puete con vigas postensadas +losa.xlsx

DISEÑO DE UN PUENTE CON VIGAS POSTENSADAS

Resumen Página 1

Datos Iniciales de las Vigas Postensadas SECCION APROPIADA DE VIGAS LONGITUDINALES "T"

Postensado: 28 Luz: 30 mhm: 1.9 m

Materiales hf1: 20 cm fig area Yc I

Concreto: f'c= 350 hf2: 10 cm 1 9000.0 90 24300000

Acero de Refuerzo: fy= 4200 bw: 50 cm 2 2400.0 185.0 20000Grado Acero de Presfuerzo: grado 270 bf: 240 cm 3 950.0 176.7 5277.778

Acero p (torón) fu= 18900 ho: 1.15 m

Peso Vol. Concreto: 2400 Caracteristicas al Centro

Sección Crítica Area: 12350.0Cargas Mcc ε= 2.533333 Yc: 115.13 cm R asumido

Peso Propio: Wo= 2964 kg/m 333450 kg-m Xcrit= 12 m Ic: 45322714 R= 80%

Carga muerta: Wm= 2145 kg/m 241313 kg-m Acrit= 11600.00 c1: 74.87 cm

Carga Viva: Wv= 2823.6 kg/m 317651 kg-m Ic= 36059062 c2: 115.13

c1= 67.91307 cm s1: 605337.614

Esfuerzos Permisibles al Centro del Claro c2= 107.09 cm s2: 393671.678

f de compresión i: fci= -210 83.27 cm 3669.86 OK!!!

f de tensión i: fti= 14.79 S1crit= 530959.1

f de compresión s: fcs= -157.5 S2crit= 336727 Modulos de Sección Requeridos

f de tensión s: fts= 29.58 Mo= 320112 kg-m 354703.372 OK!!!

f en el centroide: fcci= -73.791 Mm= 231660 kg-m 303991.126 OK!!!Mv= 304944.5 kg-m

PresfuerzoFuerza Pref Inicial Pi= 911320 kg Esfuerzos Actuantes al CC Esfuerzos en la Seccion Crítica

Pref Efectivo Pe= 729056 kg Pi+Mo f1= 1.702712 OK!!! 4.06439608 OK!!!

A de Acero de Pref Asp= 68.883 f2= -189.8757 OK!!! -208.84941 OK!!!

3/5 in #= 49 toronesPe+Mt

f1= -101.9939 OK!!! -109.86961 OK!!!

Geometría en el Centro del Claro

kg/cm2

kg/cm2

kg/cm2

ρcon= kg/m3

cm2

cm4

cm2

cm4 cm Sección Propuesta Correcta?

cm3

cm3

kg/cm2 еcrit= r2: cm2

kg/cm2 cm3

kg/cm2 cm3

kg/cm2 s1≥ cm3

kg/cm3 s2≥ cm3

kg/cm2 kg/cm2

cm2 kg/cm2 kg/cm2

Ø torón kg/cm2 kg/cm2

bf

hf1

hf2

bw

hm

1

2

3

DISEÑO DE UN PUENTE CON VIGAS POSTENSADAS

Resumen Página 2

Excentricidad al CC. 86.74 cmPe+Mt

f2= 7.027015 OK!!! 11.2925107 OK!!!еc= kg/cm2 kg/cm2

NOTA: Observar que la disposicion del Acero de Presfuerzo no sobrepase los límites de las excentricidades permisibles segun el ACI.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

-40

-20

0

20

40

60

80

100

120

Excentricidades Permisibles a lo Largo de la luz

еtsi (cm)еcii (cm)еcst (cm)еcit (cm)ecprop (cm)

Excentricidades Permisibles Página 3

Variación de la Excentricidad a lo Largo de la luz

X(m) c1 (cm)

0 115.0 8600 74 11113096 41.0 73.98 270903.857 150222.21 0.0 0 0 35.9 17.1 -27 -23.56 00.25 116 8663 74.69 11458442 41.56 74.69 275704.799 153414.46 11022.38 7976.72 10500.11 37.51 18.85 -23.69 -19.89 2.86711

0.5 117 8725 75.4 11810427 42.10 75.4 280532.396 156637.07 21859.50 15819.38 20823.76 39.1 20.54 -20.43 -16.28 5.686030.75 119 8788 76.11 12169103 42.64 76.11 285386.601 159889.97 32511.38 23527.97 30970.92 40.68 22.22 -17.24 -12.75 8.45676

1 120 8850 76.82 12534521 43.18 76.82 290267.372 163173.1 42978.00 31102.50 40941.62 42.23 23.88 -14.13 -9.281 11.17931.25 121 8913 77.52 12906733 43.73 77.52 295174.665 166486.39 53259.38 38542.97 50735.84 43.75 25.53 -11.1 -5.884 13.8537

1.5 122 8975 78.23 13285790 44.27 78.23 300108.444 169829.78 63355.50 45849.38 60353.60 45.26 27.16 -8.138 -2.556 16.47981.75 124 9038 78.93 13671742 44.82 78.93 305068.67 173203.19 73266.38 53021.72 69794.87 46.75 28.79 -5.254 0.703 19.0578

2 125 9100 79.64 14064643 45.36 79.64 310055.31 176606.56 82992.00 60060.00 79059.68 48.21 30.4 -2.444 3.893 21.58762.25 126 9163 80.34 14464541 45.91 80.34 315068.332 180039.84 92532.38 66964.22 88148.01 49.65 31.99 0.2895 7.013 24.0692

2.5 127 9225 81 14871490 46.46 81.04 320107.706 183502.97 101887.50 73734.38 97059.88 51.08 33.57 2.9483 10.06 26.50272.75 129 9288 81.74 15285539 47.01 81.74 325173.404 186995.87 111057.38 80370.47 105795.26 52.48 35.14 5.532 13.05 28.8879

3 130 9350 82.44 15706739 47.56 82.44 330265.399 190518.5 120042.00 86872.50 114354.18 53.85 36.7 8.0407 15.96 31.2253.25 131 9413 83.14 16135143 48.11 83.14 335383.665 194070.81 128841.38 93240.47 122736.62 55.21 38.24 10.474 18.8 33.5138

3.5 133 9475 83.84 16570799 48.66 83.84 340528.181 197652.72 137455.50 99474.38 130942.59 56.55 39.77 12.833 21.58 35.75453.75 134 9538 84.53 17013760 49.22 84.53 345698.923 201264.2 145884.38 105574.22 138972.09 57.86 41.28 15.117 24.28 37.947

4 135 9600 85.23 17464075 49.77 85.23 350895.871 204905.18 154128.00 111540.00 146825.12 59.16 42.79 17.326 26.92 40.09134.25 136 9663 85.92 17921797 50.33 85.92 356119.007 208575.61 162186.38 117371.72 154501.67 60.43 44.27 19.46 29.49 42.1874

4.5 138 9725 86.62 18386974 50.88 86.62 361368.311 212275.45 170059.50 123069.38 162001.76 61.68 45.75 21.519 31.99 44.23544.75 139 9788 87.31 18859658 51.44 87.31 366643.766 216004.64 177747.38 128632.97 169325.36 62.92 47.21 23.503 34.42 46.2351

5 140 9850 88 19339900 52.00 88 371945.357 219763.14 185250.00 134062.50 176472.50 64.13 48.66 25.412 36.78 48.18675.25 141 9913 88.69 19827749 52.56 88.69 377273.069 223550.89 192567.38 139357.97 183443.16 65.31 50.09 27.247 39.07 50.09

5.5 143 9975 89.38 20323257 53.12 89.38 382626.887 227367.85 199699.50 144519.38 190237.36 66.48 51.51 29.007 41.29 51.94525.75 144 10038 90.07 20826474 53.68 90.07 388006.799 231213.98 206646.38 149546.72 196855.07 67.63 52.92 30.692 43.44 53.7522

6 145 10100 90.76 21337450 54.24 90.76 393412.791 235089.22 213408.00 154440.00 203296.32 68.75 54.31 32.302 45.53 55.5116.25 146 10163 91.45 21856236 54.80 91.45 398844.852 238993.54 219984.38 159199.22 209561.09 69.86 55.69 33.838 47.54 57.2217

6.5 148 10225 92.14 22382881 55.36 92.14 404302.971 242926.89 226375.50 163824.38 215649.40 70.94 57.06 35.298 49.49 58.88416.75 149 10288 92.82 22917437 55.93 92.82 409787.139 246889.22 232581.38 168315.47 221561.22 72 58.41 36.685 51.36 60.4984

7 150 10350 93.51 23459953 56.49 93.51 415297.344 250880.5 238602.00 172672.50 227296.58 73 59.75 38 53.17 62.0644

hm (cm)

Ac (cm2)

Yc (cm) Ic (cm4) c2

(cm) S1 (cm3) S2 (cm3) Mo(x) kg-m

Mm(x) kg-m

Mv(x) kg-m

еtsi (cm)

еcii (cm)

еcst (cm)

еcit (cm)

ecprop (cm)


7.25 151 10413 94.2 24010480 57.05 94.2 420833.579 254900.69 244437.38 176895.47 232855.46 74.07 61.08 39.233 54.91 63.58237.5 153 10475 94.88 24569067 57.62 94.88 426395.835 258949.74 250087.50 180984.38 238237.88 75.07 62.39 40.396 56.58 65.052

7.75 154 10538 95.56 25135765 58.19 95.56 431984.104 263027.62 255552.38 184939.22 243443.81 76 63.69 41.483 58.18 66.47358 155 10600 96.25 25710625 58.75 96.25 437598.378 267134.28 260832.00 188760.00 248473.28 77 64.98 42.496 59.71 67.8468

8.25 156 10663 96.93 26293695 59.32 96.93 443238.651 271269.7 265926.38 192446.72 253326.27 77.94 66.25 43.435 61.17 69.17198.5 158 10725 97.61 26885027 59.89 97.61 448904.916 275433.82 270835.50 195999.38 258002.79 78.86 67.51 44.299 62.56 70.4489

8.75 159 10788 98.29 27484670 60.46 98.29 454597.168 279626.62 275559.38 199417.97 262502.84 79.76 68.75 45.089 63.89 71.67779 160 10850 99 28092674 61.03 98.97 460315.4 283848.07 280098.00 202702.50 266826.42 80.63 69.98 45.804 65.14 72.8582

9.25 161 10913 99.65 28709089 61.60 99.65 466059.607 288098.11 284451.38 205852.97 270973.52 81.49 71.2 46.444 66.33 73.99069.5 163 10975 100 29333966 62.17 100.3 471829.784 292376.72 288619.50 208869.38 274944.15 82.32 72.4 47.01 67.45 75.0748

9.75 164 11038 101 29967353 62.74 101 477625.928 296683.87 292602.38 211751.72 278738.31 83.13 73.59 47.502 68.49 76.110810 165 11100 102 30609302 63.31 101.7 483448.032 301019.53 296400.00 214500.00 282356.00 83.92 74.77 47.919 69.47 77.0987

10.25 166 11163 102 31259861 63.89 102.4 489296.094 305383.65 300012.38 217114.22 285797.21 84.7 75.93 48.262 70.38 78.038310.5 168 11225 103 31919081 64.46 103 495170.11 309776.21 303439.50 219594.38 289061.96 85.45 77.08 48.53 71.22 78.9297

10.75 169 11288 104 32587011 65.03 103.7 501070.076 314197.18 306681.38 221940.47 292150.22 86.18 78.22 48.724 72 79.77311 170 11350 104 33263702 65.61 104.4 506995.99 318646.52 309738.00 224152.50 295062.02 86.89 79.34 48.844 72.7 80.5681

11.25 171 11413 105 33949202 66.18 105.1 512947.848 323124.2 312609.38 226230.47 297797.34 87.57 80.45 48.889 73.33 81.31511.5 173 11475 106 34643563 66.76 105.7 518925.647 327630.2 315295.50 228174.38 300356.20 88.24 81.54 48.86 73.9 82.0137

11.75 174 11538 106 35346833 67.34 106.4 524929.385 332164.49 317796.38 229984.22 302738.57 88.89 82.62 48.756 74.39 82.664212 175 11600 107 36059062 67.91 107.1 530959.061 336727.03 320112.00 231660.00 304944.48 89.52 83.69 48.578 74.82 83.2665

12.25 176 11663 108 36780301 68.49 107.8 537014.67 341317.8 322242.38 233201.72 306973.91 90.12 84.75 48.326 75.18 83.820712.5 178 11725 108 37510598 69.07 108.4 543096.213 345936.77 324187.50 234609.38 308826.88 90.71 85.79 48 75.47 84.3267

12.75 179 11788 109 38250003 69.65 109.1 549203.686 350583.91 325947.38 235882.97 310503.36 91.27 86.81 47.599 75.69 84.784413 180 11850 110 38998567 70.23 109.8 555337.089 355259.2 327522.00 237022.50 312003.38 91.82 87.82 47.123 75.84 85.194

13.25 181 11913 110 39756338 70.80 110.4 561496.419 359962.61 328911.38 238027.97 313326.92 92.34 88.82 46.574 75.92 85.555413.5 183 11975 111 40523366 71.38 111.1 567681.676 364694.11 330115.50 238899.38 314474.00 92.84 89.81 45.95 75.93 85.8686

13.75 184 12038 112 41299701 71.96 111.8 573892.858 369453.68 331134.38 239636.72 315444.59 93.33 90.78 45.252 75.87 86.133714 185 12100 112 42085392 72.54 112.5 580129.964 374241.29 331968.00 240240.00 316238.72 93.79 91.74 44.48 75.75 86.3505

14.25 186 12163 113 42880490 73.13 113.1 586392.994 379056.92 332616.38 240709.22 316856.37 94.23 92.68 43.634 75.55 86.519114.5 188 12225 114 43685043 73.71 113.8 592681.946 383900.55 333079.50 241044.38 317297.56 94.65 93.61 42.713 75.29 86.6396

14.75 189 12288 114 44499101 74.29 114.5 598996.82 388772.14 333357.38 241245.47 317562.26 95 94.53 41.718 74.96 86.711915 190 12350 115 45322714 74.87 115.1 605337.614 393671.68 333450.00 241312.50 317650.50 95.43 95.43 40.649 74.56 86.736

15.25 189 12288 114 44499101 74.29 114.5 598996.82 388772.14 333357.38 241245.47 317562.26 95 94.53 41.718 74.96 86.7119


15.5 188 12225 114 43685043 73.71 113.8 592681.946 383900.55 333079.50 241044.38 317297.56 94.65 93.61 42.713 75.29 86.639615.75 186 12163 113 42880490 73.13 113.1 586392.994 379056.92 332616.38 240709.22 316856.37 94.23 92.68 43.634 75.55 86.5191

16 185 12100 112 42085392 72.54 112.5 580129.964 374241.29 331968.00 240240.00 316238.72 93.79 91.74 44.48 75.75 86.350516.25 184 12038 112 41299701 71.96 111.8 573892.858 369453.68 331134.38 239636.72 315444.59 93.33 90.78 45.252 75.87 86.1337

16.5 183 11975 111 40523366 71.38 111.1 567681.676 364694.11 330115.50 238899.38 314474.00 92.84 89.81 45.95 75.93 85.868616.75 181 11913 110 39756338 70.80 110.4 561496.419 359962.61 328911.38 238027.97 313326.92 92.34 88.82 46.574 75.92 85.5554

17 180 11850 110 38998567 70.23 109.8 555337.089 355259.2 327522.00 237022.50 312003.38 91.82 87.82 47.123 75.84 85.19417.25 179 11788 109 38250003 69.65 109.1 549203.686 350583.91 325947.38 235882.97 310503.36 91.27 86.81 47.599 75.69 84.7844

17.5 178 11725 108 37510598 69.07 108.4 543096.213 345936.77 324187.50 234609.38 308826.88 90.71 85.79 48 75.47 84.326717.75 176 11663 108 36780301 68.49 107.8 537014.67 341317.8 322242.38 233201.72 306973.91 90.12 84.75 48.326 75.18 83.8207

18 175 11600 107 36059062 67.91 107.1 530959.061 336727.03 320112.00 231660.00 304944.48 89.52 83.69 48.578 74.82 83.266518.25 174 11538 106 35346833 67.34 106.4 524929.385 332164.49 317796.38 229984.22 302738.57 88.89 82.62 48.756 74.39 82.6642

18.5 173 11475 106 34643563 66.76 105.7 518925.647 327630.2 315295.50 228174.38 300356.20 88.24 81.54 48.86 73.9 82.013718.75 171 11413 105 33949202 66.18 105.1 512947.848 323124.2 312609.38 226230.47 297797.34 87.57 80.45 48.889 73.33 81.315

19 170 11350 104 33263702 65.61 104.4 506995.99 318646.52 309738.00 224152.50 295062.02 86.89 79.34 48.844 72.7 80.568119.25 169 11288 104 32587011 65.03 103.7 501070.076 314197.18 306681.38 221940.47 292150.22 86.18 78.22 48.724 72 79.773

19.5 168 11225 103 31919081 64.46 103 495170.11 309776.21 303439.50 219594.38 289061.96 85.45 77.08 48.53 71.22 78.929719.75 166 11163 102 31259861 63.89 102.4 489296.094 305383.65 300012.38 217114.22 285797.21 84.7 75.93 48.262 70.38 78.0383

20 165 11100 102 30609302 63.31 101.7 483448.032 301019.53 296400.00 214500.00 282356.00 83.92 74.77 47.919 69.47 77.098720.25 164 11038 101 29967353 62.74 101 477625.928 296683.87 292602.38 211751.72 278738.31 83.13 73.59 47.502 68.49 76.1108

20.5 163 10975 100 29333966 62.17 100.3 471829.784 292376.72 288619.50 208869.38 274944.15 82.32 72.4 47.01 67.45 75.074820.75 161 10913 99.65 28709089 61.60 99.65 466059.607 288098.11 284451.38 205852.97 270973.52 81.49 71.2 46.444 66.33 73.9906

21 160 10850 99 28092674 61.03 98.97 460315.4 283848.07 280098.00 202702.50 266826.42 80.63 69.98 45.804 65.14 72.858221.25 159 10788 98.29 27484670 60.46 98.29 454597.168 279626.62 275559.38 199417.97 262502.84 79.76 68.75 45.089 63.89 71.6777

21.5 158 10725 97.61 26885027 59.89 97.61 448904.916 275433.82 270835.50 195999.38 258002.80 78.86 67.51 44.299 62.56 70.448921.75 156 10663 96.93 26293695 59.32 96.93 443238.651 271269.7 265926.38 192446.72 253326.27 77.94 66.25 43.435 61.17 69.1719

22 155 10600 96.25 25710625 58.75 96.25 437598.378 267134.28 260832.00 188760.00 248473.28 77 64.98 42.496 59.71 67.846822.25 154 10538 95.56 25135765 58.19 95.56 431984.104 263027.62 255552.38 184939.22 243443.81 76 63.69 41.483 58.18 66.4735

22.5 153 10475 94.88 24569067 57.62 94.88 426395.835 258949.74 250087.50 180984.38 238237.88 75.07 62.39 40.396 56.58 65.05222.75 151 10413 94.2 24010480 57.05 94.2 420833.579 254900.69 244437.38 176895.47 232855.46 74.07 61.08 39.233 54.91 63.5823

23 150 10350 93.51 23459953 56.49 93.51 415297.344 250880.5 238602.00 172672.50 227296.58 73 59.75 38 53.17 62.064423.25 149 10288 92.82 22917437 55.93 92.82 409787.139 246889.22 232581.38 168315.47 221561.22 72 58.41 36.685 51.36 60.4984

23.5 148 10225 92.14 22382881 55.36 92.14 404302.971 242926.89 226375.50 163824.38 215649.40 70.94 57.06 35.298 49.49 58.8841


23.75 146 10163 91.45 21856236 54.80 91.45 398844.852 238993.54 219984.38 159199.22 209561.09 69.86 55.69 33.838 47.54 57.221724 145 10100 90.76 21337450 54.24 90.76 393412.791 235089.22 213408.00 154440.00 203296.32 68.75 54.31 32.302 45.53 55.511

24.25 144 10038 90.07 20826474 53.68 90.07 388006.799 231213.98 206646.38 149546.72 196855.07 67.63 52.92 30.692 43.44 53.752224.5 143 9975 89.38 20323257 53.12 89.38 382626.887 227367.85 199699.50 144519.38 190237.36 66.48 51.51 29.007 41.29 51.9452

24.75 141 9913 88.69 19827749 52.56 88.69 377273.069 223550.89 192567.38 139357.97 183443.16 65.31 50.09 27.247 39.07 50.0925 140 9850 88 19339900 52.00 88 371945.357 219763.14 185250.00 134062.50 176472.50 64.13 48.66 25.412 36.78 48.1867

25.25 139 9788 87.31 18859658 51.44 87.31 366643.766 216004.64 177747.38 128632.97 169325.36 62.92 47.21 23.503 34.42 46.235125.5 138 9725 86.62 18386974 50.88 86.62 361368.311 212275.45 170059.50 123069.38 162001.76 61.68 45.75 21.519 31.99 44.2354

25.75 136 9663 85.92 17921797 50.33 85.92 356119.007 208575.61 162186.38 117371.72 154501.67 60.43 44.27 19.46 29.49 42.187426 135 9600 85.23 17464075 49.77 85.23 350895.871 204905.18 154128.00 111540.00 146825.12 59.16 42.79 17.326 26.92 40.0913

26.25 134 9538 84.53 17013760 49.22 84.53 345698.923 201264.2 145884.38 105574.22 138972.09 57.86 41.28 15.117 24.28 37.94726.5 133 9475 83.84 16570799 48.66 83.84 340528.181 197652.72 137455.50 99474.38 130942.60 56.55 39.77 12.833 21.58 35.7545

26.75 131 9413 83.14 16135143 48.11 83.14 335383.665 194070.81 128841.38 93240.47 122736.62 55.21 38.24 10.474 18.8 33.513827 130 9350 82.44 15706739 47.56 82.44 330265.399 190518.5 120042.00 86872.50 114354.18 53.85 36.7 8.0407 15.96 31.225

27.25 129 9288 81.74 15285539 47.01 81.74 325173.404 186995.87 111057.38 80370.47 105795.26 52.48 35.14 5.532 13.05 28.887927.5 128 9225 81 14871490 46.46 81.04 320107.706 183502.97 101887.50 73734.38 97059.88 51.08 33.57 2.9483 10.06 26.5027

27.75 126 9163 80.34 14464541 45.91 80.34 315068.332 180039.84 92532.38 66964.22 88148.01 49.65 31.99 0.2895 7.013 24.069228 125 9100 79.64 14064643 45.36 79.64 310055.31 176606.56 82992.00 60060.00 79059.68 48.21 30.4 -2.444 3.893 21.5876

28.25 124 9038 78.93 13671742 44.82 78.93 305068.67 173203.19 73266.38 53021.72 69794.87 46.75 28.79 -5.254 0.703 19.057828.5 123 8975 78.23 13285790 44.27 78.23 300108.444 169829.78 63355.50 45849.38 60353.59 45.26 27.16 -8.138 -2.556 16.4798

28.75 121 8913 77.52 12906733 43.73 77.52 295174.665 166486.39 53259.38 38542.97 50735.84 43.75 25.53 -11.1 -5.884 13.853729 120 8850 76.82 12534521 43.18 76.82 290267.372 163173.1 42978.00 31102.50 40941.62 42.23 23.88 -14.13 -9.281 11.1793

29.25 119 8788 76.11 12169103 42.64 76.11 285386.601 159889.97 32511.38 23527.97 30970.92 40.68 22.22 -17.24 -12.75 8.4567629.5 118 8725 75.4 11810427 42.10 75.4 280532.396 156637.07 21859.50 15819.38 20823.76 39.1 20.54 -20.43 -16.28 5.68603

29.75 116 8663 74.69 11458442 41.56 74.69 275704.799 153414.46 11022.38 7976.72 10500.11 37.51 18.85 -23.69 -19.89 2.8671130 115 8600 74 11113096 41.02 73.98 270903.857 150222.21 0.00 0.00 0.00 35.9 17.15 -27 -23.56 0

Refuerzo por Cortante Página 7

Refuerzo del Alma por Cortante a 7.5 m

Flexión-Cortante Presfuerzo Refuerzo LongitudinalPi 911320.007 kgPe 729056.0 kg

Areq= 49.4Cortante por Peso Propio Vo= 22230 kg Sección Crítica Calibre de varilla #6Momento por Peso Propio Mo= 250087.5 kg-m Xc= 7.5 m # varillas 9 #6

Esfuerzo del Peso Propio fo= 96.57762072 hm= 152.50 cm

Esfuerzo del Presfuerzo Efectivo f2= -69.61710315 Ac= 10475.00

Momento de Agrietamiento Mcr= 7697.906517 kg-m Ic= 24569067.1Cortante de Cargas de Servicio Vi= 37264.2 kg c1= 57.6203262 cmMomento Maximo Mmax= 419222.25 kg-m c2= 94.88 cm

Contribución Flexión-Cortante Vci= 41173.5464 kg 65.0519902 cmdp= 122 cm

Cortante en el AlmaRefuerzo Transversal

f de Compresión en el Centroide fcc= 69.5996187 Carga Factorada Wu= 10648.496 kg/mtanθ= 3.309385501 ° Cortante de Cargas FactoradaVu= 79863.72 kg

Fuerza Vertical del Pe Vp= 42086.62611 kg Contribución del Acero Vs= 65311.414 kgContribución Cortante en el Alma Vcw= 275586.0401 kg

Acero de Refuerzo TransversalContribución del Concreto Cuantía de Ref. Requerido Avreq/s= 0.12746

Vc= 41173.5464 kg Cuantía de Ref. Mínimo Avmin/s= 0.04454

Cuantía de Ref. a Colocar Av/s= 0.12746

Separación Máxima Smax= 60Sep min= #3@ 32.5 cm Sep. Requerida #varilla #4 S#4= 20 cm

cm2

kg/cm2

kg/cm2 cm2

cm4

еc=

kg/cm2

θ aprox de Inclinación de la е

cm2/cm

cm2/cm

cm2/cm

cm2/cm

𝑉_𝑐𝑖=0.16√( _ ^ )𝑓 𝑐 ′ 𝑏_𝑤 𝑑_𝑝+𝑉𝑜+(𝑉𝑀_𝑐𝑟)/𝑀_𝑚𝑎𝑥

𝑉_𝑐𝑤=(0.93√( _ ^ )𝑓 𝑐 ′+0.3𝑓_𝑐𝑐)𝑏_𝑤 𝑑_𝑝+𝑉𝑝 𝑉_𝑢=∅𝑉_𝑐+∅𝑉_𝑠 ∅=0.75

𝐴𝑟𝑒𝑞=0.004∗𝐴𝑐

Zona de Anclaje Página 8

Refuerzo para las Zonas de Anclaje en l= 2.75 m

Nota: El bloque de anclaje es de sección rectangular

Datos de la Viga Potensada: fs= 1400 #4b= 55 h= 128.75 e= 28.8879022983 c1= -16.55636Pi= 973498.3807 f1= 47.59846389 f2= -322.549462855 c2= 112.19364

y y/h fy Mfy Mpy Mneto (ton-m) y/h0 0 -322.5494629 0 0 0.000 01 0.00776699 -319.6745275 8843.756654 0 0.088 0.007766992 0.015533981 -316.7995921 35269.61232 0 0.353 0.0155339813 0.023300971 -313.9246568 79119.44556 0 0.791 0.0233009714 0.031067961 -311.0497214 140235.1349 0 1.402 0.0310679615 0.038834951 -308.1747861 218458.559 0 2.185 0.0388349516 0.046601942 -305.2998507 313631.5962 0 3.136 0.0466019427 0.054368932 -302.4249154 425596.1253 0 4.256 0.0543689328 0.062135922 -299.54998 554194.0247 0 5.542 0.0621359229 0.069902913 -296.6750447 699267.173 0 6.993 0.069902913

10 0.077669903 -293.8001093 860657.4488 0 8.607 0.07766990311 0.085436893 -290.925174 1038206.731 0 10.382 0.08543689312 0.093203883 -288.0502386 1231756.897 0 12.318 0.09320388313 0.100970874 -285.1753033 1441149.826 0 14.411 0.10097087414 0.108737864 -282.3003679 1666227.398 0 16.662 0.10873786415 0.116504854 -279.4254326 1906831.489 0 19.068 0.116504854

Areaestribos=

h

ye

l

a b

c d

b

f

f

1

2

c2

c1

Pi

y

l

a b

c d

f

f

1

2

c2

c1

Pi

fy

VM


16 0.124271845 -276.5504972 2162803.979 0 21.628 0.12427184517 0.132038835 -273.6755618 2433986.747 0 24.340 0.13203883518 0.139805825 -270.8006265 2720221.67 0 27.202 0.13980582519 0.147572816 -267.9256911 3021350.628 0 30.214 0.14757281620 0.155339806 -265.0507558 3337215.499 0 33.372 0.15533980621 0.163106796 -262.1758204 3667658.161 0 36.677 0.16310679622 0.170873786 -259.3008851 4012520.494 0 40.125 0.17087378623 0.178640777 -256.4259497 4371644.375 0 43.716 0.17864077724 0.186407767 -253.5510144 4744871.684 0 47.449 0.18640776725 0.194174757 -250.676079 5132044.298 0 51.320 0.19417475726 0.201941748 -247.8011437 5533004.097 0 55.330 0.20194174827 0.209708738 -244.9262083 5947592.958 0 59.476 0.20970873828 0.217475728 -242.051273 6375652.761 0 63.757 0.21747572829 0.225242718 -239.1763376 6817025.384 0 68.170 0.22524271830 0.233009709 -236.3014023 7271552.706 0 72.716 0.23300970931 0.240776699 -233.4264669 7739076.604 0 77.391 0.24077669932 0.248543689 -230.5515315 8219438.959 0 82.194 0.24854368933 0.25631068 -227.6765962 8712481.647 0 87.125 0.2563106834 0.26407767 -224.8016608 9218046.549 0 92.180 0.2640776735 0.27184466 -221.9267255 9735975.542 0 97.360 0.2718446636 0.27961165 -219.0517901 10266110.5 -499309.557 97.668 0.2796116537 0.287378641 -216.1768548 10808293.32 -1472807.94 93.355 0.28737864138 0.295145631 -213.3019194 11362365.85 -2446306.32 89.161 0.29514563139 0.302912621 -210.4269841 11928170 -3419804.7 85.084 0.30291262140 0.310679612 -207.5520487 12505547.62 -4393303.08 81.122 0.31067961241 0.318446602 -204.6771134 13094340.62 -5366801.46 77.275 0.31844660242 0.326213592 -201.802178 13694390.85 -6340299.84 73.541 0.32621359243 0.333980583 -198.9272427 14305540.2 -7313798.22 69.917 0.33398058344 0.341747573 -196.0523073 14927630.55 -8287296.6 66.403 0.34174757345 0.349514563 -193.177372 15560503.78 -9260794.98 62.997 0.34951456346 0.357281553 -190.3024366 16204001.76 -10234293.4 59.697 0.35728155347 0.365048544 -187.4275012 16857966.37 -11207791.7 56.502 0.36504854448 0.372815534 -184.5525659 17522239.5 -12181290.1 53.409 0.37281553449 0.380582524 -181.6776305 18196663 -13154788.5 50.419 0.38058252450 0.388349515 -178.8026952 18881078.81 -14128286.9 47.528 0.38834951551 0.396116505 -175.9277598 19575328.75 -15101785.3 44.735 0.39611650552 0.403883495 -173.0528245 20279254.71 -16075283.6 42.040 0.40388349553 0.411650485 -170.1778891 20992698.58 -17048782 39.439 0.41165048554 0.419417476 -167.3029538 21715502.24 -18022280.4 36.932 0.41941747655 0.427184466 -164.4280184 22447507.55 -18995778.8 34.517 0.42718446656 0.434951456 -161.5530831 23188556.41 -19969277.2 32.193 0.43495145657 0.442718447 -158.6781477 23938490.69 -20942775.6 29.957 0.44271844758 0.450485437 -155.8032124 24697152.26 -21916273.9 27.809 0.45048543759 0.458252427 -152.928277 25464383 -22889772.3 25.746 0.45825242760 0.466019417 -150.0533417 26240024.82 -23863270.7 23.768 0.466019417


61 0.473786408 -147.1784063 27023919.56 -24836769.1 21.872 0.47378640862 0.481553398 -144.3034709 27815909.12 -25810267.5 20.056 0.48155339863 0.489320388 -141.4285356 28615835.36 -26783765.8 18.321 0.48932038864 0.497087379 -138.5536002 29423540.17 -27757264.2 16.663 0.49708737965 0.504854369 -135.6786649 30238865.44 -28730762.6 15.081 0.50485436966 0.512621359 -132.8037295 31061653 -29704261 13.574 0.51262135967 0.52038835 -129.9287942 31891744.82 -30677759.4 12.140 0.5203883568 0.52815534 -127.0538588 32728982.69 -31651257.7 10.777 0.5281553469 0.53592233 -124.1789235 33573208.53 -32624756.1 9.485 0.5359223370 0.54368932 -121.3039881 34424264.21 -33598254.5 8.260 0.5436893271 0.551456311 -118.4290528 35281991.61 -34571752.9 7.102 0.55145631172 0.559223301 -115.5541174 36146232.61 -35545251.3 6.010 0.55922330173 0.566990291 -112.6791821 37016829.08 -36518749.6 4.981 0.56699029174 0.574757282 -109.8042467 37893622.91 -37492248 4.014 0.57475728275 0.582524272 -106.9293114 38776456 -38465746.4 3.107 0.58252427276 0.590291262 -104.054376 39665170.15 -39439244.8 2.259 0.59029126277 0.598058252 -101.1794406 40559607.31 -40412743.2 1.469 0.59805825278 0.605825243 -98.30450529 41459609.35 -41386241.5 0.733678007663 0.60582524379 0.613592233 -95.42956994 42365018.13 -42359739.9 0.05278202063 0.61359223380 0.621359223 -92.55463458 43275675.54 -43333238.3 -0.57562770294 0.62135922381 0.629126214 -89.67969923 44191423.45 -44306736.7 -1.15313237749 0.62912621482 0.636893204 -86.80476388 45112103.75 -45280235.1 -1.68131321746 0.63689320483 0.644660194 -83.92982852 46037558.31 -46253733.4 -2.16175143729 0.64466019484 0.652427184 -81.05489317 46967629 -47227231.8 -2.59602825144 0.65242718485 0.660194175 -78.17995782 47902157.72 -48200730.2 -2.98572487435 0.66019417586 0.667961165 -75.30502246 48840986.34 -49174228.6 -3.33242252045 0.66796116587 0.675728155 -72.43008711 49783956.73 -50147727 -3.63770240421 0.67572815588 0.683495146 -69.55515176 50730910.78 -51121225.4 -3.90314574005 0.68349514689 0.691262136 -66.6802164 51681690.36 -52094723.7 -4.13033374242 0.69126213690 0.699029126 -63.80528105 52636137.35 -53068222.1 -4.32084762577 0.69902912691 0.706796117 -60.9303457 53594093.63 -54041720.5 -4.47626860455 0.70679611792 0.714563107 -58.05541034 54555401.09 -55015218.9 -4.59817789319 0.71456310793 0.722330097 -55.18047499 55519901.59 -55988717.3 -4.68815670614 0.72233009794 0.730097087 -52.30553964 56487437 -56962215.6 -4.74778625785 0.73009708795 0.737864078 -49.43060428 57457849.24 -57935714 -4.77864776276 0.73786407896 0.745631068 -46.55566893 58430980.16 -58909212.4 -4.78232243531 0.74563106897 0.753398058 -43.68073358 59406671.63 -59882710.8 -4.76039148996 0.75339805898 0.761165049 -40.80579822 60384765.55 -60856209.2 -4.71443614113 0.76116504999 0.768932039 -37.93086287 61365103.78 -61829707.5 -4.64603760328 0.768932039

100 0.776699029 -35.05592752 62347528.21 -62803205.9 -4.55677709086 0.776699029101 0.784466019 -32.18099216 63331880.72 -63776704.3 -4.44823581829 0.784466019102 0.79223301 -29.30605681 64318003.18 -64750202.7 -4.32199500004 0.79223301103 0.8 -26.43112146 65305737.48 -65723701.1 -4.17963585055 0.8104 0.80776699 -23.5561861 66294925.49 -66697199.4 -4.02273958425 0.80776699105 0.815533981 -20.68125075 67285409.08 -67670697.8 -3.8528874156 0.815533981


106 0.823300971 -17.8063154 68277030.15 -68644196.2 -3.67166055904 0.823300971107 0.831067961 -14.93138004 69269630.56 -69617694.6 -3.480640229 0.831067961108 0.838834951 -12.05644469 70263052.2 -70591193 -3.28140763995 0.838834951109 0.846601942 -9.181509336 71257136.95 -71564691.3 -3.07554400631 0.846601942110 0.854368932 -6.306573982 72251726.67 -72538189.7 -2.86463054254 0.854368932111 0.862135922 -3.431638629 73246663.26 -73511688.1 -2.65024846308 0.862135922112 0.869902913 -0.556703276 74241788.59 -74485186.5 -2.43397898238 0.869902913113 0.877669903 2.318232078 75236944.54 -75458684.9 -2.21740331487 0.877669903114 0.885436893 5.193167431 76231973 -76432183.3 -2.00210267501 0.885436893115 0.893203883 8.068102785 77226715.8 -77405681.6 -1.78965827723 0.893203883116 0.900970874 10.94303814 78221014.88 -78379180 -1.58165133598 0.900970874117 0.908737864 13.81797349 79214712.09 -79352678.4 -1.37966306571 0.908737864118 0.916504854 16.69290884 80207649.31 -80326176.8 -1.18527468086 0.916504854119 0.924271845 19.5678442 81199668.42 -81299675.2 -1.00006739588 0.924271845120 0.932038835 22.44277955 82190611.29 -82273173.5 -0.8256224252 0.932038835121 0.939805825 25.3177149 83180319.82 -83246671.9 -0.66352098328 0.939805825122 0.947572816 28.19265026 84168635.87 -84220170.3 -0.51534428456 0.947572816123 0.955339806 31.06758561 85155401.32 -85193668.7 -0.38267354347 0.955339806124 0.963106796 33.94252097 86140458.06 -86167167.1 -0.26708997448 0.963106796125 0.970873786 36.81745632 87123648 -87140665.4 -0.17017479201 0.970873786126 0.978640777 39.69239167 88104812.9 -88114163.8 -0.09350921052 0.978640777127 0.986407767 42.56732703 89083794.76 -89087662.2 -0.03867444445 0.986407767128 0.994174757 45.44226238 90060435.41 -90061160.6 -0.00725170824 0.994174757

128.75 1 47.59846389 90791284.37 -90791284.4 0 1 No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica No Aplica


No Aplica No Aplica No Aplica No Aplica

Mmax= 97.66800947 Ton-m T= 69762.86390972 Kg

As= 49.83061708 #estribos= 20 #4@ 14.2105263cm2

-20.000 0.000 20.000 40.000 60.000 80.000 100.000 120.0000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MOMENTOS MÁXIMOS

y/h


-20.000 0.000 20.000 40.000 60.000 80.000 100.000 120.0000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MOMENTOS MÁXIMOS

y/h

Pérdidas Página 14

Pérdidas Instantáneas y Diferidas

Datos GeneralesAp= 68.8828426 Ep= 1960000 Cu= 2.35

Ac= 12350 Ec= 282495.133 Deslizamiento= 0.25 cm

Ic= 45322714 f'c= 350 86.736 cm

c1= 74.8717949 cm s1= 605337.614 Pi= 911320 kg

c2= 115.128205 s2= 393671.678 Pe= 729056 kg

3669.85536 Wo= 2964 kg/m

Pérdidas InstantáneasDeslizamiento del Anclaje

163.333333

Acortamiento Elástico para Tensado Simultáneo0

Fricción al Centro del ClaroCurvatura deseada

α= 0.23129597 rad

Coeficiente Curvatura No Deseadak= 0.001

Coeficiente de Fricciónμ= 0.4

Esfuerzo en el Presfuerzo al Aplicar los Gatos

fs= 13066.66670.06125919

776.428957

Pérdidas DiferidasFlujo Plástico

fcs= -73.194176

1193.4095Contracción

0.000448

cm2 kg/cm2

cm2 kg/cm2

cm4 kg/cm2 еc=

cm3

cm cm3

r2= cm2

ΔfDA= kg/cm2

ΔfAE= kg/cm2

kg/cm2

(μα+kx)=ΔfFR= kg/cm2

kg/cm2

ΔfFP= kg/cm2

Єsh=Considerando una deformación de 800x10-6 y

que a los 28 días se alcanza el 44% de esta deformación

∆𝑓_𝐷𝐴=∆𝑙/𝑙 𝐸_𝑝

∝=8𝑒/𝑙 ∆𝑓_𝐹𝑅=𝑓_𝑠 (1−𝑒^(−(𝜇𝛼+𝑘𝑥) ) )

∆𝑓_𝐹𝑃=𝐶𝑢∗𝑛∗𝑓_𝑐𝑠

∆𝑓_𝐶𝐶=𝐸_𝑝 𝜖_𝑠ℎ


878.08Relajamiento

Considerando Acero de Bajo Relajamiento

fi/fpu= 0.69135802C= 0.7 Ver tablasKre= 5 ksi Ver tablasJ= 0.04 Ver tablas

186.998294Efecto Elástico

507.83383

Resumen de PérdidasTipo de Pérdidas Δf %

Inst

antá

neas Esfuerzo en Gato (Pi) 13230 100.00%

Deslizamiento de Anclaje -163.333333333 -1.23%

Acortamiento Elástico 0 0.00%

Fricción -776.428956773 -5.87%

Dife

ridas

Flujo Plástico -1193.40949998 -9.02%

Contracción -878.08 -6.64%

Relajamiento -186.998294001 -1.41%

Efecto Elástico 507.833829779 3.84%

Pe= 10539.5837457 R= 79.66%

ΔfCC= kg/cm2

ΔfRE= kg/cm2

Δfw= kg/cm2

∆𝑓_𝑅𝐸=(𝐾_𝑟𝑒−𝐽(∆ _𝑓 𝐶𝐶+∆ _𝑓 𝐹𝑃+∆ _𝑓 𝐴𝐸 ))C

∆𝑓_𝑤=𝐸_𝑝/𝐸_𝑐 𝑓_𝑐𝑠


l(m)0 0 0

0.25 0.0010209865501 13.334082803140.5 0.0020419731002 26.654558634531

0.75 0.0030629596502 39.9614413796171 0.0040839462003 53.254744909673

1.25 0.0051049327504 66.5344830818241.5 0.0061259193005 79.800669739045

1.75 0.0071469058506 93.0533187101922 0.0081678924006 106.29244381001

2.25 0.0091888789507 119.518058839132.5 0.0102098655008 132.73017758413

2.75 0.0112308520509 145.92881381753 0.012251838601 159.11398129767

3.25 0.013272825151 172.285693769043.5 0.0142938117011 185.44396496199

3.75 0.0153147982512 198.588808592884 0.0163357848013 211.72023836406

4.25 0.0173567713514 224.838267963934.5 0.0183777579014 237.94291106689

4.75 0.0193987444515 251.03418133345 0.0204197310016 264.11209240999

5.25 0.0214407175517 277.176657929245.5 0.0224617041018 290.22789150983

5.75 0.0234826906518 303.265806756566 0.0245036772019 316.29041726031

6.25 0.025524663752 329.301736598136.5 0.0265456503021 342.29977833318

6.75 0.0275666368522 355.28455601487 0.0285876234022 368.25608317851

7.25 0.0296086099523 381.2143733467.5 0.0306295965024 394.15944002517

7.75 0.0316505830525 407.091296710128 0.0326715696026 420.00995688121

8.25 0.0336925561526 432.915434005038.5 0.0347135427027 445.80774153441

8.75 0.0357345292528 458.686892908489 0.0367555158029 471.55290155263

Cálculo de las Perdidas por Fricción a lo largo del Claro

(μα+kx) ΔfFR

0 5 10 15 20 250

200400600800

1000120014001600

Pérdidas por Fricción a lo largo del Claro

Estación l del claro (m)

Perd

idas

por

Fric

ción

(kg/

cm^2

)

∆𝑓_𝐹𝑅=𝑓_𝑠 (1−𝑒^(−(𝜇𝛼+𝑘𝑥) ) )


9.25 0.037776502353 484.405780878589.5 0.038797488903 497.24554428433

9.75 0.0398184754531 510.0722051542310 0.0408394620032 522.88577685897

10.25 0.0418604485533 535.6862727555910.5 0.0428814351034 548.4737061875

10.75 0.0439024216534 561.2480904844911 0.0449234082035 574.00943896276

11.25 0.0459443947536 586.7577649249111.5 0.0469653813037 599.49308165997

11.75 0.0479863678538 612.2154024434112 0.0490073544038 624.92474053715

12.25 0.0500283409539 637.6211091895712.5 0.051049327504 650.30452163555

12.75 0.0520703140541 662.9749910964413 0.0530913006041 675.63253078011

13.25 0.0541122871542 688.2771538809613.5 0.0551332737043 700.90887357992

13.75 0.0561542602544 713.5277030444514 0.0571752468045 726.13365542861

14.25 0.0581962333545 738.72674387314.5 0.0592172199046 751.30698150484

14.75 0.0602382064547 763.8743814379315 0.0612591930048 776.42895677271

15.25 0.0622801795549 788.9707205962315.5 0.0633011661049 801.4996859822

15.75 0.064322152655 814.0158659909816 0.0653431392051 826.51927366962

16.25 0.0663641257552 839.0099220518316.5 0.0673851123053 851.48782415803

16.75 0.0684060988553 863.9529929953717 0.0694270854054 876.4054415577

17.25 0.0704480719555 888.8451828256217.5 0.0714690585056 901.27222976649

17.75 0.0724900450557 913.6865953344418 0.0735110316057 926.08829247036

18.25 0.0745320181558 938.4773341019618.5 0.0755530047059 950.85373314374

18.75 0.076573991256 963.2175024970319 0.0775949778061 975.56865504998

19.25 0.0786159643561 987.9072036776219.5 0.0796369509062 1000.2331612418

19.75 0.0806579374563 1012.546540591320 0.0816789240064 1024.8473545617

20.25 0.0826999105565 1037.1356159756


20.5 0.0837208971065 1049.411337642420.75 0.0847418836566 1061.6745323585

21 0.0857628702067 1073.925212907221.25 0.0867838567568 1086.1633920588

21.5 0.0878048433069 1098.389082570621.75 0.0888258298569 1110.6022971867

22 0.089846816407 1122.803048638422.25 0.0908678029571 1134.9913496439

22.5 0.0918887895072 1147.167212908522.75 0.0929097760573 1159.3306511245

23 0.0939307626073 1171.481676971123.25 0.0949517491574 1183.6203031148

23.5 0.0959727357075 1195.746542209123.75 0.0969937222576 1207.8604068945

24 0.0980147088077 1219.961909798624.25 0.0990356953577 1232.0510635363

24.5 0.1000566819078 1244.127880709424.75 0.1010776684579 1256.192373907

25 0.102098655008 1268.244555705325.25 0.1031196415581 1280.2844386676

25.5 0.1041406281081 1292.312035344525.75 0.1051616146582 1304.3273582736

26 0.1061826012083 1316.3304199826.25 0.1072035877584 1328.3212329758

26.5 0.1082245743085 1340.299809760326.75 0.1092455608585 1352.2661628203

27 0.1102665474086 1364.2203046295

Deflexiones Página 19

Cálculo de Deflexiones: MÉTODO APROXIMADO

Contraflecha debida al Presfuerzo EfectivoTendon Parabólico:

hacia arriba 5.78781 cm

Contraflecha debida al Presfuerzo Efectivo

hacia arriba 4.61082 cm

Deflexión Total debida al Presfuerzo a los 360 días

Ct= 1.81809 cm

-14.0637 cm

Deflexión debido a las Cargas de Servicio

2.4416 cm

1.76695 cm

hacia abajo 2.32592 cm

Deflexión Neta

0.12234 cmhacia abajo

Deflexión Permisible

6.25 cmOK!!!

Δpi=

Δpe=

Δt=

Δwo=

Δwm=

Δwv=

Δnet=

Δperm=

∆_𝑝𝑖=5/48 (𝑃𝑒𝑙^2)/(𝐸_𝑐 𝐼)∆_𝑝𝑒=𝑅∆_𝑝𝑖

∆_𝑡=−∆_𝑝𝑒−(∆_𝑝𝑖+∆_𝑝𝑒)/2 Ct𝐶𝑡=𝑡^0.6/(10+ ^0.6𝑡 ) Cu

∆_𝑤𝑖=5/384 (𝑤𝑖𝑙^4)/(𝐸_𝑐 𝐼)

∆_𝑛𝑒𝑡=∆_𝑡+(∆_𝑜+∆_𝑚 )(1+Ct)+∆𝑙∆_𝑝𝑒𝑟𝑚=𝑙/48

UNSCH VERIFICACIÓN DISEÑO DE LOSA DE CONCRETO (AASHTO-LRFD)

DISEÑO DE SUPERESTRUCTURA PARA PUENTES DE SECCION COMPUESTA 20

DISEÑO DE SUPERESTRUCTURA DE PUENTES DE SECCIÓN COMPUESTA

DATOS DE DISEÑODATOS GEOMÉTRICOSL = 30.00 m Longitud del puente entre apoyosBc = 7.20 m Ancho de la calzadaNb = 3.00 Numero de vigas principalesNc = 2.00 Numero de viasS = 3.00 m Separacion de vigas principalesbv = 0.75 m Ancho de veredahv = 15.00 cm Peralte de tramo extremo de la vereda.hs = 15.00 cm Altura de vereda sobre la calzadapv = 10.00 cm Pendiente horizontal de la veredae = 20.00 cm Espesor de pavimentoav = 0.30 cm Longitud de apoyo de la vereda

PROPIEDADES MECÁNICAS

f'c = 210.0 Resistencia del concreto en la losa

fy = 4,200.0 Esfuerzo de fluencia de acero de refuerzo

Fy = 2,530.0 Esfuerzo de fluencia de acero estructural

= 2,400.0 Peso especifico del concreto

γs = 7,850.0 Peso específico del acero estructural

γa = 2,000.0 Peso específico del pavimento

Es = 2,100,000.0 Modulo de elasticidad de acero(estructural y de refuerzo)

Ec = 238,528.0 Modulo de elasticidad del concreto

CARGASP = 3.57 tn Carga de 01 rueda en eje delantero (HL-93)SCv = 0.36 tn/m2 Sobrecarga peatonal en vereda Wb = 0.10 tn/m Peso propio de la barandaWsc = 0.96 tn/m Sobre carga distribuidaØ = 0.90 Modificador de resistencia para flexion para losas de concreto.

VERIFICACIÓN DISEÑO DE LOSA DE CONCRETO (AASHTO-LRFD)

PREDIMENSIONAMIENTO DE VIGA

kgf/cm2

kgf/cm2

kgf/cm2

γc kgf/m3

kgf/m3

kgf/m3

kgf/cm2

kgf/cm2

hv

0.90

lvtc

2PPL=360kgf/m2

bv

av 0.30

X

pv

hs

bfs

hv

lv

0.30

av

bv

0.90

0.20

0.30

lvav

hs hs

bv

0.90

0.20

pv pv

Bcs%s%



Peralte minimo de la vigah=L/30 1.00 m Asumir h= 1.00 m

Peralte minimo de la viga compuestahc=L/25 1.20 m Asumir h= 1.20 m

Espesor de la losa de concretotc=hc-h 0.200tc=0.1+S/30 0.200Asumir tc= 0.200 = 20.00 cm

Ancho de ala Asumir bfs= 55.0 cm

Espesor

tfs= 2.51 cmAsumir tfs= 2.55 cm

Calculo de S' y S"

S'=S-bfs = 2.45 mS"=S-bfs/2 = 2.73 m

DISEÑO DE LOSA EN TRAMO INTERIOR

Armadura principal perpendicular a la direccion del trafico

I) CÁLCULO DE MOMENTOS

Momento debido a camión de diseño HL-93Mcd=(S"+0.61)(2P)/9.74 Mcd= 2.529 tn.m

Momento debido a sobrecarga distribuida

Msd= 0.711 tn.m

El momento se la sobrecarga vehicular sera la suma de Mcd+MsdPor continuidad se aplica un factor de 0.80 para momento positivo y de 0.90 para momentonegativo si es que número de vigas (Nb) es mayor o igual que tres.

Mll(+)=0.80(Mcd+Msd) Mll(+)= 2.592 tn.m

Mll(-)=0.9(Mcd+Msd) Mll(-)= 2.916 tn.m

Momento debido a cargas permanentesCargasPavimento Wdw=b(e)(γa) 0.400 tn/m

Losa Wdc=b(tc)(γc) 0.480 tn/m

Para obtener los momentos positivos y negativos se considerará un coeficiente de 1/9 para momentosnegativos y 1/11 para momentos positivos (recomendaciones del ACI)

Mdw(+)=1/11(Wdw)S"2 0.270 tn.m

Mdw(-)=1/9(Wdw)S"2 0.330 tn.m

Mdc(+)=1/11(Wdc)S"2 0.324 tn.m

Msd=0.1W(S"2)

FyEs

bfstfs

Fy

Es

tfs

bfs

/76.038.0

2



Mdc(-)=1/9(Wdc)S"2 0.396 tn.m

Momento debido a impactoCoeficiente de Impacto

CI=33% 0.330

Mim(+)=CI(Mcd) = 0.668 tn.m

Mim(-)=CI(Mcd) = 0.751 tn.m

Momento Ultimo

Mu=1.25Mdc+1.50Mdw+1.75(Mll+Mim) RESISTENCIA IMs=Mdc+Mdw+1.3(Mll+Mim) SERVICIO II

Mu(+)= 6.515 tn.mMu(-)= 7.424 tn.mMs(+)= 4.832 tn.mMs(-)= 5.268 tn.m Mmax(ser) 5.268 tn.m

II) VERIFICACIÓN DE PERALTE POR SERVICIO

Esfuerzo de compresion del concreto

fc=0.4f'c = 84

Esfuerzo de tension del acero=0.4fy

fy=0.4fy = 1680

Modulo de elasticidad del concreto

Ec= 217,370.65

Relacion de modulo de elasticidad n=Es/Ec = 9.66

Relacion entre la tension del acero y del concreto= 20

Factor adimensional= 0.326

j=1-k/3 = 0.891

Peralte util

= 13.146 cm

Recubrimiento (r) = 4.0 cmNumero de refuerzo = 4 1.27

d=tc-r-dr/2 = 15.37 cm OK

III) DISEÑO DE ACERO DE REFUERZO POR ROTURA

A) Refuerzo principal para momento positivo: Mu(+)

kgf/cm2

kgf/cm2

kgf/cm2

γ=fs/fc

k=n/(n+γ)

cfEc '000,15

bjkfc

Msd

...

2

fy

bdf

Mubdf

Asc

c

2'85.0

211'85.0



Mu(+)= 6.515 tn.m

As(+)= 12.388

Refuerzo minimo

Asmin=0.03f'c/fy.b.d 1.97 ¡OK!

Se selecciona el mayor As(+)= 12.388

Ø= 1/2" s= 10.00 cmρ= 0.0083

Refuerzo principal Ø 1/2" @ 10 cm As= 12.7 cm2

Refuerzo por reparto

= 66.636 %Del acero principal

Asr=%r(As) = 8.255

Ø= 3/8" s= 8.50 cm

Refuerzo por reparto Ø 3/8" @ 8.5 cm

B) Refuerzo principal para momento negativo: Mu(-)

Mu(-)= 7.424 tn.m

As(-)= 14.357

Refuerzo mínimo


Se selecciona el mayor As(-)= 14.357

Ø= 1/2" s= 8.50 cmρ= 0.0149

Refuerzo principal Ø 1/2" @ 8.5 cm As= 14.94 cm2



Asr=%r(As) = 9.567

Ø= 1/2" s= 13.00 cm

Refuerzo por reparto Ø 1/2" @ 13 cm

C) Refuerzo de temperaturaAe tomara el menor de los siguientes valores

Ast=0.0018.b.tc = 2Astm=2.64cm2/m = 5.28 cm2 En ambas direcciones (AASHTO-LRFD)

Repartiendo en ambos sentidos 2.64

cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm2

%67"

110%

Sr

%67"

110%

Sr



Ø= 3/8" s= 26.50 cm

Refuerzo por temp. Ø 3/8" @ 26.5 cm

El refuerzo por reparto se hallará adicionando el acero por temperatura al acero por repartohallado anteriormente, esto para momento negativo

Asrt=Asr+Ast/2 = 12.21

Aspt(+)=As(+)+Ast/2 = 15.028

Aspt(-)=As(-)+Ast/2 = 16.997Ø= 1/2" s= 10.00 cmØ= 1/2" s= 8.00 cmØ= 5/8" s= 11.50 cmRefuerzo de reparto Ø 1/2" @ 10 cm (incluye temperatura)Refuerzo Principal (+) Ø 1/2" @ 8 cm (incluye temperatura)Refuerzo Principal (-) Ø 5/8" @ 11.5 cm (incluye temperatura)

D) Verificacion de Cuantía

Cuantia balanceadaCuantia máximaρmax=0.75ρb= 0.0163 OK

Cuantia minimaβ=0.85 para f'c<345 kgf/cm2 ρmin=0.03f'c/fy= 0.0015 OK

ρb = 0.0217

ρmax ≥ ρ ≥ ρmin El losa fallará por fluencia del acero

RESUMEN DE REFUERZO EN TRAMO INTERIORRefuerzo principal positivo +temperatura Ø 1/2" @ 8 cmRefuerzo principal negativo+temperatura Ø 5/8" @ 11.5 cmRefuerzo por reparto en parte inferior Ø 3/8" @ 8.5 cmRefuerzo por reparto+temperatura (superior) Ø 1/2" @ 10 cmRefuerzo por temperatura:

- Sentido Longitudinal Ø 3/8" @ 26.5 cm

DISEÑO EN TRAMO EXTERIOR

Sv=[Bc+2(pv+av)-S(Nb-1)]/2 = 0.70 mLv=Sv-bfs/4 = 0.57 mX=Lv-pv-av-0.30 = 0.16 m

cm2

cm2

cm2

fyfy

cfb

6300

6300'85.0

hv

0.90

lvtc

2PPL=360kgf/m2

bv

av 0.30

X

pv

hs

bfs



lv=bv-av = 0.75 m

I) CÁLCULO DE MOMENTOSMomento por peso propio

SECCION DIMENSIONES CARGA (tn) BRAZO(m) MOMENTO(tn.m)Baranda wb(kgf/m) 0.100 1.213 0.121

1 (hv)(lv) 0.269 0.939 0.2532 (hs-hv)(lv)/2 0.000 0.815 0.0003 (hs)(av) 0.001 0.564 0.0014 (hs)(pv)/2 0.012 0.529 0.0065 (Lv)(tc) 0.271 0.283 0.077

TOTAL 0.457

Mcd=Momento por peso propio = 0.457 tn.m

Momento debido al peso del pavimento

= 0.214 tn.m

Momento debido a sobrecarga de vereda

Mpl=SCv(bv)(Lv-av+lv/2) = 0.33696 tn.m

Momento debido a sobrecarga vehicular

Momento debido a camion de diseño HL93X=Lv-av-pv-0.30 = 0.1625 mE=0.80(X)+1.143 = 1.273 m OK

Mca=2PX/E = 0.911 tn.m

Momento debido a sobrecarga distribuida

Msd=w(Lv-av-pv)(Lv-av-pv)/2 = 0.102 tn.m

El momento debido a la sobrecarga vehicular será, la suma de camion de diseño HL-93mas momento debido a sobrecarga distribuida

Mll=Mca+Msd = 1.013 tn.m

Momento debido a impacto

Coeficiente de Impacto (33%)

Cim= 0.330

Mim=CI(Mll) 0.330

Momento Ultimo

Mu=1.25Mdc+1.50Mdw+1.75(Mpl+Mll+Mim) RESISTENCIA IMs=Mdc+Mdw+1.30(Mpl+Mll+Mim) SERVICIO II

Mu(-)= 3.833 tn.mMs(-)= 2.654 tn.m

II) DISEÑO DE ACERO DE REFUERZO POR ROTURA

Mwd=γa(Lv-av-pv)2/2

fy

bdf

Mubdf

Asc

c

2'85.0

211'85.0



Refuerzo principal para momento negativo: Mu(-)3

Mu(-)= 3.833 tn.m12.388

As(-)= 6.970

Refuerzo mínimo


Se selecciona el mayor As(-)= 6.97

Ø= 1/2" s= 18.00 cmρ= 0.0046




Asr=%r(As) = 4.645

Ø= 3/8" s= 15.00 cm

Refuerzo por reparto Ø 3/8" @ 15 cm

Refuerzo de temperaturaSera el menor de los siguientes valores

Ast=0.0018.b.tc = 3.6Astm=2.64cm2/m = 5.28 cm2 En ambas direcciones (AASHTO-LRFD)

Repartiendo en ambos sentidos 2.64

Ø= 3/8" s= 26.50 cm

Refuerzo por temp. Ø 3/8" @ 26.5 cm

El refuerzo por reparto se hallará adicionando el acero por temperatura al acero por repartohallado anteriormente, esto para momento negativo

Asrt=Asr+Ast/2 = 7.29

Asp(-)=Asp(-)+Ast/2 = 9.61

Ø= 5/8" s= 27.00 cmØ= 5/8" s= 20.50 cm

Refuerzo de reparto Ø 5/8" @ 27 cm (incluye temperatura)Refuerzo principal (-) Ø 5/8" @ 20.5 cm (incluye temperatura)

Verificacion de Cuantía

Cuantia balanceada

Asmax= 43.35 cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm2

fy

bdf

Mubdf

Asc

c

2'85.0

211'85.0

%67"

110%

Sr

fyfy

cfb

6300

6300'85.0



β=0.85 para f'c<345 kgf/cm2

ρb = 0.0217

Cuantia máximaρmax=0.75ρb = 0.0163 OK

Cuantia minimaρmin=0.03f'c/fy = 0.0015 OK

ρmax ≥ ρ ≥ ρmin

El losa fallará por fluencia del acero

RESUMEN DE REFUERZO EN TRAMO EXTERIORRefuerzo principal negativo+temperatura Ø 1/2" @ 8 cmRefuerzo por reparto+temperatura (superior) Ø 5/8" @ 27 cmRefuerzo por reparto en parte inferior Ø 3/8" @ 15 cmRefuerzo por temperatura:

- Sentido Longitudinal Ø 3/8" @ 26.5 cm

Como el Momento Ultimo Mu(-) en tramo exterior es menor que el momento negativo del tramo interior, se colocará el refuerzo negativo del tramo interior en el voladizo.

DISEÑO DE VEREDA

Momento por peso propioLv=bv-av-pv = 0.747 m

SECCION DIMENSIONES CARGA BRAZO MOMENTO(tn.m)Baranda 0.100 0.647 0.065

1 (hv)(lv) 0.269 0.374 0.1002 (hs-hv)(lv)/2 0.000 0.249 0.000

TOTAL 0.165

Mcd=Momento por peso propio = 0.165 tn.m

El momento debido al peso del pavimento se considera nulo

Momento debido a sobrecarga de vereda

fyfy

cfb

6300

6300'85.0

hv

0.90

lvtc

2PPL=360kgf/m2

bv

av 0.30

X

pv

hs

bfs



= 0.100 tn.m

Momento debido a impacto

Se considera el momento de impacto debido a la sobrecarga peatonalCoeficiente de Impacto

Cim= 33% 0.330

Mim=CI(Mll) = 0.033 tn.m

Momento Ultimo

Mu=1.25Mdc+1.75(Mpl+Mim) RESISTENCIA IMs=Mdc+1.30*(Mpl+Mim) SERVICIO II

Mu= 0.438 tn.mMs= 0.337 tn.m

DISEÑO DE ACERO DE REFUERZO POR ROTURA

Recubrimiento (r) = 4.0 cmNumero de refuerzo = 3 0.95

d=tc-r-dr/2 = 10.52 cm

Verificación de Peralte

d= 3.33 cm OK

DISEÑO DE ACERO DE REFUERZO POR ROTURA

Refuerzo principalPara momento positivo y negativo

= 1.12

Refuerzo minimo


Se selecciona el mayor As(±)= 3.51

Ø= 3/8" s= 20.00 cmρ= 0.0034


Refuerzo de temperatura

Ast=0.0018.b.tc 2.70

Aspt=Asp(-)+Ast 6.21Ø= 3/8" s= 26.00 cmØ= 3/8" s= 11.00 cmRefuerzo por temperatur Ø 3/8" @ 26 cm Solo temperatuta

Mpl=SCv(Lv-av)2/2

cm2

cm2

cm2

cm2

bjkfc

Msd

...

2

fy

bdf

Mubdf

Asc

c

2'85.0

211'85.0



Principal Ø 3/8" @ 11 cm Principal+temperatura

Verificacion de Cuantía

Cuantia balanceada

β=0.85 para f'c<345 kgf/cm2

ρb = 0.0217

Cuantia máximaρmax=0.75ρb = 0.0163 OK

Cuantia minimaρmin=0.03f'c/fy = 0.0015 OK

ρmax ≥ ρ ≥ ρmin

El losa de la vereda fallará por fluencia del acero

RESUMEN DE REFUERZO EN VEREDARefuerzo principal negativo+temperatura Ø 3/8" @ 11 cmRefuerzo por temperatura:

- Sentido Longitudinal Ø 3/8" @ 26 cm

fyfy

cfb

6300

6300'85.0



14.27 Tn 14 3.57

hv

0.90

lvtc

2PPL=360kgf/m2

bv

av 0.30

X

pv

hs

bfs

hv

lv

0.30

av

bv

0.90

0.20

0.30

lvav

hs hs

bv

0.90

0.20

pv pv

Bcs%s%



fy

bdf

Mubdf

Asc

c

2'85.0

211'85.0



DIMENSIONES DEL ACERO

Nº # 2 # 3 # 4 # 5 # 6 # 8 # 10 # 11 # 14Ø 1/4" 3/8" 1/2" 5/8" 3/4" 1" 1 1/4" 1 3/8" 1 3/4"

DIAMETRO ( 6.35 9.52 12.70 15.88 19.05 25.40 32.26 35.81 43.00PERIMETRO 2.00 2.99 3.99 4.99 5.99 7.98 10.13 11.25 13.50PESO (Kg/m) 0.25 0.56 0.99 1.55 2.24 3.98 6.40 7.91 11.40

0.32 0.71 1.27 1.98 2.85 5.07 8.17 10.06 14.52


Nº # 2 # 3 # 4 # 5 # 6 # 8 # 10 # 11 # 14Ø 1/4" 3/8" 1/2" 5/8" 3/4" 1" 1 1/4" 1 3/8" 1 3/4"


0.32 0.71 1.27 1.98 2.85 5.07 8.17 10.06 14.52

AREA (cm2)

AREA (cm2)




Nº # 2 # 3 # 4 # 5 # 6 # 8 # 10 # 11 # 14Ø 1/4" 3/8" 1/2" 5/8" 3/4" 1" 1 1/4" 1 3/8" 1 3/4"


0.32 0.71 1.27 1.98 2.85 5.07 8.17 10.06 14.52AREA (cm2)



DIMENSIONES DEL ACERONº # 2 # 3 # 4 # 5 # 6 # 8 # 10 # 11Ø 1/4" 3/8" 1/2" 5/8" 3/4" 1" 1 1/4" 1 3/8"

DIAMETRO ( 6.35 9.52 12.70 15.88 19.05 25.40 32.26 35.81PERIMETRO 2.00 2.99 3.99 4.99 5.99 7.98 10.13 11.25PESO (Kg/m) 0.25 0.56 0.99 1.55 2.24 3.98 6.40 7.91

0.32 0.71 1.27 1.98 2.85 5.07 8.17 10.06AREA (cm2)



hv

0.90

lvtc

2PPL=360kgf/m2

bv

av 0.30

X

pv

hs

bfs

Documents

puete con vigas postensadas +losa.xlsx