Analisis Ultima Version

1

Predimensionamiento De

Columnas, Vigas Y Zapatas Datos: Niveles = 6

Cv = 500 kg/m2

Cm = 300 kg/m2

Cvaz = 100 kg/m2

Cp del suelo = 1.03 kg/cm2

σ del suelo = 1903 kg/m3

S/C = 500 kg/ m2

E. piso = 0.15 m

F’c = 210 kg/cm2

F’y = 4200 kg/cm2

Φ de columna central y lateral = ¾”

Φ de columna esquina = 5/8”

1. PREDIMENSIONAMIENTO DE COLUMNAS. COLUMNA 1:

At1 = 5x4.25=21.25 m2

PGp=1.2(300)+1.6(500) =1160kg/m2

PGaz = 1.2 (300)+1.6 (100) = 520 kg/m2

Pt = (5x1160x21.25)+ (520x1x21.25)=134300kg

1º piso:

Asc=(1.1)(134300)

(0.25)(210)= 2813.90 cm2= (53.05)2= 55x55 cm

2

2º piso:

Asc=(1.1)(109650)

(0.25)(210)= 2297.43 cm2= (47.93)2= 50x50 cm

3º piso:

Asc=(1.1)(85000)(0.25)(210)

= 1780.95 cm2=(42.20)2 = 45x45 cm

4º piso:

Asc=(1.1)(60350)

(0.3)(210)= 1053.73 cm2= (32.46)2= 35x35 cm

5º piso:

Asc=(1.1)(35700)

(0.3)(210)= 623.33cm2= (24.97)2= 25x25 cm

6º piso:

Asc=(1.1)(35700)

(0.3)(210)= 623.33cm2= (24.97)2= 25x25 cm

COLUMNA 2:

At =5x2.25=11.25 m2

PGp =1.2(300)+1.6(500 )=1160kg/m2

PGaz = 1.2 (300)+1.6 (100) = 520 kg/m2

Pt = (5x1160x11.25)+ (520x11.25) =71100kg

1º piso:

Asc=(1.25)(71100)

(0.25)(210)= 1692.86 cm2= (41.14)2= 45x45 cm

2º piso:

Asc=(1.25)(58050)

(0.25)(210)= 1382.14 cm2= (37.18)2= 40x40 cm

3

3º piso:

Asc=(1.8)(45000)(0.25)(210)

= 1071.43 cm2= (32.71)2= 35x35 cm

4º piso:

Asc=(1.25)(31950)

(0.25)(210)= 760.71 cm2= (27.58)2= 30x30 cm

5º piso:

Asc=(1.25)(18900)

(0.25)(210)= 450cm2= (21.21)2= 25x25 cm

6º piso:

Asc=(1.25)(18900)

(0.25)(210)= 450cm2= (21.21)2= 25x25 cm

COLUMNA 3:

At=4.25x2.5 =10.625 m2

PGp=1.2(300)+1.6(500) =1160kg/m2

PGaz= 1.2 (300)+1.6 (100) = 520 kg/m2

Pt= (5x1160x10.625)+ (520x10.625) = 67150kg

1º piso:

Asc=(1.25)(67150)

(0.25)(210)= 1598.81 cm2= (39.99)2= 40x40 cm

2º piso:

Asc=(1.25)(54825)

(0.25)(210)= 1305.36 cm2= (36.13)2= 40x40 cm

3º piso:

Asc=(1.25)(42500)

(0.25)(210)= 1011.91 cm2= (31.81)2= 35x35 cm

4

4º piso:

Asc=(1.25)(30175)

(0.25)(210)= 718.452 cm2= (26.8)2= 30x30 cm

5º piso:

Asc=(1.25)(17850)

(0.25)(210)= 425cm2= (20.6)2= 25x25 cm

6º piso:

Asc=(1.25)(17850)

(0.25)(210)= 425cm2= (20.6)2= 25x25 cm

COLUMNA 4:

At=2.25x2.5=5.625 m2

PGp=1.2(300)+1.6(500)=1160kg/m2

PGaz= 1.2 (300)+1.6 (100)= 520 kg/m2

Pt= (5x1160x5.625)+ (520x5.625)=35550kg

1º piso:

Asc=(1.5)(35550)(0.20)(210)

= 1269.64 cm2= (35.6)2= 40x40 cm

2º piso:

Asc=(1.5)(29025)(0.20)(210)

= 1036.61 cm2= (32.19)2= 35x35 cm

3º piso:

Asc=(1.5)(22500)(0.20)(210)

= 803.57 cm2= (28.3)2= 30x30 cm

4º piso:

Asc=(1.5)(15975)(0.20)(210)

= 570.54 cm2= (23.9)2= 25x25 cm

5º piso:

Asc=(1.5)(9450)(0.20)(210)

= 337.5 cm2= (18.37)2= 25x25 cm

5

6º piso:

Asc=(1.5)(2925)(0.20)(210)

= 104.46 cm2= (10.22)2= 25x25 cm

Resumen de datos

6

2. PREDIMENSIONAMIENTO DE VIGAS:

Principales:

P=(𝐿)

(10)=

(5)(10)

= 0.5

b=(𝐿)

(20)=

(5)(20)

=0.25

Vp = 50cm x 25cm

Secundaria:

P=(𝐿)

(12)=

(4.5)(12)

= 0.375= 40

b=(𝐿)

(20)=

(4.5)(20)

=0.225= 25

Vs =40 cm x 25cm

3. PREDIMENSIONAMIENTO DE ZAPATAS: Zapata N° 1

CVT = (5000(5)+100) (21.25) = 55250Kg = 55.25Tn

CMT = (300) (21.25) (6) =38250Kg = 38.25Tn

Peralte efectivo

d = 0.08 * 𝜙Ac * 𝐹ʹ𝑦√𝐹ʹ𝑐

≥ 0.004 * ∅A * Fʹy

d = 0.08 * 1.905 * 4200√210

≥ 0.004 * 1.905 * 4200

d = 44.17 ≥ 32

Altura de la zapata será:

hz = d + r + ∅b = 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m

7

El peralte efectivo de diseño será:

dʹ = 60 – 10 – 1.588 = 48.41cm = 0.4841m

Esfuerzo neto del terreno

𝜎𝑛 = 1.03 ∗ (1002) − 1903(. 6) − 500 − 24008(.15)

𝜎𝑛 = 6858.2 𝑘𝑔𝑚2 = 6.858𝑇𝑛/𝑚2

Área de zapata

Az = 𝑷𝒆𝒔𝒕.𝜎n

Az = (𝟓𝟓.𝟐𝟓+𝟑𝟖.𝟐𝟓)𝑻𝒏𝟔.𝟖𝟓𝟖𝑻𝒏/𝒎𝟐

= 13.634𝑚2

Lv1 = Lv2

T = S = √13.634 ± (.𝟓𝟓−.𝟓𝟓𝟐

) = 3.692𝑚 ≅ 3.7𝑚

S = 3.7m T = 3.7m

LV1 = LV2 = 𝟑.𝟕−𝟎.𝟓𝟓

𝟐= 1.575𝑚

Reacción ultima

Wnu = (𝟑𝟖.𝟐𝟓)(𝟏.𝟐)+𝟓𝟓.𝟐𝟓(𝟏.𝟔)

(𝟑.𝟕)𝟐= 𝟗.𝟖𝟏𝑻𝒏

𝒎𝟐 = 9810𝑘𝑔/𝑚2

verificación de cortante

∅vc > Vu

∅(0.53)√𝐹ʹ𝑐 (𝑆)dʹ > Wnu(S)(LV − dʹ)

0.75(0.53)√210(10)(3.70)(0.4841) > 9.81(3.7)(1.575 − 0.4841)

103.18 > 39.596

8

corte por punzonamiento

m = dʹ + t1 = 0.4841+0.55 = 1.034m

n = dʹ + t2 = 0.4841+0.55 = 1.034m

Vu < ∅Vc

Vu = Pdin – Wnu (m) (n)

Vu = 134.3 – 9.81 (1.034)2 = 123.812Tn

bo = 2m + 2n = 4(1.034) = 4.136m

𝛽𝑐 = 0.550.55

= 1

∅(0.27)(2 + 4𝛽𝑐

)√𝐹ʹ𝑐 𝑏𝑜𝑑

∅Vc ∅(0.27)(∝𝑠𝑑𝑏𝑜

+ 2)√𝐹ʹ𝑐 𝑏𝑜𝑑

∅ ∗ 1.1√𝐹ʹ𝑐 𝑏𝑜𝑑

0.75(0.27) �2 + 41�√210 (10)(4.136)(0.4841) = 352.53𝑇𝑛

∅Vc 0.75(0.27) �(40)(.4841)4.136

+ 2� √210 (10)(4.136)(0.4841) = 392.595𝑇𝑛

0.75 ∗ 1.1 ∗ √210 (10)(4.136)(0.4841) = 239.375𝑇𝑛

Acero

Mu = 𝑊𝑛𝑢2

(𝐿𝑣1)2 ∗ 𝑆

Mu = 9.812

(1.575)2 ∗ (3.7) = 45.02 𝑇𝑛𝑚

= 45.02 ∗ 105𝑘𝑔/𝑐𝑚

9

Área del acero

As = 𝑀𝑢

∅𝐹ʹ𝑦(𝑑ʹ−𝑎2) = As=

(𝑎)(0.85)(𝐹ʹ𝑐)(𝑆)𝐹ʹ𝑦

45.02∗105

0.9(4200)(48.41− 𝑎2) =

𝑎(0.85)(210)(370)4200

50.02∗105

6.6045∗104= 48.41𝑎 − 0.5𝑎2

0.5𝑎2 − 48.41𝑎 + 75.736 = 0

𝑎 =48.41 ± �48.412 − 4(0.5)(75.736)

1= 48.41 ± 46.81𝑎

𝒂 = 𝟏.𝟓𝟗𝟏𝒄𝒎

As1= 45.0∗105

0.9(4200)(48.41−1.5912 )

= 𝟐𝟓.𝟎𝟏𝟑𝒄𝒎𝟐

As2= 1.591(0.85)(210)(370)4200

= 𝟐𝟓.𝟎𝟏𝟖𝒄𝒎𝟐

As=25.018 𝒄𝒎𝟐

Verificación de acero mínimo

As> As𝑚𝑖𝑛𝑖𝑚𝑜

25.0188>0.0018 (48.41) (370)

25.018>32.241

As = 32.241𝒄𝒎𝟐

Nv⅝ = 32.241

2= 16.12 ≅ 17

S = 370−2(2.75)−1.588

16= 22.09 ≅ 0.22𝑚

Lv =370 – 2(7.5) = 355 = 3.55𝑚

10

17 ∅ ⅝ @ 0.22

Zapata N° 2

CVT = (500(5)+100) (11.25) = 29250Kg = 29.25Tn

CMT = (300) (11.25) (6) =20250Kg = 20.25Tn

Peralte efectivo


≥ 0.004 * ∅A * Fʹy

d = 0.08 * 1.905 * 4200√210

≥ 0.004 * 1.905 * 4200

d = 44.17 ≥ 32


hz = d + r + ∅b= 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m


dʹ = 60 – 10 – 1.588 = 48.41cm = 0.4841m


𝜎𝑛 = 1.03 ∗ (1002) − 1903(. 6) − 500 − 24008(.15) 𝜎𝑛 = 6858.2 𝑘𝑔

𝑚2 = 6.858𝑇𝑛/𝑚2

Área de zapata


Az = (𝟐𝟗.𝟐𝟓+𝟐𝟎.𝟐𝟓)𝑻𝒏𝟔.𝟖𝟓𝟖𝑻𝒏/𝒎𝟐

= 7.22𝑚2

11

Lv1 = Lv2

S= Lv2 + t2 Lv2 = S- t2

T= 2 Lv1 + t1 Lv1= 𝑇−𝑡12

2AZ=T2-T (t1-2t2)

2(7.22)= T2-T (0.45-2(0.45))

14.44= T2 + 0.45T

0= T2 + 0.45T -14.44

𝑇 =−0.45 ± �0.452 − 4(1)(14.44)

2 = 3.585 𝑚

2S2=AZ-S (t1-2t2)

2S2=7.22-S (0.45-2(0.45))

S = 0.45±�0.452−4(2)(7.22)4

= 2.015 𝑚

Lv2 = 2.015-0.45 = 1.565

Lv1 =𝟑.𝟓𝟖𝟓−𝟎.𝟒𝟓

𝟐 =1.567

Lv2=Lv1=1.60

S=1.6+ (0.45)=2.05 m

T=2(1.6)+ (0.45)= 3.65 m

Reacción ultima

Wnu = (𝟐𝟎.𝟐𝟓)(𝟏.𝟐)+𝟐𝟗.𝟓𝟓(𝟏.𝟔)

(𝟐.𝟎𝟓)(𝟑.𝟔𝟓)= 𝟗.𝟓𝟕𝑻𝒏

𝒎𝟐 = 9570𝑘𝑔/𝑚2

m = dʹ + t1 = 0.4841+0.45 = 0.934m

n = dʹ + t2 = 0.4841+0.45 = 0.934m

12


EJE “x”

∅vc > Vu


0.75(0.53)√210(10)(3.65)(0.4841) > 9.57(3.65)(1.6 − 0.4841)

101.783 > 38.979

EJE “y”


0.75(0.53)√210(10)(2.05)(0.4841) > 9.57(2.05)(1.6 − 0.4841)

57.166 > 21.8923

corte por punzonamiento

Vu < ∅Vc


Vu = 71.58 – 9.57 (0.934)2 = 63.23 Tn

bo = 2m + 2n = 4(0.934) = 3.736m

𝛽𝑐 = 0.450.45

= 1

∅(0.27)(2 + 4𝛽𝑐


∅Vc ∅(0.27)(∝𝑠𝑑𝑏𝑜



13

0.75(0.27) �2 + 41�√210 (10)(3.736)(0.4841) = 318.44 𝑇𝑛

∅Vc 0.75(0.27) �(30)(0.4841)3.736

+ 2� √210 (10)(3.736)(0.4841) = 312.46𝑇𝑛

0.75 ∗ 1.1 ∗ √210 (10)(3.736)(0.4841) = 216.225 𝑇𝑛

Acero

Mu = 𝑊𝑛𝑢2

(𝐿𝑣1)2 ∗ 𝑆

Mu = 9.572

(1.6)2 ∗ (3.65) = 44.71 𝑡𝑛.𝑚 = 44.71 ∗ 105𝑘𝑔/𝑐𝑚

Área del acero

As = 𝑀𝑢



44.71∗105

0.9(0.85)(210)(365) = 48.41 a – 0.5 a2

0.5𝑎2 − 48.41𝑎 + 76.25 = 0

𝑎 =48.41 ± �48.412 − 4(0.5)(76.25)

1 = 48.41 ± 46.81𝑎

𝒂 = 𝟏.𝟔 𝒄𝒎

As1= 44.71∗105

0.9(4200)(48.41−(0.5∗1.6))= 𝟐𝟒.𝟖𝟒 𝒄𝒎𝟐

As2= 1.6(0.85)(210)(365)4200

= 𝟐𝟒.𝟖𝟐 𝒄𝒎𝟐

As=24.84 𝒄𝒎𝟐



24.84>0.0018 (48.41) (365)

14

24.84> 31.811

As =31.81 𝒄𝒎𝟐

Nv⅝ = 31.812

= 15.91 ≅ 16

S = 365−2(7.5)−1.588

15= 23.22 ≅ 24 𝑐𝑚 ≅ 0.24 𝑚

Lv =205 – 2(7.5) = 190 cm = 1.9 𝑚

16 ∅ ⅝ @ 0.24

Ast = (𝐴𝑠)(𝑆)

𝑇=

(31.81)(205)365

= 17.87 cm2

Nºv⅝ = (17.87)

2= 8.935≅9

Se= (205)−(2∗7.5)−(1.588)

8=23.55 cm=0.24 m

Lv=365-(2*7.5)=350=3.5m

9 ∅ ⅝ @ 0.24

Zapata N° 3

CVT = (5000(5)+100) = 29.25Tn

CMT = (300) (6) (11.25) = 20.25Tn

Peralte efectivo


≥ 0.004 * ∅A * Fʹy

d = 0.08 * 1.905 * 4200√210

≥ 0.004 * 1.905 * 4200

d = 44.17 ≥ 32


hz = d + r + ∅b= 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m

15


dʹ = 60 – 10 – 1.588 = 48.41cm = 0.4841m


𝜎𝑛 = 1.03 ∗ (1002) − 1903(. 6) − 500 − 24008(.15)

𝜎𝑛 = 6858.2 𝑘𝑔𝑚2 = 6.858𝑇𝑛/𝑚2

Área de zapata


Az = (𝟐𝟕.𝟔𝟓+𝟏𝟗.𝟏𝟐𝟓)𝑻𝒏

𝟔.𝟖𝟓𝟖𝑻𝒏/𝒎𝟐= 6.817𝑚2

Lv1 = Lv2

S = Lv2 + t2 Lv = S – t2

T = 2Lv1 + t1 Lv1 = 𝑇−𝑡12

2Az = T2 – T(t1-2t2)

0 = T2 + 0.40T-13.634

T=−0.4±�4(13.634)+0.42

2

T=3.5m

S = 0.4±√4∗2∗6.817+0.42

4

S = 1.95m

Lv2 = 1.949 – 0.4 = 1.549

Lv1 = (3.498 – 0.4)/2 = 1.549

16

Lv2=Lv1=1.55m

S = 1.55 + 0.4 =1.95m

T = 2*1.55 + 0.4 = 3.50m

Reacción ultima

Wnu = (𝟐𝟕.𝟔𝟐𝟓)(𝟏.𝟔)+𝟏𝟗.𝟏𝟐𝟓(𝟏.𝟐)𝟏.𝟗𝟓∗𝟑.𝟓

= 𝟗.𝟖𝟑𝟗𝑻𝒏𝒎𝟐


Eje “ X”

∅vc > Vu


0.75(0.53)√210(10)(3.5)(0.4841) > 9.839(3.5)(1.55 − 0.4841)

97.6 > 36.71

Eje “ Y”

0.75(0.53)√210(10)(1.95)(0.4841) > 9.839(1.95)(1.55 − 0.4841)

54.38 > 20.45

verificación por punzonamiento

m = dʹ + t1 = 0.4841 + 0.4 = 0.884m

n = dʹ + t2 = 0.4841 + 0.4 = 0.884m

V𝜇 = 67.115 - 9.839(0.884)2 = 59.46Tn

bo = 3(0.884) = 2.652m

𝛽 = 0.40.4

= 1

17

0.75(0.27) �2 + 41�√210 (10)(2.652)(. 4841) = 226.04𝑇𝑛

∅Vc 0.75(0.27) �(30)(.4841)2.802

+ 2�√210 (10)(2.652)(. 4841) = 281.66𝑇𝑛

0.75 ∗ 1.1 ∗ √210 (10)(2.652)(. 4841) = 153.49𝑇𝑛

Área del acero

As = 𝑀𝑢


(𝑎)(0.85)(𝐹ʹ𝑐)(𝑇)𝐹ʹ𝑦

𝑀𝑢

0.9(0.85)𝐹ʹ𝑐(𝑇) =𝑑𝑎 − 0.5𝑎2

41.37∗105

0.9(0.85)(210)(350)= 48.41𝑎 − 0.5𝑎2

0.5𝑎2 − 48.41𝑎 + 73.576 = 0

𝑎 =48.41 ± �48.412 − 4(0.5)(73.576)

1 = 48.41 ± 46.81𝑎

𝒂 = 𝟏.𝟓𝟒𝟒𝒄𝒎

As1= 41.37∗105

0.9(4200)(48.41−0.5∗1.544)= 𝟐𝟐.𝟗𝟕𝟒𝒄𝒎𝟐

As2= 1.544(0.85)(210)(350)4200

= 𝟐𝟐.𝟗𝟔𝟕𝒄𝒎𝟐

As = 22.97𝐜𝐦𝟐


As >Aminimo

22.97 >0.0018 (48.41) (350)

22.97 >30.498

As = 30.498𝒄𝒎𝟐

18

Area del acero longitudinal “x”

Nv⅝ = 30.4982

= 15.249 ≅ 16

Se = 350−2(7.5)−1.588

15= 22.23𝑐𝑚 ≅ 0.23𝑚

Lv = 195 – 2(7.5) = 180cm = 1.8𝑚

16 ∅ ⅝ @ 0.23

Área de acero en la sección transversal ”Y”

AST=𝐴𝑠∗𝑆𝑇

= 31.84∗205365

= 17.87𝑐𝑚2

Nv⅝ = 16.962

= 8.495 ≅ 9

Se = 195−2(7.5)−1.588

8= 22.3𝑐𝑚 ≅ 0.23𝑚

Lv = 350 – 2(7.5) = 335cm = 3.5𝑚

9 ∅ ⅝ @ 0.23

Zapata N° 4

CVT = (500(5)+100) (5.625) = 14625 kg = 14.625Tn

CMT = (300) (5.625) (6) =10125 Kg = 10.125 Tn

Peralte efectivo


≥ 0.004 * ∅A * Fʹy

d = 0.08 * 1.588 * 4200√210

≥ 0.004 * 1.588 * 4200

d = 36.82 ≥ 26.68


19

hz = d + r + ∅b= 36.82 + 10 +1.588 = 48.408cm = 50cm = 0.5m

Por condiciones de diseño la altura de la zapata será 60 cm


dʹ = 60 – 10 – 1.588 = 48.41cm = 0.4841m


𝜎𝑛 = 1.03 ∗ (1002) − 1903(. 6) − 500 − 24008(.15)

𝜎𝑛 = 6858.2 𝑘𝑔𝑚2 = 6.858𝑇𝑛/𝑚2

Área de zapata


Az = (𝟏𝟒.𝟔𝟐𝟓+𝟏𝟎.𝟏𝟐𝟓)𝑻𝒏

𝟔.𝟖𝟓𝟖𝑻𝒏/𝒎𝟐= 𝟑.𝟔𝟏𝑚P

2

Debe cumplir que:

Lv1 = Lv2 S= Lv2 + t2 Lv2 = S- t2

T= Lv1 + t1 Lv1= 𝑇 − 𝑡1

Az = T2-T (t1-t2)

3.61= T2-T (0.40-0.40)

T=1.9m

Az = S2-S (t1-2t2)

3.61= S2-S (0.40-0.40)

S = 1.9 m

Lv2=1.9-0.4=1.5 m

20

Reacción ultima

Wnu = (𝟏𝟎.𝟏𝟐𝟓)(𝟏.𝟐)+𝟏𝟒.𝟔𝟐𝟓(𝟏.𝟔)

(𝟏.𝟗)𝟐= 𝟗.𝟖𝟓𝑻𝒏

𝒎𝟐 = 9850𝑘𝑔/𝑚2

m = dʹ + t1 = 0.4841+0.40 = 0.884m

n = dʹ + t2 = 0.4841+0.40 = 0.884m

bo= m+n=1.768 Bc=0.40/0.40 =1



0.75(0.53)√210(10)(1.9)(0.4841) > 9.85(1.9)(1.5 − 0.4841)

52.98 > 19.01

Corte por punzonamiento

Vu < ∅Vc


Vu = 35.55 – 9.85 (0.884)2 = 27.85 Tn

∅(0.27)(2 + 4𝛽𝑐


∅Vc ∅(0.27)(∝𝑠𝑑𝑏𝑜



0.75(0.27)(2 + 4)√210 (10)(1.768)(0.4841) = 150.70 𝑇𝑛

∅Vc 0.75(0.27) �(20)(0.4841)1.768

+ 2� √210 (10)(1.768)(0.4841) = 187.77𝑇𝑛

0.75 ∗ 1.1 ∗ √210 (10)(1.768)(0.4841) = 102.325 𝑇𝑛

21

Acero

Mu = 𝑊𝑛𝑢2

(𝐿𝑣1)2 ∗ 𝑆

Mu = 9.852

(1.5)2 ∗ (1.9) = 21.05 𝑡𝑛.𝑚 = 21.05 ∗ 105𝑘𝑔/𝑐𝑚

Área del acero

As = 𝑀𝑢



21.05∗105

0.9(0.85)(210)(1.90) = 48.41 a – 0.5 a2

0.5𝑎2 − 48.41𝑎 + 68.963 = 0

𝑎 =48.41 ± �48.412 − 4(0.5)(68.963)

1 = 48.41 ± 46.964

𝒂 = 𝟏.𝟒𝟒𝟔 𝒄𝒎

As1= 21.05∗105

0.9(4200)(48.41−(0.5∗1.446))= 11.678 𝑐𝑚2

As2= 1.446(0.85)(210)(190)4200

= 11.676 𝑐𝑚2

As=11.678 𝑐𝑚2



11.678>0.0018 (48.41) (190)

11.678> 16.556

As =16.556 𝒄𝒎𝟐

22

Nv⅝ = 16.556

2= 8.278 ≅ 9

S = 190−2(7.5)−1.588

8= 21.67 ≅ 22 𝑐𝑚 ≅ 0.22 𝑚

Lv =190 – 2(7.5) = 175 cm = 1.75 𝑚

9 ∅ ⅝ @ 0.22

RESUMEN DE DATOS:

DATOS Z1 Z2 Z3 Z4

hs 0.6m 0.6m 0.6m 0.6m

hz 0.6m 0.6m 0.6m 0.6m

Lv1=Lv2 1.575m 1.6m 1.55m 1.5m

dʹ 0.4841m 0.4841m 0.4841m 0.4841m

Az 13.63m2 7.22m2 6.817m2 3.61m2

S 3.7m 2.05m 1.949m 1.9m

T 3.7m 3.6m 3.498m 1.9m

m 1.034m 0.934m 0.884m 0,884

n 1.034m 0.934m 0.884m 0,884

ф 5/8" 5/8" 5/8" 5/8"

N°v. Long. 17 16 16 9

Sepr. Long. 0,22 0,24 0,23 0,22

N°v. Transv. 17 9 9 9

Sepr. Transv. 0,22 0,24 0,23 0,22

Analisis Ultima Version

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