cuadernillo electronico

7/26/2019 cuadernillo electronico

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Universidad Autónomade Coahuila

FACULTAD DE INGENIERIA

CIVILCUADERNILLO 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 ALTARESISTENCIA, ALUMINIO, MADERA, KEVLAR, FIBRA DEPOLICARBONATO)………………………………………………..4

ESFUERZO DE FLEION………………..! FUERZA CORTANTE Y FLEIONANTE……………."

RELACION ENTRE CAR#A Y ESFUERZO CORTANTE…………..$

TEORIA DE LA ELASTICIDAD………………….%

CURVA ELASTICA……………………&



DEFORACI&N DE LOS ATERIALES

L' *+-'/0 '-/+ 5'-'6+ + *+-' 7 78+ /+' *79+ /5+ 8+7/+ 8+ 7' + -: *79' '8/'' + -/-+ + ' +7/' /'5'/0 5;-/'.

DEFORACI&N UNIDIENSIONAL

L' -'</57 -: /-8 8'' -/ ' *+-'/0 + =7 /</>' '-' *+-'/0 '?/' + *+-'/0 7/5'/' */ +-+ '-/+ +</57 8+ 7/' +</57@

D ' -/-' -'</57

D+ ' +</57 ///' ' 9+' 57/+ ' +</57 */' +*+-''. E 5/ 8'' ?8' + '-/+ +</57 7 ' +7 8/-' -:/+. L' *+-'/0 '7'' '7+ ' '-'*+-'/0 /<//. E ' 8:5/' 87 7' +5' -/''/+'' + 5' +-+ 5/'-/5+@

L' *+-'/0 '?/' +<'>5-/' + *+-'/0 =7 */ +-+@

L' *+-'/0 #L'<'< / '' 8+@

L' *+-'/0 E7A-'/ / '' 8+@

DEFORMACIÓN DE UN CUERPO

E ' -:/' 0/+ *+-' ' *+-'/0 87 5 7<' </+ -++ /' //+, 87 '-: 8++'

/5+/+ ' *+-' 78+, ' +//+ ' *+-'/0 7

1

https://es.wikipedia.org/wiki/Esfuerzo_interno

https://es.wikipedia.org/wiki/Fuerza

https://es.wikipedia.org/wiki/Dilataci%C3%B3n_t%C3%A9rmica

https://es.wikipedia.org/wiki/Longitud

https://es.wikipedia.org/wiki/Prisma_mec%C3%A1nico

https://es.wikipedia.org/wiki/Mec%C3%A1nica_de_s%C3%B3lidos_deformables


https://es.wikipedia.org/wiki/Dilataci%C3%B3n_t%C3%A9rmica

https://es.wikipedia.org/wiki/Longitud

https://es.wikipedia.org/wiki/Prisma_mec%C3%A1nico

https://es.wikipedia.org/wiki/Mec%C3%A1nica_de_s%C3%B3lidos_deformables

https://es.wikipedia.org/wiki/Esfuerzo_interno



78+ 87 ''5/9' 8+ 7 5+ (-: ?'5'-5 7 '-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/' =787 5/' / /*/75' 78'+ 7 +</57 +/</' 7' 9 =7'8' ' '<'. E5 +-8+5'-/5+, / -'<+, + ?7/+ 5+ -'5/', -++ =7 + -5' ''/+ '8/'/05;/', 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'/'

https://es.wikipedia.org/wiki/C%C3%A1lculo_tensorial

https://es.wikipedia.org/wiki/Tensor_deformaci%C3%B3n



https://es.wikipedia.org/wiki/Plasticidad_(mec%C3%A1nica_de_s%C3%B3lidos)

https://es.wikipedia.org/wiki/Energ%C3%ADa

https://es.wikipedia.org/wiki/Elasticidad_(mec%C3%A1nica_de_s%C3%B3lidos)


https://es.wikipedia.org/wiki/Metal

https://es.wikipedia.org/wiki/Aleaci%C3%B3n

https://es.wikipedia.org/wiki/Roca

https://es.wikipedia.org/wiki/Hormig%C3%B3n

https://es.wikipedia.org/wiki/Madera

https://es.wikipedia.org/wiki/L%C3%ADmite_el%C3%A1stico

https://es.wikipedia.org/wiki/C%C3%A1lculo_tensorial




https://es.wikipedia.org/wiki/Plasticidad_(mec%C3%A1nica_de_s%C3%B3lidos)

https://es.wikipedia.org/wiki/Energ%C3%ADa

https://es.wikipedia.org/wiki/Elasticidad_(mec%C3%A1nica_de_s%C3%B3lidos)


https://es.wikipedia.org/wiki/Metal

https://es.wikipedia.org/wiki/Aleaci%C3%B3n

https://es.wikipedia.org/wiki/Roca

https://es.wikipedia.org/wiki/Hormig%C3%B3n

https://es.wikipedia.org/wiki/Madera

https://es.wikipedia.org/wiki/L%C3%ADmite_el%C3%A1stico



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(RO(IEDADES DEL )EVLAR ' FI*A DE (OLICAR*ONATO

)EVLAR

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E/'-5 G' + 5/8+ */' K'@

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K' 4&@ -8' 7'+ ' */' ' ' - 7' /' 8''*+-' 7 -'5/' +-875+. L' */' K' 4& 5: 5'5''

78*//'-5 8'' *'+ ' 7/0 + ' /'. E K' 4& -8'+-+ =7/8'-/5+ 8'' 8+5 ?5-+, 8'' '5'+ 8'' ' /75/''+:75/'.

L' >5/ 5 8+>-+ ' ' '+ ' 5'; 7' 8+/-/9'/0 8+ 8'+ ' 8'5/ ' 8*//'-/' /+7+ :/+ 5*5:/+. L''/0 1,4*//'-/' (8''*//'-/') + +7+ 5*5'+>+' 7<' ' K' E K' 7' 8+/'-/', ' 7' 5++ + <78+ '-/'5: 8''+ 8+ <78+ 8''*/+, /, + <78+ '-/' 7' '/+ */+ 8+//+ +875' 5 >, + '++ 1 4. E K'

7 8+>-+ '5'-5 /5'/+. L0 5/-8+ +5' 7' '8/'/0 5/8'' K', '+ =7 + ' +7 /< +5. P+ + 5'5+, 78+'+ +7/0 5'' '5'+. N+ *7>' 8+ '+ ! CE N+-?, 8+ +5' 8'5, 8+ <78+ -5'*/+, /, + <78+'-/' 7 ' '/+ */+ ' 8+//+ 1 3. E K' 75//9' 8''G' G'+ ' 87' '' 7-:5/+ //5' /55 ' '8/G'7'. L' -9' N+-? K' 75//9' 8'' G' +8' +/*'-', +-+ ' + 5' +-+.

(RO(IEDADES FISICAS ' +UIICAS

RESISTENCIA A LA TEMPERATURA

2

https://es.wikipedia.org/w/index.php?title=Mecanismos&action=edit&redlink=1

https://es.wikipedia.org/w/index.php?title=Mecanismos&action=edit&redlink=1



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/' ' ' '-'.

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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' +'55+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/'.

http://es.wikipedia.org/wiki/Kevlar#cite_note-dupont-6

http://es.wikipedia.org/wiki/Kevlar#cite_note-omenetto-7





(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+>-+ -58+'. L+ <78+ '+'5+ + ?5-''-5 / ' ' G/0//

+-+ 5: ' '' 8//8', 87 8++' <''/0 '8+8/' 5-+8:5/+. D/+ ' 5' '/0 8+/'+'5+



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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+, '> =78'' ++ ' 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

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(RO(IEDADES DEL (OLICAR*ONATO

(RO(IEDADES FISICAS

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(RO(IEDADES ECANICAS

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(RO(IEDADES DE LA SECCION

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Centroide

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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?//'

3



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Radio de Giro

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' /0 7'+ 7' +-+ +7-'. E radio de giro */-'5-:5/'-5 +-+ r= (I/A) ^0.5.



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odulo de la se--ión

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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

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 ,arade1ormarse /a3o -ar4a5 sin rom,erse5 una ve6 su,erado el l0mite el7sti-o!

(ro,iedades me-7ni-as.

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T'/'@ */ +-+ ' /5/' ' ' +57' 8+ *79+ =7*+-' -5', 8+ + 5'5+ 7 -5' 5'9 / 8+ /5' '8'/' /'5'/0.

D79'@ E ' 8+8/' =7 ?8' <'+ *+-'/0 8-'5 =7

4

http://www.xuletas.es/ficha/capacidad-de-difusi-1/

http://www.xuletas.es/ficha/dilatacion-termica/


http://www.xuletas.es/ficha/capacidad-de-difusi-1/





7* 7 -5' '+ ' '/0 /5' 7' *79' 5-/''. E?/5 +D79' *>/' 79' 5;/'.

D75//'@ ' '8'/' =7 5/ + -'5/' 8'' 7*/ *+-'/+

' 5'/0 '5/'-5 '5', G'5' <' ' 875+ *'57'.

(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 -'<'+

http://www.xuletas.es/ficha/el-calor/

http://www.xuletas.es/ficha/tecno-357/

http://www.xuletas.es/ficha/el-calor/

http://www.xuletas.es/ficha/tecno-357/



'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<mm9

Limite de ,ro,or-ionalidad

E >-/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 =75<' ' 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-asT'/'@ L' 5'/' */ +-+ ' +8+//0 ' ' *+-'/0. L+'5+ *79+ + ' ''5>5/' +- +5'' 5'-8'+ '+ '5' /5/'. L' *?/0 ' 875' 8790 + 7 ''++ //'+ '+ *79+ ?/+ , / + +7/+':8/'-5, ' ' ' */7' =7/ 8790.

D79'@ L' 79' ' G'//' '+ G+=7 + /-8'5+ /5+. E'+ '5' /5/' 5/ ' '5/'-5 7+, <'+ *79+/5+ 5'5+ 8790 +-+ ' -'5/9. L+ '+ '5' /5/'7* +5 /5+ /+ ' + <' *79+ 7'+ 8790



'5'/' -'5/' '+ +-+ 75'+ 7 *79+ + 7 G+=7 +5.

R/5/' ' <'5@ L' /5/' ' <'5 ' G'//' /5/ '+/0 75'5 ' *//0 5 ' G'-/5' '+ -'5/' '

8/9'. E M+/+, T7<5+ V''/+ + ' 8//8' ''/+7'' ' -'+>' + '+ 8'' G'-/5' 8'' 8+8+/+' /5/' ' <'5 <'/' ' ' '/0 '7+. D/+ ' ' '5'?/</' 5'/' 79' ' '8/'/+ 5'-8'+ '+ '5' /5/', ' /5/' ' <'5 <' ' 7+ 7/'5 5'5'-/5+ 78*//' ' G'-/5'. U '+ 8'' G'-/5' +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: <'+ -: +- '+ =787 /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'' +<' 775'+ ?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/+ :/'-58+ ' 75'/' -5'5, /, ' /</', -/5' =7 *79+ +5 + C/9''-/5+ 88/7' ' <'+, + */' ' =7 '7-5' '/5/' ' C/9''-/5+. L' -'' -7G+ -' /55 ' +588/7' =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

)EVLAR

E K' + 8+/8''*/+5*5''-/' 7' 8+/'-/', =7 *7 /55/9''

8+ 8/-' 9 8+ ' =7>-/' S58G'/ KJ+ 1&"!, =7 5'''' 8''D7P+5. L' +5/0 ' */' K' *7 +-8/'', 5''+ '8+5 5 B', =7 +7/+0 8+-' =7; /+5 -8' 8'' 8+'+. F/'-5, D7P+5 -890 ' +-/'/9'+ 1&$2.E/'-5 G' + 5/8+ */' K'@

K' 2&@ ' */' 5' +-+ +5/ 7 *'/'/0. S 7'5>8/'-5 +-+ *79+ 5/', 8+ 7 7' 8+8/' -:/', + 5/+. E5 7 '8/'/+ 5: ' *'/'/0 ', +8' /55

( 8+5/0) + G'+ '5/''.

K' 4&@ -8' 7'+ ' */' ' ' - 7' /' 8''*+-' 7 -'5/' +-875+. L' */' K' 4& 5: 5'5''78*//'-5 8'' *'+ ' 7/0 + ' /'. E K' 4& -8'+-+ =7/8'-/5+ 8'' 8+5 ?5-+, 8'' '5'+ 8'' ' /75/''+:75/'.

(ro,iedades F0si-as

RESISTENCIA A LA TEMPERATURA E K' +-8+ ' '5'5-8'57' (424% <'+ 5><'+) -'5/+ 8'5 78+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' +'55+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+>-+ -58+'. 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<-

ESFUER#O DE FLE?ION

E *79+ *?/0 87+ + /-8 +5/ 7'+ '8/' + 778+ 8' *79' 88/7' ' 7 +</57/', -++ =78++=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+ +575' 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 +

5



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 /05''. 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 [email protected]?I&N ASI@TRICA (URA

P'' ':// 5' 57/' +-8+5'-/5+ -/-++-5/+ ' *?/0 87' /0 5'' '/-;5/', +/'+ =7Q7'+ 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' ' /05'' 85' 7 -+-5+ //' -:?/-+ ->/-+, /+, E8+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





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

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



+ ' /<', 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/',

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TEORA DA LA ELASTICIDAD

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8



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1. +-+</'@ 7'=7/ -5+ +7- 0/+ 5: /;5/'8+8/' *>/'.

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E ' */<7' 2 -75' 7' 7' ' 5>8/' ' *+-'/0 + 85+ '*79+.



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CURVA ELASTICA

L' 7' :5/' + :5/' ' *+-'' 8+ *?/0 +</57/' 7' /<' 5', ' 7' ' ' '8/'/0 '<' 5'' 8'+ ? + ' /<'.

L' 7'/0 ' :5/' ' 7'/0 /*/' =7, 8'' 7' /<' 5+, 8-/5 +5' ' *+-' +5' ' 7' :5/'. C+5'-5' 7'/0 ' :5/' 7' 7'/0 8'' '-8+ 8'9'-/5+=7 7* ' /<' 7 *+-' 5' +/</' ' ' *+-' 7'' +*5'' */'. P'' 7' /<' -'5/' :5/+ /' +-5/+ ' 8=76'*+-'/+ ' 7'/0 /*/' ' :5/' / '' 8+@

L' 7'/0 (1) +5/57 0+ 7' '8+?/-'/0, ' =7 G' 7875+=7 ' *+-'/+ + -7 8=76' + 85+ ' ' /-/+ ' /<' , 8+ 5'5+, G' '8+?/-'+ </+ 7' /0 ' /<' + '/'' 8/-' ' *G'. P'' *+-'/+ -'+ +5/ '7'/0 -: ?'5' (1a)@

9

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http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FEje_longitudinal

http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FViga

http://var/www/apps/conversion/tmp/scratch_7/l%20


http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FFlexi%C3%B3n_mec%C3%A1nica

http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FEje_longitudinal

http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FViga





L' 7'/0 ' :5/' (1) 87 /5' *7/0 ' '<'/5/7/' =(?) + ' /<'@

E5' 5/-' 7'/0 /5'5 8+=7 7 <'/9'/0 ' -5+//-/+' 8/'-5 ' 7'/0 *7'-5' <+/+

8'' + 7'/0 L'<'< 8'' 8'' <''@


http://var/www/apps/conversion/tmp/scratch_7/%2Fwiki%2FPlacas_y_l%C3%A1minas






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