Download - Análisis de Viga Pretensada
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