H = 1.00 mbs = .65 mbi = .65 m

bw = .15 mts = .14 mti = .14 m

hw = .64 m

Perímetro : 4.15 m

Elemento TIPO bi hi Ai yi Aiyi1 R 0.50 0.14 0.07 0.9300 0.06510002 TI 0.50 0.04 0.01 0.8467 0.00846673 R 0.15 1.00 0.15 0.5000 0.07500004 T 0.50 0.04 0.01 0.1533 0.00153335 R 0.50 0.14 0.07 0.0700 0.00490006789

101112131415

suma 0.31 0.1550

PROPIEDADES DE LA SECCIÓN

H = 1.00 m 100 cm 1000 mmA = 0.31 m2 3100 cm2 310000 mm2ȳ = 0.50 m 50 cm 500 mm

ys = 0.50 m 50 cm 500 mmyi = 0.50 m 50 cm 500 mm

I = 0.04102 m4 4102000 cm4 4.102E+10 mm4r2 = 0.132323 m2 1323 cm2 132323 mm2Cs = 0.264645 m 26.465 cm 264.645 mmCi = 0.264645 m 26.465 cm 264.645 mmSs = 0.08204 m3 82040 cm3 82040000 mm3Si = 0.08204 m3 82040 cm3 82040000 mm3

eficiencia = 0.529

di Aidi2 Ii0.4300 0.0129430 0.000114330.3467 0.0012018 0.000000890.0000 0.0000000 0.01250000

-0.3467 0.0012018 0.00000089-0.4300 0.0129430 0.00011433

0.02828956 0.01273044

LONGITUD DE LA VIGA : 20.00 m

f´c = 35 MPaf´ci = 28 MPa

N = 2150 kNNi = 2530 kN

e = 42.00 cm

METRADO DE CARGAS :

Peso Propio : 7.285 kN/mAligerado : 15.00 kN/mAcabados : 5.00 kN/m

S/C : 5.00 kN/m

CALCULO DE MOMENTOS :

Peso Propio : 364.25 kN-mAligerado : 750.00 kN-mAcabados : 250.00 kN-m

S/C : 250.00 kN-m

Definiendo los momentos:

M1 = 364.25 kN-m

Ma = 1250.00 kN-mM2 = 1614.25 kN-m

ESFUERZOS ADMISIBLES :

NORMAfci = 16.80 MPafti = -1.32 MPafc = 15.75 MPaft = -3.67 MPa

CÁLCULO DE LOS ESFUERZOS

POSTENSADO INICIAL :

σ s = -4.791 MPaσ i = 21.114 MPa

POSTENSADO ESTABLE :

σ s = -4.071 MPaσ i = 17.942 MPa

FLEXIÓN DEBIDO A M1 :

σ s = 4.440 MPaσ i = -4.440 MPa

FLEXIÓN DEBIDO A Ma :

σ s = 15.236 MPaσ i = -15.236 MPa

Verificando La Sección con la norma:

SUPERIOR INFERIOREsfuerzo Resultado Admisible Esfuerzo

PTi -4.791 MPa 21.114 MPaM1 4.440 MPa -.351 MPa -1.32 MPa OK -4.440 MPaPT -4.071 MPa .369 MPa -3.67 MPa OK 17.942 MPaMa 15.236 MPa 15.605 MPa 15.75 MPa OK -15.236 MPa

INFERIORResultado Admisible

16.674 MPa 16.80 MPa OK13.502 MPa 15.75 MPa OK-1.734 MPa -3.67 MPa OK

2 cables de 12 cordones de 1/2'' Grado 250

Tu = 160.1 kNaps = 92.90 mm2

Aps = 2229.60 mm2

Acero de baja relajación

fpu = 1725 MPafpy = 1553 MPa

fsi = 1134.7 MPa

VERIFICACIÓN DEL ESFUERZO

0.82 fpy = 1273 MPa OK0.74 fpu = 1277 MPa OK

0.5 fpu = 862.5 MPa

fse = 964.3 MPa 0.56 MÉTODO APROXIMADO

Usando el método aproximado

CÁLCULO DE LOS VALORES

fpu = 1725 MPa0.28

β1 = 0.80920.00 mm

0.373%

fps = 1614 MPa

186.10 mm > b NO USAR FÓRMULA

3598.70 kN273.10 mm

2657.70 kN-m

Comparando valores:

MD = 1364.25 kN-m

ƴp =

dp = ρp =

a =

T = a (new) =

φ Mn =

ML = 250.00 kN-m

Mu = 2334.95 kN-m OK

Si = 82040 cm3fr = 3.668 MPa

fpe = 17.942 MPa

1.2 Mcr = 2127.49 kN-m OK

DATOS NECESARIOS :

H = 1.00 m

ESFUERZOS SUPERIOR INFERIORPTi + M1 -0.351 16.674PT + M2 15.605 -1.734

f´c = 35 MPaf´ci = 28 MPa

Es : 193000 MPaEci : 24870 MPaEc : 27806 MPa

1. Acortamiento Elástico

CABLES ADHERIDOS

Donde : Kes = 1.0fcir = 15.312 MPa

118.823 MPa

2. Acortamiento Plástico

CABLES ADHERIDOS

Momento (Aligerado) : 750.00 kN-mMomento (Acabados) : 250.00 kN-m

σ s = 12.189 MPaσ i = -12.189 MPa

Δ1 =

Donde : Kcr = 2.0fcds = -10.239 MPa

70.420 MPa

3. Contracción de Fragua del Concreto

Donde : Ksh = 1.00HR = 70 %

V/S = 7.46 cm

26.213 MPa

4. Relajación del Acero

Δ2 =

Δ3 =

Donde : Kre = 31.9 MPaJ = 0.037

fpi = 1134.7 MPafpu = 1725 MPa

fpi/fpu = 0.66

C = 0.53

12.682 MPa

Entonces :

228.138 MPa

fpe = 964.3 MPa

fpi = 1192.4 MPa 0.77

η = 0.809

N = 2150 kNNi = 2659 kN

5. Fricción en los cables

Δ4 =

ΣΔi = ≤ 276 Mpa

≤ 0.83 fpy

Para cables DYWIDAG

0.19k = 0.001

cable 1

x1 = .75 mx0 = .08 m

l = 10.00 m0.1332

0.0353 < 0.30

T0 = 1192.4 MPaT1 = 1234.5 MPa

cable 2

x1 = .25 mx0 = .08 m

l = 10.00 m0.0340

0.0165 < 0.30

T0 = 1192.4 MPaT1 = 1212.1 MPa

6. Deformación de los anclajes

μ =

α =

μα + kl =

α =

μα + kl =

6.00 mm

cable 1

s = 16.58 m > l

73.696 MPa

cable 2

s = 24.29 m > l

96.175 MPa

Δ =

Δ6 =

Δ6 =

DATOS NECESARIOS :

N = 2150 kN

WD = 27.29 kN/mWL = 5.00 kN/m

Wu = 46.70 kN/m

Vu(apoyo) 466.99 kNMu(centro) 2334.95 kN-m

0.4 Asp fpu 1538 kN < N

Método simplificado

x(m) Vu (kN) Mu(kN-m) dp(mm) d(mm) Vu*dp/Mu φVc (kN)0.0 443.641 0.000 500.000 800.000 1.00 253.4450.5 443.641 227.658 540.950 800.000 1.00 253.4451.0 420.291 443.641 579.800 800.000 0.55 253.4451.5 396.942 647.949 616.550 800.000 0.38 215.0972.0 373.592 840.582 651.200 800.000 0.29 171.8732.5 350.243 1021.541 683.750 800.000 0.23 144.9483.0 326.893 1190.825 714.200 800.000 0.20 126.1603.5 303.544 1348.434 742.550 800.000 0.17 112.0114.0 280.194 1494.368 768.800 800.000 0.14 102.5854.5 256.845 1628.628 792.950 800.000 0.13 102.5855.0 233.495 1751.212 815.000 815.000 0.11 104.5085.5 210.145 1862.123 834.950 834.950 0.09 107.0666.0 186.796 1961.358 852.800 852.800 0.08 109.3556.5 163.447 2048.919 868.550 868.550 0.07 111.3757.0 140.097 2124.804 882.200 882.200 0.06 113.1257.5 116.748 2189.016 893.750 893.750 0.05 114.6068.0 93.398 2241.552 903.200 903.200 0.04 115.8188.5 70.049 2282.414 910.550 910.550 0.03 116.7619.0 46.699 2311.601 915.800 915.800 0.02 117.4349.5 23.350 2329.113 918.950 918.950 0.01 117.838

10.0 0.000 2334.950 920.000 920.000 0.00 117.973

198 mm

750 mm600 mm

1084 mm430 mm

s =

s = s =

s = s =

Método completo

x(m) Vu (kN) Mu(kN-m) dp=d(mm) e (mm) fpe (MPa) Mct(kN-m)0.0 443.641 0.000 800.000 0.000 6.935 811.6650.5 443.641 227.658 800.000 40.950 8.009 899.7071.0 420.291 443.641 800.000 79.800 9.027 983.2351.5 396.942 647.949 800.000 116.550 9.990 1062.2472.0 373.592 840.582 800.000 151.200 10.898 1136.7452.5 350.243 1021.541 800.000 183.750 11.751 1206.7273.0 326.893 1190.825 800.000 214.200 12.549 1272.1953.5 303.544 1348.434 800.000 242.550 13.292 1333.1474.0 280.194 1494.368 800.000 268.800 13.980 1389.5854.5 256.845 1628.628 800.000 292.950 14.613 1441.5075.0 233.495 1751.212 815.000 315.000 15.191 1488.9155.5 210.145 1862.123 834.950 334.950 15.713 1531.8076.0 186.796 1961.358 852.800 352.800 16.181 1570.1856.5 163.447 2048.919 868.550 368.550 16.594 1604.0477.0 140.097 2124.804 882.200 382.200 16.952 1633.3957.5 116.748 2189.016 893.750 393.750 17.254 1658.2278.0 93.398 2241.552 903.200 403.200 17.502 1678.5458.5 70.049 2282.414 910.550 410.550 17.695 1694.3479.0 46.699 2311.601 915.800 415.800 17.832 1705.6359.5 23.350 2329.113 918.950 418.950 17.915 1712.407

10.0 0.000 2334.950 920.000 420.000 17.942 1714.665

1215 mm

750 mm600 mm

s =

s = s =

1084 mm434 mm

s = s =

φVs (kN)190.196190.196166.846181.844201.719205.294200.733191.533177.609154.260128.987103.079

77.44152.07126.972

2.1410.0000.0000.0000.0000.000

Vci (kN) Vp (kN) Vcw (kN) φVc (kN) φVs (kN)inf 180.600 636.157 540.733 0.000

1788.772 171.570 627.127 533.058 0.000966.982 162.540 618.097 525.382 0.000686.243 153.510 609.067 517.707 0.000540.716 144.480 600.037 459.609 0.000449.232 135.450 591.007 381.847 0.000384.726 126.420 581.977 327.017 0.000335.599 117.390 572.947 285.259 18.284296.044 108.360 563.917 251.637 28.557262.831 99.330 554.887 223.406 33.438234.684 90.300 554.399 199.481 34.014209.916 81.270 556.729 178.428 31.717187.381 72.240 557.864 159.274 27.522166.496 63.210 557.803 141.522 21.925146.840 54.180 556.545 124.814 15.283128.095 45.150 554.093 108.881 7.867112.211 36.120 550.444 95.380 0.000113.125 27.090 545.599 96.156 0.000113.777 18.060 539.559 96.710 0.000114.168 9.030 532.323 97.043 0.000114.299 0.000 523.891 97.154 0.000