Columna Sante

7/25/2019 Columna Sante

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DIAGRAMA DE INTERACCION DE COLUMNA RECTANGULAR

cm =0.003MODELO DE CONCRETO MODELO DE ACERO

fc = 210 [kg/cm2 A! = 6.28 [cm2

k3 = 0.85 "# = 4200 [kg/cm2

$ = 0.002 "!% = &000 [kg/cm2

' = 50 E! = 2100000 [kg/cm2

cm = 0.003 E!( = )0000 [kg/cm2

* = 40 [cm !( = 0.006

+ = ).5 [cm # = 0.002

,c = 2.5 [cm !m = 0.0682

( = 12 [cm = -0.121&

c = 20 [cm ! = -0.0016

= 1.5 Fs : Regin 1

k1 = 0.&6)44444 "! = -330&.50 [kg/cm2

c1 = 0.6666666&

c2 = 0.001

c3 = 0.000025

c4 = 0.000)5

c5 = 0.00230833


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k2 = 0.40&)4224

Cc = 109877 !g" T = #20782 !g"

E$$%$ = 1&0'(8 NO

M)%gnes = #2&720'*'7 !g*c+" M)%gnes = #27871*&991!g*c+"

,)%gnes- = 1*(00E#0. 1/c+"

%gnes- 3 M%e4% s%5s-ic% e4 ce$%

fc = 210 [kg/cm2

A! = 6.28318531 [cm2

M [T.m

0 0 0

0.0005 -0.28 1.50E-04

0.0010 -0.20 6.00E-05

0.0015 0.&4 1.00E-04

0.0020 0.26 6.00E-050.0025 2.06 &.50E-05

0.0030 1.1) 5.25E-05

0.0035 3.4) 6.000E-05

0.0040 2.3& 4.560E-05

0.0045 4.)) 5.000E-05

0.0050 3.68 4.000E-05

cm [1/cm

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012

-1

0

1

2

3

4

5

6

M%+en-% C6$-6$ # %gnes- 3 M%e4% A

C6$-6$ 1/c+

M%+en-% -%n*+


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Filas D[mm] # As[cm!] "i [cm]

10 4 3.14 2.50

! 10 4 3.14 13.05

( 12 0 0.00 23.60

) 12 0 0.00 34.15

* 12 0 0.00 44.70

+ 12 0 0.00 55.25

, 12 0 0.00 65.80

- 12 0 0.00 76.35

. 12 0 0.00 86.90

/ 12 0 0.00 97.45

25 0 0.00 0.00

! 25 0 0.00 0.00

( 25 0 0.00 0.00) 25 0 0.00 0.00

As0 = +!-

c [cm] a [cm] Cc [$%f] Cc [$%f]

! 20.00 17.00 109877 -27418

( 30.00 25.50 164815 -80968

) 40.00 34.00 219753 -136430

* 50.00 42.50 274692 -191753

+ 60.00 51.00 329630 -246949

, 70.00 59.50 384568 -302071

) 14.00 11.90

) 14.00 11.90

* 15.00 12.75

+ 16.00 13.60

, 17.00 14.45

- 18.00 15.30

. 19.00 16.15

!/ 20.00 17.00

! 21.00 17.85

2


fc = 210 [kg/cm2 A! = 6.28 [cm2

k3 = 0.85 "# = 4200 [kg/cm2

$ = 0.002 "!% = &000 [kg/cm2

' = 50 E! = 2100000 [kg/cm2

c( = 0.0012 E!( = )0000 [kg/cm2

* = 40 [cm !( = 0.006

+ = ).5 [cm # = 0.002

,c = 2.5 [cm !m = 0.0682

( = 12 [cm = -0.1066

c = 20 [cm ! = -0.0006

= 0.6 Fs : Regin 1

k1 = 0.48 "! = -1323.00 [kg/cm2

c1 = 1.6666666&

c2 = -0.0008

c3 = 0.000016

c4 = -0.000832

c5 = 0.00051&33


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k2 = 0.3541666&

Cc = #27.18 !g" T = #8&1& !g"

E$$%$ = #1910( NO

M)%gnes = 2.2188*8 !g*c+" M)%gnes = #20088*91.2 !g*c+"

,)%gnes- = '*000E#0( 1/c+"

M%e4% e %gnes-

fc = 210 [kg/cm2

M [T.m

0 0 0

0.0005 0.0 0.00E00

0.0010 2.4 6.00E-05

0.0015 0.0 0.00E00

0.0020 10.2 6.00E-050.0025 -22.& &.50E-05

0.0030 22.6 5.25E-05

0.0035 -3).5 6.00E-05

0.0040 3).5 4.56E-05

0.0045 -60.) 5.00E-05

0.0050 60.) 4.00E-05

cm [1/cm

0.00014 0.00016

e$%

0 0.00001 0.00002 0.

-80

-60

-40

-20

0

20

40

60

80

M%+en-% C6$-6$ #

M%+en-% -%n*+


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fs [$%f&cm!] T [$%f] M [$%fcm] fs! [$%f&cm!] T! [$%f]

0.0026 4200.00 13195 46181 0.0028 4200.00 13195

0.0010 2189.25 6878 -48488 0.0017 3559.50 11182

-0.0005 -1134.00 0 0 0.0006 1344.00 0

-0.0021 -4200.00 0 0 -0.0004 -871.50 0

-0.0037 -4200.00 0 0 -0.0015 -3087.00 0

-0.0053 -4200.00 0 0 -0.0025 -4200.00 0

-0.0069 -4200.00 0 0 -0.0036 -4200.00 0

-0.0085 -4200.00 0 0 -0.0046 -4200.00 0

-0.0100 -4200.00 0 0 -0.0057 -4200.00 0

-0.0116 -4200.00 0 0 -0.0067 -4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 00.0030 4200.00 0 0 0.0030 4200.00 0

+ = 600 *0 = 5400

Mc [$%cm] Mc [$%cm] 2 [$%f] M [$%fcm] /,*

-23&206.66& 242188.8 102531 2676 /,*

-1028160 1023661.8 108225 -37153 /,*

-226&346.6& 22634)1.0& 109713 -50697

-3)54&66.6& 3)51682.1) 109328 -49926

-60)0420 608&84).6 109071 -49412

-86&4306.6& 86&2103.4& 108887 -49044

&

cm =0.003MODELO DE CONCRETO MODELO DE ACERO MODE

fc = 210 [kg/cm2 A! = 6.28 [cm2 fc =

k3 = 0.85 "# = 4200 [kg/cm2 k3 =

$ = 0.002 "!% = &000 [kg/cm2 $ =

' = 50 E! = 2100000 [kg/cm2 ' =

cm = 0.003 E!( = )0000 [kg/cm2 c( =

* = 40 [cm !( = 0.006 * =

+ = ).5 [cm # = 0.002 + =

,c = 2.5 [cm !m = 0.0682 ,c =

( = 12 [cm = -0.12)4 ( =

c = 30 [cm ! = -0.0021 c =

= 1.5 Fs : Regin 1 =

k1 = 0.&6)44444 "! = -4305.00 [kg/cm2 k1 =

c1 = 0.6666666& c1 =

c2 = 0.001 c2 =

c3 = 0.000025 c3 =

c4 = 0.000)5 c4 =

c5 = 0.00230833 c5 =

s s!


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k2 = 0.40&)4224 k2 =

Cc = 1'.81( !g" T = #270.9 !g" Cc =

E$$%$ = 1918'. NO

M)%gnes = #10281'0 !g*c+" M)%gnes = 7.0'7*'9'82 !g*c+" M)%gnes =

,)%gnes- = 1*000E#0. 1/c+"

M%e4% s%5s-ic% e4 ce$%

A! = 6.28318531 [cm2

M [T.m

0 0 0

0.0005 -0.28 1.50E-04

0.0010 -0.20 6.00E-05

0.0015 0.&4 1.00E-04

0.0020 0.26 6.00E-050.0025 2.06 &.50E-05

0.0030 1.1) 5.25E-05

0.0035 3.4) 6.00E-05

0.0040 2.3& 4.56E-05

0.0045 4.)) 5.00E-05

0.0050 3.68 4.00E-05

cm [1/cm

0003 0.00004 0.00005 0.00006 0.0000& 0.00008

%gnes- C%nc$e-% c%n5n%

C6$-6$ 1/c+


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M! [$%fcm] fs( [$%f&cm!] T( [$%f] M( [$%fcm] fs) [$%f&cm!]

46181 0.0028 4200.00 13195 46181 0.0029 4200.00

-78837 0.0020 4200.00 13195 -93023 0.0022 4200.00

0 0.0012 2583.00 0 0 0.0016 3326.40

0 0.0004 921.37 0 0 0.0010 1997.10

0 -0.0004 -740.25 0 0 0.0003 667.80

0 -0.0011 -2401.88 0 0 -0.0003 -661.50

0 -0.0019 -4063.50 0 0 -0.0009 -1990.80

0 -0.0027 -4200.00 0 0 -0.0016 -3320.10

0 -0.0035 -4200.00 0 0 -0.0022 -4200.00

0 -0.0043 -4200.00 0 0 -0.0028 -4200.00

0 0.0030 4200.00 0 0 0.0030 4200.00

0 0.0030 4200.00 0 0 0.0030 4200.00

0 0.0030 4200.00 0 0 0.0030 4200.000 0.0030 4200.00 0 0 0.0030 4200.00

/, +++++++, )*-!*,*+.* *)// +// 3155.1033&

//-( +)))))))) )*-!*,*+.* 5400 600 5)56.34024

/(( )*-!*,*+.* 5400 600 36&4.&6&45

cm =0.003O DE CONCRETO MODELO DE ACERO MODELO DE CONC

210 [kg/cm2 A! = 6.28318530&2 [cm2 fc = 210

0.85 "# = 4200 [kg/cm2 k3 = 0.85

0.002 "!% = &000 [kg/cm2 $ = 0.002

50 E! = 2100000 [kg/cm2 ' = 50

0.0018 E!( = )0000 [kg/cm2 cm = 0.003

40 [cm !( = 0.006 * = 40

).5 [cm # = 0.002 + = ).5

2.5 [cm !m = 0.0682 ,c = 2.5

12 [cm = -0.1162 ( = 12

30 [cm ! = -0.0012 c = 40

0.) Fs : Regin 1 = 1.5

0.63 "! = -2583.00 [kg/cm2 k1 = 0.&6)44444

1.11111111 c1 = 0.6666666&

-0.0002 c2 = 0.001

0.000001 c3 = 0.000025

-0.000202 c4 = 0.000)5

0.00113233 c5 = 0.00230833

s( s)


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0.36)04&62 k2 = 0.40&)4224

#809'8 !g" T = #1'229 !g" Cc = 2197(&

E$$%$ = #'.7&8 NO E$$%$ =

102&''1*8 !g*c+" M)%gnes = 2((0&*..91' !g*c+" M)%gnes = #22'7&.7

,)%gnes- = '*000E#0( 1/c+"


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T) [$%f] M) [$%fcm] fs* [$%f&cm!] T* [$%f] M* [$%fcm]

13195 46181 0.0029 4200.00 13195 46181 0.0029

13195 -93023 0.0023 4200.00 13195 -93023 0.0024

0 0 0.0018 3822.00 0 0 0.0020

0 0 0.0013 2714.25 0 0 0.0015

0 0 0.0008 1606.50 0 0 0.0011

0 0 0.0002 498.75 0 0 0.0006

0 0 -0.0003 -609.00 0 0 0.0002

0 0 -0.0008 -1716.75 0 0 -0.0003

0 0 -0.0013 -2824.50 0 0 -0.0007

0 0 -0.0019 -3932.25 0 0 -0.0012

0 0 0.0030 4200.00 0 0 0.0030

0 0 0.0030 4200.00 0 0 0.0030

0 0 0.0030 4200.00 0 0 0.00300 0 0.0030 4200.00 0 0 0.0030

.

cm =0.003 cm = ETO MODELO DE ACERO MODELO DE CONCRETO

[kg/cm2 A! = 6.28 [cm2 fc = 210 [kg/cm2

"# = 4200 [kg/cm2 k3 = 0.85

"!% = &000 [kg/cm2 $ = 0.002

E! = 2100000 [kg/cm2 ' = 50

E!( = )0000 [kg/cm2 c( = 0.0021

[cm !( = 0.006 * = 40 [cm

[cm # = 0.002 + = ).5 [cm

[cm !m = 0.0682 ,c = 2.5 [cm

[cm = -0.1332 ( = 12 [cm

[cm ! = -0.0023 c = 40 [cm

Fs : Regin 1 = 1.05

"! = -4803.&5 [kg/cm2 k1 = 0.68242063

c1 = 0.)52380)5

c2 = 0.0001

c3 = 0.00000025

c4 = 0.0000))5

c5 = 0.00143308

s* s+


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k2 = 0.3&824&04

!g" T = #&018& !g" Cc = #1&'.&0 !g"

2.99&' NO E$$%$ = #11

!g*c+" M)%gnes = 20(777*&101 !g*c+" M)%gnes = 22'&.91*1 !g*c+"

,)%gnes- = 7*(00E#0( 1/c+"


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fs+ [$%f&cm!] T+ [$%f] M+ [$%fcm] fs, [$%f&cm!] T, [$%f] M, [$%fcm]

4200.00 13195 46181 0.0025 4200.00 13195 46181

4200.00 13195 -93023 0.0002 427.50 1343 -9468

4176.00 0 0 -0.0021 -4200.00 0 0

3226.50 0 0 -0.0043 -4200.00 0 0

2277.00 0 0 -0.0066 -4200.00 0 0

1327.50 0 0 -0.0088 -4200.00 0 0

378.00 0 0 -0.0111 -4200.00 0 0

-571.50 0 0 -0.0134 -4200.00 0 0

-1521.00 0 0 -0.0156 -4200.00 0 0

-2470.50 0 0 -0.0179 -4200.00 0 0

4200.00 0 0 0.0030 4200.00 0 0

4200.00 0 0 0.0030 4200.00 0 0

4200.00 0 0 0.0030 4200.00 0 04200.00 0 0 0.0030 4200.00 0 0

0.003MODELO DE ACERO

A! = 6.28318530&2 [cm2

"# = 4200 [kg/cm2

"!% = &000 [kg/cm2

E! = 2100000 [kg/cm2

E!( = )0000 [kg/cm2

!( = 0.006

# = 0.002

!m = 0.0682

= -0.1222

! = -0.0016

Fs : Regin 1

"! = -3362.63 [kg/cm2

s,


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T = #21128 !g"

(&02 NO

M)%gnes = 1189.8*1129!g*c+"

,)%gnes- = (*2(0E#0( 1/c+"


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fs- [$%f&cm!] T- [$%f] M- [$%fcm] fs. [$%f&cm!] T. [$%f]

0.0025 4200.00 13195 46181 0.0025 4200.00 13195

0.0002 427.50 1343 -9468 0.0004 819.00 2573

-0.0021 -4200.00 0 0 -0.0017 -3612.00 0

-0.0043 -4200.00 0 0 -0.0038 -4200.00 0

-0.0066 -4200.00 0 0 -0.0059 -4200.00 0

-0.0088 -4200.00 0 0 -0.0081 -4200.00 0

-0.0111 -4200.00 0 0 -0.0102 -4200.00 0

-0.0134 -4200.00 0 0 -0.0123 -4200.00 0

-0.0156 -4200.00 0 0 -0.0144 -4200.00 0

-0.0179 -4200.00 0 0 -0.0165 -4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 0

0.0030 4200.00 0 0 0.0030 4200.00 00.0030 4200.00 0 0 0.0030 4200.00 0

s- s.


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MATERIALES

f'c = 210

Fy = 4200

M. [$%fcm] fs/ [$%f&cm!] T/ [$%f] M/ [$%fcm] Ec = 2.10E+05

46181 0.0025 4200.00 13195 46181 Es = 2.10E+06

-18139 0.0006 1161.56 3649 -25727 0.85

0 -0.0014 -2992.50 0 0 0.003

0 -0.0034 -4200.00 0 0

0 -0.0054 -4200.00 0 0

0 -0.0074 -4200.00 0 0

0 -0.0093 -4200.00 0 0

0 -0.0113 -4200.00 0 0

0 -0.0133 -4200.00 0 0

0 -0.0153 -4200.00 0 0

0 0.0030 4200.00 0 0

0 0.0030 4200.00 0 0

0 0.0030 4200.00 0 00 0.0030 4200.00 0 0

MODELO DE CONC

fc = 210

k3 = 0.85

$ = 0.002

' = 50

cm = 0.003

* = 40

+ = ).5

,c = 2.5

( = 12

c = 50

= 1.5

k1 = 0.&6)44444

c1 = 0.6666666&

c2 = 0.001

c3 = 0.000025

c4 = 0.000)5

c5 = 0.00230833

s/

=c =


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k2 = 0.40&)4224

Cc = 27.'92

E$$%$ =

M)%gnes = #&9(.7'7


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SECCION

[kgf/cm2] B = 40 [cm]

[kgf/cm2] H = 12 [cm]

[kgf/cm2] A% = 480 [cm2]

[kgf/cm2]

(


[kg/cm2 A! = 6.28 [cm2 fc = 210 [kg/cm2

"# = 4200 [kg/cm2 k3 = 0.85

"!% = &000 [kg/cm2 $ = 0.002

E! = 2100000 [kg/cm2 ' = 50

E!( = )0000 [kg/cm2 c( = 0.00228

[cm !( = 0.006 * = 40 [cm

[cm # = 0.002 + = ).5 [cm

[cm !m = 0.0682 ,c = 2.5 [cm

[cm = -0.1355 ( = 12 [cm

[cm ! = -0.0024 c = 50 [cm

Fs : Regin 1 = 1.14

"! = -5103.00 [kg/cm2 k1 = 0.&06&426)

c1 = 0.8&&1)2)8

c2 = 0.00028

c3 = 0.000001)6

c4 = 0.0002&608

c5 = 0.0016113&


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k2 = 0.38442484

!g" T = #&20'& !g" Cc = #1917(& !g"

&0'7(( NO E$$%$ = #1'

!g*c+" M)%gnes = &.9&9(*1&0. !g*c+" M)%gnes = &9(1'82*2 !g*c+"

,)%gnes- = '*000E#0( 1/c+"


20/49

0.003 cm =0.003MODELO DE ACERO MODELO DE CONCRETO MO

A! = 6.28318530&2 [cm2 fc = 210 [kg/cm2 A! =

"# = 4200 [kg/cm2 k3 = 0.85 "# =

"!% = &000 [kg/cm2 $ = 0.002 "!% =

E! = 2100000 [kg/cm2 ' = 50 E! =

E!( = )0000 [kg/cm2 cm = 0.003 E!( =

!( = 0.006 * = 40 [cm !( =

# = 0.002 + = ).5 [cm # =

!m = 0.0682 ,c = 2.5 [cm !m =

= -0.1261 ( = 12 [cm =

! = -0.0018 c = 60 [cm ! =

Fs : Regin 1 = 1.5 Fs :

"! = -38&8.28 [kg/cm2 k1 = 0.&6)44444 "! =

c1 = 0.6666666&

c2 = 0.001

c3 = 0.000025

c4 = 0.000)5

c5 = 0.00230833


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k2 = 0.40&)4224

T = #2.&'8 !g" Cc = &29'&0 !g" T =

7&8( NO E$$%$ = &'29.7

M)%gnes = 2&'88'*7(& !g*c+" M)%gnes = #'090.20 !g*c+" M)%gnes =

,)%gnes- = .*('0E#0( 1/c+" ,)%gnes- =


22/49

'

cm =0.003ELO DE ACERO MODELO DE CONCRETO MO

6.28 [cm2 fc = 210 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 c( = 0.0024 E!( =

0.006 * = 40 [cm !( =

0.002 + = ).5 [cm # =

0.0682 ,c = 2.5 [cm !m =

-0.13&0 ( = 12 [cm =

-0.0025 c = 60 [cm ! =

Regin 1 = 1.2 Fs :

-5302.50 [kg/cm2 k1 = 0.&2055556 "! =

c1 = 0.83333333

c2 = 0.0004

c3 = 0.000004

c4 = 0.0003)2

c5 = 0.001&2)33


23/49

k2 = 0.38858)05

#&&&17 !g" Cc = #2.'9.9 !g" T =

NO E$$%$ = #22029'

.989'7*0(.1 !g*c+" M)%gnes = '0878.9*' !g*c+" M)%gnes =

(*000E#0( 1/c+" ,)%gnes- =


24/49


6.28318530&2 [cm2 fc = 210 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 cm = 0.003 E!( =

0.006 * = 40 [cm !( =

0.002 + = ).5 [cm # =

0.0682 ,c = 2.5 [cm !m =

-0.128) ( = 12 [cm =

-0.0020 c = &0 [cm ! =

Regin 1 = 1.5 Fs :

-4242.00 [kg/cm2 k1 = 0.&6)44444 "! =

c1 = 0.6666666&

c2 = 0.001

c3 = 0.000025

c4 = 0.000)5

c5 = 0.00230833


25/49

k2 = 0.40&)4224

#2''(& !g" Cc = &8.('8 !g" T =

NO E$$%$ = .18780

&'822.*098.!g*c+" M)%gnes = #8'7.&07 !g*c+" M)%gnes =

.*000E#0( 1/c+" ,)%gnes- =


26/49

7


6.28 [cm2 fc = 210 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 c( = 0.002485&1 E!( =

0.006 * = 40 [cm !( =

0.002 + = ).5 [cm # =

0.0682 ,c = 2.5 [cm !m =

-0.1381 ( = 12 [cm =

-0.0026 c = &0 [cm ! =

Regin 1 = 1.24285&14 Fs :

-5445.00 [kg/cm2 k1 = 0.&2)42802 "! =

c1 = 0.8045)&&

c2 = 0.000485&1

c3 = 5.8)80E-006

c4 = 0.0004&3)2

c5 = 0.00181315


27/49

k2 = 0.3)1531)

#&.212 !g" Cc = #&02071 !g" T =

NO E$$%$ = #27&72.

'(19.1*&2!g*c+" M)%gnes = 8'7210&*(!g*c+" M)%gnes =

.*28'E#0( 1/c+" ,)%gnes- =


28/49

ELO DE ACERO

6.28318531 [cm2

4200[kg/cm2

&000[kg/cm2

2100000[kg/cm2

)0000 [kg/cm2

0.006

0.002

0.0682

-0.1310

-0.0021

Regin 1

-4511.5& [kg/cm2


29/49

#28&.7 !g"

NO

(07'17*0.!g*c+"

&*((1E#0(1/c+"


30/49


fc = 250 [kg/cm2 A! = 60.8 [cm2

k3 = 0.85 "# = 4200 [kg/cm2

$ = 0.002 "!% = &000 [kg/cm2

' = 50 E! = 2100000 [kg/cm2

cm = 0.0005 E!( = )0000 [kg/cm2

* = 60 [cm !( = 0.006

+ = 55 [cm # = 0.002

!m = 0.0682

= -0.08)1

c = 28.&8 [cm ! = 0.0005

= 0.25 "! Rg 1

k1 = 0.22)1666& "! = )56.60 [kg/cm2

c1 = 4

c2 = -0.0015c3 = 0.00005625

c4 = -0.0016125

c5 = -0.000222)2

k2 = 0.340)0)0)

Cc = 8.092 !g" T = (81'1 !g"

E$$%$ = 2(9&0 NO

M)%gnes = &79998& !g*c+" M)%gnes = 2'282&&*897 !g*c+"

,)%gnes- = 1*7&7E#0( 1/c+"

%gnes- 3 M%e4% s%5s-ic% e4 ce$%

fc = 250 [kg/cm2

A! = 60.8 [cm2

M [T.m

0 0 0

0.0005 26.28 1.&4E-05

0.0010 48.&6 3.3&E-05

0.0015 11).32 6.55E-05

0.0020 122.15 1.05E-040.0025 122.&3 1.41E-04

0.0030 -2&.24 3.33E-05

0.0035 126.33 2.03&E-04

0.0040 12&.82 2.2)4E-04

0.0045 128.&2 2.522E-04

0.0050 12).11 2.&23E-04

cm [1/cm

20

40

60

80

100

120

140

M%+en-% C6$-6$ # %gnes- 3 M%e4% A

M%+en-% -%n*+


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0 0.00005 0.0001 0.00015 0.0002 0.0

-40

-20

0

C6$-6$ 1/c+


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cm =0.001MODELO DE CONCRETO MODELO DE ACERO MODE

fc = 250 [kg/cm2 A! = 60.8 [cm2 fc =

k3 = 0.85 "# = 4200 [kg/cm2 k3 =

$ = 0.002 "!% = &000 [kg/cm2 $ =

' = 50 E! = 2100000 [kg/cm2 ' =

cm = 0.001 E!( = )0000 [kg/cm2 cm =

* = 60 [cm !( = 0.006 * =

+ = 55 [cm # = 0.002 + =

!m = 0.0682

= -0.082&

c = 2).63& [cm ! = 0.000) c =

= 0.5 "! Rg 1 =

k1 = 0.4166666& "! = 1&)&.16 [kg/cm2 k1 =

c1 = 2 c1 =

c2 = -0.001 c2 =c3 = 0.000025 c3 =

c4 = -0.00105 c4 =

c5 = 0.00030833 c5 =

k2 = 0.35 k2 =

Cc = 1(7..7 !g" T = 1092'7 !g" Cc =

E$$%$ = .8180 NO

M)%gnes = 702'&7(*' !g*c+" M)%gnes = .87'2''*(2. !g*c+" M)%gnes =

,)%gnes- = &*&7.E#0( 1/c+"

M%e4% e %gnes- M%e4%

fc = 250 [kg/cm2

A! =

M [T.m

0 0 0 0

0.0005 38.0 1.&4E-05 0.0005

0.0010 &0.3 3.3&E-05 0.0010

0.0015 &6.8 6.55E-05 0.0015

0.0020 &&.& 1.05E-04 0.00200.0025 &).3 1.41E-04 0.0025

0.0030 161.4 3.33E-05 0.0030

0.0035 83.0 2.04E-04 0.0035

0.0040 85.3 2.2)E-04 0.0040

0.0045 8&.6 2.52E-04 0.0045

0.0050 8).) 2.&2E-04 0.0050

cm [1/cm cm

e$%

60

80

100

120

140

160

180

M%+en-% C6$-6$ # %gnes

M%+en-% -%n*+


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0025 0.0003

0 0.00005 0.0001 0.00

20

40

C6$-


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cm =0.0015O DE CONCRETO MODELO DE ACERO MODELO DE CONC

250 [kg/cm2 A! = 60.8 [cm2 fc = 250

0.85 "# = 4200 [kg/cm2 k3 = 0.85

0.002 "!% = &000 [kg/cm2 $ = 0.002

50 E! = 2100000 [kg/cm2 ' = 50

0.0015 E!( = )0000 [kg/cm2 cm = 0.002

60 [cm !( = 0.006 * = 60

55 [cm # = 0.002 + = 55

!m = 0.0682

= -0.062&

22.)1& [cm ! = 0.0021 c = 1).108

0.&5 "! Rg 2 = 1

0.5625 "! = 4200.00 [kg/cm2 k1 = 0.6666666&

1.33333333 c1 = 1

-0.0005 c2 = 00.00000625 c3 = 0

-0.0005125 c4 = 0

0.00082&08 c5 = 0.00133333

0.36111111 k2 = 0.3&5

1'.&(8 !g" T = 2((&'0 !g" Cc = 1'2.18

E$$%$ = #91002 NO E$$%$ =

7'79(2(*1 !g*c+" M)%gnes = 119&1(.7*0. !g*c+" M)%gnes = 77'918&*8

,)%gnes- = '*(.(E#0( 1/c+"

%5s-ic% e4 ce$%

60.8 [cm2

M [T.m

0 0

26.28 1.&4E-05

48.&6 3.3&E-05

11).32 6.55E-05

122.15 1.05E-04122.&3 1.41E-04

-2&.24 3.33E-05

126.33 2.04E-04

12&.82 2.2)E-04

128.&2 2.52E-04

12).11 2.&2E-04

[1/cm

C%nc$e-% c%n5n%


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015 0.0002 0.00025 0.0003

$ 1/c+


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[kg/cm2 A! = 60.8 [cm2 fc = 250 [kg/cm2

"# = 4200 [kg/cm2 k3 = 0.85

"!% = &000 [kg/cm2 $ = 0.002

E! = 2100000 [kg/cm2 ' = 50

E!( = )0000 [kg/cm2 cm = 0.0025

[cm !( = 0.006 * = 60 [cm

[cm # = 0.002 + = 55 [cm

!m = 0.0682

= -0.0361

[cm ! = 0.0038 c = 1&.&04 [cm

"! Rg 2 = 1.25

"! = 4200.00 [kg/cm2 k1 = 0.&3083333

c1 = 0.8

c2 = 0.0005c3 = 0.00000625

c4 = 0.00048&5

c5 = 0.00182&08

k2 = 0.3)201824

!g" T = 2((&'0 !g" Cc = 1'.9'8 !g"

#929.2 NO E$$%$ = #9

!g*c+" M)%gnes = 1221(017*92 !g*c+" M)%gnes = 7928&18*2 !g*c+"

,)%gnes- = 1*0.7E#0. 1/c+"


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0.0025 cm =0.003MODELO DE ACERO MODELO DE CONCRETO MO

A! = 60.8 [cm2 fc = 250 [kg/cm2 A! =

"# = 4200 [kg/cm2 k3 = 0.85 "# =

"!% = &000 [kg/cm2 $ = 0.002 "!% =

E! = 2100000 [kg/cm2 ' = 50 E! =

E!( = )0000 [kg/cm2 cm = 0.003 E!( =

!( = 0.006 * = 60 [cm !( =

# = 0.002 + = 55 [cm # =

!m = 0.0682 !m =

= -0.0118 =

! = 0.0053 c = )0 [cm ! =

"! Rg 2 = 1.5 Fs :

"! = 4200.00 [kg/cm2 k1 = 0.&6)44444 "! =

c1 = 0.6666666&

c2 = 0.001c3 = 0.000025

c4 = 0.000)5

c5 = 0.00230833

k2 = 0.40&)4224

T = 2((&'0 !g" Cc = 8829&8 !g" T =

&92 NO E$$%$ = 10&1898

M)%gnes = 12272(27*29 !g*c+" M)%gnes = 1'1..'88 !g*c+" M)%gnes =

,)%gnes- = 1*.12E#0. 1/c+" ,)%gnes- =


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60.8 [cm2 fc = 250 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 cm = 0.0035 E!( =

0.006 * = 60 [cm !( =

0.002 + = 55 [cm # =

0.0682 !m =

-0.1152 =

-0.0012 c = 1&.186 [cm ! =

Regin 1 = 1.&5 Fs :

-2450.00 [kg/cm2 k1 = 0.&)345238 "! =

c1 = 0.5&14285&

c2 = 0.0015c3 = 0.00005625

c4 = 0.00138&5

c5 = 0.002&&&08

k2 = 0.4214)823

#1.89'0 !g" Cc = 17&8'2 !g" T =

NO E$$%$ = #90'78

#272&7'&*18 !g*c+" M)%gnes = 8&02999*2 !g*c+" M)%gnes =

&*&&&E#0( 1/c+" ,)%gnes- =


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60.8 [cm2 fc = 250 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 cm = 0.004 E!( =

0.006 * = 60 [cm !( =

0.002 + = 55 [cm # =

0.0682 !m =

0.02&3 =

0.00&& c = 1&.436 [cm ! =

Regin & = 2 Fs :

4351.00 [kg/cm2 k1 = 0.80833333 "! =

c1 = 0.5

c2 = 0.002c3 = 0.0001

c4 = 0.0018

c5 = 0.00323333

k2 = 0.432)8)6)

2'.(.1 !g" Cc = 179700 !g" T =

NO E$$%$ = #89'82

12'&&.&2*09 !g*c+" M)%gnes = 8(2'82.*7 !g*c+" M)%gnes =

2*0&7E#0. 1/c+" ,)%gnes- =


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44/49


60.8 [cm2 fc = 250 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 cm = 0.0045 E!( =

0.006 * = 60 [cm !( =

0.002 + = 55 [cm # =

0.0682 !m =

0.0421 =

0.0086 c = 1&.845 [cm ! =

Regin & = 2.25 "!

4430.63 [kg/cm2 k1 = 0.81&12)63 "! =

c1 = 0.44444444

c2 = 0.0025c3 = 0.00015625

c4 = 0.00218&5

c5 = 0.0036&&08

k2 = 0.4428&063

2'9&82 !g" Cc = 18(91' !g" T =

NO E$$%$ = #87&82

1278228(*2& !g*c+" M)%gnes = 87('099*7 !g*c+" M)%gnes =

2*29.E#0. 1/c+" ,)%gnes- =


45/49


46/49


60.8 [cm2 fc = 250 [kg/cm2 A! =

4200 [kg/cm2 k3 = 0.85 "# =

&000 [kg/cm2 $ = 0.002 "!% =

2100000 [kg/cm2 ' = 50 E! =

)0000 [kg/cm2 cm = 0.005 E!( =

0.006 * = 60 [cm !( =

0.002 + = 55 [cm # =

0.0682 !m =

0.0542 =

0.00)4 c = 18.365 [cm ! =

Rg 3 = 2.5 "!

44)5.04 [kg/cm2 k1 = 0.8216666& "! =

c1 = 0.4

c2 = 0.003c3 = 0.000225

c4 = 0.00255

c5 = 0.00410833

k2 = 0.4515213

27&298 !g" Cc = 192&9' !g" T =

NO E$$%$ = #8.01'

12871(2&*'1 !g*c+" M)%gnes = 898'.11*( !g*c+" M)%gnes =

2*(22E#0. 1/c+" ,)%gnes- =


47/49


48/49

ELO DE ACERO

60.8 [cm2

4200[kg/cm2

&000[kg/cm2

2100000 [kg/cm2

)0000 [kg/cm2

0.006

0.002

0.0682

0.063)

0.0100

Rg 3

4546.25 [kg/cm2

27'.12 !g"

NO

12910(99*&7 !g*c+"

2*72&E#0.1/c+"


49/49

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