Trabajo Diseño Madera

UNIVERSIDAD JO JOSE CA CARLOS MARIATEGUI FACUL ACULT TAD DE INGENIERI INGENIERIA A CIVIL CI VIL

INDICE .............................. ..................... ...................... ..................... ...................................... ............................ 2 1. Introducción....................

1.1. 1.1. Estruc Estructur tura a del Tronco ronco....................................................................4 ............................... ..................... ..................... ............................. .................. 5 1.2. 1.2. Famil amilia ias s Mader Maderab able les s.................... ................................ ...................... ..................... ............................. ...................6 6 1.3. 1.3. Prop Propie ieda dade des s fs fsic icas as.....................

1.!. 1.!. El merc mercad ado o mad mader erer ero o....................................................................8 1.". 1.". Norm Normas as de dise dise# #o..........................................................................9 2. MET$D$ MET$D$% % DE DI%E DI%E&$ &$ ' (N() (N()I%I I%I% % E%T*+ E%T*+CT+ CT+*() *().........................10 2.1. 2.1. M,to M,todo dos s de Dis Dise# e#o o......................................................................10 2.2. 2.2. Esfuer Esfuer-os -os ue resist resiste e la madera madera...............................................10 2.3. 2.3. P*$P P*$PIE IED( D(DE DE% % E)/%T E)/%TIC IC(% (%..................... ............................... ..................... ............................ .................12 12 ................................ ...................... ..................... ..................... ..................... ..................... ................ .....14 14 2.!. C0lculos..................... ............................... ..................... ..................... ..................................... ........................... 15 3. DI%E& I%E&$ $ DE I I(% (%.....................

3.1. 3.1. P*$PIE P*$PIED(D D(DE% E% DE DE )(% )(% %ECCI$ %ECCI$NE% NE%..................... ................................ ..................... .............15 ...15 3.2. 3.2. DEF) DEF)E EI$ I$NE NE% % (DMI% (DMI%I4 I4)E% )E%.........................................................17 ............................... ..................... ...................... ............18 18 3.3. 3.3. *E5+ *E5+I% I%IT IT$% $% DE *E%I *E%I%T %TEN ENCI CI( (.................... ............................... ..................... ...................................... ........................... 22 3.!. 3.!. E%C+ E%C+(D (D*6 *6( ( 7PTIM 7PTIM( (.....................

3.". 3.". I( I(% % C$MP C$MP+E +E%T %T(% (%....................................................................24 :............................... ..................... ..................... ..................... ........................................... ................................. 29 E8emplo 1:.................... :............................... ..................... ..................... ..................... ........................................... ................................. 35 E8emplo 2:.................... .............................. ..................... ............................39 .................39 E8emplo 39 DINTE) DE ENT(N(.................... :............................... ..................... ..................... ..................... ........................................... ................................. 43 E8emplo !:....................

1. Introd Int roducci ucción ón

DISEÑO EN ACERO  MADERA

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UNIVERSIDAD JO JOSE CA CARLOS MARIATEGUI FACUL ACULT TAD DE INGENIERI INGENIERIA A CIVIL CI VIL •

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Estructura Tronco

UNIVERSIDAD JO JOSE CA CARLOS MARIATEGUI FACUL ACULT TAD DE INGENIERI INGENIERIA A CIVIL CI VIL

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UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL

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A


b*h = ESCUADRIA h

b

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Listones :

1 b (2 - 2 )" 2

b (3 - 4)" •

Viguetas :

b (15 - 20)cm •

Vigas :

h (15 - 25)cm

b (25 - 30) cm •

Basas(grandes vigas) :

h (35 - 45)cm

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B


Tablas

(1 -121)" Virutas

L! )*(*!*/ #$ (!' +(!/!' +$%"*)$ / ', +)*", #$ (!' "!#$%!' (!"$/)!($"$/)$ $/ $')$ %!", (! */#')%*! ,(*;*!/! $' +,%$.

1.".

Normas de dise#o L!' /,%"!' #$ #*'$>, ',/ #,"$/),' )/*,' $ )*$/$/ ?$%! #$ ($= $/ $',' #,"$/),' $/$/)%! $( */$/*$%, ?%"(!'& ;!(,%$' = %$,"$/#!*,/$' $ ($ +$%"*)$/ #*'$>!% $')%)%!' #$ "!/$%! '$%! = $,/"*!& !
MANUAL DE DISEÑO ARA MADERAS DEL GRUO ANDINO DIN 1052 BC,/?$%!' CILENA NC5006 BC,/?$%!' TIMER DESIGN MANUAL B,/ ' '+($"$/), NDS LRFD MANUAL FOR ENGINEERED POOD CONSTRUCTION

2. MET$D$% DE DI%E&$ ' (N()I%I% E%T*+CT+*() L! +!%)$ +%*/*+!( #$ ),#, )%!!, #$ #*'$>, $')%)%!( $' (! /$$'*#!# #$ ,/$*% = $;!(!% $( ,"+,%)!"*$/), ?'*, #$ (! $')%)%! !( %$'*')*% (!' !%!' $ #$$ ',+,%)!% +!%! (, !( #$$ !$%'$ / )%!!, "!)$")*, +!%! !+,=!% $')$ !/(*'*'. C,/(*#, $( !/(*'*' '$ #$$ %$!(*!% $( )%!!, #$


UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL #*'$>, +$%, +!%! $'), #$$/ ,/'*#$%!%'$ (,' ,"+,%)!"*$/),' $')%)%!($' '*"+($' = (! "etodolog#a de diseño ! '$*%. 2.1.

M,todos de Dise#o A)!("$/)$ '$ )*(*!/ 2 "),#,' +%*/*+!($' #$ #*'$>, $ ',/: 

E( "$todo tradicional $ '$ ,/,$ ,", diseño por es%uerzos de tra&a'o ad"isi&les. E/ $')$ "),#, '$ )*(*!/ %$(!*,/$' '*!'

#$%*;!#!' #$ (! )$,%! ('*! #$( ,"+,%)!"*$/), $(')*, #$ (,' "!)$%*!($' (! !#$!*/ , '$%*#!# #$ (,' #*'$>,' '$ "*#$ !( ,"+!%!% ,/ %$'+$), ! #,' ("*)$' +%*/*+!($': / !$+)!($ +!%! $( $'?$%, "-*", = / /*;$( ),($%!($ +!%! $( !(!/$ #$ (! #$?,%"!*/. E/ $'$/*! $( "),#, #$ (,' $'?$%,' #$ )%!!, ,/'*')$ $/ #*'$>!% /! $')%)%! +!%! traba8ar a aln porcenta8e apropiado $')!($*#, #$ ' !+!*#!# ),)!(. S*/ $"!%, (, $ $' ;$%#!#$%!"$/)$ !+%,+*!#, ,", /! ,/#**/ #$ )%!!, )*$/$ muc;o de especulación teórica. C,/ $( ,$), #$ $')!($$% $/ ?,%"! ,/;*/$/)$ !",' ("*)$' #$ $'?$%, = #$?,%"!*/& ?$ /$$'!%*, $$)!% $/'!=,' #$ $')%)%!' %$!($'. 

M$todo de la resistencia , LRD& $/ $( !( '$ '!/ lmites de falla

+!%! $( )%!!, #$ #*'$>,. E( "),#, #$ (! %$'*')$/*! ,/'*')$ $/ dise#ar una estructura para fallar& +$%, +!%! /! ,/#**/ #$ !%! m0s all0 #$ (, $ #$$%! $-+$%*"$/)!% #%!/)$ ' ',. U/! %!/ +%*/*+!( +!%! ?!;,%$$% (,' "),#,' #$ %$'*')$/*! $' $ (! ?!((! #$ /! $')%)%! se demuestra con relati:a facilidad "$#*!/)$ +%$!' ?'*!'.

2.2.

Esfuer-os ue resiste la madera L! !*/ #$ (!' !%!' ',"$)$ ! (!' "!#$%!' ! (,' '**$/)$' $'?$%,':

2.2.1 C$MP*E%I7N9 E')$ $'?$%, '$ +%,#$ !/#, /! ?$%! )*$/#$ ! ,"+%*"*% , !+(!')!% / "*$"%,. E')$ $'?$%, '$ +%$'$/)! $/ (!' ,("/!' #$ $#*@!*,/$'& !' ,", $/ !(/!' !%%!' $ ,/?,%"!/ #*')*/),' )*+,' #$ !%"!#%!'.

Paralelas a las ?bras:etaG adσ CII Perpendicular a las ?bras DISEÑO EN ACERO  MADERA

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11


2.2.2 T*(CCI7N9 E' / $'?$%, $ '$ +%,#$ !/#, /! ?$%! )*$/#$ ! $')*%!% , !(!%!% / "*$"%,. L! $%#! */?$%*,% = *$%)!' !("!' #$ "*$"%,' #$ !%"!#%!' = !*,' !)*%!/)!#,' )%!!!/ ! )%!*/. S* '$ ,/,$ (! ?$%! ),)!( #$ )%!*/ !-*!( B#$/,)!#, +,%  $/ / "*$"%,& !' ,", $( %$! #$ ' '$*/ )%!/';$%'!( B#$/,)!#, +,% A& $( $'?$%, /*)!%*, #$ )%!*/ '$

σ! =

P 

$/$/)%! ! +!%)*% #$ (! ?%"(! '*! #$( $'?$%, #*%$), : adσ !II •

Paralelas a las ?bras

2.2.3 F)EI7N9 E')$ )*+, #$ $'?$%, +,% (, ,"
adσ  •

2.2.! C$*TE9 S$ +%,#$ / $'?$%, ,%)!/)$ !/#, #,' ?$%!' *!($'& +!%!($(!' = #$ '$/)*#, ,/)%!%*, )*$/#$/ ! !$% %$'!(!%& /! ',%$ ,)%!& (!' '+$%@*$' ,/)*!' #$( "*$"%,. E')$ $'?$%, $ $' "= ,"!(!% $ $-*')$/ 2 )*+,' #$ $'?$%, ,%)!/)$& $( ;$%)*!( = $( ,%*,/)!( = +,% (, $/$%!( (!' ?!((!' +,% ,%)!/)$ $/ ;*!' #$ "!#$%! '$ #$$/ !( $'?$%, ,%)!/)$ ,%*,/)!(& = /, !( ;$%)*!(.

ad# •

2.2." DEF$*M(CI7N9 L! #$?,%"!*/ $' $( !"*, #$ )!"!>, , ?,%"! $ '*$"+%$ '?%$ / $%+, $ $') ',"$)*#, ! /! ?$%!. C!/#, (!' ?$%!' ',/ #$ ,"+%$'*/ = #$ )%!*/ !-*!(& (!' #$?,%"!*,/$' ',/ !,%)!"*$/),'


12

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL , !(!%!"*$/),'& %$'+$)*;!"$/)$. C!/#, /! ?$%! !)
Flec;as  $')$ ?$/"$/, $/ (!' "!#$%!' $' $-)%$"!#!"$/)$ +$(*%,',& (!' Q$!' !#"*'*($' #$+$/#$/ #$( %+, #$ (!' "!#$%!': ↔

•

•

2.3.

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$ (cm) 250 - 300

G%+, A ↔ G%+,  ↔

$ (cm) 225 - 2%5

P*$PIED(DE% E)/%TIC(%

2.3.1 )imite El0stico. H E( #*'$>, #$ (!' $')%)%!' #$ "!#$%! '$ !'! $/ (! )$,%! $(')*!& $/ (! !( '$ $')!($$ $ (!' #$?,%"!*,/$' ',/ #*%$)!"$/)$ +%,+,%*,/!($' ! (,' $'?$%,'& $' #$*% $ !( '$% !+(*!#! /! ?$%! '$ +%,#$ /! *$%)! #$?,%"!*/& = !( '$% !+(*!#! $( #,($ #$ $')! ?$%! '$ +%,#*% $( #,($ #$ (! !/)*#!# #$ #$?,%"!*/. E')! %$(!*/ '$ "!/)*$/$ '(, !')! / *$%), ("*)$& #$'+' #$( !( (! #$?,%"!*/ ,"*$/! ! !"$/)!% $/ / %!#, "!=,% $ (,' */%$"$/),' #$ !%! !+(*!#! $( $'?$%, /*)!%*, +!%! $( !( ,%%$ $')$ ("*)$ '$ ,/,$ ,", l#"ite el*stico , l#"ite de proporcionalidad #$( "!)$%*!(.

2.3.2 Módulo De Elasticidad (ial. J E( M+dulo de elasticidad #$ / "!)$%*!( $' (! "$#*#! #$ ' rigidez & = $')$ $' (! %$(!*/ $/)%$ $( $'?$%, /*)!%*, = (! #$?,%"!*/ /*)!%*!& '*$"+%$ $ $( $'?$%, /*)!%*, /, $-$#! $( ("*)$ $(')*, #$( "!)$%*!(. E( "#(, #$ $(!')**#!# !-*!( E ;!%! $/)%$: 55000E130000 K"2 #$+$/#*$/#, #$( %+, #$ (! "!#$%!& '*$/#, $( +%*"$%, +!%! "!#$%!' #$( )*+, C = $( <()*", +!%! "!#$%!' #$( %+, A. L,' ;!(,%$' '!#,' '!("$/)$ +!%! $( #*'$>, ',/:

A("$/#%*((, DISEÑO EN ACERO  MADERA

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13




E ≈ 100000 kg/cm2

GRUO A:

V$%#,(!,

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E ≈ 80000 kg/cm2 !(, M!%!

G!/ 

2.!.

GRUO C:

E ≈ 65000 kg/cm2

C0lculos E' "= %$,"$/#!($ $ '$ !!/ (,' ((,' $')%)%!($' ,/ +%,%!"!' , +!$)$' $/ ,"+)!#,%!& #$*#, ! $ $/ $( #*'$>, +%,?$'*,/!( $( )%!!, $' ,"+($, = #$$ %$!(*!%'$ #$ (! "!/$%! "' %+*#! +,'*($ +,% )!( ",)*;, $/ $( +%$'$/)$ )$-), '$ !$ / )),%*!( #$ (,' +%,%!"!' SA2000 = R,,) M*(($/*" +!%! (! '*"(!*/ $')%)%!( #$ !%"!#%!'. T!"*/ +!%! / #*'$>, = ;$%*@!*/ %+*#! #$ %$'()!#,' '$ !#/)!% !( +%$'$/)$ #,"$/), /!' +(!/*((!' E-$( $/ (!' $ $?$),' !),")*,' #$ (,' #*?$%$/)$' )*+,' #$ +%,($"!' $ '$ !!%$/ $/ $( +%$'$/)$ )$-),.



3. DI%E&$ DE I(% U/! ;*! $' / $($"$/), $')%)%!( $ %$'*')$ !%!' )%!/';$%'!($'. G$/$%!("$/)$& (!' !%!' !)
3.1.

P*$PIED(DE% DE )(% %ECCI$NE% A#$"' #$ (! %$'*')$/*! #$ (! "!#$%!& !%!)$%*!#! +,% (,' $'?$%,' /*)!%*,' !#"*'*($'& $( ,"+,%)!"*$/), #$ / "*$"%, $')%)%!( )!"*/ #$+$/#$ #$ (!' #*"$/'*,/$' = (! ?,%"! #$ ' '$*/ )%!/';$%'!(& $'),' #,' ?!),%$' '$ ,/'*#$%!/ #$/)%, #$ (!' +%,+*$#!#$' #$ (! '$*/.


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UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL 3.1.1. Centroides.J E( $/)%, #$ %!;$#!# #$ / '(*#, $' / +/), *"!*/!%*, $/ $( !( '$ ,/'*#$%! $ ),#, ' +$', $') ,/$/)%!#, , $( +/), ! )%!;' #$( !( +!'! (! %$'()!/)$ #$ ' +$',.

E( +/), $/ / %$! +(!/! $

,%%$'+,/#$ !( $/)%, #$ %!;$#!# #$ /! +(!! "= #$(!#! $ )*$/$ (!' "*'"!' %$!' = ?,%"! '$ ,/,$ ,", $( $/)%,*#$ #$( %$!. C!/#, /! ;*! '$ Q$-*,/! #$*#, ! /! !%! !+(*!#!& (!' @%!' +,% $/*"! #$ / *$%), +(!/, $/ (! ;*! )%!!!/ $/ ,"+%$'*/ = !$((!' +,% #$!, #$ $')$ +(!/,& ! )$/'*/. E')$ +(!/, '$ ,/,$ ,", (! '+$%@*$ /$)%!. L! */)$%'$*/ #$ (! '+$%@*$ /$)%! = (! '$*/ )%!/';$%'!( #$ (! ;*! '$ ,/,$ ,", $( e8e neutro. 3.1.2. Momento de inercia E/ (! @%! 31 '$ *(')%! /! '$*/ %$)!/(!% #$ !/, & = !(), ! ,/ $( $$ ,%*,/)!( - $ +!'! +,% ' $/)%,*#$ ! /! #*')!/*!   !2 ! +!%)*% #$ (! !%! '+$%*,%. E/ (! '$*/&

a %$+%$'$/)! / %$! */@/*)!"$/)$

+$$>! ! /! #*')!/*! z #$( $$ - . S* '$ "()*+(*! $')! %$! */@/*)$'*"!( +,% $( !#%!#, #$ ' #*')!/*! !( $$& '$ ,)*$/$ (! !/)*#!# B a - z 2. E( %$! ,"+($)! #$ (! '$*/ $')!% ,/')*)*#! +,% / /<"$%, */@/*), #$ $')!' +$$>!' %$!' $($"$/)!($' ! #*?$%$/)$' #*')!/*!' +,% !%%*! = +,% #$!, #$( $$ -. E/),/$'& $( ","$/), #$ */$%*! '$ #$@/$ ,", (! '"! #$ (,' +%,#),' $ '$ ,)*$/$/ !( "()*+(*!% ),#!' (!' %$!' */@/*)!"$/)$ +$$>!' +,% $( !#%!#, #$ '' #*')!/*!' ! / $$.

FIGURA 3.1 Y b

a c

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h X

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Y

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L,' #,' $$' +%*/*+!($' #$ (! @%! ',/ - = /-/, +!'!/ +,% $( $/)%,*#$ #$ (! '$*/ %$)!/(!%& ,/ %$'+$), ! / $$ $ +!'! +,% $( $/)%,*#$ = $' +!%!($(, ! (! !'$ $' I -  &!312& ,/ %$'+$), !( $$ ;$%)*!(& (! $-+%$'*/ '$%! I/-/  !&312.

3.1.3. *adio de iro. H E')! +%,+*$#!# #$ (! '$*/ )%!/';$%'!( #$ / "*$"%, $')%)%!( $') %$(!*,/!#! ,/ $( #*'$>, #$ "*$"%,' '$),' ! ,"+%$'*/. D$+$/#$ #$ (!' #*"$/'*,/$' = #$ (! ?,%"! $,")%*! #$ (! '$*/ = $' / /#*$ #$ (! %**#$ #$ (! '$*/ !/#, '$ '! ,", ,("/!. E( radio de giro '$ #$@/$ I & A

"!)$")*!"$/)$ ,", r0

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D,/#$ 1 $' $( ","$/), #$ */$%*! = A $( %$! #$ (! '$*/. S$ $-+%$'! $/ $/)"$)%,' +,%$ $( ","$/), #$ */$%*! $') $/ $/)"$)%,' ! (! !%)! +,)$/*! = $( %$! #$ (! '$*/ )%!/';$%'!( $') $/ $/)"$)%,' !#%!#,'. E( %!#*, #$ *%, /, '$ '! )!/ !"+(*!"$/)$ $/ $( #*'$>, #$ "!#$%! $')%)%!( ,", $/ $( #*'$>, #$ !$%, $')%)%!(. !%! (!' '$*,/$' %$)!/(!%$' $ '$ $"+($!/ ,", #$ ,("/!'.

3.2.

DEF)EI$NE% (DMI%I4)E% S$ ((!"! ec!a , dee2i+n ! (! #$?,%"!*/ $ !,"+!>! ! (! Q$-*/ #$ /! ;*!& ;*$)! , $/)!(!#,. L! Q$! '$ +%$'$/)! $/ !(

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UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL . S,%$!%!' #$ '$%;**, !)!/#, ',(!'. S$ %$,"*$/#! $ +!%! ,/')%*,/$' %$'*#$/*!($' $')!' /, $-$#!/ (,' ("*)$' */#*!#,' $/ (! '**$/)$ T!(!: TABLA 3.1: DEFLEXIONES MAXIMAS ADMISIBLES

Cara (ctuante

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C!%!' +$%"!/$/)$' ',%$!%!' S,%$!%!

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L $' (! ( $/)%$ !%!' #$ !+,=,' , (! #*')!/*! #$ (! !%! #$( !+,=, !( $-)%$",& $/ $( !', #$ ;,(!#,'. L,' ;!(,%$' */#*!#,' $/ (! ,("/! B! #$$/ '$% )*(*!#,' !/#, '$ )$/!/ *$(,' %!',' #$ =$',  ,)%,' !!!#,' $ +#*$%!/ '$% !?$)!#,' +,% (!' #$?,%"!*,/$': $/ ,)%,' !',' #$$/ )*(*!%'$ (,' ;!(,%$' #$ (! ,("/! B. A/$ (!' ,/'*#$%!*,/$' +!%! #$@/*% (! Q$! +$#$/ '$% *"+,%)!/)$'& (! #$)$%"*/!*/ +%$*'! #$ (! Q$! $' / ,$)*;, */!(!/!($ +,% (!' '**$/)$' %!,/$': 

L! #$)$%"*/!*/ #$ (!' !%!' '*$"+%$ */(=$ !(
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E( "#(, #$ $(!')**#!# #$ !(*$% +*$! */#*;*#!( #$ "!#$%! '*$"+%$ $' / ;!(,% !+%,-*"!#,.

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E-*')$/ #*?$%$/)$' %$')%**,/$' $/ (! #$?,%"!*/ $')%)%!( #$*#, ! (! #*')%**/ #$ !%!'& %$'*')$/*!' $/ (!' /*,/$'& %**#$ #$*#! ! $($"$/),' /, $')%)%!($' #$ (! ,/')%*/& $).

L!' #$Q$-*,/$' $/ ;*!' #$$/ '$% !((!#!' ,/ $( "#(, #$ $(!')**#!# E "*/ #$( %+, #$ (! "!#$%! $')%)%!( $'+$*@!#,. !%! $/)!(!#,' #$$ )*(*!%'$ $( E +%,"$#*,& (!' #$Q$-*,/$' $/ ;*$)!' = $($"$/),' '*"*(!%$' +$#$/ )!"*/ #$)$%"*/!%'$ ,/ $( E +%,"$#*,& '*$"+%$ = !/#, '$ )$/!/ +,% (, "$/,' !)%, $($"$/),' '*"*(!%$'& = '$! +,'*($ /! %$#*')%**/ #$ (! !%!. L,' "#(,' #$ $(!')**#!# +!%! (,' )%$' %+,' #$ "!#$%!' $')%)%!($' ,/'*#$%!#,' '$ */#*!/ $/ (! )!(! 3.2.: TABLA 3.2: MODULO DE ELASTICIDAD k /cm2


1A


Emnimo Epromedio

*+P$ ( 95&000 130&000

*+P$ 4 75&000 100&000

*+P$ C 55&000 90&000

R$?.: TALA 8.2 #$ . 83 #$(  Manual de Diseño para Maderas del Grupo Andino 

3.3. *E5+I%IT$% DE *E%I%TENCI( 3.3.1. Fleión. H E( ","$/), Q$-*,/!/)$ $' /! "$#*#! #$ (! )$/#$/*! #$ (!' ?$%!' $-)$%/!' $ !)
!%! !(*$% )*+, #$ ;*! '$ +$#$ !((!% $( ","$/), Q$-*,/!/)$ "-*", $/$%!#, +,% (! !%!. S* '$ #$'$! #*'$>!% /! ;*! +!%! %$'*')*% $')! !%!& '$ #$$ '$($*,/!% / "*$"%, ,/ /! '$*/ )%!/';$%'!( #$ ?,%"!& %$! = "!)$%*!( )!($'& $ '$! !+! #$ +%,#*% / ","$/), %$'*')$/)$ *!( ","$/), Q$-*,/!/)$ "-*", (, !/)$%*,% '$ (,%! '!/#, (! ?%"(! #$ (! e2i+n. ,% (, ,"
⋅' I

D,/#$ $( )!"!>, = (! ?,%"! #$ (! '$*/ )%!/';$%'!( $')/ %$+%$'$/)!#,' +,% (! */$%*! BI = $( "!)$%*!( #$( !( $') $! (! ;*! $') %$+%$'$/)!#, +,% & (! #*')!/*! #$( +(!/, /$)%, ! !(*$% ?*%! #$ (! '$*/ $')! %$+%$'$/)! +,% =& $( $'?$%, $/ (! @%! "' !($!#! #$( $$ /$)%, '$ ($ ((!"! es%uerzo de la 3&ra e2tre"a B. !%! ;*!' %$)!/(!%$': FIGURA 3.2 SECCION TRANSVERSAL DISTRIBUCION DE ESFUER!OS

N$*M()E% P*$D+CID$% P$* F)EI$N

b c=h2

y

c=h2

R$?.: E(!,%!*/


Mc I My I EJE NEUTRO

1B


S')*)=$/#, (,' #!),' +!%! /! ;*! %$)!/(!% = +!%! ,)$/$% $( $'?$%, #$ (! @%! $-)%$"! )$/#%$",':

σ =

⋅c I

=

⋅

h

2 b ⋅ h 3 12

+ 

=

* ⋅  ma b ⋅ h 2

L,' $'?$%,' #$ ,"+%$'*/ = #$ )$/'*/ +%,#*#,' +,% ?($-*/ B& $ !)
GRUO A GRUO  GRUO C

210 150 100

R$?.: TALA 8.3 #$ . 84 #$(  Manual de Diseño para Maderas del Grupo A ndino E'),' $'?$%,' +$#$/ */%$"$/)!%'$ $/ / 10 !( #*'$>!% $/)!(!#,' , ;*$)!' '* != /! !*/ #$ ,//), !%!/)*!#!.

3.3.2. Corte.J C,", "$/*,/!",' $/ $( !+)(, !/)$%*,%& '$ +%,#$ / es%uerzo cortante !/#, #,' ?$%!' *!($'& +!%!($(!' = #$ '$/)*#, ,/)%!%*, )*$/#$/ ! !$% %$'!(!%& /! ',%$ ,)%!& (!' '+$%@*$' ,/)*!' #$ / "*$"%,. E/ (! @%! 3.3! '$ %$+%$'$/)! /! ;*! ,/ /! !%! /*?,%"$"$/)$ #*')%**#!. E-*')$ /! )$/#$/*! $/ (! ;*! ! ?!((!% ,(!+'/#,'$ $/)%$ !+,=,'& ,", '$ */#*! $/ (! @%! 3.3. ')$ $' / $$"+(, #$ ,%)!/)$ ;$%)*!(. E/ (! @%! 3.3 '$ "$')%!& $/ ?,%"! $-!$%!#!& (! Q$-*/ #$ /! ;*! = (! ?!((! #$ +!%)$' #$ (! ;*! +,% #$'(*!"*$/), ,%*,/)!(& $')$ $' / $$"+(, #$ ,%)!/)$ ,%*,/)!(. L!' ?!((!' +,% ,%)!/)$ $/ (!' ;*!' #$ "!#$%! '$ #$$/


2

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL !( $'?$%, ,%)!/)$ ,%*,/)!(& /, !( ;$%)*!(. E'), $' ;$%#!# #$*#, $ (! %$'*')$/*! !( $'?$%, ,%)!/)$ #$ (! "!#$%! $' ", "$/,% $/ $( '$/)*#, +!%!($(, ! (!' @%!' $ $/ $( )%!/';$%'!( ! ')!'.

FI+*( 3.3 ENE*(CI$N DE) E%F+E*L$ C$*T(NTE

B!

B

B

R$?.: E(!,%!*/

L,' $'?$%,' ,%)!/)$' /*)!%*,' ,%*,/)!($' /, $')/ /*?,%"$"$/)$ #*')%**#,' ',%$ (! '$*/ )%!/';$%'!( #$ /! ;*!. E( $'?$%, #$ ,%)$ $/ /! '$*/ )%!/';$%'!( #$ / $($"$/), ! /! *$%)! #*')!/*! #$( +(!/, /$)%, +$#$ ,)$/$%'$ "$#*!/)$: τ =

 ⋅, b ⋅ I

E/ $')! $-+%$'*/ '$ )*$/$: W $'?$%, ,%)!/)$ /*)!%*, ,%*,/)!(& $/ !(*$% +/), $'+$?*, #$ (! '$*/. V ?$%! ,%)!/)$ ;$%)*!( ),)!( $/ (! '$*/ $($*#! S ","$/), $'))*, ,/ %$'+$), !( $$ /$)%, #$( %$! #$ (! '$*/ )%!/';$%'!(. I ","$/), #$ */$%*! #$ (! '$*/ )%!/';$%'!( #$ (! ;*! ,/ %$'+$), ! ' $$ /$)%,.  !/, #$ (! ;*! $/ $( +/), $/ $( $ '$ !((! W. !%! /! ;*! #$ '$*/ %$)!/(!% $( "-*", $'?$%, #$ ,%)$ %$'()! !( '')*)*%: h  h b ⋅ h 2  , =  b ×  × = /  2  4


.

I=

b ⋅ h 3 12

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL τ =

 ⋅, I ⋅ b

#

=

 × bh 2 & / bh 3 & 12 × b

3  ma

= ⋅

2 b ⋅ h

 V 2 bh

b h 2

21

h 4

x h

R$?.: E(!,%!*/

FI+*( 3.! ENE*(CI$N DE) E%F+E*L$ C$*T(NTE EN +N( I( L,' $'?$%,' ,%)!/)$'& W& /, #$$/ $-$#$% $( $'?$%, "-*", !#"*'*($ +!%! ,%)$ +!%!($(, ! (!' @%!'& ? ;& #$( %+, #$ "!#$%! $')%)%! $'+$*@!#,. TABLA 3.#: ESFUER!O MAXIMO ADMISIBLE $ARA CORTE $ARALELO A LAS FIBRAS "%(kg/cm2)

GRUO A

15

GRUO 

12

GRUO C

8

R$?.: TALA 8.4 #$ . 85 #$(  Manual de Diseño para Maderas del Grupo Andino 

E'),' $'?$%,' +$#$/ */%$"$/)!%'$ $/ / 10 !( #*'$>!% $/)!(!#,' , ;*$)!' '* != /! !*/ #$ ,//), !%!/)*!#!.

3.!.

E%C+(D*6( 7PTIM(

FI+*( 3."



y R : Rai! "r!#$i! $ tr!%&!

R

y

x

h

R y

x

x b

R$?.: E(!,%!*/ S$ #$'$! $')!($$% /! %$(!*/ $/)%$ (! !'$ = (! !()%! #$ /! ;*! #$ '$*/ %$)!/(!%& #$ )!( "!/$%! $ (! !+!*#!# %$'*')$/)$ #$ $')! ;*! '$! (! "!=,% +,'*($& #$ $')! ?,%"! '$ +$#$ )*(*!% / )%,/, #$ "!#$%! ,/ $( "$/,% #$'+$%#**,. C,", (! #$?,%"!*/ ,*$%/! $( #*'$>,& $/),/$' #$$ $/,/)%!%'$ #*"$/'*,/$' $ $/$%$/ $( "!=,% ","$/), #$ */$%*! +,'*($.

I=

 2

=

 2


4 3

= 2 + '2

−  2  ( 1)

I=

I=

12

=  2 −  2

'2

'

b ⋅ h 3

2 ⋅ (2') 3

⋅ ⋅(

12

 2 −  2 )3

22

23

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL I=

4

I=

4

3

3

⋅⋅

⋅

( 2

−  2 )3

 2 ⋅ ( 2

−  2 )3

D$%*;!/#, (! */$%*! $/ ?/*/ #$ -:

 1 [ 2 2 2 3 ] −21  [ 2 I = ⋅  ⋅  ⋅ ( −  )  ⋅ {  ⋅ (3 ⋅ ( 2 −  2 ) 2 ) ⋅ ( −2) ] +[( 2 −  2 )3 ⋅ (2) ] } 3 2  4

S*"+(*@!/#, (! $-+%$'*/:

I =

4 3

{ [  ⋅ (3 ⋅ ( −  2

⋅

2

) ) ⋅ ( −2) ] +[( 2 −  2 )3 ⋅ (2) ]

2 2

}

2 ⋅  2 ⋅ ( 2 −  2 )3

A,%! '$ *!(! ! $%, (! $-+%$'*/ #$%*;!#!& $'), ,/ $( @/ #$ $/,/)%!% $( +/), %)*,& , '$! +!%! "!-*"*!% (! */$%*!:

I =

4 3

⋅

{

+ ( 2 −  2 )3 ⋅ (2) } =0 2 2 2 3 2 ⋅  ⋅ ( −  )

 2 ⋅ (3 ⋅ ( 2 −  2 ) 2 ) ⋅ ( −2)

S*"+(*@!/#, (! $-+%$'*/:

I   = −  2 ⋅ (3 ⋅ ( 2 I 

−  2 ) 2 ) + ( 2 −  2 )3 = 0

= −3 2 + ( 2 −  2 ) = 0  2

= 4 2

 =

 2

∴ b = 


UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL R$$"+(!!/#, - $/ $!*/ B1:

'

=

'=

2



−

 2 4

3 2 ⋅  4

' =  ⋅

3 4

' = 0/  h = 2'

A,%! ,",

$/),/$':

h = 1%3

 )!"*/ ,",   R:

h b

∴

= 1%3

Toda :e- ue se asume una escuadra para el dise#o de una :ia se debe procurar ue la altura sea 1.@3

3.". I(% C$MP+E%T(% 3.".1. ias refor-adas lateralmente con per?les de acero

FI+*( 3.>


2!

2"


1

2 'a$ra

'a$ra

($r%!s

($r%!s

h

h

(la%&has

b

b

R$?.: E(!,%!*/ C!/#, (!' !%!' $ !)
e



14XX

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18XX

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116



132

N, $' ,/;$/*$/)$ '!% "!=,%$' $'+$',%$' #$ +(!/!& #$*#, ! ' "!=,% +$', +%,+*,. Principio9 4La de%or"aci+n vertical de a"&os "ateriales de&e ser la "is"a5 .


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UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL C!/#, (!' ;*!' #$ "!#$%! '$ %$?$%!/ +,% "$#*, #$ +$%@($' #$ !$%, #*'+$'),' (!)$%!("$/)$& !% $ )$/$% $/ $/)! +!%! $?$),' #$ ((,& (,' #*')*/),' "#(,' #$ $(!')**#!#& #$( !$%, E ! = #$ (! "!#$%! E ". !, (! *+)$'*' #$ $ )!/), (,' +$%@($' #$ !$%, ,", (! ;*! #$ "!#$%! $-+$%*"$/)!/ (! "*'"! #$?,%"!*/ ;$%)*!(& $'), ,%%$ '*$"+%$ = !/#, $( $($"$/), #$ /*/ B+$%/, $')$ !#$!#!"$/)$ !+%$)!#,. E/),/$' '**$/#, $( +%*/*+*,& = +!%! /! ;*! '*"+($"$/)$ !+,=!#! ,/ /! !%!  /*?,%"$"$/)$ #*')%**#! '$ )*$/$:

 mad

=

5 ⋅  m ⋅ $4 3/4 ⋅  m ⋅ I m

F($! +!%! (! "!#$%!:

 ac

=

5 ⋅  a ⋅ $4 3/4 ⋅  a ⋅ I a

F($! +!%! $( !$%,: E/),/$' +,% $( +%*/*+*,:

 mad

=  ac

E/),/$':

m  m ⋅ Im

=

a  a ⋅ Ia

m a

=

 m ⋅ Im  a ⋅ Ia

 !O!$

= m + a

& #,/#$

3.".2 ias acopladas mediante cu#a ;ori-ontal de madera L! @%! 3.7. "$')%! $( !,+(!"*$/), #$ 2 ;*!' "$#*!/)$ / %+, #$ >! +$%/,. E'),' !,+(!"*$/),' '$ )*(*!/ $'+$*!("$/)$ $/ (! ,/')%*/ #$


2@

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL +$/)$'. C,/ $( !,+(!"*$/), '$ +%$)$/#$ ,/')%*% %!/#$' !'!' #$ !()%!  ,"+%$/#*#!' $/)%$ 60 " = 80 ": 6080 ".

FI+*( 3.@

&

a

"U#$

h 2

T2

!

σa

%

h

T1 T

h 2

'ERNO

b

R$?.: E(!,%!*/

t⇔

h 6cm7 12 - 20

.

d ≥ 5 ⋅ t.

e⇔

h 6cm7 15 - 20

≥ 1" .

φ ≅

b 6cm7 10

E( $')#*, #$ $'),' !,+(!"*$/),' /, ,$#$$ ! #$'!%%,((,' )$%*,' B)$,%$"!'& $).& E'),' ;!(,%$' %$?$%$/*!($' !/ '*#, #$)$%"*/!#,' $-+$%*"$/)!("$/)$ BN,%"! A($"!/! DIN L! '$+!%!*/ $ '$ #$! +!%! +$%"*)*% !*%$!*/ $/)%$ (!' ;*!' $;*)!/#, #$ $')! ?,%"! (! +)%$?!*/ #$ $((!'& '*/ $"!%, #$$ +%,$#$%'$ ! ' "!/)$/*"*$/), = (*"+*$! !/#, '$! /$$'!%*,. L! "!#$%! #$ (! >! #$$ '$% +,% (, "$/,' #$( "*'", %+, $ (! "!#$%! #$ (!' ;*!' = $( !$%, #$( +$%/, /, #$$ '$% ,%%!#,. A/)$ (! !*/ #$ (!' !%!'& (!' ;*!' $ */)$%;*$/$/ $/ $( !,+(!"*$/), )*$/#$/ ! #$'(*!%'$ (!' /!' %$'+$), ! (!' ,)%!'. E/),/$' '$ ,%**/! (! ?$%! T 1 #$ !+(!')!"*$/), ',%$ (! +$/$)%!*/ #$ (! >! $/ (! "!#$%!.

!1

= σ a ⋅ b ⋅ t

D,/#$: !  E'?$%, #$ !+(!')!"*$/), #$ (! "!#$%! $/ (! >!& B30 K" 2  50 K"2. C!/#, '$ !+%$)!/ (,' +$%/,' '$ $/$%!/ (!' ?$%!' T2 ',%$ (! !$! #$ (!' >!'& $-+$%*"$/)!("$/)$ '$ ! #$)$%"*/!#, $ T 2 #$+$/#$ #$( #*"$)%, B  

#$( +$%/,:



= µ ⋅  s ⋅  8 . ⇔ µ ⋅

!2

π ⋅ φ 2 4

⋅  s

µ = (05 - 0*)

.

A/)$ (! !*/ #$ !%!' (,' +$%/,' +%$'*,/!/ ',%$ $( $, $ '$ ! $, $/ (! "!#$%! +!%! */)%,#*% (,' +$%/,'& $') +%$'*/ $')! %$+%$'$/)!#! +,% T 3. !3

= (150 - 1%0) ⋅ φ 2 .

9onde φ en cm

E/),/$' (! !+!*#!# #$ !%! B#$ %$'*')$/*! #$( %+, >!+$%/, '$%: TT1T2T3 E/ $')! '"! T1 $' #,"*/!/)$ = "!' ;$$' ',(!"$/)$ '$ ),"! ')$& #$!/#, T 2 = T3 ,", ?!),%$' #$ '$%*#!#. A,%! #$)$%"*/!%$",' $( /<"$%, #$ >!':

FI+*( 3.A

h 2

h h 2

b

R$?.: E(!,%!*/

?=

I c@ ( omento de ;ne=c;a de toda la esca)  (omento estt;co)

b ⋅ h 3 ?= b ⋅

12 h h

⋅

2

= ⋅h 3

2 4

C,/ $')$ ;!(,% $' +,'*($ !((!% (! ?$%! ,%*,/)!( $ ,%**/! $( #$'(*!"*$/), $/)%$ ;*!':


2A

2B

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL H=

 A ?

E/),/$' $( /<"$%, #$ >!' '$%: n ≅

H !

E' ,/;$/*$/)$& +!%! $')!% #$( (!#, #$ (! '$%*#!# '')*)*% T +,% T 1. F*/!("$/)$ $/ $( +/), "$#*, $/)%$ 2 >!' !#=!$/)$' '$ *!% / +$%/,.

E8emplo 1: E/,/)%!% (! $'!#%! #$ /! ;*! #$ 6.5 "$)%,' #$ (,/*)#& $ '$ $/$/)%! '*"+($"$/)$ !+,=!#!& = ',+,%)! /! !%! /*?,%"$"$/)$ #*')%**#! #$ 0.3 ),/$(!#!' +,% "$)%,. E( $'$"! $' $( '**$/)$:

, = -*. t/#

A

0 )*+#

S$ #$$ $($*% $( %+, !( !( +$%)$/$$ (! "!#$%! ! )*(*!% $/ $')$ !', '$ '!% "!#$%! #$( GRUO A& $ '$% $( ALMENDRILLO.



adσ 

210 K"2 ad#

15 K"2

E •

95000 K"2

G%+, A BA("$/#%*((,

!%! !((!% (! !%! #$*#, !( +$', +%,+*, '$ #$$ !'"*% (! !'$ = (! !()%! #$ (! '$*/ #$ (! "!#$%! +!%! !'"*% /! '$*/ !+%,-*"!#! '$ #$$ %$%%*% ! (!' '**$/)$' $!*,/$':

h

= 1%3 ⋅ b

•

adσ 

= ?

•

D,/#$ (! +%*"$%! $!*/ $' (! %$(!*/ #$ $'!#%! +)*"!& = (! '$/#! $!*/ $' (! $!*/ #$ Q$-*/& #,/#$ M $' $( ","$/), +,% !%! ;*;! = Y $' $( "#(, #$ (! '$*/& $/),/$':

adσ 

=

 ?

=

 b ⋅ h 2

=

 b ⋅ h 2

 S')*)=$/#, (! $( ;!(,% #$ (! !()%! #$ (! $'#!%! +)*"!:

adσ 

=

* b ⋅ (1%3 ⋅ b)

2

=

2⋅ b 3

E/),/$':

b = 3

2⋅ adσ 

A,%! '$ !((! $( ","$/), +%,#*#, +,% (! !%! ;*;!:


3


=

C ! ⋅ $2 /

300 ⋅ *52 = /

= 15/43/ B ⋅ m

$%, !#$"' '$ #$$ !$% */*#*% $( ,$@*$/)$ #$ '$%*#!# ! Q$-*/ B'$ ),"!% $( ;!(,% #$ 2.E/),/$' (! !'$ '$%:

b =

3

2 ⋅ 15/43/ 210

= 1445cm

2

h

= 1%3 ⋅ 1445 = 25cm

$%, ,", +,% (, $/$%!( (! ,"$%*!(*!*/ #$ (! "!#$%! '$ %$!(*! $/ +(!#!'& '$ ;$ +,% ,/;$/*$/)$ %$#,/#$!% (!' #*"$/'*,/$' #$ (! '$*/& = !#$"' !"$/)!%(! / +,, #$*#, ! $ /, '$ )," $/ $/)! $( +$', +%,+*,:

ESCUADR1A:

 15 "

E( +$', +%,+*, '$%:

P 8

= γ ⋅ b ⋅ h

+  800 K" 3 . 0.15 " . 0.25 "  30 K"

C! L! !%! ),)!( '$%: C T  330 K"

L!' %$!*,/$' '$%/:  

=

⋅$ 2


=  + P8

31

32


 

=

*50 ⋅ *5 2

= 10%2 5

B

  = 10%2 5 B

L,' $'?$%,' */)$%/,' '$%/ (,' $ '$ +%$'$/)!/ $/ $( '**$/)$ #*!%!"! $( ","$/), "-*", '$ !((! ,/:

 A

=

C ! ⋅ $2 /

=

330 ⋅ *5 2 /

= 1%42 /1 B ⋅ m

Diarama de esfuer-os internos9 , = -*. t/#

(" A

0 )*+#

1-2*+ 3

1-2*+ 3

1-2*+ 3 C6RTA7TES

.*2+#

1-2*+ 3 '#ax=142*51 3*#* '6'E7T6S

x a # '

+ 

F)EI7N 9


=

 ⋅  ma b ⋅ h 2


=

+ 

 ⋅ 1%42/1

= 111 54

2

15 ⋅ 25

B & cm 2

C,", $')$ ;!(,% $' "$/,% !( !#"*'*($& $/),/$' "+($.

E( ,$@*$/)$ #$ '$%*#!# ! (! Q$-*/ '$%:

C,e@ 

σ 

= ad

σ 

=

210 11154

= 1//

E')$ ,$@*$/)$ $' "= !,& #$$ '!(*% "!=,% , *!( ! 2& $/),/$' '$ ','+$! $ '$ #$$% !"*!% #$ $'!#%!& +$%, +,% %!,/$' !!#"*!' '$ ,/)*/!%! $( $$%**,. C$*TE9

#

3  ma

= ⋅

2 b ⋅ h

τ=

3 ⋅ 10%2 5 2 ⋅ 15 ⋅ 25

= 42D

B & cm 2

C,", $')$ ;!(,% $' "$/,% !( !#"*'*($& $/),/$' "+($. E( ,$@*$/)$ #$ '$%*#!# !( ,%)$ '$%:

C,e@ τ

=

τ = 15 = 350 τ 42D

ad

E')$ ,$@*$/)$ $' / ;!(,% !$+)!($. DEF$*M(CI$N9 L! #$?,%"!*/ !#"*'*($ '$%9 $ (cm)



ad

2%5

=

50 2%5

= 23

 L! Q$! $ +%,#$ (! !%! '$%:


cm

33

3!


 =

5 ⋅  ⋅ l4 3/4 ⋅  ⋅ I

5 ⋅ 33 ⋅ 50 4

=

3/4 ⋅ D5000 ⋅

15 ⋅ 253

= 413

cm

12

∴ CAMBIAR ESCUADRIA! C,", $')$ ;!(,% $' "!=,% !( !#"*'*($& $/),/$' ?!((!& L,' )%$' ?$/"$/,' BQ$-*/& ,%)$ = #$?,%"!*/ /, ',/ !*'(!#,'& '$ +%$'$/)!/ '*"()/$!"$/)$. E/ $/$%!( $/ (!' "!#$%!' (! #$?,%"!*/ $' $( ?$/"$/, "' +$(*%,',& "!' $ (! Q$-*/& "!' $ $( ,%)$. ,% $', '$ $-*$ $/ (!' "!#$%!' / ,$@*$/)$ #$ '$%*#!# +!%! (! #$?,%"!*/ $/)%$ 1.5 ! 2. C,", (! $'!#%! !'"*#! $' */'@*$/)$: AFINAMIENTO

!%! $( !@/!"*$/), '$ ;! !>!#*$/#, #$ +(!#! $/

+(!#!.

 15 "

ESCUADR1A:

 35 " E( +$', +%,+*, '$%:

= γ ⋅ b ⋅ h

P 8

+  800 K" 3 . 0.15 " . 0.35 "  42 K" L! !%! ),)!( '$%:

C!

=  + P8

C T  342 K" DEF$*M(CI$N 9 L! Q$! $ +%,#$ (! !%! '$%:

f =

5 ⋅ q ⋅ l 4 384 ⋅ E ⋅ I

=

5 ⋅ 342 ⋅ *50 4 3/4 ⋅ D5000 ⋅

15 ⋅ 353

= 15*

cm

12

C,", $')$ ;!(,% $' "$/,% !( !#"*'*($& $/),/$' "+($. DISEÑO EN ACERO  MADERA

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL E( ,$@*$/)$ #$ '$%*#!# ! (! #$?,%"!*/ '$%:

C.Seg 

=

ad 



=

23 15

= 151

E')$ ;!(,% #$ ,$@*$/)$ #$ '$%*#!# ! (! #$?,%"!*/ $/)%! $/ $( %!/, %$,"$/#!#, #$ 1.5 ! 2& +,% (, )!/), (! $'!#%! !'"*#! "+($. Nota.J L! #$?,%"!*/ ,*$%/! $( #*'$>, B$' $( $?$), "' #$'?!;,%!($ +!%! "!#$%!'. L,' ,$@*$/)$' #$ '$%*#!# '*%;$/ +!%! !'$%!% (! $')%)%! !/)$ !%!' $ /, *$'$/ '*#, ,/'*#$%!#!'& , !(/,' #$?$),' #$ (! "!#$%! $ '$ ;! ! $"+($!%. O)%! !()$%/!)*;! #$( $$%**, !/)$%*,% *$'$ '*#, ",#*@!% (!' ,/#**,/$' #$ !+,=,& ,", +,% $$"+(, $/ ;$ #$ '$% '*"+($"$/)$ !+,=!#,& $ ?$'$ $"+,)%!#,$"+,)%!#, +!%! !' #*'"*/*% (! #$?,%"!*/.


3"

3>


E8emplo 2: S$ #*'+,/$ #$ "!#$%! #$( %+, A +!%! ,/')%*% /! ;*! #$ +$/)$& +,% $( +$/)$ )%!/'*)! $( )%$/ $ '$ ,'$%;! $/ (! @%!. D$)$%"*/$ (! $'!#%! #$ (! ;*!. E( $'$"! $' $( '**$/)$:

-2 t

-2 t (" A

0

1+ 8#9

)- 8#9

S$ !'"*% (,' '**$/)$' #!),' #$( GRUO A.

adσ 

210 K"2 ad# o

15 K"2

G%+, A

95000 K"2

E

!%! +%$#*"$/'*,/!% (! '$*/ B(, $-+(*!#, $/ $( !/)$%*,% $$"+(,:

2⋅

b = 3

adσ 

A,%! '$ !((! $( ","$/), +%,#*#, +,% (! !%! ;*;!& +!%! $'), '$ *! (! !%! $/ (! +,'**/ "' #$'?!;,%!($ B!/(*'*' #$ (/$! #$ */Q$/*!:

-*2 t

-*2 t

A

0

2*2+#

 = P⋅a D$ (,' ?,%"(!%*,' #$ (,' !/$-,' #$( !+*)(, 3:


= 200 ⋅ 225 = 450 B ⋅ m

3@

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL $%, !#$"' '$ #$$ !$% */*#*% $( ,$@*$/)$ #$ '$%*#!# ! Q$-*/ B'$ ),"!% $( ;!(,% #$ 2.E/),/$' (! !'$ '$%:

b =

3

2 ⋅ 45000 210

= D50cm

2

h = 1%3 ⋅ D50 = 1*435cm $%, ,", +,% (, $/$%!( (! ,"$%*!(*!*/ #$ (! "!#$%! '$ %$!(*! $/ +(!#!'& '$ ;$ +,% ,/;$/*$/)$ %$#,/#$!% (!' #*"$/'*,/$' #$ (! '$*/& = !#$"' !"$/)!%(! / +,, #$*#, ! $ /, '$ )," $/ $/)! $( +$', +%,+*,:

 12.5 " ESCUADR1A:

 25 " E( +$', +%,+*, '$%: +  750 K" 3 . 0.125 " . 0.25 "  23.44 K"

+25 K"



E%T/TIC(9 D$$ +,'**,/!%'$ $( )%$/ #$ )!( "!/$%! $ $'! +,'**/ $/$%$ (,' $'?$%,' "-*",' BF($-*/& ,%)!/)$ = #$?,%"!*/.S$ ,(,!/ (!' #,' !%!' '*")%*!' %$'+$), $( $/)%, #$ (! ;*! B!/(*'*' #$ (/$! #$ */Q$/*!. F)EI7N 9 L! '$*/ %)*! +!%! $( ","$/), "-*", $' $( $/)%, #$( )%!", +,% )!/), #$$ '*)!%'$ $( )%$/ #$ "!/$%! ,"+!%)*#! %$'+$), !( $/)%,.

-*2 t

-*2 t

A

0

x 2+ 3

∑ 



= 0 ⇒ ( 225 + 3%5) ⋅ 200 −  ⋅  + 150 ⋅ 3 = 0

= 2%5B ⇒  =  = 2%5B


2+ 3

3A


555.46 K Z "

= 2%5 ⋅  - 25 ⋅  0 <  < 225



2

0 K Z"

2

562.50 K Z "

= 2%5 ⋅  - 25 ⋅  225 <  < 3

+ 

=

+ 

=



2

2

− 200 ⋅ ( x − 225 )

555.46 K Z "

 ⋅  ma b ⋅ h

2

* ⋅ 5*250 125 ⋅ 252

= 432

< adσ  ⇒ IE

B&cm 2

C$*TE9 L! '$*/ %)*! +!%! $( ,%)!/)$ "-*", $' $/ $( $-)%$", #$( )%!", B!(*$% $-)%$",& +,% )!/), $( )%$/ #$ !%!' #$$ '*)!%'$:

-*2 t

-*2 t

A

0

42+ 3

∑



= 0 ⇒ 15 ⋅ 200 + 150 ⋅ 3 −  ⋅  = 0

 = 125B * ⋅  - * ⋅ 200 - 45 ⋅ 200 - 3 ⋅ 150 = 0


12+ 3

3B

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL 

#

= 425B ⇒  A

= 3⋅

 ma

3

τ =

2 b ⋅ h

⋅

425

= 204

2 125 ⋅ 25

[

B&cm 2

< adτ ⇒ IE

DEF$*M(CI7N9 L! Q$! $ +%,#$ (! !%! '$%:

- *2 t

-*2 t

A

 1

=

5 ⋅  ⋅ $4 3/4 ⋅  ⋅ I

5 ⋅ 025 ⋅ ( *00)

=

3/4 ⋅ D5000 ⋅

-*2

0

A

0

t

A

4

125 ⋅ 25 3

= 02% cm

12

  2

 !

=

P⋅a 24 ⋅  ⋅ I

(3 ⋅ $2

200 ⋅ 225

− 4⋅a2) =

24 ⋅ D5000 ⋅

125 ⋅ 25

3

⋅ (3 ⋅ *00 2 − 4 ⋅ 225 2 ) = 10* cm

12

=  1 +  2 = 02% + 10* = 133 cm

ad =

$(cm) 250

=

*00 250

= 24 cm ⇒  ! < ad ⇒ IE

C$EFICIENTE% DE %E+*ID(D =$)+*(G9 F($-*/:

C,e@ 

=

adσ 

σ 

=

210 432

= 4/*

C,%)!/)$:


-*2 t

0

!


C,e@τ

=

adτ

τ

=

15 204

= %35

D$?,%"!*/

C,e@ f =

ad f

f

=

240 133

= 1/1

L! $'!#%! $/,/)%!#! '$ $/$/)%! #$/)%, (, !$+)!($ #$/)%, #$( "!%, #$ (! '$%*#!# B+$%, $' antieconómico.

E8emplo 39 DINTE) DE ENT(N( Madera rupo9 4

'*./ )1%+*/+ Mam1/.!%+*a 7% (a7+*66/ 8amb/!% 7% "a+ga 2,-0 m

3*!%6 7% Ma7%+a

()z (*b+% = 2m 0 cm 2,0 m

E!+%ga / 3%.ca./ 4m**m/ 0 cm5

A #*?$%$/*! #$ (,' !/)$%*,%$' $$%**,' !,%! (! !%! /, $')! #!#!& #$$ $( */$/*$%, +%,%!% $')*"!% (! !%! ,/ (! "!=,% +%$*'*/ +,'*($. D$ /!#! '$%;*% !(*$% !@/!"*$/), !%*)")*, , !($%!*, '* (! !%! /, ! '*#, !#$!#!"$/)$ $')*"!#!. E-*')$/ #,' +,'**(*#!#$' +!%! $')*"!% (! !%!:


!1


2,0m 1m

α

α

9 2,0m

S$ ,/'*#$%!% $( $?$), !%, ,/:

50° < α < 5°

C((, #$ :

tan( 0F ) =

h 230 & 2

C,/ / α  60\:

h

= 1DDm ≅ 20m

C((, #$( %$!:

 1 ⋅115 ⋅ 2    2 

 = 2

 = 23m 2 C((, #$ -:

2 115

=

1 

 = 05%5m !%! $( (!#%*((,:


!2


G $ad=;llos ≅ 130

Peso 8 & cada $ad=;llo = 25B@

Peso total de $ad=;llo = 130 ⋅ 25 ⋅ 23 = %4%5B@ ≅ %4/B@

!%! $( ",%)$%,:

ol
ol
Peso es8ec;;co del mo=te=o = 2200

B@ m3

Peso total del mo=te=o = 01/ ⋅ 2200 = 3DB@

P!

= Plad + Pmo=t = %4/ + 3D* = 1144B@

Peso total9 A,%!& #*')%*=$/#, $( $', ),)!( $/ (! (,/*)#: !

=

P! $

=

1144 230

= 4D%4

B m

A,%!& (, $ ?!()! $' !'"*% (! $'!#%! #$( #*/)$(: E/),/$':

b = 3

2⋅ adσ 


!3

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL A,%! '$ !((! $( ","$/), +%,#*#, +,% (! ',%$!%!:



=

C ! ⋅ $2 /

4D%40 ⋅ 23 2

=

/

= 32/D1 B ⋅ m

$%, !#$"' '$ #$$ !$% */*#*% $( ,$@*$/)$ #$ '$%*#!# ! Q$-*/ B'$ ),"!% $( ;!(,% #$ 2.E/),/$' (! !'$ '$%:

b =

3

2 ⋅ 32/D1 150

= D5%cm

2

h

= 1%3 ⋅ D5% = 155cm

$%, ,", +,% (, $/$%!( (! ,"$%*!(*!*/ #$ (! "!#$%! '$ %$!(*! $/ +(!#!'& '$ ;$ +,% ,/;$/*$/)$ %$#,/#$!% (!' #*"$/'*,/$' #$ (! '$*/& = !#$"' !"$/)!%(! / +,, #$*#, ! $ /, '$ )," $/ $/)! $( +$', +%,+*,:

 10 "

ESCUADR1A:

$', +%,+*, #$ (! "!#$%!:

Pmad

= 010 ⋅ 01%5 ⋅ %00 = 1225

 !otal

B m

= 4D%4 + 1225 = 50D5

B@ m

Cara total9 F)EC=(9 L! Q$! $ +%,#$ (! !%! '$%:

f =

5 ⋅ q ⋅ L4 384 ⋅ E ⋅ I

=

5 ⋅ 50D% ⋅ 230 4 3/4 ⋅ %5000 ⋅


10 ⋅ 1%53 12

= 052

cm

!!

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL C,", $')$ ;!(,% $' "$/,% !( !#"*'*($& $/),/$' "+($. E( ,$@*$/)$ #$ '$%*#!# ! (! #$?,%"!*/ '$%:

C,e@  =

ad



=

0D2 052

= 1%%

E')$ ;!(,% #$ ,$@*$/)$ #$ '$%*#!# ! (! #$?,%"!*/ $/)%! $/ $( %!/, %$,"$/#!#, #$ 1.5 ! 2& +,% (, )!/), (! $'!#%! !'"*#! "+($ B'$ +$#$ !@/!% !/ "'& $/ '! #$ ba8ar los costos. DET())E C$N%T*+CTI$9 ,% %!,/$' ,/')%)*;!' : !'$ #$ #*/)$(  7.5" ,% %!,/$' )$%*!'

: !'$ #$ #*/)$(  5"

%,?/#*#!# #$ (!;,

: +%,?.  18 "

1-,5

"($VO

-,5

E8emplo !: D$)$%"*/!% (! $'!#%! #$ "!#$%! +!%! (! ;*! A& = #$)$%"*/!% '* ,%%$'+,/#$ %$?,%!% (! $'!#%! ,/ +$%@($' #$ !$%,. E/ $( '*)*, (,' )%,/,' ',/ ;$/$' = +,% ,/'**$/)$ #$ +,, #*"$)%,.

, =1 t/#

A

0 2*- #


UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL S$ #$$ $($*% $( %+, !( !( +$%)$/$$ (! "!#$%! ! )*(*!% $/ $')$ !', '$ '!% "!#$%! #$( GRUO A& $ '$% $( ALMENDRILLO.

adσ 

210 K"2 ad# •

15 K"2

G%+, A BA("$/#%*((,

E

95000 K"2

!%! !((!% (! !%! #$*#, !( +$', +%,+*, '$ #$$ !'"*% (! !'$ = (! !()%! #$ (! '$*/ #$ (! "!#$%!& (! "-*"! $'!#%! $ '$ +$#$ $/,/)%!% $/ / ,'$ ,;$/:

 17.5 " ESCUADR1A:

 30 "

E( +$', +%,+*, '$%:

P 8

= γ ⋅ b ⋅ h

+  800 K"3 . 0.175 " . 0.30 " ≈ 42 K" L! !%! ),)!( '$% B'*/ !$%,:

!

=  + P8

 T  1000 K" 42 K"  1042 K" A,%! '$ #$'$! '!$% !/), #$ (! !%! ),)!( +$#$ !'"*% (! $'!#%! #$ "!#$%!: DEF$*M(CI$N9 L! #$?,%"!*/ !#"*'*($ '$%9 DISEÑO EN ACERO  MADERA

!"

!>


$ (cm)



ad

2%5

=

%00 2%5

= 254

cm

 E( ,$@*$/)$ #$ '$%*#!# #$ #$?,%"!*/ $' #$ 1.5 ! 2& +,% (, '$ !'"$ / ;!(,% #$ 1.6& +,% (, )!/),:

C,e@ f =

ad



ad

⇒  =

C,e@ f

=

254 1*

= 15D cm

L! Q$! $ +%,#$ (! !%! '$%:

 m

=

5 ⋅  ⋅ $4 3/4 ⋅  m ⋅ I

= 15D =

5 ⋅  m ⋅ %00 4 3/4 ⋅ D5000 ⋅

∴

 T ] "

1%5 ⋅ 303

⇒  m = 1D0 B&cm

12

REFORYAR



! 1042  190  852 K" N$$'!%*!"$/)$ #$$ %$?,%!%'$ (! $'!#%!& +$' $((! ',(! /, $' !+! #$ %$'*')*% ! (! !%! ),)!(. C,/)*/!%$",' $( $$%**, ',(!"$/)$ +,% ",)*;,' !!#"*,'& +$' $ $' )!/ %!/#$ (! !%! $ #$$ !'"*% $( !$%, $/ +%,+,%*/ ! (! "!#$%! B%$(!*/ !+%,-*"!#! #$ 4 ! 1 $ '$%! +%$?$%*($ ,/')%*% (! ;*! #$ ,)%, "!)$%*!( BC,/%$), +%, , !$%, +%,. G$/$%!("$/)$ / $/ %$?$%, #$ !$%, #$$ %*% ,", "-*", $( 50 #$ (! !%! ),)!(. E($*",' $( ', #$ +(!/!' +!%! $( %$?$%,:


!@


'a$ra ($r%!s

.

(la%&has

12*+

e = 1 " = 04 cm 4

A,%! '$ #$$ $($*% $'+$',% #$ +(!/!: E( ","$/), #$ */$%*! $' !?$)!#, +,% !#! /! #$ (!' +(!/!' #$ !$%,.

 a

=

5 ⋅  a ⋅ $4 3/4 ⋅  a ⋅ I

5 ⋅ /52 ⋅ %00 4

= 15D =

3/4 ⋅ 21 × 10 ⋅ 2 ⋅

04 ⋅ h a

3

⇒ h a = 53cm > h m = 30cm

12

L! !()%! #$( !$%, '+$%! ! (! !()%! #$ (! "!#$%! $ *"+,'**(*)! , +,% (, "$/,' #*@()! $( +%,$', ,/')%)*;,& !#$"' #$ $ ),#!;! /, $')! ,/'*#$%!#, $( +$', #$( !$%,. γ CO

= %/50 B&m 3

+  2. 0.0064 " . 0.53 ". 7850 K"3 = 53.25 K"  TOTAL≈ 1100 K" E/),/$' /,' ;$",' $/ (! /$$'*#!# #$ !"*!% #$ $'!#%! #$ (! ;*! #$ "!#$%!& +!%! $', #*%$",' */**!("$/)$ $ (! "!#$%! ',+,%)!% $( 50 #$ (! !/)$%*,% !%! ),)!( = ,/ $')! !+%,-*"!*/ '!!%$",' (,' ;!(,%$' #$ (! !'$ = (! !()%! #$ (! ;*!.

 m

=

5 ⋅  m ⋅ $4 3/4 ⋅  m ⋅ I

= 15D =


5 ⋅ 550 ⋅ %00 4 b ⋅ h a 3/4 ⋅ D5000 ⋅ 12

3

⇒

b ⋅ h 3 12

= 113/3424 cm 4

!A

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL S')*)=$/#, (! %$(!*/ #$ $'!#%! +)*"!: b ⋅ (1%3 ⋅ b) 3

= 113/3424 cm 4 ⇒ b = 22** cm

12

E/),/$':

 25 "

ESCUADR1A:

+  800 K"3 . 0.25 " . 0.45 "  90 K" L! !%! ),)!( '$% B'*/ !$%,:

!

=  + P8

 T  1000 K" 90 K"  1090 K"

L! Q$! $ +%,#$ (! !%! '$%:

 m

=

5 ⋅  ⋅ $4 3/4 ⋅  m ⋅ I

= 15D =

5 ⋅  m ⋅ %00 4 3/4 ⋅ D5000 ⋅

∴

 T ] "

25 ⋅ 453

⇒  m = D1% B&cm

12

REFORYAR



! 1090  917  173 K" !%! (! $'!#%! #$ (! !'! (! "!#$%! %$'*')$ $( 84.12 #$ (! !%! ),)!( '*/ ),"!% $/ $/)! ),#!;! $( +$', #$( !$%,.

 a

=

5 ⋅  a ⋅ $4 3/4 ⋅  a ⋅ I

5 ⋅115 ⋅1%3 ⋅ %00 4

= 15D =

3/4 ⋅ 21× 10  ⋅ 2 ⋅


04 ⋅ h a 12

3

⇒ h a = 32%cm ⇒ sa= h a = 35cm

!B

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL E/ (! !/)$%*,% $!*/ '$ $')! "!=,%!/#, $/ / 15 (! !%! #$( !$%, ,/ ,$), #$ ),"!% $/ $/)! $( +$', +%,+*, #$( "*'",. A/$ (,' $($"$/),' #$( #$)!(($ ,/')%)*;, '$ $')#*!%/ #$ ?,%"! "' +%,?/#! $/ (,' +%-*",' !+)(,'& ! "!/$%! #$ */)%,#*/ '$ +%$'$/)! (,' #$)!(($' #$ /*/ #$ ;*! %$?,%!#!. S$ '!%/:

L,/*)# +$%/,  30 ". $%/,'

D*"$)%, +$%/,  ^

L! +(!/! #$ !$%, '$ $-)$/#$% /! #*')!/*! # ! !#! (!#, #$( $/)%, (/$! #$ (! ;*!& $')! #*')!/*! +$#$ !((!%'$ $-!)!"$/)$ #$ (! )$,%! #$ (!' #$?,%"!*,/$'& '*/ $"!%,& '$ )*$/$: d=

1  $  1  %00 

  = 

3  2  3  2

 = 11% ≅ 120 cm 

S$ +$#$ #$)$%"*/!% $-!)!"$/)$ $')! #*')!/*! +,% (! )$,%! #$ (!' #$?,%"!*,/$': D,/#$:

∂2' ⋅I⋅ 2 =  ∂ !%! (! ,/#**/ #$ !%!& $( ","$/), $/ ?/*/ #$ - '$%: =

⋅$⋅ 2

−

 ⋅ 2 2

E/),/$':

∂2'  ⋅ $ ⋅   ⋅ 2 − ⋅I⋅ 2 = 2 2 ∂ I/)$%!/#,:

∂'  ⋅ $ ⋅  2  ⋅  3 ⋅I⋅ = − + C1  4 * ∂


"


L$,: ⋅I⋅ ' =

 ⋅ $ ⋅ 3

−

12

 ⋅ 4 24

+ C1 ⋅  + C 2

!((!",' C1 = C2 ,/ (!' ,/#**,/$' #$ ,%#$: C20 C1

=−

 ⋅ $3 24

L! $!*/ $/$%!( #$ (! $(')*! '$%: ⋅I⋅' =

 ⋅ $ ⋅ 3 12

−

 ⋅ 4 24

−

 ⋅ $3 ⋅  24

A,%! '$ #$$ !((!% ! $ #*')!/*! - (! "!#$%! '$ #$?,%"! 1.59 ". !, (! !+(*!*/ #$ (! !%! ),)!(  TOTAL  1090 K". ; ;

,t =1-<- 3/# A

# & < + * 1

# & < + * 1

0

:=#

E/),/$' %$$"+(!!/#, $/ (! $!*/ #$ (! $(')*!: D5000 ⋅

25 ⋅ 45 3 12

0454 ⋅  4

⋅ (−15D) =

10D0 ⋅ %00 ⋅  3 12

−

10D0 ⋅  4 24

−

10D0 ⋅ %00 3 ⋅  24

− *35/3 ⋅  3 + 155%%D1**% ⋅  - 2/*%5/D/440 = 0


"1

UNIVERSIDAD JOSE CARLOS MARIATEGUI FACULTAD DE INGENIERIA CIVIL R$',(;*$/#, (! $!*/ +,(*/,"*!(:

D$ (!' !($' '$ #$'!%)!/ (!' #,' <()*"!' +,% '$% ',(*,/$' */,$%$/)$'. E/),/$' # '$% *!(: d

=

2

− 1

=

2

4%/55 - 22135 2

= 12/*

cm

U'!",' $( "!=,% $/)%$ $( !((!#, = $( ;!(,% %$?$%$/*!( #!#, !/)$%*,%"$/)$. # 128.6 _ 130 ".



L! '$+!%!*/ $/)%$ +$%/,' '$% #$ 10 ". E%5+EM( E%T*+CT+*()

" ( 1

 = 1.

.+ 

%ECCI$N T*(N%E*%()9


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