Informede Resistencia Esfuerzos Combinados y Circulo de Mohr

INGENIERÍA EN MINAS

ESFUERZOS COMBINADOS Y CIRCULO DE MOHR

INTEGRANTES CARRERA ASIGNATURA ASIGNATURA PROFESOR FECHA

: CELSO GREGORY CHAMBE MAMANI RODRIGO FELIPE ARAYA ARAYA ALMONTE YERKO MILENKO PELAYO PELAYO MARINOVICH : INGENIERÍA EN MINAS : RESISTENCIA DE MATERIALES MATERIALES : DAVID ARTURO GOMEZ VILAXA : 20 DE JUNIO, 201

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INTRODUCCIÓN.............. INTRODUCCIÓN....................... .................. .................. .................. .................. ................. ................. .................. .............................3 ....................3

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ESFUERZOS ESFUERZOS COMBINADOS COMBINADOS.... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .........! .....!

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E"ERCICIO E"ERCICIO DE APLICACI APLICACIÓN... ÓN....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ........... ...........# ......#

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CIRCULO CIRCULO DE MOHR..... MOHR......... ........ ........ ........ ........ ........ ........ ....... ....... ........ ........ ........ ........ ........ ........ ........ .......... ............ ........... ........... ............ .......$ .$ !"1

CONSTRUCCI CONSTRUCCI#N #N CIRCULO CIRCULO MORH"""" MORH"""""""" """""""" """""""" """""""" """""""" """""""" """""""" """""""" """""""" """"""""" """"""""""" """""""""""" """"""""""" """"""""""$ """""$

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CONCLUSIÓN............... CONCLUSIÓN........................ .................. .................. ................. ................. .................. .................. .................. ................. .....................1# .............1#

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BIBLIOGRAFÍA.............. BIBLIOGRAFÍA....................... .................. ................. ................. .................. .................. .................. ................. ........................ .....................1% .....1%







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INTRODUCCIÓN

L& '()&*(+&+ '()&*(+&+ +* -(./() -(./() ()'3 ()'3 -*(4(&+ -*(4(&+ 5 * +4) D&6(+ D&6(+ G738 V(*&9& V(*&9& +* I)-(/ P'-()&* INACAP - 4)4 5()4(5&*3) *- -'/8- 43()&+- ; * 4<4/* + M="

R&'i'(&n)ia *& +a(&,ia-&'. •

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A* (./&* >/ &- +(-4(5*()&- ; 4()4(&-, - 5/+ +'()( -(-)4(& + 3&( 3&(&* &*-- 43 43 /)& 4()4(& 4()4(&  +(-4(5 +(-4(5*() *()& & >/ () () 43 43 ?( ?(6 6 5()4(5&*, 5()4(5&*, -/ -/+( +(& & * 435 435 &3 &3( () )  >/ >/ 5/+ 5/+) ) ) ) **- -7*( -7*(+ +-- +' +'3 3& &* *-- ; +3()& *- 4((- >/ )- 53(&) -&*4 * (5 + 3&(&* 3@&+4/&+ & *& =& + &*(8& /)& 4)-/44(7) ;& -& + /)& 4&-&, +('(4(, .&*57), ; &-< /)& ()'()(+&+ + 4-&-" L& -(-)4(& + 3&(&*- )- &;/+& & -& -& 4/@) 4/@)  5/+ 5/+  -( -(- -( ( /) + +3 3() ()&+ &+  -7*( -7*(+ +,, ))- +(-5 +(-5) )  ) )  ()'3&4(7) + 4/&) - * 5/+ 4&.& & /)& +3()&+& -/4/&" L& -(-)4(& + 3&(&*- - 3/; /(*(8&+& ) * @& + *& 4)-/44(7) ;& >/ - 554()& 554()& ()'3&4(7 ()'3&4(7) ) + *- 3&(&*3&(&*- 3@- &+4/&+- ; & *& 68 &;/+& & *& 5& 4)73(4&, ;& >/ )- &;/+& & *.( * (5 + 3&(&* 3@4)73(4"

O/&(i0' a (,a(a, &n &- 2,&'&n(& in,+& 1" S 4)4@ 4)4@ * 4)45 4)45 + -'/8-'/8- 43()&+ 43()&+-, -, 43 &3() &3() - - &*(8&@ &*(8&@ /) ?4(4( + &5*(4&4(7) 5&& +?& ) 4*& 3@- ) >/ 4)-(-" 2" S 4)4 4)4@ @ * 4)45 4)45  + C<4/* C<4/*  + M=, M=, 43 43 &3() &3() - &*(8& &*(8&@ @ /) ?4(4( + &5*(4&4(7) 5&& +?& 3@- ) 4*& ) >/ 4-(-"







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ESFUERZOS COMB COMBIINADO NADOS S

P&& =&*& + -'/8- 43()&+- &)- - + -& ) >/ 4)-(- * 4)45 + -'/8 E* -'/ -'/8 8  - +'( +'() ) 43 43 *& () ())-( )-(+& +&+ + + *&*&- '/ '/8&8&- 435 435) )) )- () ()) )&&+(-(/(+&- >/ -(-) /) 4&3(& ) *& '3& + /) 4/5, - =&*& - '/8& 5 /)(+&+ + @&" E9(-) - 4*&-- @-(4&- + -'/8-: + (&n'i4n5 )+2,&'i4n 6 *& ),(&. •

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-'/ 88 () ()) )  -/* -/*&) &) + *&- )-( )-() )E'7&, E'7&,8 8 a9i a9iaa-: E- * -'/ 55)+(4/*&- )3&*- & *& -44(7) &)-6-&*" 43()&4(7 4(7) ) + -'/8 -'/8-- + 435435-(7) (7) ; E'7&,8 *& -&9i4n: E- /)& 43()& )-(7)" E'7&,8 ),(an(& 2, (,'i4n: E- * -'/8 3@9(3 ) *& -/5'(4( 9("

T)()+ T)()+ -- 4)45- 4*&-, - 5/+ =&*& + -'/8- 43()&+- *& 4/&* - +'() 43 * -/*&+ + *& -/3&  *& 43()&4(7) + -- - -'/8-, &9(&*, /)& 4&.& 5 '*9(7)  /)& 4&.& 5 -(7)"

E9i'(&n ! (i2' *& )+ina)in&' *& 2'i-&' )a,ga': 1" 2" %" !"

C&. C&.& & &9( &9(&* &* ; '* '*9( 9(7) 7) C&.& C&.& &9(& &9(&*,*, -( -(7) 7) ; '*9(7 '*9(7) ) C&. C&.& & &9( &9(&* &* ; -(7 (7) ) C&. C&.& & +  -( -(7) 7) ; '*9 '*9(7 (7) )

E'7&,8 )+ina* ; E'7&,8 A9iaF,+7-a G&n&,a-

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E"ER E"ERCI CICI CIO OD DE E APL APLIC ICA ACIÓN CIÓN

E) *& -(./() && , *& 4/&* ) /) 93 -@ 35&+& & *& 5&+ ; *  933 - )4/)& ) *&+(8 , C&*4/*& * -'/8 43()&+"

P,i+&, '& *&(&,+ina,á &- áng7- a =a-a>

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E'7&,8 T&n'ina- ; F9 A E-'/8 )-()&*  !$$ *  ?? 2'i ! () 9  ()









C7a,( )á-)7- *& &'7&,8 *& -&9i4n

E- - + *&4()& * 33) >/ - .)& ) *& && , * 4)(+ ; * 33) 5*& + ()4(&" F3/*& : E-'/8  M 4 I M  M3) 4  C)(+ I  M3) 5*& + ()4(& •

C@4/* 33)

M  1!0%"% * 9 20 ()  @?%% - in •

C@*4/* 4)(+







U)& 68 >/ - 4/)& 4) + - 54+ & &5*(4& *& '3/*&" E-'/8  M 4 I

E-'/8 + 435-(7)  20 * () 9 % ()  11%$.! 2'i  in!

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S&9( )á)7- *& &'7&,8 *& )+2,&'i4n 200 5-(  11$"!2 11$"!2 5-(  $%$.! 2'i







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CIRCULO DE MOHR

E* 4(4/* + 3= '/ 4&+ 5 * - C=(-(&) M= , - 4(4/* - /) 3+ .@'(4 5&& +3()& * -&+ )-()&* ) *- +(-()- 5/)- + /) 4/5" E) *&- )-()- >/ 9(-)- ) /) 4/5 -3(+ & /) 4( -&+ + 4&.&- ; 4) /)&- 4(&- -(44()-, (35&) ) .)&* *&- )-()- 5()4(5&*-, >/ -) *&)-()- >/ 9(-) - 4(- 5*&)- +* 4/5, +)+ *&- )-()- + 4 )/*&-" E-&- )-()- -) + (35&)4(& 5&& * -/+( + *& -(-)4(& 34@)(4& + /)& 5(8&" E- 3+ () &5*(4&4(7) 5&& -&+- )-()&*- ) +- ; +(3)-()-"

!.11 CONS !. CONSTR TRUC UCCI CIÓN ÓN CIRC CIRCUL ULO O MO MORH RH







!.1.1 Pa' 1 S + /-4& * &+( +* 4(4/* 3+(&) *& -(./() '3/*&:

D)+ *& )-(7) &).)4(&*  5/+ - &) ).&(6 43 &3() 5-((6 "







!.1. Pa'  S 4&*4/*& * E-'/8 53+( >/ & *& 68 5&-& & - * 4) +* 4(4/*, - - 4@*4/*& 3+(&) *& -(./() '3/*&:









!.1.3 Pa' 3 C&*4/*& *- -'/8- 3@9(3- ; 3()(3- 3+(&) *&- -(./()- '3/*&-"

F()&*3) * 4(4/* >/+&(& + *& -(./() 3&)&







!. !. E"ER E"ERCI CICI CIO O DE APL APLIC ICA ACIÓN CIÓN S () * -(./() *3) 9&(+ + /)& && ) 4/&* () /)& 4&.& + )-(7) + !0 M5& ) * ? ? Y F Y ; /)& 4&.& + )-(7) + + 0 M5& ) * ? X F9" T&3() T&3() () /)& )-(7) &).)-(&* + 10 M5&"







Pa' 3 C@*4/* -'/8 3@9(3 ; 3()(3

E'7&,8 Má9i+ ; ## < 1@.?3 ; 3.?3 E'7&,8 Mini+ ; ##  1@.?3 ; 3%.$ Fina-+&n(& &- )i,)7- 7&*a,ia *& -a 'ig7i&n(& +an&,a







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CONCLUSIÓN

E* 5-) ()'3 +?& ) 4*& 473 - 3&)('(-&) 3&)('(-&) *- -'/8- ;& -& /)& &&  )  *3) -7*(+, -&- 43()&4()- 5/+) - + 6&(&3&)&-  (5-" E) 4/&) &* 4<4/* + M= )- &;/+& & +3()& @5(+&3) ; 3+(&) -(35* 5&-- 4/&* - * -'/8 4&) 3@9(3" A * *&. +* (35 *& +(-4(5*()& + *& -(-)4(& + 3&(&*- =& (+ 6*/4()&)+ ) .&) 4&)(+&+, + .&4(&- & 4()<'(4- ; 3&3@(4- >/ =&) 5/- 3/4=& ++(4&4(7), 43 * -)  M , J&3- G, ) -"







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BIBLIOGRAFÍA

L( + -(-)4(& + 3&(&*- + R M , /()& +(4(7)" M4@)(4& + M&(&*- II: E-'/8- 43()&+- 5 A)+- G" C*&6(? V", U)(6-(+&+ S(37) B*<6&" A5/)- + 4*&- + -(-)4(& + 3&(&*-, 5 * +4) D&6(+ G38 G38 V(*&9& +* I)-(/ P'-()&* INACAP" L( L( + 34@) 34@)(4 (4& & + 3& 3&( (&* &*- /() /()& & +(4 +(4(7 (7) ) , 5 5 F+( F+()&) )&)+ + P" B B E"R/--** J=)-)  J=) T" D*'  D&6(+ F" M&8/

Informede Resistencia Esfuerzos Combinados y Circulo de Mohr

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