472:Strength of Materials
1448:Strength of Materials
1313:Strength of Materials
1311:Den Hartog, Jacob P.
805:stress concentrations
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256:parameters. The term
224:stress concentrations
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32:strength of materials
1540:Building engineering
1330:. McGraw-Hill, 1967.
848:Forensic engineering
746:George Rankine Irwin
742:Alan Arnold Griffith
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335:is a limit state of
315:is a limit state of
312:Compressive strength
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1342:Groover, Mikell P.
1143:Structural Analysis
877:Molecular diffusion
818:Creep (deformation)
784:plastic deformation
500:Stress–strain curve
474:reduced deformation
266:physical quantities
96:stress–strain curve
81:plastic deformation
1339:. Princeton, 1984.
871:Material selection
860:Fracture toughness
854:Fracture mechanics
842:Fatigue (material)
789:compressive stress
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442:Charpy impact test
418:). In the case of
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317:compressive stress
204:compression member
195:Compressive stress
187:engineering stress
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69:Stephen Timoshenko
1535:Materials science
1287:. Pergamon, 1992.
1227:978-0-07-352938-7
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883:Specific strength
677:{\displaystyle F}
262:mechanical stress
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254:mechanical stress
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102:Types of loadings
53:ultimate strength
16:(Redirected from
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797:shear stresses
793:tensile stress
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762:work hardening
754:microstructure
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911:
751:
730:
724:
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531:
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288:between the
273:
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232:Shear stress
230:
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182:
178:
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126:Stress terms
93:
89:
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35:
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1282:Ashby, M.F.
460:Deformation
200:compression
1524:Categories
903:References
533:Plasticity
515:Elasticity
486:Deflection
446:elasticity
284:, and the
108:Transverse
75:Definition
464:material.
424:amplitude
392:σ
388:−
371:σ
364:σ
361:Δ
227:strength.
149:σ
121:rotation.
118:Torsional
833:Dynamics
811:See also
270:pressure
241:scissors
208:buckling
40:stresses
889:Statics
801:fatigue
280:in the
237:sliding
220:pulling
44:strains
1478:
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772:, and
479:tensor
469:Strain
177:where
59:, and
519:line.
351:range
1476:ISBN
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1422:ISBN
1407:ISBN
1393:ISBN
1378:ISBN
1363:ISBN
1348:ISBN
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1122:ISBN
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997:ISBN
972:ISBN
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922:ISBN
744:and
272:and
198:(or
42:and
565:ksi
561:psi
553:MPa
472:or
440:or
331:or
286:psi
278:MPa
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353:(
183:A
179:P
160:A
157:P
152:=
20:)
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