Universidad Autónoma de Coahuila FACULTAD DE INGENIERIA CIVIL CUADERNILLO ELECTRONICO RESISTENCIA DE LOS ATERIALES ING! "ESUS OLINA #AORA "OSE FRANCISCO TRE"O SIFUENTES $% A
DEFORMACIÓN DE LOS MATERIALES………. 1 PROPIEDADES DEL KEVLAR Y POLICARBONATO………..2 PROPIEDADES DE LA SECCION…………….3 PROPIEDADES DE LOS MATERIALES (ACERO, ACERO DE ALTA RESISTENCIA, ALUMINIO, ALUMINIO, MADERA, KEVLAR, FIBRA DE POLICARBONATO)………………………………………………..4 ESFUERZO DE FLEION………………..! FUERZA CORTANTE Y FLEIONANTE……………." RELACION ENTRE CAR#A Y ESFUERZO CORTANTE…………..$ TEORIA DE LA ELASTICIDAD………………….% CURVA ELASTICA……………………&
DEFORMACIÓN DE LOS MATERIALES………. 1 PROPIEDADES DEL KEVLAR Y POLICARBONATO………..2 PROPIEDADES DE LA SECCION…………….3 PROPIEDADES DE LOS MATERIALES (ACERO, ACERO DE ALTA RESISTENCIA, ALUMINIO, ALUMINIO, MADERA, KEVLAR, FIBRA DE POLICARBONATO)………………………………………………..4 ESFUERZO DE FLEION………………..! FUERZA CORTANTE Y FLEIONANTE……………." RELACION ENTRE CAR#A Y ESFUERZO CORTANTE…………..$ TEORIA DE LA ELASTICIDAD………………….% CURVA ELASTICA……………………&
1 DEFORACI&N DE LOS ATERIALES L' *+-'/0 '-/+ 5'-'6+ + *+-' 7 78+ /+ ' *79+ *79+ /5+ /5+ 8+ 8+7 7/ /+ + 8+ 8+ 7' 7' + -: -: *79' '8/ '8/'' '' + + -/-+ + ' +7/' /'5'/0 5;-/'. 5;-/'.
DEFORACI&N UNIDIENSIONAL UNIDIENSIONAL L' -'</57 -: /-8 8'' -/ ' *+-'/0 + =7 /</>' '-' *+-'/0 '?/' + *+-'/0 7/5'/' */ +-+ '-/+ +57 8+ +57 8+ 7/' +57@
D ' -/-' -'</57 D+ D+ ' ' + +57 57 ///' ///' ' 9+' 9+' 57 57/+ /+ ' + +57 57 */' */' + *+-''. E 5/ 8'' ?8' + '-/+ +57 7 ' + 7 8/8/-' ' -: -:/+ /+.. L' *+ *+-' '/0 /0 ' '7 7' '' ' '7 '7 + + ' ''-' ' *+ *+-' '/0 /0 /< /</ / //.. E ' 8: 8:5/5/' ' 87 87 7' 7' +5' +5' -/ -/' ' '/+'' + 5' +-+ 5/'-/5+@
L' *+-'/0 '?/' +<'>5-/' + *+-'/0 =7 */ +-+@
L' *+-'/0 #L'<'< / '' 8+@
L' *+-'/0 E7A-'/ / '' 8+@
DEFORACI&N DE UN CUER'O E ' -:/' 0/+ *+-' ' *+-'/0 87 5 7<' < / /+ + -++ -++ / / ' ' / / /+ /+ , , 87 87 ''-: : 8+ 8++ +' ' /5+/+ ' *+-' 78+, ' +//+ ' *+-'/0 7 7 78+ 8+ 87 87 '' ''5 5 /9 /9' ' 8+ 8+ 7 5+ (-: 5+ (-: ?'5 ?'5'- '-5 5 7 '-8+ '-8+ 5+/') ' *+-'@
D+ '' 7' ' +-8+5 ' -'5/9 '5/+, '-'' 5+ *+-'/0 85' 7' *7/0 *//' + ' ++'' 78+ =7 +5/ +-+ +-/'/0 /'' '-8+ 8'9'-/5+ + 875+ 78+.
DEFORACION ELASTICA ( 'LASTICA T'5+ 8'' ' *+-'/0 7/5'/' +-+ 8'' 5+ *+-'/0 87 +-8+ '+ ' *+-'/0 @ •
•
D*+-'/0 8:5/', // + 8-'5. M++ *+-'/0 =7 -'5/' + <' ' 7 *+-' +/' 87; 5/' ' '<' '8/''. E5+ 7 8+=7, ' *+-'/0 8:5/', -'5/' ?8/-5' '-/+ 5-+/:-/+ // ' '=7// -'+ <>' 8+5/' :5/'. L' *+-'/0 8:5/' + +5'/+ ' ' *+-'/0 /. D*+-'/0 :5/', / + + 8-'5, 78+ 78' 7 *+-' +/' ' 5/' ' *79' =7 8++' ' *+-'/0. E 5 5/8+ *+-'/0, 0/+, ' '/' 7 5'+ 5/0 ' '7-5' 7 <>' /5' *+-' <>' 8+5/' :5/', ++ 8'' 8+ '-/+ 5-+/:-/+ /.
C+--5 5/ 8+ -'5/' :5/+, '=7+ =7 7* <' +<'/+ 7'+ '8/' 7' *79', +-+ ' <+-' :5/' =7 87 5/' / /*/75' 78'+ 7 +57 +/' 7' 9 =7 '8' ' '<'. E5 +-8+5'-/5+, / -'<+, + ?7/+ 5+ -'5/', -++ =7 + -5' ''/+ '8/'/0 5;/', 8/', G+-/<+ -'' -8'+ +57/0 , <', 7'=7/ -'5/', 85' 5 +-8+5'-/5+ G'5' 7 /5+ '+ ' *79' '8/''H / / + '+ '875'+ ' *+-'/+ + 8=76', ' 5/' ' '<' '8'. A '+ -:?/-+ ' *79' '8/'' + 7 +5+ 8'' =7 7 *+-'/0 ' :5/' +-/' >-/5 :5/+ <' /-8+5'/' /6+ -:/+, ' =7 ' -'+>' '8/'/+ ;5 + ' +57', =7 '+85' +-+ '/' /6+ (8'5/7'-5 -'/-+). U' 9 78'+ >-/5 :5/+ '8' *+-'/+ 8:5/' (=7 + 8-'5 5' 5/' ' '<') +-8+-5/+ ' *7/+'/' /5+ -5+ -:/+.
'RO'IEDADES DEL )EVLAR ( FI*A DE 'OLICAR*ONATO
2
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
'RO'IEDADES FISICAS ( +UIICAS RESISTENCIA A LA TEMPERATURA
E K' +-8+ ' '5' 5-8'57' (424% <'+ 5><'+) -'5/+ 8'5 7 8+8/' -:/' /7+ ' 5-8'57' '' ' 7 5-8'57' +-8+//0. ELASTICIDAD
E -07+ :5/+ 7 5++ ' 7 2 7'+ -8' ' */' '
1% <'+ 5><'+ 7'5 ! G. "E5' 8+8/' 75+ + 7 /5/' =7>-/' G' K' 7 -'5/' -7 75//9'+ =7/8+ 8+5/0. TENACIDAD
L' 5'/' (<>' '+/' '5 ' +57') K' 5++ ' + ! M -3, *5 ' + " M - 3 '+$. VENTAJAS •
• • • • • • • • •
A5' /5/' ' ' 5'/0 (/+ -: *75 8+ 8+ =7 '+ 7)H A5+ -07+ '5//'H A'<'-/5+ -7 '+ G'5' 875+ 7857'H E '+ 8+H A5' //' =7>-/'H M7 '+ +*//5 ?8'/0 5;-/'H T'/' ' ' *'57' (/5/' ' /-8'5+)H A5' /5/' ' + +5H P+'//' T?5/H R/5/' ' ' '-'.
L' 5'' K' +@ '8'/' '+ G7-', /*/75' ' *79' +5, +-8/0 ''. PROPIEDADES QUIMICAS
L' ' ' /5/' K' ' + 5++ ' 5757' 5//-/+' 8+>-+. L+ ' /5' /5-+7' ' 5 / 5: ' ' ' ?8/+' 8+8/' K'. L+ 5+ =7 *+-' + ' +'5 ' 5757' 8+/-;/' 5: *75-5 +'/9'+ ' 7<' ' 7' 5757' +'5 5+5'-5 8'' /'-5 /'. A-:, ' '' +5/<7' 8'+ 7 ' 5'; ' G/0<+. E ' 5' /-/0, 5 ' '8' 8+>-+, + ' *79' V' '' ' =7 +5/7 ' +-8'5' -'5/'.
'RO'IEDADES DE CO'RESION E5' 8+8/' + /*>/ -/ ++ 87 /*/ ' 8'5/ ' 8+8/' + -'5/' +-875+ *'/'+ + /G' */'. S G' +5'+ =7 ' /9 '?/' +-8/0 '8+?/-''-5 ' -/-' =7 5'/0 8'' 5+' ' */'. S/ -'<+ ' /5/' ' +-8/0 +57/' :-/' 7///+' +/5'' *'/'' + ' ++ 7 2 7 /5/' ' 5'/0. E +5'5, + +8+/5 '5+ 8'' ' */' '++ //+ -75' =7 5/ /5/' 8'/' 5'/0 +-8/0. L' '' /5/' ' +-8/0 ' /' ' ' 8+8/' '/05+8' ' */' ' ' '' /9 ' +5'7'. B:/'-5, +-+ +5' */' 5?5/, -'5/' 5/ ++ 7' /-/5'' '5//' +-8/0. A 5'/0, ' '<' + +8+5'' 8+ + ' +'5, 8+ ' +-8/0 + ;/ ' G/0<+ ' *79' V' '' G' =7 8+79' 5' ''/0 +' G/'G'-/5+. E5+ +7 ' ' *+-'/0 7 +5/'-/5+ ' */' G'' + ' '/0 ' ' *?///' ' */'.
FI*RA DE 'OLICAR*ONATO E 8+/'+'5+ 75'5 ' '/0 5 /'+ :/+ '0/+ /*+ A 7 5-+8:5/+ /</>' =7 G' 5+'+ -7 ++/+ 8+ 5'8'5 +-+ //+ /55 +-+ '+. L' '' 8+/-;/' 8+/'+'5+ /-;5/'. P+ +, 8+/'+'5+ 8+ 7' 8+8/' /;5/' ' 5'; 7' 'G' '' *7/', G'5' 7' 5-8'57' 12!C. L' 8+8/' =7>-/' 8+/'+'5+ + ' 7 8+>-+ -5 8+'. L+ <78+ '+'5+ + ?5-''-5 / ' ' G/0// +-+ 5: ' '' 8//8', 87 8++' <''/0 ' 8+8/' 5-+8:5/+. D/+ ' 5' '/0 8+/'+'5+ 5' /-8 + 8'' 8++, +5' *+-' -'5/' >' 7 8+ -+7' 7/+ :5/'-5 ' 8+8/' '8'//' 5/+''. L' 8/9' 8+/'+'5+, 8-'5 +5'5+ + '<7', 5/ 7 /' 5/ 7/' / ' 5-8'57' 5''+ 78' "C. E '8/'/+ + +5'5+ + '<7' + +5'5, 5 8+-' + '8', +-+ '+ + /+ + ;. #'-5 8+/'+'5+ + / ' :/+ +<:/+ /+<:/+ +//+ +-' 5-8'57' +5'/0, / -'<+ 7 /5/' ' + -: +-875+ +<:/+ ''. E5' '' /5/' ' -: '*5'' + ' '8'//0 -/+*/7'-/5+ + 5/0, =7 8++' 8++/' ' 78*// -'5/', *'//5'+ '5'=7 =7>-/+.
E 8+/'+'5+ 8+ 085/-' 5'//' ' ' '/'/+ UV. L+ 5/8+ +-' 8+/'+'5+ 8+ 7' /5' 5'//' '57'. E '5'=7 ' '/'/0 //'+ 8+ 7' <''/0 + 8/-+ !1 -/0-5+ ' 78*// ' 8/9'. E5' 5'//' -'5/ ' 8+8/' 8+/'+'5+ G'5' 7 /5+ >-/5, / -'<+ + 7*//5 8'' -'5 ' ++'/0 '''+ 78*//' ' 8/9' -+''. P+ +, 8+/'+'5+ //'+ 8'' '8/'/+ /5/+. E '8/'/+ 8'' ?5/+, + '5'=7 '/'/+ 5/8+ UV + -: ', '/+ 5' 7' 8+5/0 ?5' ' 8+/'+'5+, '<<:+ 7 '+5 UV. L' 8+8/' 8+/'+'5+ 87 -+/*/' 75//9'+ /5/5+ '/5/+ + '/9'+ 5'5'-/5+ 78*//' + 8+/'+'5+, '> =7 8'' ++ ' 8+8/' 7 -'5/' +5+ G' =7 7/ ' ' 5'' =7 8+8+/+' + *'/'5. P+ -8+ B' G' +<'+ *'/' 7 8+/'+'5+ =7 5''' +5'-5 ' 5-8'57' G'5' 22C *5 ' + 13C 8+/'+'5+ +-', Apec, =7 75//9' 8'' ' *'/'/0 *'+ 8'' G>7+.
'OLICAR*ONATO EN LA CONSTRUCCION POLICARBONATO EN PLANCHAS
Com,a-to.(L?', M'++, A8) E 8+/'+'5+ +-8'5+ 8'' 75//9' +57/+ + '+ =7 +5 5'8'/' 78*//, 5'5+ G+/9+5' +-+ 5/' + 7'. D'+ =7 + 5/ 5'5' /9 +-+ //+, 7 -++ -: *//5 75//9'/0 78*// 7', + ' *+-' *:/-5 +5/ '' 7 '5//'. E 8+/'+'5+ +-8'5+ +5/ ++ </ ('-'+ 5'-/; 7 + *7-;), ++ '5'6+ ('-'+ ++ + +) 5'8'5. 'oli-ar/onato en ,el0-ulas o 1ilms.(M'+*+, B'*+, L?') E 8+/'+'5+ 85' 75//' '-8+ ' +57/0, 8'' '/9' '-/5+ 5/' G+/9+5' <7/', 8+=7 + Q/+-8/Q 8+=7 87 -+' *:/-5 8'' ' 75'+ + 7' 5;5/' -7G+ -: '<'' =7 //+ + -+ 8+. A> -/-+ ?/5 -'+ /5/5+ 5/8+ 8+/'+'5+ =7 */5' 8'+ '+ UV@
'RO'IEDADES DEL 'OLICAR*ONATO 'RO'IEDADES FISICAS A+/0 A<7' E=7///+ ()
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3 'RO'IEDADES DE LA SECCION 2rea
E 7' 8+8/' ' *+-' =7 + //' ' '5/' 7/' 78*// =7 5/ 7' */<7' + 78+. E5' *//' 8+ + +5+<+' 5 /, 8/'-5 8+ + =7 5' 7/' 7''', / U2. E5' 8+8/' 5/ 7' <' '5/' '8/'/+ '-8+ A=7/550/+ +-+ 87 +5 ' 78*// 7 5+ + ' '5/' -7+ =7 ' ' +57/, 5'-'6+ ' +' 58/+, 5.
Centroide E 5+ <'' 7 0/+ 7 875+ /-''/+ 7' +/' =7 5++ 7 8+ 5: +5'+ + 875+ ' 5'; 7' 8'' ' 75'5 7 8+. E 875+ 7 :' 8'' =7 +8+ ' 5+ <'' 7' 8'' -7 <'' =7 5/ ' -/-' :' *+-' ++ +-+ C5+/ :'. C7'+ 7' /<' *?/+' /+ ' 7' '<' '8/'', ' */' 8+ /-' 7 /5+ 8'+ ' /<' 5''' +-8/0 '=7' 8+ '+ 5 8'+, ' 5/0. E5 8'+ ++ +-+ ' 78*// 75'. L' /5/0 ' 78*// 75' ' /0 5'' ' /<' ++ +-+ 75+. C'7+ C5+/ A. D/// ' */<7' -+ -+ */<7' <+-;5/' /-8 =7 ' 8+/. B. E+< 7 8' 7'=7/' *//+. C. C'7' ' :' '' 7' ' */<7' <+-;5/' /-8. D. '7' ' /5'/' ?1, ?2, ?3, ?4, ?… 1, 2, 3, 4, ,… =7 + ' /5'/' + 5+ <'' ' */<7' ' + '7?//' E. A8/' ' 7'/+ <' ?, (A11A22A33A44ANN) (A1A2A3A4AN) Y (A1Y1A2Y2A3Y3A4Y4ANYN) (A1A2A3A4AN)
omento de iner-ia E ' */<7' /75' 7' /0 5'<7' 'G+ b '5+ h +
G+/9+5' X-X =7 8'' 8+ 7 5+/ ' 7' /5'/' h2 ' 8'5/ ' '' 78/+. E ' /0, a 85' 7 :' /*//5'-5 8=76' ' 7' /5'/' z X-X . S/ -75/8/' 5' :' /*//5/-' 8+ 7''+ 7 /5'/' ' , +5/ ' '5/' ( a ? z 2). E :' +-85' ' /0 5': +5/57/' 8+ 7 -+ /*//5+ 5' 8=76' :' -5' ' /*5 /5'/' 8+ '/' 8+ '+ X-X. E5+, -+-5+ //' */ +-+ ' 7-' + 8+75+ =7 +5/ ' -75/8/' 5+' ' :' /*//5'-5 8=76' 8+ 7''+ 7 /5'/' ' 7 .
L+ + 8//8' ' */<7' + X-X Y-Y, 8'' 8+ 5+/ ' /0 5'<7', + 85+ ' 7 =7 8'' 8+ 5+/ 8''+ ' ' ' I X-X bh312, + 85+ ' 5/', ' ?8/0 >' I Y3 Y hb 12.
Radio de Giro E5' 8+8/' ' /0 5'' 7 -/-+ 5757' 5: '/+'' + /6+ -/-+ 75+ ' +-8/0. D8 ' /-/+ ' *+-' <+-;5/' ' /0 7 >/ ' /9 ' /0 7'+ 7' +-+ +7-'. E radio de giro */ -'5-:5/'-5 +-+ r= (I/A) ^0.5. D+ I -+-5+ //' A :' ' /0. S ?8' 5>-5+ 8+=7 -+-5+ //' 5: 5>-5+ ' ' 7'5' 8+5/' :' ' /0 5'' 5: 5>-5+ 7''+. E '/+ + + 7' 5' '-8/'-5 /6+ -'' 5757' +-+ /6+ '+ 5757'. P'' ' /+ 5'<7' =7 -8' +--5 ' +7-' -'', -: +/5 75/57/ '/+ + 8+ ' /-/0 '5' ->/-' + 8++ /6+ +7-'.
odulo de la se--ión
E 7 5;-/+ 5757' /</>' =7 *+'/9' ' *79' 7 +5+ +-8''' + + +5+ +5+ + + =7 5' +5'+. E -07+ ' /0 7 57+ -/ 875+ =7 57+ +-/9' ' . E -07+ ' /0 '7'+ 75//9'+ + /:-5+ /5+ ?5+ 57+ 75//9' +5'5 -'5-:5/+ 8/ + W, =7 7 -+ =7 + 8/5 / 5-/', =7 *7/+' -'+-5 :' + +- /7'. C'7' -07+ ' /0 7 57+ /-8+5'5 8'' -'5 ' /5</' 7' 5757'. E5' 7' -' ' 8+8/' <+-5/' =7 5/ ' /+ + -5+ 5757'. A -+7+ /+ +-/' + 7' -'77' ( S ) 5' */'+ ' '<7+ + 5+/' / S? + S. Y +-+ 75'+ /// M+-5+ //' (U4 ) 5 /5'/' (U1), 75'+ 5' 7/' 7/' (U3 ), / 5'5' 7 +7-. E -+7+ /+ / ' +/5 =7 75' /// -+-5+ //' (I) + ' /5'/' 5+/ ' '<7+ + '7?//'.
'RO'IEDADES DE LOS ATERIALES A-ero
4
E '+ 7' ''/0 G/+ '++ (-:?/-+ 2.11 '++), ' 7' '//+' '/'+ -5+ ''/0, + 7' +*/ 8+8/' -:/' 8/*/' 8'' 7 /*5 75//9'/0 ' /75/'. L+ 8//8' -5+ ''/0 +@ C+-+, T7<5+, M'<'+, N>=7, V''/+, C+'5+, M+/+, C+, A97* F0*++. L+ 8+75+ *++ + -' 2.11 '++ +-/' *7//+ G/+.
La du-tilidad de un a-ero sometido a tra--ión es la -a,a-idad ,ara de1ormarse /a3o -ar4a5 sin rom,erse5 una ve6 su,erado el l0mite el7sti-o! 'ro,iedades me-7ni-as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
'ro,iedades F0si-as.
P+8/' + 78+@ M'5/', C78+, E5'+ '<<'/0, P+, M'', V+7-, D/', 8+ 8/*/+ (-). P+8/' T;-/'@ 5: */' ' + -'/-+ '+ ?/5 5 -'/-+@ C+7/0@ 8+7 7'+ ' *75 -/+' 5' +5'5+ /5+ + =7 ' '7-5' T. C+/0@ 8'' =7 +7' 5'*/' '+ 8+ +/0 '/+ =7 ?/5' 7 *7/+ =7/ ' '<'+ 5'-/5/ '+ ' *75 -/+' G'/' 78+ + '-/5. R'/'/0@ S 8+7 8+=7 ' *75 '+ 75' +5'5+ *+-' /5' + '-/5. E5' *75 -/+' <' '+ /*'++ =7 / -/+ 5'*/' '+. P+8/' E;5/'@ E5: '/+'' + ' '8'/' +7/ ' +/5 ;5/'. P+8/' Ó85/'@ 5: */+ ' ' '8'/' =7 8+ + -'5/' 8'' *' + '+ '+ '7+ ' ' /<7/5 ''5>5/'@ C++B/+P7/+. P+8/' M'<;5/'@ E5: */' ' ' '8'/' =7 8+ + -'5/' -5:/+ 8'' /7/ + /7/+ 8+ 7 '-8+ 5+-'<;5/+, / '57' +-+ /-: + '5'>+ 8+ 7 /-:.
'ro,iedades +u0mi-as. E '+ 5: +-875+ 8//8'-5 8+ G/+, 8+ 5'-/; +5/ ,! ' 2 8+ /5+ '++. L+ :5+-+ '++ /5'' 5 + :5+-+ G/+ -+' +5'-5 7 /9. A'/+ E '+ 87 +5 7+ + -: -5' '5/' -7 8=76'. L+ /*5 -5+ /-8'5 /*5 8+8/'. E +'5+, 8+ -8+, + G' -: 7+ -: /*>/ -'. E >=7 -'<'+ '7-5' 7 *79' 5'/0, G'/+ =7 ' 8/9' 5/8+ '+ ' -: /*>/ +-8. E +-+ '7-5' 7 79' -+' 7 /5/' ' ' ++/0.
odulo El7sti-o
E M07+ E'5//' + M07+ Y+7<, 8'' :7+ /6+ 5757' '+ '<+ :5/+, 5+-' +/+'-5 /<7/5 '+@
E8 9:;!;;; N-/5 8+8+/+' *79+ -:?/-+ =7 *79+ ' *+-'/0 8-' /5'-5 8+8+/+'. E >-/5 8+8+/+' 5-/' -/'5 ' 7' *79+ *+-'/0, 5'9'+ 7' >' 5' 5'<5 ' ' 7', +/<, '+5'+ ' 8/-' /'/0 =7 5<' ' 7' 7 /'/'.
Alrededor de 9;; ;;; 'a ,ara la ma=or0a de a-eros!
ACERO DE ALTA RESISTENCIA L+ '+ 8'' G'-/5' 5/ 5 ''5>5/' 8//8'@ 5'/', 79' /5/' ' <'5. T+' 75' ' 5'5'-/5+ 5;-/+ =7 /. E5' ''5>5/' ?'-/'' 8'' -86+ 085/-+ 879+ 7'+ 5'-8'+ '+ '5' /5/'.
'ro,iedades F0si-as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
7 7 5-8'+ =7 ' 5'/' 5'5'-/5+ 5;-/+ 085/-+, 7'+ 7'+ +/ 5'5'-/5+ 78*//' ' G'-/5'. Propiedades mecáicas!
Los aceros HSLA ie!e! "#$ies e"%sicos hasa &0.000 psi. '! co$paraci!, oros aceros esrcra"es !or$a"$e!e posee! "#$ies e"%sicos de $e!os de "a $iad de eso. Si! e$bargo, e" "#$ie e"%sico a$e!ado redce "a dci"idad hasa e! ! *0 + e! co$paraci! co! oros aceros esrcra"es. "ormas com#es
L+ '+ SLA + 7' *'-//' '+ + 8+8/' 8>*/' 5;/' 8+7/0. E A3" =7/9: <'+ -: +- '+ =7 87 /5+ +-+ '+ '+ SLA. O5' '/' + ASTM A$1! ASTM A"!".
odulo el7sti-o 14 MP' (2 8/) 8'' '+ '5' /5/'.
Normas P'' -'5/' ASTM A!14, +-/' 8*5-5 8'' 5757' '5' ?/</' -:/' +'//', 5' +-+ 875 <', '9+ 508/+, 875, '9+ '5, 5. P'' -'5/' 1!M+3, +-/' 7 7+ ' *'/'/0 +-8+5 ' 8/0, +/, 75+ ?875+ ' '5' 5-8'57', +5/+ *7//0, 5.
ALUINIO E-5+ =7>-/+ -5:/+, >-++ A, -+ '50-/+ 13, 8+ '50-/+ 2".&%1!, =7 85 ' <78+ IIIA /5-' 8/0/+. E '7-//+ 87+ '+ 5/ 8+' /5/' -:/', 8+ 87 *+-' ''/+ + +5+ -5+ 8'' '7-5' 7 /5/' '=7// '/' 8+8/' 5/. L' ''/+ '7-//+ + /<', *75, *:/ *+-'/0 8'' -7G+ 8++ -5'/5>'H + *:/ '-', *7/ + -'=7/' '85' <' '/' '''+. P+ 7 8+8/' *>/', =7>-/' -5'', '7-//+ G' +5/+ -5' + *++ -'+ 7+.
'ro,iedades 10si-as E '7-//+ 5/ 7 ++ '+ 8'5'+. S /5 ' + 1.22,!$" F'GG/5 ("",32 C/7) G/ ' + 4.4$2,33 (2.4"",%! C/7). E
'7-//+ 5/ 7 8+ '50-/+ 2",&%1!4 7 '/+ '50-/+ 143,1 8-. E 7+ + -5' -: 5/ -''. N+ -'<;5/+.
'ro,iedades e-ani-as L' ''5>5/' -:/' '7-//+ '>' +/'-5 8/+ 5/8+ ''/0 =7 5; +/'+. L' /5/' ' /9''-/5+ 7 '+ /-8+5'5 ' 5 75' 8'' '7' ' *79' '/' 8'' +5, '> +-+ 8'' 5-/'' +57/+. N+ ?/5 '+ +-'/9'+ ' 5 85+, 8+ <'-5 7 '+ =7 5: 5 !! % ' /5/' ' ' 5'/0.
'ro,iedades >u0mi-as C7'+ 5' +5'5+ + +?><+, '7-//+ *+-' 7' '8' 0?/+ =7 ++ +-+ 0?/+ '7-//+. E5' '8' + '7' ' 8+5<+ ' ++/0. E '7-//+ 8++ 8 *7<+ + *'//' / + ?8+ ' 7' '-'. T'-/; '/+' 5'5+ + + :/+ +-+ + + :'/ .
ódulo de elasti-idad lon4itudinal o ódulo de (oun4 E -07+ '5//' +57/' + -07+ Y+7< (E) '/+' ' 5/0 '8/'' ' 7' 8/9' < 7' //0 + ' *+-'/0 +/'' ' -/-' //0, /-8 +/'+ 7 +-8+5'-/5+ :5/+ ' 8/9'. P'' ' ''/+ '7-//+, -07+ '5//' +57/', E, 5/ /<7/5 '+@ '= 0.000 MP' (0.000 N--2)
ADERA L' -'' 7 -'5/' 7+ /55 =7 8+7 -/'5 ' 5'*+-'/0 :+. E 7 7+ *+5' /8+/ =7 G' 75//9'+ 7'5 -7G+ 5/-8+ +-+ -'5/' +57/0. L' -'' 7+ + -5+ +575/+ -: '5/<7+ =7 G+- G' 75//9'+ 8'' ' +57/0 7 //' +5' /*/'/+. P+ 8'' +<' 7 75'+ ?5 7 5'''//' G' =7 5 85 /5+ '85+ '/+'+ + ' *+-' +5, 7'+ '+.
'ro,iedades F0si-as D/' +5/+ G7-' D/'@ ' '/0 5 ' -'' (-) 7' 8/9' -'' + 7 +7- () ' ?8' <'-+ 8+ 5>-5+ /+. L' /' '/+' /5'-5 + +5' 8+8/' ' -''. P+8+/+' 7' 8/-' //'/0 '' 7 +-8+5'-/5+ 8+' *5 ' ' '+/0 8/' '<7' 7 +8+/5 <'+ '/'/0 /-/+' '+ 875+ '57'/0 ' */'. C+5/+ 7-'@ ' '5/' '<7' 85 ' -''H ?8' +-+ 8+5' 8+ ' -'' ' + 'G/'.
'ro,iedades e-7ni-as C+-8/0@ L' -'' +-8+5' ' -'' 7 +75+ 57+ ''<'+ =7 7*/' 7' 8/0 88/7' ' 7 +57H 7 /+ 5'' : '8'5'' , +7/', 7*/: /-/7/0 7 /-/+ '+ *79+ 7*//5-5 '5+. T'/0@ E '7-/' :/'-5 8+ ' /</' ' -'' =7 7-8 7' *7/0 -5'5 5 */'. L' -'' 5/ -+ /5/' ' 5 5/8+ *79+ '/0 + +5' +//5'/+. E +5 + C/9''-/5+@ E -'5 ' +-8+5'-/5+ 7 8'=75 57+ =7 G'' 'G/+ 5 +H 8+ 5' '90, '+ X+5 + C/9''-/5+ 8''+ ' <'+, *79+ +5 /5/+ :/'-5 8+ ' 75'/' -5'5, /, ' /</', -/5' =7 *79+ +5 + C/9''-/5+ 88/7' ' <'+, + */' ' =7 '7-5' ' /5/' ' C/9''-/5+. L' -'' -7G+ -' /55 ' +5 88/7' =7 ' +5 8''+. F?/0@ E +-8+5'-/5+ *?/0 7' 8/9' -'' +-/', /-75:'-5, + +-8+5'-/5+ ' 5'/0, +-8/0 +5, 8/5/;+ + -/-+ *0-+ '5/+-5 /5+. L' -'' 7 -'5/' 8'5/7'-5 '85+ 8'' +8+5' 5'/0 +-8/0 8''', /+ ' 7 '5' '8'/' 8+ 7/' 8+.
odulo de elasti-idad. 12! <C- 2
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
'ro,iedades F0si-as RESISTENCIA A LA TEMPERATURA E K' +-8+ ' '5' 5-8'57' (424% <'+ 5><'+) -'5/+ 8'5 7 8+8/' -:/' /7+ ' 5-8'57' '' ' 7 5-8'57' +-8+//0. ELASTICIDAD@ E -07+ :5/+ 7 5++ ' 7 2 7'+ -8' ' */' ' 1% <'+ 5><'+ 7'5 ! G. "E5' 8+8/' 75+ + 7 /5/' =7>-/' G' K' 7 -'5/' -7 75//9'+ =7/8+ 8+5/0. TENACIDAD L' 5'/' (<>' '+/' '5 ' +57') K' 5++ ' + ! M - 3, *5 ' + " M - 3 '+$.
'ro,iedades >u0mi-as L' ' ' /5/' K' ' + 5++ ' 5757' 5//-/+' 8+>-+. L+ ' /5' /5-+7' ' 5 / 5: ' ' ' ?8/+' 8+8/' K'. L+ 5+ =7 *+-' + ' +'5 ' 5757' 8+/-;/' 5: *75-5 +'/9'+ ' 7<' ' 7' 5757' +'5 5+5'-5 8'' /'-5 /'. A-:, ' '' +5/<7' 8'+ 7 ' 5'; ' G/0<+. E ' 5' /-/0, 5 ' '8' 8+>-+, + ' *79' V' '' ' =7 +5/7 ' +-8'5' -'5/'.
odulo el7sti-o. E '+ -07+ '5//' ' 5-8'57' '-/5 5++ ' % #P'.
FI*RA DE 'OLICAR*ONATO E 8+/'+'5+ 75'5 ' '/0 5 /'+ :/+ '0/+ /*+ A 7 5-+8:5/+ /</>' =7 G' 5+'+ -7 ++/+ 8+ 5'8'5 +-+ //+ /55 +-+ '+. L' '' 8+/-;/' 8+/'+'5+ /-;5/'. P+ +, 8+/'+'5+ 8+ 7' 8+8/' /;5/' ' 5'; 7' 'G' '' *7/', G'5' 7' 5-8'57' 12!C.
'ro,iedades F0si-as A+/0 A<7' E=7///+ ( )
,3!
A+/0 A<7' 24 G+' ( )
,1
D/' ( < -3 )
1,2
I/ R*'5/+
1,!%4"
I/ O?><+ L>-/5 ( )
2!2$
I*'-'//'
VV2
N-+ A
34,
R/5/' ' + U5'/+5'
A85'
'ro,iedades +u0mi-as L' 8+8/' =7>-/' 8+/'+'5+ + ' 7 8+>-+ -5 8+'. L+ <78+ '+'5+ + ?5-''-5 / ' ' G/0// +-+ 5: ' '' 8//8', 87 8++' <''/0 ' 8+8/' 5-+8:5/+. D/+ ' 5' '/0 8+/'+'5+ 5' /-8 + 8'' 8++, +5' *+-' -'5/' >' 7 8+ -+7' 7/+ :5/'-5 ' 8+8/' '8'//' 5/+''. L' 8/9' 8+/'+'5+, 8-'5 +5'5+ + '<7', 5/ 7 /' 5/ 7/' / ' 5-8'57' 5''+ 78' "C. E '8/'/+ + +5'5+ + '<7' + +5'5, 5 8+-' + '8', +-+ '+ + /+ + ;.
odulo de elasti-idad. 23 K<-
5
ESFUER#O DE FLE?ION E *79+ *?/0 87+ + /-8 +5/ 7'+ '8/' + 7 78+ 8' *79' 88/7' ' 7 +57/', -++ =7 8++=7 + ' /+ 5'' + 85+ ' + /-/'5+. S/ -'<+ 8+ +-+/' 8'' '/9' '+ + /5/5+ -'5/' '+ ' '/0 5 *79+ -8' <'-5 ' ' -/-' +-8+5:+ +-+ /<' /-8-5 '8+'', + ' '<' +5'' 7 875+ -/+ (*?/0 8'5/' 7 +/'/')E 5' +//+ '-: 8+7/ -+-5+ *?/0 =7/+, 788+ ' 7 *79+ +5'5, 7' /*7/' '7+ ' /5/' -'5/' '/' + ' /5'/' 5 '8++, /+ ' =7 -/5' + -+-5+ *5+ '7-5' + /-/7 + 5', + *79+ +5'5 -'5/ +5'5, +-+ 87 +-8+' *:/-5 ' */<7', 8+ + =7 : 5'5+ -+ 7 /*7/' 7'5+ -'+ ' ' 79 5 '8++. E 8+ 5' '90 =7 ' /5'/' 5 + +8+5 ' 8+5' G' +-'/9'+ +/5-5 *7/0 ' '57' + /:-5+ ' -/-', 87/+ '85' 5+ =7 ' '/0 *79+ +5 75' 8:5/'-5 8/'. P'' '+ -: 8/+ ' '8/'/0 ' '<' G' 8+ /5-/+ + *79' + + =7 +<' X*?/0 87'.
ESFUER#OS ( DEFORACIONES 'OR FLE?I&N L+ -+-5+ *5+ + '7'+ 8+ ' '8/'/0 '<' +-' ' +57/' -5+ G'/+ =7 -/-+ *?/+. D8/+ 8'+ + =7 '5 ' *79', 7 //'/0 + 85+ ' +57/' 7 7/'/0 + 85+ ' 5+ +5'5 ' /0 5'' -5+, 87 8+7/ + 5 *?/0 /-8, *?/0 87', *?/0 /'?/' + *?/0 '/-;5/'.
FLE?I&N 'URA L' *?/0 87' */ ' ' *?/0 7 -5+ '+ ' '/0 7 -+-5+ *?/+'5 +5'5. C7'+ 7 -5+ 75' +-5/+ ' *?/0 87', + *79+ +5'5 + ; + +. U -8+ 7 -5+ +-5/+ ' *?/0 87' + +5/57 ' 8'5 ' /<' 5 ' + '<' 8757' P. E /'<'-' +5'5 (V) /75' =7 ' 8'5 5' ' /<' + ?/5 *79' +5'5 ' =7 5: +-5/' /'-5 ' 7 -+-5+ +5'5 /<7' ' P. . L' 8'5 +57 + 75' *?/0 87' 875+ =7 -+-5+ + +5'5 ?/5 *79' +5'5.
P'' 8+ 5-/' + *79+ 8+7/+ 7 -5+ +-5/+ ' *?/0, '/+ '/9' 8/-+ 7 57/+ ' *+-'/+ +-' 8+7/' + ' /0 5'' -5+.
FLE?I&N SI'LE E ' /' 8:5/' + 8++ + -5+ =7 75' +-5/+ ' *?/0 87'. P+ + <' + -/-+ 75' *?/0 + 7/*+- + =7 //' =7 85' *+-' /-75'' -+-5+ *5+ *79' +5'5. P+ + 5'5+ G' '/+ ' =7 7 + + *79+ ' *+-'/+ 7'+ 75' 5' /57'/0. P'' + ++ ' *79' /5' =7 '5' + + -5+ 5-/:+' 8'' ' +5/0 + /'<'-' -+-5+ *5+ *79' +5'5 =7 '5' + 7 -5+ '+.
FLE?I&N *IA?IAL L' *?/0 /'?/' 85' 7'+ 7 -5+ +-5/+ ' '<' =7 '5' + //+ =7 + +/7' ' + /-5>' 7 /0 5''. U -8+ + +5/57 ' /<' +'/9+ ' /<7/5 */<7' +-5/' ' ' '/0 7' '<' P, 7' //0 +/7' ' + /-5>'. S+ 5', 85' '-: + -+-5+ *5+, *79' +5'5. P'' ''/9' + *79+ '7'+ 8+ *?/0 +-8+ ' *79' P '' 7+ + /-5>' ' /0 5'' 8'' '/9' 7 ':// *?/0 8+ 8''+ 8'' '' //0 7<+ 788++ 8'' 5-/' + *79+ *?/+ 5+5'.
FLE?I&N ASI@TRICA.
FLE?I&N ASI@TRICA 'URA P'' ':// 5' 57/' +-8+5'-/5+ -/-+ +-5/+ ' *?/0 87' /0 5'' '/-;5/', +/'+ =7 Q7'+ 7' /<' '/-;5/' 75' +-5/' ' *?/0 87', 8'+ -+-5+ *?/+'5 88/7' ' ' 78*// 75' 0+ / + 5+/' ' /0 5'' + + 8//8' ' -/-'Q. L+ 8//8' + '=7+ + 85+ ' + 7' ' /0 5'' 85' 7 -+-5+ //' -:?/-+ ->/-+, /+, E 8+75+ //' 8'' 5+ +. P+ 5'5+ / 7 -+-5+ *?/+'5 '5' 7+ + 8'+ 8//8', 5 8'+ : 8'+ *?/0 8+: '8/' ' 5+>' *?/0 /5' '5/+-5 (MI). P'' 5+ G'' + 5+/' ' /0 + 85+ ' + 7' +-8+ -+-5+ '8/'+ M, +5/;+ + -+-5+M M9 -+5'+ ' */<7' =7 85' ' +5/7'/0. P+ + <' 75+ + 88/7' ' 8'+ =7 '5' -+-5+ '8/'+H 8+ + 5'5+ + :<7+ = + + /<7' '+ 7'+ = , = &, I9 I.
RESISTENCIA A LA FLE?ION L' *+-7' ' 5/0 :, +-+ ' '-+ ' '/0 *79+ + ' /0 + '5'. E -+-5+ *5+ -:?/-+ ' /<' /<7'@ M* -'? P . ( L [ ) 4 S/+ P ' '<' 5+5', L ' /5'/' 5 '8++ ' 8''/0 5 ' '<' ( /7+ ' 8'<. S/<7/5) S/ -+7+ /55 9 @ 9 8 . \ 32 R-8'9'+ ' *+-7' =7 5-/' ' 5/0 +/'+ -+-5+ *5+ -:?/-+, +5-+ ' X/5/' 5:5/' + -+7+ +57' ' *?/0.
6 FUER#A CORTANTE VB ( OENTO FLECTOR B T++ ':// 5757' '/9' 8''@ ') D5-/' ' '8'/' +8+5' ' '<' 8'' ' 7' *7 /6'' ' 5757'. ) D5-/' ' /-/+ -: '7'' 8'' /5/ , (+-8'' + *79+ =7 +8+5' -'5/' +5' + *79+ '57'5 + + 8/5+.). L+ E*79+ 7' /0 '' 87 5-/'+ > G' 7' /0 /-''/' 7 875+ /5;, +/' +-+ 7 78+ >+ =7///+ '' 7' ' 8'5 ' =7 *7 ///+ 5+5'. E5+ *79+ 8+: ++/+ / ++ 5+' ' *79' ?5'.
FUER#A CORTANTE VB E ' 7-' '<'/' 5+' ' *79' ?5' 88/7' ' ' /<' (+ -5+ 5757') =7 '5' ' 7 '+ ' /0 +/''. L' *79' +5'5 8+/5/' 7'+ ' 8'5 /57'' ' ' /9=7/' ' /0 5/ ' 7/ + 85+ ' ' 8'5 G'. S/ 7 5'-+ -5+ 5757' (/<', +7-', //'+) + '5' /<7' '<' ' 7' ' *79' +5'5 8-': 5' 8''' ' -5+ 5757'.
C7'+ 7 5'-+ -5+ 5757' '8/=7 7' '<' /5/7/' 7/*+--5, ' >' ' *79' +5'5 : //'', + ' 5: 7' 8/5 +5'5 + 85+ ' -5+. P'' C'<' /5/7/' + '/'/0 /' 7 /5/', ' 7' *79' +5'5 : 7' >' 7' <7+ <'+.
E + 875+ '8/'/0 '<' +5'' (8757') EISTIR] 7' /+5/7/' /'<'-' *79' +5'5.
OENTO FLECTOR B E ' 7-' '<'/' + -+-5+ 8+7/+ 8+ 5+' ' *79' ?5' ' 7 -/-+ '+ ' /0 85+ ' 7 875+ /G' /0. E -+-5+ *5+ 8+/5/+ 7'+ +/'' ' /0 ' ' /9=7/' 5/ 7' +5'/0 5/+ G+'/+. C7'+ 7 5'-+ -5+ 5757' '8/=7 7' '<' /5/7/' 7/*+--5, ' >' ' *79' +5'5 : //'', + ' 5: 7' 8/5 +5'5 + 85+ ' -5+.
DIAGRAAS DE FUER#A CORTANTE ( OENTO FLECTOR E5+ 8-/5 ' 85'/0 <'*/' + '+ XV XM ' + '<+ + + -5+ 5757'. S +57 /7'+ 7' >' ' =7 +8+ +57 ' ' /<' (E-5+ E5757', ) 7' +'' //'' '+ XV XM + 875+ ' /<'. L' F79' +5'5 (V) 5+-' 8+/5/' 8+ /-' */'. L+ '+ -+-5+ *5+ (M) +/' 8+/5/+ 8+ '+ */', / + /'<'-' 5'9' 8+ '+ ' 5'/0.
L+ -:?/-+ ->/-+ 7 /'<'-' -+-5+ *5+ +8+ /-8 ' /+ *79' +5'5 7'. P'' 8+ +5 ' /5'/' (, Y+ ) + -+-5+ *5+ -:?/-+ + ->/-+ /<7'': ' + ' ?8/0 F79' +5'5, 7<+ 8' /G' /5'/' (, Y + ).
L+ 875+ + -+-5+ *5+ 7+ +-/' + 875+ /*?/0 + ' :5/'.
RELACIONES ENTRE CARGA ( FUER#A CORTANTE
7
E /-5+ ' *79' +5'5 + 85+ ' ' /5'/' (, Y + ) 7' /0 7'=7/' 7' /<' + -5+ 5757' (/57'' ' 7' /5'/', ?, + , 7 ?5-+ /9=7/+) /<7' ' '+ :' ' '<' /G' /0.
RELACIONES ENTRE ESFUER#OS ( FUER#AS E?TERIORES E5' '/+ + -7 5/ ' /5/<' +-8+5'-/5+ 5+ *79+ 5+' ' +57 7' /<'H '-:, + 8'5/7' 75//' ' +57/ + /'<'-' +8+/5 +-+ -+ -: ''5. P'' +5 ' '/+, +/-+ 7 -5+ 7' /<' 8''+ 8+ + /+ 5'' ''5 - 8= ' 7' /5'/' ? (*/<7' !.11). L' '<' =7 '5' + ' 78*// 78/+ -5+ 87 7' '<' /5/7/', 7' '<' +5'' + 7 -+-5+ (*/<7' !.11.', ). L+ +/+ /<+ 8'' 5' '<' + + /<7/5@ ' '<' /5/7/' ' '<' +5'' + 8+/5/' 7'+ '5' G'/' ''+ + ' /<', 7 -+-5+ =7 '5' +-+ '<' + 7' /<' 8+/5/+ 7'+ '5/ G+'/+ <'5/+ 7'+ G+'/+.
P'' '' 5/8+ '<' 8+-+ // + 7'/+ =7///+ 8'' -5+, 7' 7'/0 =7///+ *79' //0 5/' 7' =7///+ -+-5+. L' 8/-' + ': 7' '/0 5 ' '<' *79+ +5'5H ' <7', ' '/0 5 *79+ +5'5 -+-5+ *5+.
P'' 8/- '+ '<' (*/<7' !.11.'). E =7///+ *79' //0 5/' '@
RELACION ENTRE CARGA5 ESFUER#O CORTANTE ( OENTO FLECTOR R75' 8'5/7'-5 /-8+5'5, ++ + ++ '+ +5 -+-5+ *?/+'5 7 875+ ' /<', /+ -: / ' + '<+ 5++ -5+, /+ ' =7 7 /6+, +/' ' +//0 -: *'+' *79+ /55 /5/+ 0/+, 8+ +<' 5+ +57 + '-'+ /'<'-' *79' +5'5 -+-5+ *5+. L' '/9'/0 5+ /'<'-' =7/ ++ ' '/0 ?/55 5 ' '<' ?5' ' *79' /5' +5 -+-5+ *5+.
RELACION CARGA CORTE P+ 7-'5+/' *79' 5/',
D 5' -'' 75' ' /<7/5 '/+@
I5/' '<'
8/5 /'<'-' +5.
E /<+ ' '<', */ ' //'/0 ' 8/5 /'<'-' +5.
L' /5/' ' '<' X= */ ' '/'/0 ' 8/5 /'<'-' +5.
S 87 '7' +5 ' /0 2, + +5 '5/+ ' /0 1, -: :' /'<'-' '<' ?/55 5 ' /+ 1 2@
TEORA DA LA ELASTICIDAD
8
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