Diseño de Columnas l

 ANÁLISIS Y DISEÑO EN CONCRETO CONCRETO ARMADO

DISEÑO DE COLUMNAS - GEOMETRÍA "L"  Datos a b bw1 bw2  !  pm$n.  sm$n.  sb n  s)mien%o: n

= = = = = = = = =

0.600 m 0.600 m 0.250 m 0.250 m 2"#5.000 m2 0.010 2".#50 cm2 1.(80 cm2 11.((5

=

Las barras principales son: Extremos: 4.000 Conexión: 4.000 8.000 Canti%a% %e repartición en el alma: &' = 4.000 Canti%a% %e repartición en ca%a sector   &' = 2.000

12.000

1-. Determinacin !e centr#i!e $%&tic# !e eement# C)an%o se trata %e )na sección con re*)er+o asim,trico el p)nto %on%e se %ebe tomar momentos para la obtención %e momentos resistentes -tra+o %el %ia!rama %e interacción no %ebe ser el centro %e !ra/e%a% %e la sección -consi%eran%o sólo el rea %e concreto sino el %enomina%o centro plstico 3 )e consiste en el centro %e *)er+as obteni%o consi%eran%o to%a la sección comprimi%a en s) capaci%a% mxima. Esta con%ición se c)mple c)an%o el concreto est trabaan%o a 0.85*7c 3 ca%a )no %e los *ierros a )n es*)er+o *73. ara ello se 9ar la si!)iente repartición sien%o el p)nto %e parti%a la c)ant$a m$nima.

DIRECCI'N ((  Centros %e barras: %1 = %2 = %" = %4 = %5 =

0.060 m 0.1#0 m 0.280 m 0.410 m 0.540 m

s1 s2 s" s4 s5

= = = = =

".(60 cm2 ".(60 cm2 ".(60 cm2 (.(00 cm2 (.(00 cm2

Centroi%e plstico: o =

-s1x%1*73;-s2x%2x*73 ; < ; -six%ix*73 ; -0.85x*7cx!xi -s1x*73;-s2x*73 ; < ; -six%ix*73 ; -0.85x*7cx!xi

%i -m 6.000 1#.000 28.000 41.000 54.000

si -cm2 ".(60 ".(60 ".(60 (.(00 (.(00 "1.680 o =

six%i 2".#60 6#."20 110.880 405.(00 5"4.600 1142.460

c1

9 2

c2

92

1500.000

"0.000

8#5.000

4#.500

8##04.(60 2424.8(6

)-. C%c*# !e #& $*nt#& !e Dia+rama !e Interaccin 1- CARGA CONC,NTRICA n = 0.80x>0.85*7c-!?st ; -stx*73@ =  ! =  st = *7c =

2"#5.000 cm2 "1.680 cm2 0.210 0.210 Ancm2 Ancm2

441.0#1 An

=

"6.16( cm

Centroi%e plstico: o =

-s1x%1*73;-s2x%2x*73 ; < ; -six%ix*73 ; -0.85x*7cx!xi -s1x*73;-s2x*73 ; < ; -six%ix*73 ; -0.85x*7cx!xi

%i -m 6.000 1#.000 28.000 41.000 54.000

si -cm2 ".(60 ".(60 ".(60 (.(00 (.(00 "1.680 o =

six%i 2".#60 6#."20 110.880 405.(00 5"4.600 1142.460

c1

9 2

c2

92

1500.000

"0.000

8#5.000

4#.500

8##04.(60 2424.8(6

=

"6.16( cm

)-. C%c*# !e #& $*nt#& !e Dia+rama !e Interaccin 1- CARGA CONC,NTRICA n = 0.80x>0.85*7c-!?st ; -stx*73@ =  !  st *7c *73

= = = =

441.0#1 An

2"#5.000 cm2 "1.680 cm2 0.210 0.210 Ancm2 Ancm2 4.200 Ancm2

)-. CARGA ALANCEADA El p)nto %e la *alla balancea%a se calc)la consi%eran%o las %e*ormaciones )nitarias tales ec=0.00" 3 es=0.0021 para el concreto 3 acero respecti/amente.

C%c*# !e a $r#*n!i!a! !e e/e ne*tr# "c"  Del trin!)lo %e %e*ormaciones )nitarias se tiene )e: -ec;es% = ecc <. -B eempla+an%o ec 3 es: c = 0.411#65x% =

0.222 m

or lo tanto: a=

0.18( m

C%c*# !e e&*er0#& en a& arra& Del trin!)lo %e %e*ormaciones )nitarias se tiene )e: ecc = es1-c?%7 abien%o )e las %e*ormaciones )nitarias esi /arian se!n la pro*)n%i%a% %el ee ne) tro !enerali+an%o se tiene: esi = ecx-c?%ic 

)-. CARGA ALANCEADA El p)nto %e la *alla balancea%a se calc)la consi%eran%o las %e*ormaciones )nitarias tales ec=0.00" 3 es=0.0021 para el concreto 3 acero respecti/amente.

C%c*# !e a $r#*n!i!a! !e e/e ne*tr# "c"  Del trin!)lo %e %e*ormaciones )nitarias se tiene )e: -ec;es% = ecc <. -B eempla+an%o ec 3 es: c = 0.411#65x% =

or lo tanto: a=

0.222 m

0.18( m

C%c*# !e e&*er0#& en a& arra& Del trin!)lo %e %e*ormaciones )nitarias se tiene )e: ecc = es1-c?%7 abien%o )e las %e*ormaciones )nitarias esi /arian se!n la pro*)n%i%a% %el ee ne) tro !enerali+an%o se tiene: esi = ecx-c?%ic  abien%o )e es=*7sEs se obtiene: *7s = ecxEsx-c?%ic  e obten%r$a )e: *7si = 6x-c?%ic 

-Ancm2

M#ment# Re&i&tente !e a Seccin %i -m 0.060 0.1#0 0.280 0.410 0.540

si -cm2 ".(60 ".(60 ".(60 (.(00 (.(00

c -m

0.222

*si -Acm2 4."81 1.41" ?1.556 ?5.06" ?8.5#1

*si -Acm2 4.200 1.41" ?1.556 ?4.200 ?4.200

esi 0.00210 0.000#1 ?0.000#8 ?0.00210 ?0.00210

Fi -An 16.6"2 5.5(5 ?6.162 ?41.580 ?41.580 ?6#.0(4

Cc -An

o -m

210.85"

0."62

Gra+o -m 0."02 0.1(2 0.082 0.048 0.1#8

Hn -A?m 5.018 1.0#" 0.50" 2.00( #.414 16.01#

or lo tanto: 84."41 n = Hn =

14".#5( An 56.""# A?m

Hn -A?m

56.""# 

 

M#ment# Re&i&tente !e a Seccin %i -m 0.060 0.1#0 0.280 0.410 0.540

si -cm2 ".(60 ".(60 ".(60 (.(00 (.(00

c -m

0.222

*si -Acm2 4."81 1.41" ?1.556 ?5.06" ?8.5#1

*si -Acm2 4.200 1.41" ?1.556 ?4.200 ?4.200

esi 0.00210 0.000#1 ?0.000#8 ?0.00210 ?0.00210

Fi -An 16.6"2 5.5(5 ?6.162 ?41.580 ?41.580 ?6#.0(4

Cc -An

o -m

210.85"

0."62

Gra+o -m 0."02 0.1(2 0.082 0.048 0.1#8

Hn -A?m 5.018 1.0#" 0.50" 2.00( #.414 16.01#

or lo tanto: 84."41 n = Hn =

14".#5( An 56.""# A?m

concreto #80("#5.000 acero as1x*73 = as2x*73 = as"x*73 =

42840.000 64260.000 64260 000

Hn -A?m

56.""# 

 

concreto #80("#5.000 acero as1x*73 = as2x*73 = as"x*73 =

"(.4"6

42840.000 64260.000 64260.000

"(.4"6

 ANÁLISIS Y DISEÑO EN CONCRETO ARMADO DE COLUMNAS  DATOS GEOM,TRICOS2 b 9 %7 %

= = = =

3RO3IEDADES GEOM,TRICAS 0.250 m 0.600 m 0.060 m 0.540 m

*7c = *73 =

3ROGRAMA MAT4CAD

0.210 Acm2 4.200 Acm2

SECCI5N DE 3ERALTE MAYOR *7c *73 Ec Es I

= = = = =

0.210 Acm2 4.200 Acm2 21#."#1 Acm2 2000.000 Acm2 0.#00 -Col)mna Estriba%a

Centr#i!e !e a Seccin  Jc = c =

s1 = s2 = s" = s4 = s5 =  st =

De#rmaci#ne& Unitaria& 0.125 m 0."62 m

ec = e3 =

0.00" 0.002

0 0026#

*s1 =

".(60 cm2 ".(60 cm2 ".(60 cm2 (.(00 cm2 (.(00 cm2 "1.680 cm2

%1 = %2 = %" = %4 = %5 =

0.060 m 0.1#0 m 0.280 m 0.410 m 0.540 m

A& M6nim# 7 M%8im# sm$n. = smx. =  sopt. =

15.000 cm2 (0.000 cm2 "0.000 cm2

KMN KMN

3*nt# !e a car+a m%8ima a c#m$re&in  ! = o = I o = 0.80xo =

2"#5.000 cm2 551.""( An. "85.("# An. 441.0#1 An.

3* 9 :.;:8<=83#> 9

?:;.@: Tn.

3*nt# !e i&*racin inci$iente ec = 0.00" e3 = 0.002 O= 0.000 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0 06000 m

0.540 m es1 =

4 20000 Acm2

Fs1 =

16 6"200 An

 ANÁLISIS Y DISEÑO EN CONCRETO ARMADO DE COLUMNAS  DATOS GEOM,TRICOS2 b 9 %7 %

= = = =

3RO3IEDADES GEOM,TRICAS 0.250 m 0.600 m 0.060 m 0.540 m

*7c = *73 =

3ROGRAMA MAT4CAD

0.210 Acm2 4.200 Acm2

SECCI5N DE 3ERALTE MAYOR *7c *73 Ec Es I

= = = = =

0.210 Acm2 4.200 Acm2 21#."#1 Acm2 2000.000 Acm2 0.#00 -Col)mna Estriba%a

Centr#i!e !e a Seccin  Jc = c =

s1 = s2 = s" = s4 = s5 =  st =

".(60 cm2 ".(60 cm2 ".(60 cm2 (.(00 cm2 (.(00 cm2 "1.680 cm2

De#rmaci#ne& Unitaria& 0.125 m 0."62 m

ec = e3 =

%1 = %2 = %" = %4 = %5 =

0.060 m 0.1#0 m 0.280 m 0.410 m 0.540 m

A& M6nim# 7 M%8im#

0.00" 0.002

sm$n. = smx. =  sopt. =

15.000 cm2 (0.000 cm2 "0.000 cm2

KMN KMN

3*nt# !e a car+a m%8ima a c#m$re&in  ! = o = I o = 0.80xo =

2"#5.000 cm2 551.""( An. "85.("# An. 441.0#1 An.

3* 9 :.;:8<=83#> 9

?:;.@: Tn.

3*nt# !e i&*racin inci$iente ec = 0.00" e3 = 0.002 O= 0.000 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

0.540 m es1 es2 es" es4 es5

= = = = =

0.0026# 0.00206 0.00144 0.000#2 0.00000

Garra  s1  s2  s"  s4

*s1 -Acm2 4.20000 4.11111 2.8888( 1.44444

Fs1 -An 16.6"200 16.28000 11.44000 14."0000

%i -m 0.060 0.1#0 0.280 0.410

 s5

0.00000

0.00000 58.65200

0.540

Cc =

204.82( An.

3n 9  = 3n 9

)B?.;1 Tn. 1;.?@ Tn.

Mn 9 =Mn 9

*s1 *s2 *s" *s4 *s5

= = = = =

4.20000 Acm2 4.11111 Acm2 2.8888( Acm2 1.44444 Acm2 0.00000 Acm2

c -m

o -m

0.540

0."62

Fs1 Fs2 Fs" Fs4 Fs5

Gra+o -o?%i 0."02 0.1(2 0.082 0.048

Hni -A?m 5.018 ".121 0.("5  0.6(1

0.1#8

0.000 (.#64

= = = = =

16.6"200 An 16.28000 An 11.44000 An 14."0000 An 0.00000 An Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

204.82(

"6.840

25.#88

?B.;: T-m ).@;; T-m

3*nt# !e 9 -:.: ec = 0.00" e3 = 0.002 O= ?0.500 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"  s4  s5

*s1 -Acm2 4.20000 ".45000 1.80000 ?0.15000 ?2.10000

Cc =

151.#25 An.

3n 9  = 3n 9

1BB.;@) Tn. 11B.;1: Tn.

0.400 m es1 es2 es" es4 es5

Fs1 -An 16.6"200 1".66200 #.12800 1.48500 20.#(000

3*nt# !e aa aancea!a  9-1.::

= = = = =

0.00255 0.001#" 0.000(0 ?0.0000# ?0.00105

%i -m 0.060 0.1#0 0.280 0.410 0.540

Mn 9 =Mn 9

*s1 *s2 *s" *s4 *s5

= = = = =

4.20000 Acm2 ".45000 Acm2 1.80000 Acm2 ?0.15000 Acm2 ?2.10000 Acm2

c -m

o -m

0.400

0."62

1.:;) T-m );.@@ T-m

Gra+o -o?%i 0."02 0.1(2 0.082 0.048 0.1#8

Fs1 Fs2 Fs" Fs4 Fs5

Hni -A?m 5.018 2.61( 0.582 0.0#2 ".#0#  11.((8

= = = = =

16.6"200 An 1".66200 An #.12800 An ?1.48500 An ?20.#(000 An 15.14# An Cc = 0.85x*cxaxb

Hn -A?m

151.#25

41.082

I Hn -A?m

28.#5#  

 s5

0.00000

Cc =

204.82( An.

3n 9  = 3n 9

)B?.;1 Tn. 1;.?@ Tn.

0.00000 58.65200

0.540

Mn 9 =Mn 9

0.1#8

0.000 (.#64

?B.;: T-m ).@;; T-m

3*nt# !e 9 -:.: ec = 0.00" e3 = 0.002 O= ?0.500 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"  s4  s5

*s1 -Acm2 4.20000 ".45000 1.80000 ?0.15000 ?2.10000

Cc =

151.#25 An.

3n 9  = 3n 9

1BB.;@) Tn. 11B.;1: Tn.

0.400 m es1 es2 es" es4 es5

= = = = =

Fs1 -An 16.6"200 1".66200 #.12800 1.48500 20.#(000

0.00255 0.001#" 0.000(0 ?0.0000# ?0.00105

%i -m 0.060 0.1#0 0.280 0.410 0.540

Mn 9 =Mn 9

*s1 *s2 *s" *s4 *s5

= = = = =

4.20000 Acm2 ".45000 Acm2 1.80000 Acm2 ?0.15000 Acm2 ?2.10000 Acm2

c -m

o -m

0.400

0."62

Gra+o -o?%i 0."02 0.1(2 0.082 0.048 0.1#8

Fs1 Fs2 Fs" Fs4 Fs5

= = = = =

Hni -A?m 5.018 2.61( 0.582 0.0#2 ".#0#  11.((8

16.6"200 An 1".66200 An #.12800 An ?1.48500 An ?20.#(000 An 15.14# An Cc = 0.85x*cxaxb

Hn -A?m

151.#25

41.082

I Hn -A?m

28.#5#  

1.:;) T-m );.@@ T-m

3*nt# !e aa aancea!a  9-1.:: ec = 0.00" e3 = 0.002 O= ?1.000 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m

%5 =

Garra  s1  s2  s"  s4  s5

0.54000 m

0."18 m es1 es2 es" es4

= = = =

0.0024" 0.001"( 0.000"6 ?0.0008#

*s1 *s2 *s" *s4

= = = =

4.20000 Acm2 2.#888( Acm2 0.#1111 Acm2 ?1.#4444 Acm2

Fs1 Fs2 Fs" Fs4

es5 =

?0.00210

*s5 =

?4.20000 Acm2

Fs5 =

*s1 -Acm2 4.20000 2.#888( 0.#1111 ?1.#4444 ?4.20000

Fs1 -An 16.6"200 11.04400 2.81600 1#.2#000 41.58000 8(."4200 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc = 120.488 An.

3n 9  = 3n 9

F).1?: Tn. B.F1 Tn.

%i -m 0.060 0.1#0 0.280 0.410 0.540

GP -m o ?- a2 Gra+o -m 0."02 0.1(2 0.22#   0.082 0.048 0.1#8

o -m

0."62

= = = =

Hni -A?m 5.018 2.11#  0.2"0 0.8"4 #.414 15.61"

16.6"200 An 11.04400 An 2.81600 An ?1#.2#000 An

-

C C C A

?41.58000 An - A  ?28."58 An

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

120.488

42.(2#

"0.04(

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

).F)@ T-m ?:.:F T-m

3*nt# !e Cami# !e = ec = 0.00" e3 = 0.002 O= ?".000 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"

*s1 -Acm2 ".("""" 0.14444 ?".64444

0.1#4 m es1 es2 es" es4 es5

= = = = =

Fs1 -An 15.5#5(( 0.5#1(8 ?14.4"1(8

0.001(# 0.0000# ?0.00182 ?0.00406 ?0.006"0

%i -m 0.060 0.1#0 0.280

*s1 *s2 *s" *s4 *s5

o -m

0 "62

= = = = =

".("""" Acm2 0.14444 Acm2 ?".64444 Acm2 ?8.12222 Acm2 ?12.60000 Acm2 GP -m c ?- a2 Gra+o -m 0."02 0.1(2 0 100 0.082

*s1 *s2 *s" *s4 *s5

Hni -A?m 4.6(( 0.110 1.1#(

= = = = =

".("""" Acm2 0.14444 Acm2 ?".64444 Acm2 ?4.20000 Acm2 ?4.20000 Acm2

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

66 0#4

22 02(

15 420

%5 =

Garra  s1  s2  s"  s4  s5

0.54000 m

es5 =

*s1 -Acm2 4.20000 2.#888( 0.#1111 ?1.#4444 ?4.20000

Fs1 -An 16.6"200 11.04400 2.81600 1#.2#000 41.58000 8(."4200 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc = 120.488 An.

3n 9  = 3n 9

F).1?: Tn. B.F1 Tn.

?0.00210

%i -m 0.060 0.1#0 0.280 0.410 0.540

*s5 =

?4.20000 Acm2

GP -m o ?- a2 Gra+o -m 0."02 0.1(2 0.22#   0.082 0.048 0.1#8

o -m

0."62

Fs5 =

Hni -A?m 5.018 2.11#  0.2"0 0.8"4 #.414 15.61"

?41.58000 An - A  ?28."58 An

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

120.488

42.(2#

"0.04(

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

).F)@ T-m ?:.:F T-m

3*nt# !e Cami# !e = ec = 0.00" e3 = 0.002 O= ?".000 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"  s4  s5

0.1#4 m es1 es2 es" es4 es5

= = = = =

Fs1 -An 15.5#5(( 0.5#1(8 ?14.4"1(8 ?41.58000 ?41.58000 ?81.44401 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc = 66.0#4 An.

3n 9  = 3n 9

*s1 -Acm2 ".("""" 0.14444 ?".64444 ?4.20000 ?4.20000

-1.?@: Tn. -1:.@F Tn.

0.001(# 0.0000# ?0.00182 ?0.00406 ?0.006"0

%i -m 0.060 0.1#0 0.280 0.410 0.540

*s1 *s2 *s" *s4 *s5

= = = = =

".("""" Acm2 0.14444 Acm2 ?".64444 Acm2 ?8.12222 Acm2 ?12.60000 Acm2 GP -m c ?- a2 Gra+o -m 0."02 0.1(2 0.100 0.082 0.048 0.1#8

o -m

0."62

*s1 *s2 *s" *s4 *s5

= = = = =

Hni -A?m 4.6(( 0.110 1.1#( 2.00( #.414 15.411

".("""" Acm2 0.14444 Acm2 ?".64444 Acm2 ?4.20000 Acm2 ?4.20000 Acm2

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

66.0#4

22.02(

15.420

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

)).:)F T-m 1.): T-m

3*nt# !e Cami# !e = 9 :.F: ec = 0.00" e3 = 0.002 O= ?4.660 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"  s4  s5

0.12# m es1 es2 es" es4 es5

Fs1 -An 12.508"" ?8.11(#4 ?16.6"200 ?41.58000 ?41.58000 ?(5.40"41 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc = 48.05( An.

3n 9  = 3n 9

*s1 -Acm2 ".1586# ?2.05044 ?4.20000 ?4.20000 ?4.20000

= = = = =

-@.? Tn. -).B1: Tn.

3*nt# e8in 3*ra <3n9:.:: Tn>

0.00158 ?0.0010" ?0.00"6" ?0.006#1 ?0.00(#(

%i -m 0.060 0.1#0 0.280 0.410 0.540

*s1 *s2 *s" *s4 *s5

o -m

0."62

= = = = =

".1586# Acm2 ?2.05044 Acm2 ?#.25(56 Acm2 ?1".415#8 Acm2 ?1(.5#200 Acm2 GP -m o ?- a2 Gra+o -m 0."02 0.1(2 0."08 0.082 0.048 0.1#8

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

?:.F:B T-m )@.;1B T-m

*s1 *s2 *s" *s4 *s5

Hni -A?m ".##4 1.556 1."5( 2.00( #.414 16.112

= = = = =

".1586# Acm2 ?2.05044 Acm2 ?4.20000 Acm2 ?4.20000 Acm2 ?4.20000 Acm2

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

48.05(

"0.(06

2#.816

3*nt# !e Cami# !e = 9 :.F: ec = 0.00" e3 = 0.002 O= ?4.660 %= 0.540 m c = ecx%-ec ? - Oxe3  = Es = 2000.000 Acm2 %1 = 0.06000 m %2 = 0.1#000 m %" = 0.28000 m %4 = 0.41000 m %5 = 0.54000 m

Garra  s1  s2  s"  s4  s5

0.12# m es1 es2 es" es4 es5

= = = = =

0.00158 ?0.0010" ?0.00"6" ?0.006#1 ?0.00(#(

*s1 -Acm2 ".1586# ?2.05044 ?4.20000 ?4.20000 ?4.20000

Fs1 -An 12.508"" ?8.11(#4 ?16.6"200 ?41.58000 ?41.58000 ?(5.40"41 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc = 48.05( An.

3n 9  = 3n 9

-@.? Tn. -).B1: Tn.

%i -m 0.060 0.1#0 0.280 0.410 0.540

*s1 *s2 *s" *s4 *s5

= = = = =

".1586# Acm2 ?2.05044 Acm2 ?#.25(56 Acm2 ?1".415#8 Acm2 ?1(.5#200 Acm2

*s1 *s2 *s" *s4 *s5

GP -m o ?- a2 Gra+o -m 0."02 0.1(2 0."08 0.082 0.048 0.1#8

o -m

0."62

= = = = =

Hni -A?m ".##4 1.556 1."5( 2.00( #.414 16.112

".1586# Acm2 ?2.05044 Acm2 ?4.20000 Acm2 ?4.20000 Acm2 ?4.20000 Acm2

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

48.05(

"0.(06

2#.816

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

?:.F:B T-m )@.;1B T-m

3*nt# e8in 3*ra <3n9:.:: Tn> % c Es %1 %2 %" %4 %5

= = = = = = = =

0.540 m 0.1(# m 2000.000 Acm2 0.06000 m 0.1#000 m 0.28000 m 0.41000 m 0.54000 m

es1 es2 es" es4 es5

= = = = =

0.0020( 0.00041 ?0.0012# ?0.00"25 ?0.0052"

*s1 *s2 *s" *s4 *s5

= = = = =

4.1#0#" Acm2 0.81#0# Acm2 ?2.5"65( Acm2 ?6.50000 Acm2 ?10.46"41 Acm2

*s1 *s2 *s" *s4 *s5

= = = = =

4.1##0" Acm2 0.81#0# Acm2 ?2.5"64( Acm2 ?4.20000 Acm2 ?4.20000 Acm2

GP -m

Garra  s1  s2  s"  s4  s5

*s1 -Acm2 4.1##0" 0.81#0# ?2.5"64( ?4.20000 ?4.20000

Fs1 -An 16.54104 ".2"560 ?10.04450 ?41.58000 ?41.58000 ?#".42#86 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc =

#4.64( An.

3n 9  = 3n 9

1.))1 Tn. 1.:FF Tn.

%i -m 0.060 0.1#0 0.280 0.410 0.540

o -m

o ?- a2

0."62

0.11"

Gra+o -m 0."02 0.1(2 0.082 0.048 0.1#8

Hni -A?m 4.((0 0.620 0.821 2.00( #.414 15.854

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

#4.64(

24."01

21.8#1

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

).?:1 T-m )1.;@1 T-m

s1 s2 s" s4 s5

".(6000 cm2 ".(6000 cm2 ".(6000 cm2 (.(0000 cm2 (.(0000 cm2

3*nt#2 Traccin 3*ra *73 %1 %2 %" %4 %5

= = = = = =

3n 9  = 3n 9

4.200 Acm2 0.06000 m 0.1#000 m 0.28000 m 0.41000 m 0.54000 m

= = = = =

Fs1 Fs2 Fs" Fs4 Fs5

= = = = =

16.6"2 An 16.6"2 An 16.6"2 An 41.58 An 41.58 An 1"".056 An

1??.:B Tn. 11F.@: Tn. TALA RESUMEN

3n

= 3n

Mn

)nto %e car!a mxima a compresión )nto %e Fis)ración Bncipiente )nto %e O =0.50 )nto %e Falla Galancea%a )nto %e cambio %e I )nto %e Flexión )ra )nto %e Aracción )ra

441.0#1 26".481 166.8#2 (2.1"0 ?4#."44 0 ?1"".056

"08.#50 184.4"# 116.810 64.4(1 ?42.610 0 ?11(.#50

0 "6.840 41.082 42.(2# "0.(06 24."01 0.000

=Mn 0 25.#88 28.#5#   "0.04( 2#.816 21.8#1 0.000

Garra  s1  s2  s"  s4  s5

*s1 -Acm2 4.1##0" 0.81#0# ?2.5"64( ?4.20000 ?4.20000

Fs1 -An 16.54104 ".2"560 ?10.04450 ?41.58000 ?41.58000 ?#".42#86 Q&ota: i los es*)er+os R*siR son ne!ati/os eso )iere Cc =

#4.64( An.

3n 9  = 3n 9

1.))1 Tn. 1.:FF Tn.

%i -m 0.060 0.1#0 0.280 0.410 0.540

o -m

o ?- a2

0."62

0.11"

Gra+o -m 0."02 0.1(2 0.082 0.048 0.1#8

Hni -A?m 4.((0 0.620 0.821 2.00( #.414 15.854

Cc = 0.85x*cxaxb

Hn -A?m

I Hn -A?m

#4.64(

24."01

21.8#1

%ecir )e las barras estarn exp)estas a Aracción.

Mn 9 =Mn 9

).?:1 T-m )1.;@1 T-m

s1 s2 s" s4 s5

".(6000 cm2 ".(6000 cm2 ".(6000 cm2 (.(0000 cm2 (.(0000 cm2

3*nt#2 Traccin 3*ra *73 %1 %2 %" %4 %5

= = = = = =

3n 9  = 3n 9

4.200 Acm2 0.06000 m 0.1#000 m 0.28000 m 0.41000 m 0.54000 m

= = = = =

Fs1 Fs2 Fs" Fs4 Fs5

= = = = =

16.6"2 An 16.6"2 An 16.6"2 An 41.58 An 41.58 An 1"".056 An

1??.:B Tn. 11F.@: Tn. TALA RESUMEN

3n

= 3n

Mn

)nto %e car!a mxima a compresión )nto %e Fis)ración Bncipiente )nto %e O =0.50 )nto %e Falla Galancea%a )nto %e cambio %e I )nto %e Flexión )ra )nto %e Aracción )ra

441.0#1 26".481 166.8#2 (2.1"0 ?4#."44 0 ?1"".056

"08.#50 184.4"# 116.810 64.4(1 ?42.610 0 ?11(.#50

0 "6.840 41.082 42.(2# "0.(06 24."01 0.000

=Mn 0 25.#88 28.#5#   "0.04( 2#.816 21.8#1 0.000

CARGAS ACTUANTES  ) = H) =

126.00 An. "(.00 An.

N#ta2 i las car!as act)antes )?H) se enc)entran %entro %el %ia!rama %e interacción )iere %ecir )e las col)mna soportar sin problema las car!as )e en ella act)arn.

Diagrama de Interacción Principal 500.000 400.000 300.000 200.000 100.000 0.000 -10

0

10

20

30

40

-100.000 -200.000 Col umn F

126.00

Col umn G

Col umn B

Col umn D

50

Diagrama de Interacción Principal 500.000 400.000 300.000 200.000 100.000 0.000 -10

0

10

20

30

40

-100.000 -200.000

Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Col umn F

126.00

Col umn G

Col umn B

Load (ton) Moment (ton-m) -114.62 0.66 -74.14 13.88 -57.04 19.35 -39.63 24.18 -20.54 28.93 13.13 33.6 42.76 32.6 69.19 31.6 106.58 31.09 157.14 28.09 206.15 23.56 252.1 17.47 283.72 11.91 283.72 1.67 283.72 0

Col umn D

50

Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 2 3 4 5 6 7 8 9 10 11

Load (ton) Moment (ton-m) -114.62 0.66 -74.14 13.88 -57.04 19.35 -39.63 24.18 -20.54 28.93 13.13 33.6 42.76 32.6 69.19 31.6 106.58 31.09 157.14 28.09 206.15 23.56 252.1 17.47 283.72 11.91 283.72 1.67 283.72 0

Curve 1

0 degree

296.0746 284.698 229.7872 171.0014 110.9466 64.1382 32.9429 -3.0109 -41.556 -84.759 -136.6765

-1.2446 4.7552 8.2782 12.0642 15.3377 15.0145 16.4042 16.4645 12.2585 7.5376 1.7994

1.2446 15.0893 22.3368 26.8942 29.0391 30.5199 33.4838 34.833 26.8826 15.0343 -1.7994

Curve 2

15 degree

-296.0746 -296.0746 -267.4378 -198.3197 -136.9991 -86.1729 -48.412 -4.6913 45.5001 99.6842 136.6765

-1.2446 6.4025 12.6143 17.2612 18.8193 18.1972 19.3149 18.2339 12.8002 6.83 1.7994

Curve 3 1.2446 8.5387 16.8294 24.2953 28.0073 30.1386 34.6539 35.5683 25.4477 10.2333 -1.7994

-296.0746 -296.0746 -287.6646 -227.4364 -163.7307 -107.541 -66.4452 -14.1189 48.0398 109.7281 136.6765

Diagrama Intera

1 2 3 4 5 6 7 8 9 10 11

Curve 1

0 degree

296.0746 284.698 229.7872 171.0014 110.9466 64.1382 32.9429 -3.0109 -41.556 -84.759 -136.6765

-1.2446 4.7552 8.2782 12.0642 15.3377 15.0145 16.4042 16.4645 12.2585 7.5376 1.7994

1.2446 15.0893 22.3368 26.8942 29.0391 30.5199 33.4838 34.833 26.8826 15.0343 -1.7994

Curve 2

15 degree

-296.0746 -296.0746 -267.4378 -198.3197 -136.9991 -86.1729 -48.412 -4.6913 45.5001 99.6842 136.6765

-1.2446 6.4025 12.6143 17.2612 18.8193 18.1972 19.3149 18.2339 12.8002 6.83 1.7994

Curve 3 1.2446 8.5387 16.8294 24.2953 28.0073 30.1386 34.6539 35.5683 25.4477 10.2333 -1.7994

-296.0746 -296.0746 -287.6646 -227.4364 -163.7307 -107.541 -66.4452 -14.1189 48.0398 109.7281 136.6765

Diagrama Intera 400 300 200 100 0 -50

-40

-30

-20

-10

0 -100 -200

Column AL

30 degree -1.2446 6.311 14.1824 21.516 22.2277 21.2839 22.3558 20.4024 13.5471 6.2479 1.7994

 

1.2446 7.1715 12.879 19.5429 25.8498 29.4359 34.5685 35.7942 24.0699 6.9028 -1.7994

Curve 4

45 degree

-296.0746 -296.0746 -294.6845 -246.1739 -193.3108 -132.2146 -89.004 -28.6341 48.1788 113.0865 136.6765

-1.2446 6.6488 15.1007 22.5008 25.5744 24.8863 25.7999 23.3911 14.7943 6.02 1.7994

cción

10

Column B

20

30

40

1.2446 6.5302 11.2122 16.3408 21.8595 27.5032 33.7685 35.4773 22.646 5.7529 -1.7994

Curve 5

60 degree

-296.0746 -296.0746 -296.0746 -258.6132 -214.2118 -161.9539 -121.9079 -51.0253 41.3527 111.5607 136.6765

-1.2446 7.3489 15.9254 22.6229 26.7608 28.7455 30.7961 27.9794 17.0315 6.5247 1.7994

1.2446 6.1038 10.0367 14.2818 18.7076 23.6658 30.9942 33.7321 21.7234 5.7903 -1.7994

Curve 6

75 degree

-296.0746 -296.0746 -296.0746 -268.5081 -231.0264 -186.3332 -160.8137 -95.2988 12.9375 104.8222 136.6765

-1.2446 8.8384 16.4209 22.4555 27.1196 30.6674 35.6205 36.2516 23.2543 8.0957 1.7994

1.2446 5.8793 9.0948 12.3994 16.0326 20.1556 25.9971 27.51 19.9336 6.6349 -1.7994

Curve 7

90 degree

-296.0746 -296.0746 -296.0746 -276.3398 -244.664 -206.8478 -190.6662 -149.473 -59.0658 33.8386 136.6765

-1.2446 10.3421 16.5738 21.8704 26.6439 31.1276 37.6953 42.6613 35.4801 22.0874 1.7994

1.2446 5.6347 8.1159 10.74 13.6418 16.7008 19.2911 18.977 12.3788 4.8309 -1.7994

Curve 8

105 degree

-296.0746 -296.0746 -296.0746 -273.4889 -234.4826 -168.9874 -122.452 -48.4691 45.9484 112.9459 136.6765

-1.2446 7.579 14.628 20.5275 25.3522 28.9259 32.4703 31.0447 18.553 6.5359 1.7994

1.2446 3.3362 5.7082 8.1504 9.7054 7.2936 4.5904 -1.3387 -6.6832 -5.4541 -1.7994

Curve 9

120 degree

-296.0746 -296.0746 -296.0746 -258.2797 -194.4933 -110.987 -50.2225 22.8619 83.3443 122.76 136.6765

-1.2446 5.0512 11.773 18.0612 21.7781 22.0749 22.3145 19.3089 11.2871 4.5569 1.7994

1.2446 0.8712 2.2973 1.718 -1.5627 -5.7638 -9.7011 -12.3826 -9.2456 -4.4547 -1.7994

Curve 10

135 degree

-296.0746 -296.0746 -280.6882 -216.3927 -141.8359 -63.7922 -7.485 52.8486 96.8183 125.791 136.6765

-1.2446 3.1932 7.3207 11.5953 13.9613 14.5201 15.3862 13.8343 8.6073 3.935 1.7994

Curve 11 1.2446 -3.1932 -7.3207 -11.5953 -13.9613 -14.5201 -15.3862 -13.8343 -8.6073 -3.935 -1.7994

-296.0746 -296.0746 -296.0746 -258.2797 -194.4933 -110.987 -50.2225 22.8619 83.3443 122.76 136.6765

150 degree -1.2446 -0.8712 -2.2973 -1.718 1.5627 5.7638 9.7011 12.3826 9.2456 4.4547 1.7994

1.2446 -5.0512 -11.773 -18.0612 -21.7781 -22.0749 -22.3145 -19.3089 -11.2871 -4.5569 -1.7994

Curve 12

165 degree

-296.0746 -296.0746 -296.0746 -273.4889 -234.4826 -168.9874 -122.452 -48.4691 45.9484 112.9459 136.6765

-1.2446 -3.3362 -5.7082 -8.1504 -9.7054 -7.2936 -4.5904 1.3387 6.6832 5.4541 1.7994

1.2446 -7.579 -14.628 -20.5275 -25.3522 -28.9259 -32.4703 -31.0447 -18.553 -6.5359 -1.7994

Curve 13

180 degree

296.0746 296.0746 296.0746 276.3398 244.664 206.8478 190.6662 149.473 59.0658 -33.8386 -136.6765

-1.2446 -5.6347 -8.1159 -10.74 -13.6418 -16.7008 -19.2911 -18.977 -12.3788 -4.8309 1.7994

1.2446 -10.3421 -16.5738 -21.8704 -26.6439 -31.1276 -37.6953 -42.6613 -35.4801 -22.0874 -1.7994

Curve 14

195 degree

-296.0746 -296.0746 -296.0746 -268.5081 -231.0264 -186.3332 -160.8137 -95.2988 12.9375 104.8222 136.6765

-1.2446 -5.8793 -9.0948 -12.3994 -16.0326 -20.1556 -25.9971 -27.51 -19.9336 -6.6349 1.7994

1.2446 -8.8384 -16.4209 -22.4555 -27.1196 -30.6674 -35.6205 -36.2516 -23.2543 -8.0957 -1.7994

Curve 15

210 degree

-296.0746 -296.0746 -296.0746 -258.6132 -214.2118 -161.9539 -121.9079 -51.0253 41.3527 111.5607 136.6765

-1.2446 -6.1038 -10.0367 -14.2818 -18.7076 -23.6658 -30.9942 -33.7321 -21.7234 -5.7903 1.7994

1.2446 -7.3489 -15.9254 -22.6229 -26.7608 -28.7455 -30.7961 -27.9794 -17.0315 -6.5247 -1.7994

Curve 16

225 degree

-296.0746 -296.0746 -294.6845 -246.1739 -193.3108 -132.2146 -89.004 -28.6341 48.1788 113.0865 136.6765

-1.2446 -6.5302 -11.2122 -16.3408 -21.8595 -27.5032 -33.7685 -35.4773 -22.646 -5.7529 1.7994

1.2446 -6.6488 -15.1007 -22.5008 -25.5744 -24.8863 -25.7999 -23.3911 -14.7943 -6.02 -1.7994

Curve 17

240 degree

-296.0746 -296.0746 -287.6646 -227.4364 -163.7307 -107.541 -66.4452 -14.1189 48.0398 109.7281 136.6765

-1.2446 -7.1715 -12.879 -19.5429 -25.8498 -29.4359 -34.5685 -35.7942 -24.0699 -6.9028 1.7994

1.2446 -6.311 -14.1824 -21.516 -22.2277 -21.2839 -22.3558 -20.4024 -13.5471 -6.2479 -1.7994

Curve 18

255 degree

-296.0746 -296.0746 -267.4378 -198.3197 -136.9991 -86.1729 -48.412 -4.6913 45.5001 99.6842 136.6765

-1.2446 -8.5387 -16.8294 -24.2953 -28.0073 -30.1386 -34.6539 -35.5683 -25.4477 -10.2333 1.7994

Curve 19 1.2446 -6.4025 -12.6143 -17.2612 -18.8193 -18.1972 -19.3149 -18.2339 -12.8002 -6.83 -1.7994

-296.0746 -284.698 -229.7872 -171.0014 -110.9466 -64.1382 -32.9429 3.0109 41.556 84.759 136.6765

270 degree -1.2446 -15.0893 -22.3368 -26.8942 -29.0391 -30.5199 -33.4838 -34.833 -26.8826 -15.0343 1.7994

1.2446 -4.7552 -8.2782 -12.0642 -15.3377 -15.0145 -16.4042 -16.4645 -12.2585 -7.5376 -1.7994

Curve 20

285 degree

-296.0746 -296.0746 -283.2205 -221.2861 -153.7751 -82.4338 -39.3554 12.4246 59.8826 108.1978 136.6765

-1.2446 -7.4399 -14.3305 -21.9668 -26.4895 -28.2089 -31.7477 -31.9476 -21.8179 -7.492 1.7994

1.2446 1.6861 2.1632 -1.3245 -5.1617 -8.992 -12.028 -13.3076 -9.2086 -3.9314 -1.7994

Curve 21

300 degree

-296.0746 -296.0746 -296.0746 -266.5211 -203.7568 -123.7497 -67.7569 4.3497 74.2391 121.1677 136.6765

-1.2446 -5.3692 -9.4958 -14.7776 -20.1623 -23.9237 -27.4561 -27.1803 -16.4178 -3.2539 1.7994

1.2446 3.1578 5.618 7.3385 6.5636 2.9292 -0.5471 -4.8551 -5.5067 -2.3963 -1.7994

Curve 22

315 degree

-296.0746 -296.0746 -296.0746 -289.5642 -239.8815 -171.5015 -123.6517 -47.5923 43.5016 114.9055 136.6765

-1.2446 -4.1336 -7.0479 -10.52 -13.6717 -15.5899 -17.6187 -16.6564 -9.5377 -1.4692 1.7994

1.2446 4.1336 7.0479 10.52 13.6717 15.5899 17.6187 16.6564 9.5377 1.4692 -1.7994

Curve 23

330 degree

-296.0746 -296.0746 -296.0746 -266.5211 -203.7568 -123.7497 -67.7569 4.3497 74.2391 121.1677 136.6765

-1.2446 -3.1578 -5.618 -7.3385 -6.5636 -2.9292 0.5471 4.8551 5.5067 2.3963 1.7994

1.2446 5.3692 9.4958 14.7776 20.1623 23.9237 27.4561 27.1803 16.4178 3.2539 -1.7994

Curve 24

345 degree

-296.0746 -296.0746 -283.2205 -221.2861 -153.7751 -82.4338 -39.3554 12.4246 59.8826 108.1978 136.6765

-1.2446 -1.6861 -2.1632 1.3245 5.1617 8.992 12.028 13.3076 9.2086 3.9314 1.7994

1.2446 7.4399 14.3305 21.9668 26.4895 28.2089 31.7477 31.9476 21.8179 7.492 -1.7994