basic of som Part-2

8/10/2019 basic of som Part-2

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Bengali Wikipedia 10th Anniversary Celebration and International Conference, KolkataThe conference will be held on th and 10th !an"ary #01$ at !adavp"r %niversity&egistration for the conference is now open

Strength of materials'ro( Wikipedia, the free encyclopedia

This articleneeds additional citations for verification ) *lease helpi(prove thisarticle byadding citations to reliable so"rces) %nso"rced (aterial (ay be challengedand re(oved)(August 2010)

Internalforce lines are denser near the hole, a co((onstress concentration

Mechanics of materials , also calledstrength of materials , is a s"b+ect which deals with the behavior of solid ob+ects s"b+ect tostresses andstrains) The co(plete theory began with theconsideration of the behavior of one and two di(ensional (e(bers of str"ct"res, whosestates of stress can be appro i(ated as two di(ensional, and was then generali-ed to threedi(ensions to develop a (ore co(plete theory of the elastic and plastic behavior of(aterials) An i(portant fo"nding pioneer in (echanics of (aterials was .tephenTi(oshenko)

The st"dy of strength of (aterials often refers to vario"s (ethods of calc"lating the stresses

and strains in str"ct"ral (e(bers, s"ch as bea(s, col"(ns, and shafts) The (ethodse(ployed to predict the response of a str"ct"re "nder loading and its s"sceptibility to vario"s
http://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://en.wikipedia.org/wiki/Wikipedia:Verifiabilityhttp://en.wikipedia.org/w/index.php?title=Strength_of_materials&action=edithttp://en.wikipedia.org/w/index.php?title=Strength_of_materials&action=edithttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Force_lineshttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Strain_(physics)http://en.wikipedia.org/wiki/Stephen_Timoshenkohttp://en.wikipedia.org/wiki/Stephen_Timoshenkohttp://en.wikipedia.org/wiki/Stephen_Timoshenkohttp://en.wikipedia.org/wiki/File:HoleForceLines.svghttp://en.wikipedia.org/wiki/File:Question_book-new.svghttp://en.wikipedia.org/wiki/Strength_of_materialshttp://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://meta.wikimedia.org/wiki/Bengali_Wikipedia_10th_Anniversary_Celebration_Kolkatahttp://en.wikipedia.org/wiki/Wikipedia:Verifiabilityhttp://en.wikipedia.org/w/index.php?title=Strength_of_materials&action=edithttp://en.wikipedia.org/w/index.php?title=Strength_of_materials&action=edithttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/wiki/Force_lineshttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Strain_(physics)http://en.wikipedia.org/wiki/Stephen_Timoshenkohttp://en.wikipedia.org/wiki/Stephen_Timoshenko


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fail"re (odes takes into acco"nt the properties of the (aterials s"ch as itsyield strength,"lti(ate strength, /o"ng s (od"l"s , and*oisson s ratio in addition the (echanical ele(ent s(acroscopic properties 2geo(etric properties3, s"ch as it length, width, thickness, bo"ndaryconstraints and abr"pt changes in geo(etry s"ch as holes are considered)

Contents 1 4efinition

o 1)1 Types of loadings

o 1)# .tress ter(s

o 1)5 .trength ter(s

o 1)6 .train 2defor(ation3 ter(s

o 1)$ .tress7strain relations # 4esign ter(s

o #)1 'ail"re theories

5 8icrostr"ct"re

6 .ee also

$ &eferences

9 '"rther reading

: ; ternal links

Definition

In (aterials science, the strength of a (aterial is its ability to withstand an applied loadwitho"t fail"re) The field of strength of (aterials deals with forces and defor(ations thatres"lt fro( their acting on a (aterial) A load applied to a (echanical (e(ber will ind"ceinternal forces within the (e(ber called stresses when those forces are e pressed on a "nit basis) The stresses acting on the (aterial ca"se defor(ation of the (aterial in vario"s(anner) 4efor(ation of the (aterial is called strain when those defor(ations too are placedon a "nit basis) The applied loads (ay be a ial 2tensile or co(pressive3, orshear ) The stressesand strains that develop within a (echanical (e(ber ("st be calc"lated in order to assess theload capacity of that (e(ber) This re


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be co(pared to the applied load) The calc"lated stiffness and (ass distrib"tion of the (e(ber (ay be "sed to calc"late the (e(ber s dyna(ic response and then co(pared to the aco"sticenviron(ent in which it will be "sed)

8aterial strength refers to the point on the engineering stress7strain c"rve 2yield stress3 beyond which the (aterial e periences defor(ations that will not be co(pletely reversed"pon re(oval of the loading and as a res"lt the (e(ber will have a per(anent deflection)The "lti(ate strength refers to the point on the engineering stress7strain c"rve correspondingto the stress that prod"ces fract"re)

Types of loadings

Transverse loading > 'orces applied perpendic"lar to the longit"dinal a is of a(e(ber) Transverse loading ca"ses the (e(ber to bend and deflect fro( its original position, with internal tensile and co(pressive strains acco(panying the change inc"rvat"re of the (e(ber )?1@ Transverse loading also ind"ces shear forces that ca"seshear defor(ation of the (aterial and increase the transverse deflection of the(e(ber)

A ial loading > The applied forces are collinear with the longit"dinal a is of the(e(ber) The forces ca"se the (e(ber to either stretch or shorten)?#@

Torsional loading > Twisting action ca"sed by a pair of e ternally applied e


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their tensile strength) owever, str"ct"res loaded in co(pression are s"b+ect toadditional fail"re (odes, s"ch as b"ckling, that are dependent on the (e(ber sgeo(etry)

Tensile stress is the stress state ca"sed by an applied load that tends to elongate the(aterial along the a is of the applied load, in other words the stress ca"sed by pulling the (aterial) The strength of str"ct"res of e see shearstrength3)

Tensile strength or ultimate tensile strength is a li(it state oftensile stress that leads totensile fail"re in the (anner of d"ctile fail"re 2yield as the first stage of that fail"re,so(e hardening in the second stage and breakage after a possible DneckD for(ation3 or brittle fail"re 2s"dden breaking in two or (ore pieces at a low stress state3) Tensilestrength can be


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("st have a large vol"(e with a low (od"l"s of elasticity and a high (aterial yieldstrength)?:@

Strain (deformation) terms

De ormation of the (aterial is the change in geo(etry created when stress is applied2as a res"lt of applied forces, gravitational fields, accelerations, ther(al e pansion,etc)3) 4efor(ation is e pressed by the displace(ent field of the (aterial)?F@

Strain or reduced de ormation is a (athe(atical ter( that e presses the trend of thedefor(ation change a(ong the (aterial field) .train is the defor(ation per "nitlength)? @ In the case of "nia ial loading the displace(ents of a speci(en 2for e a(plea bar ele(ent3lead to a calc"lation of strain e pressed as the elastic region is either below the yield point, or if a yield point is not easily identified on the stress7strain plot it is defined to be between 0 and 0)# strain, and is defined as the region of strain in which no yielding2per(anent defor(ation3 occ"rs)?11@

#lasticit" or plastic defor(ation is the opposite of elastic defor(ation and is defined

as "nrecoverable strain) *lastic defor(ation is retained after the release of the appliedstress) 8ost (aterials in the linear>elastic category are "s"ally capable of plastic
http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-7http://en.wikipedia.org/wiki/Deformation_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-8http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-9http://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Deflection_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-10http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Young's_modulushttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Plasticity_(physics)http://en.wikipedia.org/wiki/Plasticity_(physics)http://en.wikipedia.org/wiki/File:Tension_test.svghttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-7http://en.wikipedia.org/wiki/Deformation_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-8http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-9http://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Deflection_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-10http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Young's_modulushttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Plasticity_(physics)


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defor(ation) Brittle (aterials, like cera(ics, do not e perience any plasticdefor(ation and will fract"re "nder relatively low stress) 8aterials s"ch as (etals"s"ally e perience a s(all a(o"nt of plastic defor(ation before fail"re while d"ctile(etals s"ch as copper and lead or poly(ers will plasticly defor( ("ch (ore)

Consider the difference between a carrot and chewed b"bble g"() The carrot will stretch verylittle before breaking) The chewed b"bble g"(, on the other hand, will plastically defor(enor(o"sly before finally breaking)

Design terms

%lti(ate strength is an attrib"te related to a (aterial, rather than +"st a specific speci(en(ade of the (aterial, and as s"ch it is


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on how to increase the strength of a (aterial depending its (icrostr"ct"ral properties and thedesired end effect) .trength is e pressed in ter(s of the li(iting val"es of theco(pressivestress, tensile stress, andshear stresses that wo"ld ca"se fail"re) The effects of dyna(icloading are probably the (ost i(portant practical consideration of the strength of (aterials,especially the proble( of fatig"e) &epeated loading often initiates brittle cracks, which grow"ntil fail"re occ"rs) The cracks always start atstress concentrations, especially changes incross>section of the prod"ct, near holes and corners at no(inal stress levels far lower thanthose 0>0:>5$# 5F>:)

#) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) :)I.B :F>0>0:>5$# 5F>:)

5) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) $)I.B :F>0>0:>5$# 5F>:)

6) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) 710)I.B :F>0>0:>5$# 5F>:)

$) Beer P !ohnston) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) $#)I.B :F>0>0:>5$# 5F>:)

9) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 90)I.B :F>0>0:>5$# 5F>:)
http://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Brittlehttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Creep_of_materialshttp://en.wikipedia.org/wiki/Deformation-mechanism_mapshttp://en.wikipedia.org/wiki/Diffusion_in_materialshttp://en.wikipedia.org/wiki/Dynamics_(mechanics)http://en.wikipedia.org/wiki/Fatigue_of_materialshttp://en.wikipedia.org/wiki/Forensic_engineeringhttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/Material_selectionhttp://en.wikipedia.org/wiki/Specific_strengthhttp://en.wikipedia.org/wiki/Staticshttp://en.wikipedia.org/wiki/Universal_testing_machinehttp://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Brittlehttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Creep_of_materialshttp://en.wikipedia.org/wiki/Deformation-mechanism_mapshttp://en.wikipedia.org/wiki/Diffusion_in_materialshttp://en.wikipedia.org/wiki/Dynamics_(mechanics)http://en.wikipedia.org/wiki/Fatigue_of_materialshttp://en.wikipedia.org/wiki/Forensic_engineeringhttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/Material_selectionhttp://en.wikipedia.org/wiki/Specific_strengthhttp://en.wikipedia.org/wiki/Staticshttp://en.wikipedia.org/wiki/Universal_testing_machinehttp://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7


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:) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) 9 579 9)I.B :F>0>0:>5$# 5F>:)

F) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 6:)I.B :F>0>0:>5$# 5F>:)

) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 6 )I.B :F>0>0:>5$# 5F>:)

10) &) C) ibbeler 2#00 3)Structural Anal"sis 2: ed)3) *earson *rentice all) p) 50$)I.B :F>0>15>90#090>F)

11) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) $57$9)I.B :F>0>0:>5$# 5F>:)

1#) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) #:7#F)I.B :F>0>0:>5$# 5F>:)

15) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) #F)I.B :F>0>0:>5$# 5F>:)

Further reading 'a> wa Cheng, Initials) 21 :3) .trength of (aterial) =hioJ 8cOraw> ill 8echanics of 8aterials, ;)!) earn

AlfireviQ, Ivo)Strength o $aterials I ) TehniRka kn+iga, 1 $)I.B $5>1:#>010>S)

AlfireviQ, Ivo)Strength o $aterials II ) TehniRka kn+iga, 1 )I.B $5>919F>F$>$) Ashby, 8)') $aterials Selection in Design ) *erga(on, 1 #)

Beer, ')*), ;)&) !ohnston, et al) $echanics o $aterials , 5rd edition) 8cOraw> ill,#001)I.B 0>0:>#6F9:5>#

Cottrell, A) ) $echanical #roperties o $atter ) Wiley, ew /ork, 1 96)

4en artog, !acob *)Strength o $aterials ) 4over *"blications, Inc), 1 91,I.B 0>6F9>90:$$>0)

4r"cker, 4)C) Introduction to $echanics o De orma%le Solids ) 8cOraw> ill, 1 9:) Oordon, !);) The &e' Science o Strong $aterials ) *rinceton, 1 F6)

Oroover, 8ikell *) Fundamentals o $odern $anu acturing , #nd edition) !ohn WileyP .ons,Inc), #00#)I.B 0>6:1>600$1>5)

ashe(i, !avad and Willia( ') .(ith) Foundations o $aterials Science and !ngineering , 6th edition) 8cOraw> ill, #009)I.B 0>0:>1#$9 0>5)

ibbeler, &)C)Statics and $echanics o $aterials , .I ;dition) *rentice> all, #006)I.B 0>15>1# 011>F)
http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/953172010Xhttp://en.wikipedia.org/wiki/Special:BookSources/9536168855http://en.wikipedia.org/wiki/M._F._Ashbyhttp://en.wikipedia.org/wiki/Special:BookSources/0072486732http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/J.E._Gordonhttp://en.wikipedia.org/wiki/Special:BookSources/0471400513http://en.wikipedia.org/wiki/Special:BookSources/0071256903http://en.wikipedia.org/wiki/Special:BookSources/0131290118http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/953172010Xhttp://en.wikipedia.org/wiki/Special:BookSources/9536168855http://en.wikipedia.org/wiki/M._F._Ashbyhttp://en.wikipedia.org/wiki/Special:BookSources/0072486732http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/J.E._Gordonhttp://en.wikipedia.org/wiki/Special:BookSources/0471400513http://en.wikipedia.org/wiki/Special:BookSources/0071256903http://en.wikipedia.org/wiki/Special:BookSources/0131290118


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ebedev, eonid *) and 8ichael !) Clo"d) Appro imating #er ection A $athematician*s +ourne" into the ,orld o $echanics ) *rinceton %niversity *ress,#006)I.B 0>9 1>11:#9>F)

Chapter 10 7 .trength of ;lasto(ers, A) ) Oent, W)E) 8ars, InJ !a(es ;) 8ark,

B"rak ;r(an and 8ike &oland, ;ditor2s3, The .cience and Technology of &"bber2'o"rth ;dition3, Acade(ic *ress, Boston, #015, *ages 6:5>$19,I.B:F01#5 6$F69, 10)1019GB :F>0>1#>5 6$F6>9)00010>F

8ott, &obert ) Applied Strength o $aterials , 6th edition) *rentice> all, #00#) I.B0>15>0FF$:F>)

*opov, ;gor *) !ngineering $echanics o Solids ) *rentice all, ;nglewood Cliffs, )!), 1 0)I.B 0>15>#: #$F>5)

&a(a(r"tha(, .) Strength o $aterials )

.ha(es, I) ) and ')A) Co--arelli) !lastic and inelastic stress anal"sis ) *rentice> all,1 1)I.B 1>$905#>9F9>:) Ti(oshenko .) Strength o $aterials , 5rd edition) Krieger *"blishing Co(pany, 1 :9,

I.B 0>FF#:$>6#0>5) Ti(oshenko, .)*) and 4) ) /o"ng) !lements o Strength o $aterials , $th edition)

28K. .yste(3 4avidge, &)W), 8echanical Behavior of Cera(ics, Ca(bridge .olid .tate .cience

.eries, 21 : 3 awn, B)&), 'ract"re of Brittle .olids, Ca(bridge .olid .tate .cience .eries, #nd

;dn) 21 53 Oreen, 4), An Introd"ction to the 8echanical *roperties of Cera(ics, Ca(bridge

.olid .tate .cience .eries, ;ds) Clarke, 4)&), ."resh, .), Ward, I)8)Bab" To()K21 F3

!ternal links 'ail"re theories

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Bengali Wikipedia 10th Anniversary Celebration and International Conference, KolkataThe conference will be held on th and 10th !an"ary #01$ at !adavp"r %niversity&egistration for the conference is now open

Strength of materials'ro( Wikipedia, the free encyclopedia

This articleneeds additional citations for verification ) *lease helpi(prove thisarticle byadding citations to reliable so"rces) %nso"rced (aterial (ay be challengedand re(oved)(August 2010)

Internalforce lines are denser near the hole, a co((onstress concentration

Mechanics of materials , also calledstrength of materials , is a s"b+ect which deals with the behavior of solid ob+ects s"b+ect tostresses andstrains) The co(plete theory began with theconsideration of the behavior of one and two di(ensional (e(bers of str"ct"res, whosestates of stress can be appro i(ated as two di(ensional, and was then generali-ed to threedi(ensions to develop a (ore co(plete theory of the elastic and plastic behavior of(aterials) An i(portant fo"nding pioneer in (echanics of (aterials was .tephenTi(oshenko)

The st"dy of strength of (aterials often refers to vario"s (ethods of calc"lating the stresses

and strains in str"ct"ral (e(bers, s"ch as bea(s, col"(ns, and shafts) The (ethodse(ployed to predict the response of a str"ct"re "nder loading and its s"sceptibility to vario"s
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fail"re (odes takes into acco"nt the properties of the (aterials s"ch as itsyield strength,"lti(ate strength, /o"ng s (od"l"s , and*oisson s ratio in addition the (echanical ele(ent s(acroscopic properties 2geo(etric properties3, s"ch as it length, width, thickness, bo"ndaryconstraints and abr"pt changes in geo(etry s"ch as holes are considered)

Contents 1 4efinition

o 1)1 Types of loadings

o 1)# .tress ter(s

o 1)5 .trength ter(s

o 1)6 .train 2defor(ation3 ter(s

o 1)$ .tress7strain relations # 4esign ter(s

o #)1 'ail"re theories

5 8icrostr"ct"re

6 .ee also

$ &eferences

9 '"rther reading

: ; ternal links

Definition

In (aterials science, the strength of a (aterial is its ability to withstand an applied loadwitho"t fail"re) The field of strength of (aterials deals with forces and defor(ations thatres"lt fro( their acting on a (aterial) A load applied to a (echanical (e(ber will ind"ceinternal forces within the (e(ber called stresses when those forces are e pressed on a "nit basis) The stresses acting on the (aterial ca"se defor(ation of the (aterial in vario"s(anner) 4efor(ation of the (aterial is called strain when those defor(ations too are placedon a "nit basis) The applied loads (ay be a ial 2tensile or co(pressive3, orshear ) The stressesand strains that develop within a (echanical (e(ber ("st be calc"lated in order to assess theload capacity of that (e(ber) This re


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be co(pared to the applied load) The calc"lated stiffness and (ass distrib"tion of the (e(ber (ay be "sed to calc"late the (e(ber s dyna(ic response and then co(pared to the aco"sticenviron(ent in which it will be "sed)

8aterial strength refers to the point on the engineering stress7strain c"rve 2yield stress3 beyond which the (aterial e periences defor(ations that will not be co(pletely reversed"pon re(oval of the loading and as a res"lt the (e(ber will have a per(anent deflection)The "lti(ate strength refers to the point on the engineering stress7strain c"rve correspondingto the stress that prod"ces fract"re)

Types of loadings

Transverse loading > 'orces applied perpendic"lar to the longit"dinal a is of a(e(ber) Transverse loading ca"ses the (e(ber to bend and deflect fro( its original position, with internal tensile and co(pressive strains acco(panying the change inc"rvat"re of the (e(ber )?1@ Transverse loading also ind"ces shear forces that ca"seshear defor(ation of the (aterial and increase the transverse deflection of the(e(ber)

A ial loading > The applied forces are collinear with the longit"dinal a is of the(e(ber) The forces ca"se the (e(ber to either stretch or shorten)?#@

Torsional loading > Twisting action ca"sed by a pair of e ternally applied e


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their tensile strength) owever, str"ct"res loaded in co(pression are s"b+ect toadditional fail"re (odes, s"ch as b"ckling, that are dependent on the (e(ber sgeo(etry)

Tensile stress is the stress state ca"sed by an applied load that tends to elongate the(aterial along the a is of the applied load, in other words the stress ca"sed by pulling the (aterial) The strength of str"ct"res of e see shearstrength3)

Tensile strength or ultimate tensile strength is a li(it state oftensile stress that leads totensile fail"re in the (anner of d"ctile fail"re 2yield as the first stage of that fail"re,so(e hardening in the second stage and breakage after a possible DneckD for(ation3 or brittle fail"re 2s"dden breaking in two or (ore pieces at a low stress state3) Tensilestrength can be


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("st have a large vol"(e with a low (od"l"s of elasticity and a high (aterial yieldstrength)?:@

Strain (deformation) terms

De ormation of the (aterial is the change in geo(etry created when stress is applied2as a res"lt of applied forces, gravitational fields, accelerations, ther(al e pansion,etc)3) 4efor(ation is e pressed by the displace(ent field of the (aterial)?F@

Strain or reduced de ormation is a (athe(atical ter( that e presses the trend of thedefor(ation change a(ong the (aterial field) .train is the defor(ation per "nitlength)? @ In the case of "nia ial loading the displace(ents of a speci(en 2for e a(plea bar ele(ent3lead to a calc"lation of strain e pressed as the elastic region is either below the yield point, or if a yield point is not easily identified on the stress7strain plot it is defined to be between 0 and 0)# strain, and is defined as the region of strain in which no yielding2per(anent defor(ation3 occ"rs)?11@

#lasticit" or plastic defor(ation is the opposite of elastic defor(ation and is defined

as "nrecoverable strain) *lastic defor(ation is retained after the release of the appliedstress) 8ost (aterials in the linear>elastic category are "s"ally capable of plastic
http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-7http://en.wikipedia.org/wiki/Deformation_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-8http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-9http://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Deflection_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-10http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Young's_modulushttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Plasticity_(physics)http://en.wikipedia.org/wiki/Plasticity_(physics)http://en.wikipedia.org/wiki/File:Tension_test.svghttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-7http://en.wikipedia.org/wiki/Deformation_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-8http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-9http://en.wikipedia.org/wiki/Tensorhttp://en.wikipedia.org/wiki/Deflection_(engineering)http://en.wikipedia.org/wiki/Strength_of_materials#cite_note-10http://en.wikipedia.org/wiki/Elasticity_(physics)http://en.wikipedia.org/wiki/Young's_modulushttp://en.wikipedia.org/wiki/Strength_of_materials#cite_note-11http://en.wikipedia.org/wiki/Plasticity_(physics)


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defor(ation) Brittle (aterials, like cera(ics, do not e perience any plasticdefor(ation and will fract"re "nder relatively low stress) 8aterials s"ch as (etals"s"ally e perience a s(all a(o"nt of plastic defor(ation before fail"re while d"ctile(etals s"ch as copper and lead or poly(ers will plasticly defor( ("ch (ore)

Consider the difference between a carrot and chewed b"bble g"() The carrot will stretch verylittle before breaking) The chewed b"bble g"(, on the other hand, will plastically defor(enor(o"sly before finally breaking)

Design terms

%lti(ate strength is an attrib"te related to a (aterial, rather than +"st a specific speci(en(ade of the (aterial, and as s"ch it is


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(aterials, and the re(aining three theories are applicable for d"ctile (aterials) =f the latterthree, the distortion energy theory provides (ost acc"rate res"lts in (a+ority of the stressconditions) The strain energy theory needs the val"e of *oissonNs ratio of the part (aterial,which is often not readily available) The (a i("( shear stress theory is conservative) 'orsi(ple "nidirectional nor(al stresses all theories are e This theory post"lates that fail"re will occ"r if the(a i("( nor(al stress in the part e ceeds the "lti(ate tensile stress of the (aterialas deter(ined fro( "nia ial testing) This theory deals with brittle (aterials only) The(a i("( tensile stress sho"ld be less than or e This theory is also known as shear energy theoryor von 8ises> encky theory) This theory post"lates that fail"re will occ"r when thedistortion energy per "nit vol"(e d"e to the applied stresses in a part e


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on how to increase the strength of a (aterial depending its (icrostr"ct"ral properties and thedesired end effect) .trength is e pressed in ter(s of the li(iting val"es of theco(pressivestress, tensile stress, andshear stresses that wo"ld ca"se fail"re) The effects of dyna(icloading are probably the (ost i(portant practical consideration of the strength of (aterials,especially the proble( of fatig"e) &epeated loading often initiates brittle cracks, which grow"ntil fail"re occ"rs) The cracks always start atstress concentrations, especially changes incross>section of the prod"ct, near holes and corners at no(inal stress levels far lower thanthose 0>0:>5$# 5F>:)

1$) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) :)I.B :F>0>0:>5$# 5F>:)

19) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) $)I.B :F>0>0:>5$# 5F>:)

1:) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) 710)I.B :F>0>0:>5$# 5F>:)

1F) Beer P !ohnston) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) $#)I.B :F>0>0:>5$# 5F>:)

1 ) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 90)I.B :F>0>0:>5$# 5F>:)
http://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Brittlehttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Creep_of_materialshttp://en.wikipedia.org/wiki/Deformation-mechanism_mapshttp://en.wikipedia.org/wiki/Diffusion_in_materialshttp://en.wikipedia.org/wiki/Dynamics_(mechanics)http://en.wikipedia.org/wiki/Fatigue_of_materialshttp://en.wikipedia.org/wiki/Forensic_engineeringhttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/Material_selectionhttp://en.wikipedia.org/wiki/Specific_strengthhttp://en.wikipedia.org/wiki/Staticshttp://en.wikipedia.org/wiki/Universal_testing_machinehttp://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Fatigue_(material)http://en.wikipedia.org/wiki/Brittlehttp://en.wikipedia.org/wiki/Stress_concentrationhttp://en.wikipedia.org/wiki/Creep_of_materialshttp://en.wikipedia.org/wiki/Deformation-mechanism_mapshttp://en.wikipedia.org/wiki/Diffusion_in_materialshttp://en.wikipedia.org/wiki/Dynamics_(mechanics)http://en.wikipedia.org/wiki/Fatigue_of_materialshttp://en.wikipedia.org/wiki/Forensic_engineeringhttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/Material_selectionhttp://en.wikipedia.org/wiki/Specific_strengthhttp://en.wikipedia.org/wiki/Staticshttp://en.wikipedia.org/wiki/Universal_testing_machinehttp://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7


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#0) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) 9 579 9)I.B :F>0>0:>5$# 5F>:)

#1) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 6:)I.B :F>0>0:>5$# 5F>:)

##) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) 6 )I.B :F>0>0:>5$# 5F>:)

#5) &) C) ibbeler 2#00 3)Structural Anal"sis 2: ed)3) *earson *rentice all) p) 50$)I.B :F>0>15>90#090>F)

#6) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) $57$9)I.B :F>0>0:>5$# 5F>:)

#$) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) pp) #:7#F)I.B :F>0>0:>5$# 5F>:)

#9) Beer P !ohnston 2#0093) $echanics o $aterials 2$th ed)3) 8cOraw ill) p) #F)I.B :F>0>0:>5$# 5F>:)

Further reading 'a> wa Cheng, Initials) 21 :3) .trength of (aterial) =hioJ 8cOraw> ill 8echanics of 8aterials, ;)!) earn

AlfireviQ, Ivo)Strength o $aterials I ) TehniRka kn+iga, 1 $)I.B $5>1:#>010>S)

AlfireviQ, Ivo)Strength o $aterials II ) TehniRka kn+iga, 1 )I.B $5>919F>F$>$) Ashby, 8)') $aterials Selection in Design ) *erga(on, 1 #)

Beer, ')*), ;)&) !ohnston, et al) $echanics o $aterials , 5rd edition) 8cOraw> ill,#001)I.B 0>0:>#6F9:5>#

Cottrell, A) ) $echanical #roperties o $atter ) Wiley, ew /ork, 1 96)

4en artog, !acob *)Strength o $aterials ) 4over *"blications, Inc), 1 91,I.B 0>6F9>90:$$>0)

4r"cker, 4)C) Introduction to $echanics o De orma%le Solids ) 8cOraw> ill, 1 9:) Oordon, !);) The &e' Science o Strong $aterials ) *rinceton, 1 F6)

Oroover, 8ikell *) Fundamentals o $odern $anu acturing , #nd edition) !ohn WileyP .ons,Inc), #00#)I.B 0>6:1>600$1>5)

ashe(i, !avad and Willia( ') .(ith) Foundations o $aterials Science and !ngineering , 6th edition) 8cOraw> ill, #009)I.B 0>0:>1#$9 0>5)

ibbeler, &)C)Statics and $echanics o $aterials , .I ;dition) *rentice> all, #006)I.B 0>15>1# 011>F)
http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/953172010Xhttp://en.wikipedia.org/wiki/Special:BookSources/9536168855http://en.wikipedia.org/wiki/M._F._Ashbyhttp://en.wikipedia.org/wiki/Special:BookSources/0072486732http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/J.E._Gordonhttp://en.wikipedia.org/wiki/Special:BookSources/0471400513http://en.wikipedia.org/wiki/Special:BookSources/0071256903http://en.wikipedia.org/wiki/Special:BookSources/0131290118http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-13-602060-8http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/978-0-07-352938-7http://en.wikipedia.org/wiki/Special:BookSources/953172010Xhttp://en.wikipedia.org/wiki/Special:BookSources/9536168855http://en.wikipedia.org/wiki/M._F._Ashbyhttp://en.wikipedia.org/wiki/Special:BookSources/0072486732http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/Special:BookSources/0486607550http://en.wikipedia.org/wiki/J.E._Gordonhttp://en.wikipedia.org/wiki/Special:BookSources/0471400513http://en.wikipedia.org/wiki/Special:BookSources/0071256903http://en.wikipedia.org/wiki/Special:BookSources/0131290118


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ebedev, eonid *) and 8ichael !) Clo"d) Appro imating #er ection A $athematician*s +ourne" into the ,orld o $echanics ) *rinceton %niversity *ress,#006)I.B 0>9 1>11:#9>F)

Chapter 10 7 .trength of ;lasto(ers, A) ) Oent, W)E) 8ars, InJ !a(es ;) 8ark,

B"rak ;r(an and 8ike &oland, ;ditor2s3, The .cience and Technology of &"bber2'o"rth ;dition3, Acade(ic *ress, Boston, #015, *ages 6:5>$19,I.B:F01#5 6$F69, 10)1019GB :F>0>1#>5 6$F6>9)00010>F

8ott, &obert ) Applied Strength o $aterials , 6th edition) *rentice> all, #00#) I.B0>15>0FF$:F>)

*opov, ;gor *) !ngineering $echanics o Solids ) *rentice all, ;nglewood Cliffs, )!), 1 0)I.B 0>15>#: #$F>5)

&a(a(r"tha(, .) Strength o $aterials )

.ha(es, I) ) and ')A) Co--arelli) !lastic and inelastic stress anal"sis ) *rentice> all,1 1)I.B 1>$905#>9F9>:) Ti(oshenko .) Strength o $aterials , 5rd edition) Krieger *"blishing Co(pany, 1 :9,

I.B 0>FF#:$>6#0>5) Ti(oshenko, .)*) and 4) ) /o"ng) !lements o Strength o $aterials , $th edition)

28K. .yste(3 4avidge, &)W), 8echanical Behavior of Cera(ics, Ca(bridge .olid .tate .cience

.eries, 21 : 3 awn, B)&), 'ract"re of Brittle .olids, Ca(bridge .olid .tate .cience .eries, #nd

;dn) 21 53 Oreen, 4), An Introd"ction to the 8echanical *roperties of Cera(ics, Ca(bridge

.olid .tate .cience .eries, ;ds) Clarke, 4)&), ."resh, .), Ward, I)8)Bab" To()K21 F3

!ternal links 'ail"re theories

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