Grafico () $x V M .-M

0 0 0 0 0 01 0 21326.36 0 0 0 202 0.319444 18957.1 6434.164 -6434.1643 0.638889 16587.85 12111.48 -12111.484 0.958333 14218.59 17031.96 -170325 1.277778 11849.34 21195.58 -21195.586 1.597222 9480.082 24602.37 -24602.377 1.916667 7110.827 27252.3 -27252.38 2.236111 4741.571 29145.4 -29145.49 2.555556 2372.316 30281.64 -30281.64

10 2.875 3.06 30661.04 -306611 2.875 3.06 30661.04 -306612 3.388889 -3808.351 29683.29 -29683.293 3.902778 -7619.762 26746.9 -26746.94 4.416667 -11431.17 21851.87 -21851.875 4.930556 -15242.58 14998.2 -14998.26 5.444444 -19054 6185.881 -6185.8817 5.958333 -22865.41 -4585.077 4585.0778 6.472222 -26676.82 -17314.68 17314.689 6.986111 -30488.23 -32002.92 32002.92

10 7.5 -34299.64 -48649.8 48649.81 7.5 35938.36 -48649.8 48649.82 7.861111 33260.07 -36155.64 36155.643 8.222222 30581.78 -24628.64 24628.644 8.583333 27903.49 -14068.8 14068.85 8.944444 25225.2 -4476.115 4476.1156 9.305556 22546.92 4149.407 -4149.4077 9.666667 19868.63 11807.77 -11807.778 10.02778 17190.34 18498.97 -184999 10.38889 14512.05 24223.01 -24223

10 10.75 11833.76 28979.9 -28979.91 10.75 -9566 28979.89 -28979.892 11.11111 -12244.29 25041.93 -25041.933 11.47222 -14922.58 20136.8 -20136.84 11.83333 -17600.87 14264.51 -14264.515 12.19444 -20279.16 7425.06 -7425.066 12.55556 -22957.44 -381.5479 381.54797 12.91667 -25635.73 -9155.316 9155.3168 13.27778 -28314 -18896.24 18896.249 13.63889 -30992.31 -29604.33 29604.33

10 14 -33670.6 -41279.58 41279.581 14 35148.12 -41279.58 41279.582 14.33333 32675.85 -29975.58 29975.583 14.66667 30203.59 -19495.68 19495.684 15 27731.32 -9839.86 9839.865 15.33333 25259.05 -1008.131 1008.131

6 15.66667 22786.79 6999.509 -6999.5097 16 20314.52 14183.06 -14183.068 16.33333 17842.25 20542.52 -20542.529 16.66667 15369.99 26077.9 -26077.9

10 17 12897.72 30789.18 -30789.181 17 -13152.28 30789.18 -30789.182 17.33333 -15624.55 25993.04 -259933 17.66667 -18096.81 20372.82 -20372.824 18 -20569.08 13928.5 -13928.55 18.33333 -23041.35 6660.096 -6660.0966 18.66667 -25513.61 -1432.398 1432.3987 19 -27985.88 -10348.98 10348.988 19.33333 -30458.15 -20089.65 20089.659 19.66667 -32930.41 -30654.41 30654.41

10 20 -35402.68 -42043.26 42043.2620 0 0 0

Ecuaciones de Corte: VTramosx inicial x final Ax+ B

0.00 2.88 -7416.80 21326.362.88 7.50 -7416.80 21326.367.50 10.75 -7416.80 91564.3610.75 14.00 -7416.80 70164.6014.00 17.00 -7416.80 138983.3217.00 -7416.80 112933.3220.00

"" & () Ecuaciones de Momento: M

Ax^2+ Bx+ C-3708.40 21326.36 0.00-3708.40 21326.36 0.00-3708.40 91564.36 -526785.00-3708.40 70164.60 -296737.58-3708.40 138983.32 -1260199.66-3708.40 112933.32 -817349.66

Momento de resitencia de aceroponer todo con signo positivo x global x localM1- n n nM2- 33347.01 7.03 7.03M3- 33347.01 7.95 0.45M4- 33347.01 13.76 6.26M5- 33347.01 14.23 0.23M6- 33347.01 19.75 5.75

x global x localM1+ 23768.61 1.51 1.51M2+ 23768.61 4.24 4.24M3+ 23768.61 10.36 2.86M4+ 23768.61 11.21 3.71M5+ 23768.61 16.52 2.52M6+ 23768.61 17.47 3.47

Momento maximoM+ M-

0.0030661.04 -48649.8028979.90 -41279.5830789.18 -42043.26

x global: V=0x local: V=02.88 2.88 x global x local2.88 2.88 2.88 2.8810.75 3.25 10.75 3.250.00 -7.50 17.00 3.0017.00 3.000.00 -14.00

PI ix global: x local V

n n n5.75 5.75 -21326.369.13 1.63 23872.8712.54 5.04 -22833.8515.37 1.37 24961.2818.61 4.61 -25093.76

$Vc/2 kg: 6267.23

x global x local2.03 2.033.72 3.72

11.50 3.2510.31 3.2517.89 3.0016.07 3.00

d 0.64Vcx=d local16579.61

-29552.8931191.61

-28923.8530401.37

-30655.93 & ()

Vu= 23349.18 23349.18 23349.18 23349.18 23349.18 23349.18x global= 0.00 6.02 9.20 12.61 15.59 18.37x local= 0.00 6.02 1.70 5.11 1.59 4.37

m kg-m0.00

30661.04-48649.8028979.90

-41279.5830789.18

-42043.26

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CALCULO DE REFUERZO LONGITUDINAL

no E X Tramo AB Tramo BC Tramo CDn 1.Xim1= n 0.45 0.23 ()

2.PI1= n 1.63 1.37 $n 3.Xim21= 1.51 2.86 2.52

4.mmax= 2.88 3.25 3.00n 5.Xim22= 4.24 3.71 3.47

6.PI2= 5.75 5.04 4.61n 7.Xim3= 7.03 6.26 5.75

8.Xt= 7.50 6.50 6.00

ACERO POSITIVO:

Datos d o 12dbarra: d: 64.00 cm12x N° de barra 8.00 30.48 cmpositivo 8.00 30.48 cm

6.00 22.86 cm 0.64 m

Barras (m) N°b(+)1i= n 0.64 b(+)1d= 5.75 0.64b(+)2i= 1.51 0.64 0.87 b(+)2d= 4.24 0.64b(+)3i= 1.63 0.64 0.99 b(+)3d= 5.04 0.64b(+)4i= 2.86 0.64 2.22 b(+)4d= 3.71 0.64b(+)5i= 1.37 0.64 0.73 b(+)5d= 4.61 0.64b(+)6i= 2.52 0.64 1.88 b(+)6d= 3.47 0.64

Longitud de anclaje minL anclaje m (m)

1.40 b(+)1i= 1.51 1.40 0.11 b(+)1d= 4.240.70 b(+)2i= 2.88 0.70 2.18 b(+)2d= 2.881.40 b(+)3i= 2.86 1.40 1.46 b(+)3d= 3.710.84 b(+)4i= 3.25 0.84 2.41 b(+)4d= 3.251.40 b(+)5i= 2.52 1.40 1.12 b(+)5d= 3.470.70 b(+)6i= 3.00 0.70 2.30 b(+)6d= 3.00

Resultado Final Cuadro de colocacióninferior b(+)1i= 0.11 b(+)1d= 6.39 inferior 0.11superior b(+)2i= 0.87 b(+)2d= 4.88 superior 0.87inferior b(+)3i= 0.99 b(+)3d= 5.68 inferior 0.99superior b(+)4i= 2.22 b(+)4d= 4.35 superior 2.22inferior b(+)5i= 0.73 b(+)5d= 5.25 inferior 0.73superior b(+)6i= 1.88 b(+)6d= 4.11 superior 1.88

3. Verficación de el momento resistente sea mayor al momento último

PI1 A PI2 PI3 PI4 PI5 PI6Mu 23768.61 23768.61 23768.61 23768.61 23768.61 23768.61 23768.61

Vu #VALUE! 21326.36 21326.36 23872.87 22833.85 24961.28 25093.76La 0.64 0.15 0.64 0.64 0.64 0.64 0.64Ld #VALUE! 1.60 1.75 1.64 1.68 1.59 1.59

ACERO NEGATIVOBarras (m) N°yob(-)1i= 0.00 0.00 0.00 b(-)1d= n 0.64b(-)2i= 0.00 0.00 0.00 b(-)2d= n 0.64b(-)3i= 5.75 0.64 5.11 b(-)3d= 1.63 0.64b(-)4i= 7.03 0.64 6.39 b(-)4d= 0.45 0.64b(-)5i= 5.04 0.64 4.40 b(-)5d= 1.37 0.64b(-)6i= 6.26 0.64 5.62 b(-)6d= 0.23 0.64b(-)7i= 4.61 0.64 3.97 b(-)7d= 6.00 0.00b(-)8i= 5.75 0.64 5.11 b(-)8d= 6.00 0.00

()Longitud de anclaje mín ""L anclaje m

1.20 b(-)1i= n 1.56 b(-)1d= n1.20 b(-)2i= 0.00 1.56 -1.56 b(-)2d= 0.001.40 b(-)3i= 7.03 1.82 5.21 b(-)3d= 0.450.84 b(-)4i= 7.50 1.09 6.41 b(-)4d= 0.001.40 b(-)5i= 6.26 1.82 4.44 b(-)5d= 0.230.84 b(-)6i= 6.50 1.09 5.41 b(-)6d= 0.001.40 b(-)7i= 5.75 1.82 3.93 b(-)7d= 6.000.84 b(-)8i= 6.00 1.09 4.91 b(-)8d= 6.00

Resultado Final Cuadro de colocaciónsuperior b(-)1i= 0.00 b(-)1d= 0.00 superior 0.00 0.00inferior b(-)2i= 0.00 b(-)2d= 1.56 inferior 1.56 1.56superior b(-)3i= 5.11 b(-)3d= 2.27 superior 2.39 2.27inferior b(-)4i= 6.39 b(-)4d= 1.09 inferior 1.11 1.09superior b(-)5i= 4.40 b(-)5d= 2.05 superior 2.10 2.05inferior b(-)6i= 5.41 b(-)6d= 1.09 inferior 1.09 1.09superior b(-)7i= 3.93 b(-)7d= 6.00 superior 2.07 6.00inferior b(-)8i= 4.91 b(-)8d= 6.00 inferior 1.09 6.00

5. Finalmente en Tensión debe pasar 1/4 de acero mínimoMientras en compresión 1/3 como mínimo

6. REFUERZO TRANSVERSAL: ESTRIBOS ()bw= 30.00 cm $f'c= 210.00 kg/cm^2 ""fy= 4200.00 kg/cm^2 Smin=Av*fy/3.5/bwǾ= 0.85acero 1.42 cm^2

x: m local x: m local x: m localVc kg: 14746.42 No es necesario

ǾVc/2 kg: 6267.23 2.03 3.72 3.25 3.25 3.00 3.00

Vsmax:kg 58429.23 2.1r2fcbd kgespacimiento max 1.1r2fcbd kg 30605.79 kg

.+ .- .+ .- .+ .-AB iz BA der BC iz CB der CD iz DC der

Vu(xi=d, xd=L-d): kg 16579.61 29552.89 31191.61 28923.85 30401.37 30655.93Vus:kg 4759.00 20021.68 21949.58 19281.63 21019.89 21319.37Vs:kg 5598.82 23554.92 25823.04 22684.27 24729.28 25081.61

Espaciamiento: el menor entre Vus y Vs maxvsf: kg 4759.00 20021.68 21949.58 19281.63 21019.89 21319.37s1: cm 80.21 19.06 17.39 19.80 18.16 17.90

espac: 1 cm 32.00 19.06 17.39 19.80 18.16 17.90espac. Modificado 1 30.00 15.00 15.00 20.00 15.00 15.00

s2: cm 56.80 56.80 56.80 56.80 56.80 56.80espac. 2 cm 32.00 32.00 32.00 32.00 32.00 32.00

espac. Modificado 2 30.00 30.00 30.00 30.00 30.00 30.00Reduciendo por fuerza cortanteVu=Ǿ*(vc+av*fy*d/s2)

Vu= 23349.18 23349.18 23349.18 23349.18 23349.18 23349.18Local x m= 0.00 6.02 1.70 5.11 1.59 4.37

Puede variar depende a la existenciaDenominación de espaciamiento: .------------------> ""izquierda cantidad espaciam. cantidad espaciam. cantidad espaciam.ABiz 1.00 0.05 -0.17 30.00 6.77 30.00 6.60BCiz 1.00 0.05 10.98 15.00 5.18 30.00 16.16CDiz 1.00 0.05 10.27 15.00 4.70 30.00 14.97

(m)6.394.885.684.355.254.11

()""

(m)1.40 5.640.70 3.581.40 5.110.84 4.091.40 4.870.70 3.70

Cuadro de colocación6.28 Longitud de anclaje si si sobrepasa4.01 Gancho: 12*diametro de la barra4.69 Ldh 318*Db/(f'c)^0.52.134.522.23

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(m)

2.271.092.010.876.006.00

1.56 1.56 1.561.82 2.271.09 1.091.82 2.051.09 1.09

6.006.00

Recordar criterio el menor: s1=Av*fy*d/Vs

d/2 32.00 cm s2=Av*fy/3.5/bw60.00 cm

Nombrar

Nombrar

<-------------------------Derecha cantidad espaciam. cantidad espaciam. cantidad espaciam.BA der 1.00 0.05 9.51 15.00 7.68 30.00CB der 1.00 0.05 6.71 20.00 6.19 30.00DC der 1.00 0.05 10.50 15.00 4.58 30.00

17.1912.9015.08

Viga "T"

Datos: hf(cm) 15.000 Seccion APOYO TRAMO APOYO TRAMObw(cm) 30.000 Mu=ΦMn 0.000 30661.041 48649.800 28979.895bf(cm) 60.000 d 64.000 64.000 64.000 64.000f´c(kg/cm2) 210.000 As(cm2) - 14.356 - 13.569fy(kg/cm2) 4200.000 a(cm) - 5.630 - 5.321

Condi - a<hf - a<hfANALISIS DE ACERO ELEGIDO Tipo Rec(bw) Rec(bf) Rec(bw) Rec(bf)Varillas - - - w1 0.000 0.069 0.245 0.065As(cm2) 10.140 11.400 15.200 w2 1.695 1.626 1.450 1.630b(cm) 60.000 60.000 30.000 w 0.000 0.069 0.245 0.065a(cm) 3.976 4.471 11.922 ρ 0.000 0.003 0.012 0.003d(cm) 64.000 64.000 64.000 ρmax 0.016 0.016 0.016 0.016Mn(Kg-m) 26409.570 29572.941 37052.235 ρ<ρmax OK OK OK OKMu(Kg-m) 23768.613 26615.647 33347.012 a(cm) 0.000 5.181 18.436 4.885

As(cm2) 0.000 13.210 23.505 12.456Asmin 6.446 12.891 6.446 12.891As(prvt) 6.446 13.210 23.505 12.891

APOYO TRAMO APOYO41279.580 30789.180 42043.260

64.000 64.000 64.000- 14.416 -- 5.654 -- a<hf -Rec(bw) Rec(bf) Rec(bw)

0.202 0.069 0.206 Mnf(kg-m)1.493 1.626 1.489 Asf(cm2)0.202 0.069 0.206 Mnw(kg-m)0.010 0.003 0.010 Muw(kg-m)0.016 0.016 0.016 w

OK OK OK Asw(cm2)15.191 5.203 15.517 As(cm2)19.369 13.268 19.785

6.446 12.891 6.44619.369 13.268 19.785