Memoria Diseño Edificio Encanto

MEMORIA DE DISEÑO ESTRUCTURAL ESTRUCTURAL MULTIFAMILIAR “EL ENCANTO” ING. JULIE MARCELA URIBE SERRANO

MEMORIA DE DISEÑO ESTRUCTURAL NSR-10

Noviembre de 2013

EDIFICIO MULTIFAMILIAR “EL ENCANTO” Dirección: DUITAMA – BOYAC

JULIE MARCELA URIBE SERRANO INGENIERO CIVIL ESPECIALISTA ESPECIALISTA EN ESTRUCTURAS M.P. M.P. 12021!1 120 21!11 1 B"C

Ingeniero Civil Mat. Profesional N° 15202191715 BYC Cel. 3212368817

MEMORIA DE DISEÑO ESTRUCTURAL ESTRUCTURAL MULTIFAMILIAR “EL ENCANTO” ING. JULIE MARCELA URIBE SERRANO

CONTENIDO Página

1.

GENERALIDADES.........................................................................................................3

2.

CRIT CRITER ERIO IOS S PA PARA EL DISE DISEÑO ÑO SISM SISMIC ICO O......................................................................4

3.

CARA CARACTE CTERIS RISTIC TICAS AS DE DE LOS LOS MAT MATERIAL ERIALES ES A EMPLEA EMPLEAR R..........................................4

4.

EVA EVALUA LUACIO CION DE DE CA CARGAS GAS..........................................................................................5

5.

DISEÑ ISEÑO O DE LAS LAS CO CORREA REAS..........................................................................................6

6.

CONFOR CONFORMA MACIO CION N DE DE LOS LOS ELEMEN ELEMENTO TOS S ESTR ESTRUCT UCTURA URALES LES.....................................7

7.

MODE MO DELA LACI CIÓN ÓN ESTR ESTRUC UCTU TURA RAL L....................................................................................8

8.

COM OM INA INACION CIONE ES DE CARGA.....................................................................................9

!.

AN"L AN"LISI ISIS S POR POR EL M#TOD M#TODO O DEL DEL ANAL ANALISI ISIS S DIN" DIN"MIC MICO O ............................................9

1$. DERIVAS......................................................................................................................10 11. DISE DISEÑO ÑO COL COLUM UMNA NAS S...................................................................................................1 

RESULTADOS EN EL DISEÑO DE COLUMNAS .........................................................1

12 12.. DISEÑ ISEÑO O VIG VIGAS............................................................................................................14 

RESULTADOS EN EL DISEÑO DE VIGAS ..................................................................14

13 13.. DISE DISEÑO ÑO DE LA PLAC PLACA A................................................................................................15 

RESULTADOS DE DISEÑO PARA LOS ELEMENTOS DE LA PLACA .......................16

14 14.. DISE DISEÑO ÑO CIME CIMENT NTA ACION CION...............................................................................................18 

VIGAS DE AMARRE.....................................................................................................18

15 15.. DISE DISEÑO ÑO DE DE LA ESCA ESCALE LERA RA........................................................................................0 16. ELEMEN ELEMENTO TOS S NO ESTRUC ESTRUCTUR TURAL ALES ES......................................................................... MUROS INTERIORES DE ALTURA TOTAL % MUROS &UE ENCIERRAN ESCALERAS........................................................................................................................ 



MURO DE FAC'ADA ...................................................................................................6



PARAPETO DE FAC'ADA..........................................................................................7



PLACA DE TAN&UES..................................................................................................9


MEMORIA DE DISEÑO ESTRUCTURAL MULTIFAMILIAR “EL ENCANTO” ING. JULIE MARCELA URIBE SERRANO

ANE(OS Anexo A. Diseño de Correas Metálicas Anexo B. Parámetros y Análisis de los Muros Anexo C. Diseño de los Muros



1. GENERALIDADES E! P"#$%&'# E('")&')"a! &#n'%*+!a !a &#n('")&&i,n -% )na E-ii&a&i,n &#n CINCO /5 +!an'a( -%('ina-a( a )n M)!'ia*i!ia" (#2"% %! L#'% )2i&a-# %n )i'a*a  B#$a&á. #-a !a &#n('")&&i,n (% )'i!ia"á %n )n (#!# )(# RESIENCIAL. E! +"#$%&'# (% )2i&a %n #na -% a*%naa ((*i&a A!'a -% a&)%"-# a !a n#"*a (i(*#""%(i('%n'% -% 010 NSR10. La %-ii&a&i,n (% +!an'%a %n %('")&')"a -% *a*+#('%"a E('")&')"a! &#n Ca:i-a- R%#"a-a )na &)2i%"'a (#+#"'a-a +#" &#""%a( *%'á!i&a( an&!a-a( a !a ;iga Cin'a -% C)!a'a $ +!a&a *a&ia %n -#( -i"%&&i#n%(. E! &,-ig# 2a(% %*+!%a-# +a"a %! aná!i(i( $ -i(%<# -% !a %('")&')"a %( !a N#"*a C#!#*2iana -% i(%<# $ C#n('")&&i,n Si(*# R%(i('%n'% -% 010 -% !a A(#&ia&i,n C#!#*2iana -% Ing%ni%"a S(*i&a AIS. L#( +"#g"a*a( )'i!ia-#( +a"a %! aná!i(i( $ -i(%<# -% !a %('")&')"a (#n EngSolutions RCB v8. y Ar!uimet c #n !#( &)a!%( (% #2'i%n% '#-# %! aná!i(i( %('")&')"a! -% !a %-ii&a&i,n =)% in&!)$% a&&i#n%( $ -%(+!aa*i%n'#( -% '#-#( !#( %!%*%n'#( -%! (i('%*a $ AUOCA +a"a !a +"%(%n'a&i,n -% !#( +!an#(. E('% in#"*% +"%(%n'a %(+%&i&a*%n'% !#( &á!&)!#( "%a!ia-#( +a"a &a-a )n# -% !#( %!%*%n'#( -% !a E-ii&a&i,n !#( "%()!'a-#( -% -i(%<# $ !#( +!an#( =)% (% %n'"%ga"an +a"a !a %>%&)&i,n -% !a #2"a.

2. CRITERIOS PARA EL DISEÑO SISMICO E! +"#$%&'# (% )2i&a"a %n )na #na -% a*%naa ((*i&a In'%"*%-ia -% a&)%"-# a !a NSR 10 !a %('")&')"a 'i%n% )n g"a-# -% -i(i+a&i,n -% %n%"ga ES $ ()( +a"á*%'"#( ((*i&#( (#n • • • •

A&%!%"a&i,n ?#"i#n'a! +i&# %%&'i:a Aa @ 0.0 ;%!#&i-a- ?#"i#n'a! +i&# %%&'i:a A: @ 0.5 C#%i&i%n'% -% i*+#"'an&ia I @ 1.0 P%"i! -%! ()%!# 

3. CARACTERISTICAS DE LOS MATERIALES A EMPLEAR La( (ig)i%n'%( (#n !a( %(+%&ii&a&i#n%( *ni*a( %('a2!%&i-a( +a"a !#( *a'%"ia!%( )'i!ia2!%( %n !a &#n('")&&i,n /a Pi%a( -% Ma*+#('%"a %n La-"i!!# P#"'an'% 30 /14.5&*  9&*  9&* &#n "%(i('%n&ia a !a &#*+"%(i,n -% 4.7 MPa a2(#"&i,n -% ag)a 9 *ái*a $ %n &)*+!i*%n'# &#n !a NC 4051 NC 4053. /2 M#"'%"# -% R%!!%n# %2% '%n%" )na "%(i('%n&ia a !a &#*+"%(i,n a !#( 8 -a( &" ig)a! # ()+%"i#" a 7.4 M+a %! &)a! (%"á )'i!ia-# %n +!a&a( -% &#n'"a+i(# &#!)*na( a+a'a( :iga( *)"#( $ +!a&a( -% %n'"%+i(#.



/& M#"'%"# -% P%ga %2% '%n%" )na "%(i('%n&ia a !a &#*+"%(i,n a !#( 8 -a( &" ig)a! # ()+%"i#" a 1.5 M+a i+# S (%gDn NSR10 .3.41 +a"a !a &#n('")&&i,n -% !a *a*+#('%"a. /- C#n&"%'# %2% '%n%" )na "%(i('%n&ia a !a &#*+"%(i,n a !#( 8 -a( &" ig)a! # ()+%"i#" a 1 M+a %! &)a! (%"á )'i!ia-# %n +!a&a( -% &#n'"a+i(# $ +!a&a( -% %n'"%+i(# L#( (#!a-#( -% !i*+i%a -%2%n '%n%" )na "%(i('%n&ia a !a &#*+"%(i,n -% 14 MPa. /% A&%"# -% "%)%"# %2% (%" &#"")ga-#. En ningDn &a(# %! a&%"# -% "%)%"# +)%-% '%n%" )n !*i'% -% !)%n&ia $ in%"i#" a 40 MPa. R%(i('%n&ia '#'a! * @ 10 MPa )'i!ia-a %n %! -i(%<#.

4. EVALUACION DE CARGAS P)*) +, -/+0 -+ ,/ +,++/ + C*+ R+*)- /+ 9/)* ,)/ /:9++/ )*:)/; C)*:) V<) R+/-+),; 1.8 FN*  (%gDn a2!a B.4..11 NSR10 C)*:) V<) C9=+*); 0.5 FN* C)*:) M9+*) R+/-+),; @ 4.6 FN*(%gDn a2!a B.3.4.31 NSR10 C)*:) M9+*) C9=+*); 1.8 FN* C)*:) V<) E/),+*)/; 3.0 FN*  C)*:) V<) -+ G*); 0.5 FN*

EngSolutions RCB v8." &#n:i%"'% &a"ga( :%"'i&a!%( (#2"% +an%!%( -% +i(# a)'#*á'i&a*%n'% %n &a"ga( (#2"% !a( :iga( $ *)"#( a-$a&%n'%( )(an-# !a( +"#+i%-a-%( a(igna-a( a !a( !#(a( %(+%(#" -i"%&&i,n -% a"*a-# &a"ga *)%"'a ()+%"i*+)%('a $ &a"ga :i:a. E! +"#g"a*a +"%(%n'a !a &a"ga *)%"'a '#'a! /+%(# +"#+i# -% !a !#(a *a( &a"ga ()+%"i*+)%('a / DL $ &a"ga :i:a / LL +a"a &a-a +i(# $ %! '#'a! -% !a %-ii&a&i,n $ -i2)>a a-%*á( +a"a &a-a :iga $ *)"# %('")&')"a! %! á"%a '"i2)'a"ia -% !#(a &#""%(+#n-i%n'%.

Cargas ara el !ise"o !e las Correas #et$li%as& 

Ca"ga ;i:a -% &)2i%"'a S%gDn 'a2!a B.4..1 -% !a NSR  10 +a"a &)2i%"'a( in&!ina-a( &#n +%n-i%n'%( *a$#"%( a 15 %( 0.5 FN* 



Ca"ga M)%"'a *a(a -% !a '%>a %( 13 Fg*  +a"a %('% +"#$%&'# (% )'i!ia"a )na &a"ga -% 30 Fg*  @ 0.3 FN* 


MEMORIA DE DISEÑO ESTRUCTURAL MULTIFAMILIAR “EL ENCANTO” ING. JULIE MARCELA URIBE SERRANO 

Ca"ga ;i:a -% G"ani# 0.5 FN* 



Ca"ga -% ;i%n'# (ig)i%n-# !a( "%&#*%n-a&i#n%( -% !a NSR  10 &a+i')!# B.6 $ &#n %! P"#&%-i*i%n'# Ana!'i&# (% 'i%n% P

=

qh( GCpf

−

GCpi ) B.6.5.1.. +a"a E-ii&i#( Ba>#(

En -#n-% qh

= 0.613 * kz * kzt * kd * V

kz =

V I

* I

0.70

kzt = 1.0 kd

2

Según NSR

− 10 B.6.5.7.2

= 0.85

= 17 m / s = 0.87

qh

= 0.613 * kz * kzt * kd * V

GCpf Barlovento GCpi

2

2

* I = 0.613 * 0.70 * 1.0 * 0.85 * 17 * 0.87 = 91.71 N / m

= −1 y − 0.18

2

Sotavento = −0.60

= ±0.18

P#" 'an'# Ba"!#:%n'# S#'a:%n'#

P& @ 108. N*  a &#*+"%(i,n P& @ 71.54 N*  a &#*+"%(i,n

S% )(a"á %! -i(%<# +a"a )na &#""%a =)% (#+#"'% &a"ga( -% :i%n'# a Ba"!#:%n'# $a =)% %( !a *á( &"'i&a -% !a( &a"ga( -% ;i%n'#. S%gDn NSR10 B.4.8.3.1 !a( &a"ga( -% g"ani# -%2%n '%n%"(% %n &)%n'a %n !a( "%gi#n%( -%! +a( &#n *á( -%  000 *%'"#( -% a!')"a (#2"% %! ni:%! -%! *a" &#*# %( %! &a(# -% )i'a*a. E('% :a!#" (%gDn B.4.8.3. +a"a &)2i%"'a( &#n )na in&!ina&i,n *a$#" a 15H +)%-% "%-)&i"(% a 0.5 FN* .

5. DISEÑO DE LAS CORREAS E! -i(%<# -% !a( C#""%a( (% %%&'), a '"a:( -%! (#'a"% -% &á!&)!# A"=)i*%' .0 '%ni%n-# %n &)%n'a !a( &a"ga( -% ;i%n'# Ca"ga *)%"'a $ &a"ga :i:a -% &)2i%"'aK &#*# (% *)%('"a %n !#( "%()!'a-#(.

6. CONFORMACION DE LOS ELEMENTOS ESTRUCTURALES Ingeniero Civil Mat. Profesional N° 15202191715 BYC Cel. 3212368817


C#n !#( an'%"i#"%( -a'#( -% %:a!)a&i,n -% &a"ga( $ &#n !a &#nig)"a&i,n (i&a -% !a E('")&')"a (% %(')-ia '"i-i*%n(i#na! *%n'% -% a&)%"-# a %('% aná!i(i( (% -i(%
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Pi(# 1 Ni:%!  1.00 /Ci*%n'a&i,n Pi(#  Ni:%!  0.00 /P"i*%" Pi(# Pi(# 3 Ni:%!  .45 /S%g)n-# Pi(# Pi(# 4 Ni:%!  4.90 /%"&%" Pi(# Pi(# 5 Ni:%!  7.35 /C)a"'# Pi(# Pi(# 6 Ni:%!  8.90 /)in'# Pi(# Pi(# 4 Ni:%!  1.35 /C)2i%"'a

7. MODELACIÓN ESTRUCTURAL



Una :% (% -i*%n(i#na !a %('")&')"a (% +"#&%-% a !a *#-%!a&i,n -% %('a %n %! (#'a"% RCB +a"a +#-%" "%a!ia" %! aná!i(i( &#n %! *'#-# -% !a )%"a E=)i:a!%n'% E('á'i&a %! *#-%!# -%2% (%" &a"ga-# -% a&)%"-# a !a %:a!)a&i,n -% &a"ga( *)%"'a( $ :i:a( .L#( %(+%&'"#( %!á('i&#( -% a&%!%"a&i#n%( $ :%!#&i-a-%( +a"a %! -i(%<# +"#+)%('# +#" !a n#"*a NSR10 (#n

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ig)"a 3. E(+%&'"# E!á('i&# -% ;%!#&i-a-%( /*( -% i(%<#



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8. COMINACIONES DE CARGA



A &#n'in)a&i,n (% *)%('"an !a( &a"ga( )'i!ia-a( %n %! RCB +a"a %! -i(%<# -% &#!)*na( $ :iga(

!. AN"LISIS POR EL M#TODO DE LA FUER>A 'ORI>ONTAL E&UIVALENTE RCB %%&'Da %! &a!&)!# -% !a( )%"a( ((*i&a( %n %! -i(%<# a '"a:( -%! M'#-# -% !a )%"a #"i#n'a! E=)i:a!%n'% +a"a %('# 'i%n% %n &)%n'a !a '#"(i,n a&&i-%n'a! $ &a!&)!a !a i""%g)!a"i-a- '#"(i#na! a -%*a( RCB %:a!)a i""%g)!a"i-a-%( -%! 'i+# 1 $  %n a!')"a $ +!an'a +a"a !a %('")&')"a a +a"'i" -% %!!# (% -%'%"*in# =)% !a %('")')"a %( i""%g)!a" %n +!an'a $ (% *#-ii&# %! :a!#" -%! &#%i&i%n'% -% &a+a&i-a- -% -i(i+a&i,n -% %n%"ga R )'i!ia-# %n %! -i(%<# ((*i&# -% !a %-ii&a&i,n. N# )% n%&%(a"i# %! )(# -% )n *%'#-# -% ana!i(i( -i%"%n'% a E $a =)% (%gDn NSR10 A.3.4..1 /- %('% *%'#-# %( )'i!ia2!% %n %-ii&a&i#n%( i""%g)!a"%( =)% n# '%ngan *á( -% 6 ni:%!%( ni *á( -% 18 * -% a!')"a *%-i-#( a +a"'i" -% !a 2a(%K A &#n'in)a&i,n (% *)%('"an %('#( aná!i(i( %n !a %('")&')"a

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1$. DERIVAS



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11. DISEÑO DE LOS MUROS Una :% (% 'i%n% %! *#-%!# %n RCB (% &#*+!%'a %! aná!i(i( -% !a E('")&')"a $ (% %('a2!%&%n !#( :a!#"%( -% Aia! C#"'an'% $ M#*%n'# +a"a &a-a &a(# -% &#*2ina&i,n -% &a"ga )'i!ia-a $ +a"a &a-a +i(#. A &#n'in)a&i,n (% *)%('"an !#( "%()!'a-#( +a"a )n *)"# %n g%n%"a!



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Pa"a !a( :iga( -% a*a""% (% 'i%n%n %n &)%n'a !a( "%&#*%n-a&i#n%( -% !a NSR 10 =)% (% '"an(&"i2%n a &#n'in)a&i,n.

C.15.13.1  FUER>AS DE DISEÑO  En %! -i(%<# -% !a( :iga( -% a*a""% -% &i*%n'a&i,n -%2%n &)*+!i"(% !#( "%=)i(i'#( -% A.3.6.4.3 "%(+%&'# a !a( )%"a( aia!%( =)% -%2% "%(i('i" !a :iga -% a*a""% $ !a( "%&#*%n-a&i#n%( =)% a! "%(+%&'# -%! %(')-i# g%#'&ni&# $ %! ')!#  -%! R%g!a*%n'#.

C.15.13.3  DIMENSIONES MINIMAS  La( -i*%n(i#n%( -% !a( :iga( -% a*a""% -%2%n %('a2!%&%"(% %n )n&i,n -% !a( (#!i&i'a&i#n%( =)% !a( a%&'%n -%n'"# -% !a( &)a!%( (% &)%n'an !a "%(i('%n&ia a )%"a( aia!%( +#" "a#n%( ((*i&a( $ !a "igi-% $ &a"a&'%"('i&a( +a"a %%&'#( -% -i%"%n&ia( -% &a"ga :%"'i&a! (#2"% !#( %!%*%n'#( -% &i*%n'a&i,n $ !a +#(i2i!i-a- -% #&)""%n&ia -% a(%n'a*i%n'#( '#'a!%( $ -i%"%n&ia!%(.

C.15.13.3.1  La( :iga( -% a*a""% -%2%n '%n%" )na (%&&i,n 'a! =)% () *a$#" -i*%n(i,n -%2% (%" *a$#" # ig)a! a !a !) -i:i-i-a +#" 0 +a"a %('")&')"a( &#n &a+a&i-a- %(+%&ia! -% -i(i+a&i,n -% %n%"ga /DES a !a !) -i:i-i-a +#" 30 +a"a %('")&')"a( &#n &a+a&i-a*#-%"a-a -% -i(i+a&i,n -% %n%"ga / DM% $ a !a !) -i:i-i-a +#" 40 +a"a %('")&')"a( &#n &a+a&i-a- *ni*a -% -i(i+a&i,n -% %n%"ga / DM& .

C.15.13.2  REFUER>O LONGITUDINAL  La( :iga( -% a*a""% (#2"% %! '%""%n# =)% %n!a&%n -a-#( # a+a'a( -%2%n '%n%" "%)%"# !#ngi')-ina! &#n'in)# %! &)a! -%2% (%" &a+a -% -%(a""#!!a" Q +#" *%-i# -% an&!a>% %n !a &#!)*na %'%"i#" -%! :an# ina!.

C.15.13.4  REFUER>O TRANSVERSAL  %2%n &#!#&a"(% %('"i2#( &%""a-#( %n '#-a () !#ngi')- &#n )na (%+a"a&i,n =)% n# %&%-a !a *i'a- -% !a *%n#" -i*%n(i,n -% !a (%&&i,n , 300 **. La( :iga( -% a*a""% =)% "%(i('an *#*%n'#( !%&'#"%( +"#:%ni%n'%( -% &#!)*na( -%2%n &)*+!i" !#( "%=)i(i'#( -% (%+a"a&i,n $ &an'i-a- -% "%)%"# '"an(:%"(a! =)% i>% %! "%g!a*%n'# +a"a %! ni:%! -% &a+a&i-a- -% -i(i+a&i,n -% %n%"ga %n %! "ang# in%!á('i&# -%! (i('%*a -% "%(i('%n&ia ((*i&a. En RC !#( "%()!'a-#( -% aná!i(i( =)% +"%(%n'a %! +"#g"a*a +a"a %('% 'i+# -% %!%*%n'# in&!)$%n -%#"*a&i#n%( )%"a( &#"'an'%( $ *#*%n'#( -% !%i,n a !# !a"g# -%! %!%*%n'#. E! +"#&%(# -% -i(%<# %( %! *i(*# =)% )'i!ia +a"a !a( :iga( a"%a( !#( "%()!'a-#( (% *)%('"an %n an%# B -%! C- a->)n'# -%n'"# -% !#( "%()!'a-#( -% !a :iga( a"%a( $ (% -i%"%n&ian +#" %! +i(# -% !a( :iga( -% &i*%n'a&i#n %( -%&i" %! +"#g"a*a !a( *)%'("a &#*# +i(# 1 /!##" 1 +a"a !a( :iga( -% &i*%n'a&i,n %n a+a'a( %&%n'"i&a( (% -%2% '%n%" %n &)%n'a =)% (i !#( &i*i%n'#( (#n i>#( n# (% +)%-%n *#-%!a" !a( :iga( -% a*a""% /tie 'eams ni !a( -% &#n'"a+%(# / stra( 'eams. Si (% =)i%"% *#-%!a" %('#( %!%*%n'#( $ #2'%n%" () -i(%<# "%a! %( n%&%(a"i# %-i'a" !a( +"#+i%-a-%( -% !#( &i*i%n'#( % in-i&a" =)% (% +%"*i'% () "#'a&i,n. Pa"a %! -i(%<# -% a+a'a( %&n'"i&a( &#n :iga( -% &#n'"a+%(# %( n%&%(a"i# +%"*i'i" "#'a&i#n%( a! *%n#( %n !#( &i*i%n'#( %&n'"i&#(. A *an%"a -% %>%*+!# (% *)%'"a %! -i(%<# +a"a )na :iga. A &#n'in)a&),n (% *)%('"an !#( "%()!'a-#( +a"a a!g)na( :iga( -% Ci*i%n'#( !#( -%*á( (% *)%('"an %n %! an%# B %n %! -i(%<# &#n "#'a&i#n%(.



14. DISEÑO DE LA ESCALERA En !a E-ii&a&i,n (% *)%('"a !a %(&a!%"a -% !a ig)"a 7 (% -i(%<, !a +!a&a &#n *á( !) !i2"% %n'"% a+#$#( &#*# (% *)%('"a a &#n'in)a&i,n t =

l

245 =

20 tan α

20 20

=

=

= 12.25cm ≈ 15cm

0.68 ⇒ α

=

tan

28

−1

( 0.68) = 35.5 = 36

o

CARGAS "a*# In&!ina-# P%(# P"#+i# @

0.15 *1 *1 * 2.4 cos( 36 )

0.20 * 0.28 * 2.4

=

0.45 ton

0.27 ton



P%!-a<#( @



A&a2a-#( @ 0.0017 ton



Aina-# in%"i#" %n +a<%'% @ 0.01ton



#'a! 0.74 '#n* 

=

2 * 0.25

m

2

/ mm

* 4mm

m

=

m

m2

2

0.007 ton m

2

2



X) @ 1.Q0.741.6Q0.30 @ 1.37 '#n* 

ig)"a 17. Ca"ga( -% i(%<# E(&a!%"a

∑ 

B

= 1.37 * 2.45 *1.225 − R " * 2.45 = 0

⇒ R " =

∑

4.11

= 1.68ton 2.45  " = −1.37 * 2.45 *1.225 + R B * 2.45 = 0

⇒ R B = $0 =

4.11

2.45 1.68ton

= 1.68ton

1.37 ton

+

 m#$. =

= 1.226 m

m 1.68 *1.226 2

= 1.03ton * m ⇒ 10 .3kN * m

ρ + = 0.0019 + 2 "s = 0.0019 *12 * 100 = 2.32 cm ⇒

4 n°3 / m

⇒ 1n°3 c / 25cm

V!a = 1.68ton = 16 .8kN v!a =

16800 1000 *150

= 0.112 Pa < 0.573 Pa → φ vc

N# n%&%(i'a "%)%"# a C#"'an'%.




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