ZONA DE ANCLAJE

A) ALTURA DE SECCION

h [cm] 90

B) EFICIENCIA DE SECCION Q:

h[cm] 100b1 [cm] 60b2 [cm] 55tf1 [cm] 15tf2 [cm] 20bw [cm] 20D3 [cm] 10D5 [cm] 10Ac [cm2] 3675.0C1 [cm] 50.2C2 [cm] 49.8I [cm4] 4231894.4

84255.8S2[cm3] 85023.5r 33.9K1 23.1K2 22.9Q 0.46COND OK

DATOS:L [m] 20f'c [kg/cm2] 350fy [kg/cm2] 16600fu [kg/cm2] 19000Peh [kg/m3] 2500

PESO PROPIO:Viga:

qo1= 946.3125 [Kg/m]

Efecto de Diafragma:Como: eD [cm]= 30

s1 [cm]= 150 Po2= 780 KghD [cm]= 80

S1[cm3]

h=0.045∙𝐿_𝑡𝑟𝑎𝑚𝑜

0.45≤𝑄≤0.55SI:Q< 0.45 "SP" seccion pesadaQ> 0.55 "SE" seccion esbelta

ESFUERZOS ADMISIBLES EN EL HORMIGON:

EN t=0:fci= 210 [kg/cm2] fcs= 157.5 [kg/cm2]

fti= 14.9666 [kg/cm2] fts= 29.93 [kg/cm2]

ESTADO PI+Mo:

Pe= 208.25 [T]Pe= 208250.00 [kg]

Pi= 245000.00 [kg]

Pj= 277666.6666667 [kg]

ZONA DE CLAVAJE:LIMITES DE LA ZONA DE CLAVAJE:

EN EL CASO DE Pi+Mo:

CASO I II

X[m] Mo1 [T-m] Moi [T-m] Mo [T-m] e [cm] e [cm] eI [cm] eII [cm]0 0.00 0 0.00 28.074 -96.0129 21.7 145.81 8.99 0.39 9.38 31.902 -92.1844 17.9 142.02 17.03 0.78 17.81 35.345 -88.742 14.4 138.53 24.13 1.17 25.30 38.401 -85.686 11.4 135.54 30.28 1.56 31.84 41.071 -83.0162 8.7 132.85 35.49 1.95 37.44 43.354 -80.7326 6.4 130.56 39.75 2.34 42.09 45.251 -78.8353 4.5 128.67 43.06 2.73 45.79 46.762 -77.3243 3.0 127.18 45.42 3.12 48.54 47.887 -76.1994 1.9 126.09 46.84 3.51 50.35 48.626 -75.4609 1.1 125.2

10 47.32 3.9 51.22 48.978 -75.1086 0.8 124.911 46.84 4.29 51.13 48.944 -75.1425 0.8 124.912 45.42 4.68 50.10 48.524 -75.5627 1.2 125.313 43.06 5.07 48.13 47.718 -76.3691 2.1 126.114 39.75 5.46 45.21 46.525 -77.5618 3.2 127.315 35.49 5.85 41.34 44.946 -79.1408 4.8 128.916 30.28 6.24 36.52 42.981 -81.106 6.8 130.917 24.13 6.63 30.76 40.629 -83.4574 9.1 133.218 17.03 7.02 24.05 37.892 -86.1951 11.9 136.0

EN t=∞:

𝑀(𝑥)=(𝑞∙𝐿)/2∙x−q∙𝑥^2/2

19 8.99 7.41 16.40 34.768 -89.319 15.0 139.120 0.00 7.8 7.80 31.257 -92.8292 18.5 142.6

EN EL ESTADO Pe+Mo+Ma+Mll:

h[cm] 100b1 [cm] 60b2 [cm] 55tf1 [cm] 15tf2 [cm] 20bw [cm] 20D3 [cm] 10D5 [cm] 10 Pe= 245 [T]Ac [cm2] 5423.571 Pe= 245000.00 [kg]C1 [cm] 45.842C2 [cm] 68.236 Pi= 288235.29 [kg] q'o [kg/m] 1355.89 [kg/m]I [cm4] 6477962.06

141310.633 Pj= 326666.6666667 [kg] qa [kg/m] 918.99 [kg/m]S2[cm3] 94934.6688

EN EL CASO DE Pe+Mo+Ma+Mll:

P1 [T]= 14.51 X [m]= 4.3 qcc [T/m] 0.95P2 [T]= 14.51 gmi= 0.507P3 [T]= 3.63 %P 33

X[m] y1 y2 y3 M'tren Mtren M'carril Mcarril Mt+Mc Mim Mll0 0 0 0 0 0 0.0 0.0 0.0 0 0.01 0.95 0.735 0.52 26.337 13.3528 9.0 4.6 17.9 4.40644 22.32 1.8 1.37 0.94 49.409 25.0503 17.1 8.7 33.7 8.2666 42.03 2.55 1.905 1.26 69.216 35.0924 24.2 12.3 47.4 11.5805 59.04 3.2 2.34 1.48 85.758 43.4792 30.4 15.4 58.9 14.3481 73.25 3.75 2.675 0.525 71.741 36.3724 35.6 18.1 54.4 12.0029 66.46 4.2 2.91 1.19 88.772 45.0075 39.9 20.2 65.2 14.8525 80.17 4.55 3.045 1.755 102.54 51.9872 43.2 21.9 73.9 17.1558 91.18 4.8 3.08 2.22 113.04 57.3116 45.6 23.1 80.4 18.9128 99.39 4.95 3.015 2.585 120.28 60.9806 47.0 23.8 84.8 20.1236 104.9

10 5 2.85 2.85 124.25 63.0 47.5 24.1 87.1 20.7881 107.911 4.95 3.015 2.585 120.28 60.9806 47.0 23.8 84.8 20.1236 104.912 4.8 3.08 2.22 113.04 57.3116 45.6 23.1 80.4 18.9128 99.313 4.55 3.045 1.755 102.54 51.9872 43.2 21.9 73.9 17.1558 91.114 4.2 2.91 1.19 88.772 45.0075 39.9 20.2 65.2 14.8525 80.115 3.75 2.675 0.525 71.741 36.3724 35.6 18.1 54.4 12.0029 66.4

S1[cm3]

16 3.2 2.34 1.48 76.401 38.7353 30.4 15.4 54.1 12.7827 66.917 2.55 1.905 1.26 62.198 31.5345 24.2 12.3 43.8 10.4064 54.218 1.8 1.37 0.94 44.73 22.6784 17.1 8.7 31.3 7.48386 38.819 0.95 0.735 0.52 23.998 12.1669 9.0 4.6 16.7 4.01506 20.820 0 0 0 0 0 0.0 0.0 0.0 0 0.0

CASO III IV

X[m] M'o [T-m] Mo [T-m] Ma [T-m] Mll [kg-m] e [cm] e [cm] eIII [cm] eIV [cm]

0 0.00 0.00 0.00 0.00 116.897 -29.10 -48.66 97.341 12.88 9.38 8.73 22.33 133.406 -12.59 -65.17 80.832 24.41 17.81 16.54 41.99 148.057 2.06 -79.82 66.183 34.58 25.30 23.43 58.96 160.853 14.85 -92.62 53.384 43.39 31.84 29.41 73.24 171.791 25.79 -103.6 42.455 50.85 37.44 34.46 66.44 173.361 27.36 -105.1 40.886 56.95 42.09 38.60 80.09 182.519 36.52 -114.3 31.727 61.69 45.79 41.81 91.06 189.82 43.82 -121.6 24.428 65.08 48.54 44.11 99.34 195.264 49.26 -127 18.979 67.12 50.35 45.49 104.95 198.852 52.85 -130.6 15.38

10 67.79 51.22 45.95 107.86 200.583 54.58 -132.3 13.6511 67.12 51.13 45.49 104.95 199.17 53.17 -130.9 15.0712 65.08 50.10 44.11 99.34 195.901 49.90 -127.7 18.3413 61.69 48.13 41.81 91.06 190.775 44.77 -122.5 23.4614 56.95 45.21 38.60 80.09 183.792 37.79 -115.6 30.4415 50.85 41.34 34.46 66.44 174.953 28.95 -106.7 39.2816 43.39 36.52 29.41 66.93 171.126 25.13 -102.9 43.1117 34.58 30.76 23.43 54.22 161.15 15.15 -92.91 53.0918 24.41 24.05 16.54 38.83 149.317 3.32 -81.08 64.9219 12.88 16.40 8.73 20.76 135.627 -10.37 -67.39 78.6120 0.00 7.80 0.00 0.00 120.081 -25.92 -51.85 94.16

CASO III:

CASO IV:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

ZONA DE CLAVAJE (Pi+Mo)

CASO I Polynomial (CASO I)CASO IV Polynomial (CASO IV)

𝑀(𝑥)=(𝑞∙𝐿)/2∙x−q∙𝑥^2/2

𝑒(𝑥)≥𝑓_𝑐𝑠∙(𝑆_1/𝑃_𝑒 )+(〖 〗𝑀𝑜 _((𝑥) )+〖 〗𝑀𝑎 _((𝑥) )+〖 〗𝑀𝑙𝑙 _((𝑥) ))/𝑃_𝑒 +𝑆_1/𝐴_𝑐 𝑒(𝑥)≥〖− 〗𝑓 _𝑡𝑠∙(𝑆_2/𝑃_𝑒 )+(〖 〗𝑀𝑜 _((𝑥) )+〖 〗𝑀𝑎_((𝑥) )+〖 〗𝑀𝑙𝑙 _((𝑥) ))/𝑃_𝑒 −𝑆_2/𝐴_𝑐

Graficando el caso I y caso IV, tenemos:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

ZONA DE CLAVAJE (Pi+Mo)

CASO I Polynomial (CASO I)CASO IV Polynomial (CASO IV)

CASO I:

CASO II:

𝑒(𝑥)≤𝑓_𝑡𝑖∙(𝑆_1/𝑃_𝑖 )+〖 〗𝑀𝑜 _((𝑥) )/𝑃_𝑖 +𝑆_1/𝐴_𝑐 𝑒(𝑥)≤−𝑓_𝑐𝑖∙(𝑆_2/𝑃_𝑖 )+〖 〗𝑀𝑜 _((𝑥) )/𝑃_𝑖 −𝑆_2/𝐴_𝑐