Basic of Som

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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

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Internal force linesare denser near the hole, a co((on stress concentration

Mechanics of materials, also called strength of materials, is a s"b+ect which deals with thebehavior of solid ob+ects s"b+ect to stressesand strains) 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 approi(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 its yield strength,"lti(ate strength, /o"ngs (od"l"s, and *oissons ratio in addition the (echanical ele(ents(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 4efinitiono 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 epressed 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 aial 2tensile or co(pressive3, or shear) 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(bers 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 eperiences 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 ais 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)

Aial loading > The applied forces are collinear with the longit"dinal ais 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 eternally applied e


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defor(ation) Brittle (aterials, like cera(ics, do not eperience any plasticdefor(ation and will fract"re "nder relatively low stress) 8aterials s"ch as (etals"s"ally eperience 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 (ai("( 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(ai("( nor(al stress in the part eceeds the "lti(ate tensile stress of the (aterialas deter(ined fro( "niaial testing) This theory deals with brittle (aterials only) The(ai("( 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 epressed in ter(s of the li(iting val"es of the co(pressivestress, tensile stress, and shear stressesthat 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( offatig"e) &epeated loading often initiatesbrittlecracks, which grow

"ntil fail"re occ"rs) The cracks always start at stress 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 $aterials2$th ed)3) 8cOraw ill) p) :)I.B:F>0>0:>5$#5F>:)

5) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill) p) $)I.B:F>0>0:>5$#5F>:)

6) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill)pp) 710) I.B:F>0>0:>5$#5F>:)

$) Beer P !ohnston)$echanics o $aterials2$th ed)3) 8cOraw ill) p) $#)I.B:F>0>0:>5$#5F>:)

9) Beer P !ohnston 2#0093)$echanics o $aterials2$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 $aterials2$th ed)3) 8cOraw ill)pp) 95799) I.B:F>0>0:>5$#5F>:)

F) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill)p) 6:) I.B:F>0>0:>5$#5F>:)

) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill)p) 6) I.B:F>0>0:>5$#5F>:)

10) &) C) ibbeler 2#003) Structural Anal"sis2: ed)3) *earson *rentice all)p) 50$) I.B:F>0>15>90#090>F)

11) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill)pp) $57$9) I.B:F>0>0:>5$#5F>:)

1#) Beer P !ohnston 2#0093)$echanics o $aterials2$th ed)3) 8cOraw ill)pp) #:7#F) I.B:F>0>0:>5$#5F>:)

15) Beer P !ohnston 2#0093)$echanics o $aterials2$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, 196)

4en artog, !acob *) Strength o $aterials) 4over *"blications, Inc), 191, I.B 0>6F9>90:$$>0)

4r"cker, 4)C)Introduction to $echanics o Deorma%le Solids) 8cOraw>ill, 19:) Oordon, !);)The &e' Science o Strong $aterials) *rinceton, 1F6)

Oroover, 8ikell *)Fundamentals o $odern $anuacturing, #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#$90>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)Approimating #erection A$athematician*s +ourne" into the ,orld o $echanics) *rinceton %niversity *ress,#006) I.B 0>91>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>$19, I.B:F01#56$F69, 10)1019GB:F>0>1#>56$F6>9)00010>F

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

*opov, ;gor *)!ngineering $echanics o Solids) *rentice all, ;nglewood Cliffs, )!), 10) I.B 0>15>#:#$F>5)

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

.ha(es, I)) and ')A) Co--arelli)!lastic and inelastic stress anal"sis) *rentice>all,11) 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) 2153

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()K21F3

!ternal links

'ail"re theories

case st"dies in str"ct"ral fail"re

CategoriesJ .olid (echanics 8aterials science

B"ilding engineering

4efor(ation 2(echanics3

Condensed (atter physics

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