traçado e dimensionamento laje protendida

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γ 1.4 g (kgf/m² 950 q (kgf/m²) 1330 lx (m) 11.50 ly (m) 24.00 ly/lx 2.086957 2 αx 14.2 mx (kgf.m) 12386.8 αy 42.5 my (kgf.m) 4138.647 βx 8 mbx (kgf.m) 21986.56 βy - mby (kgf.m) -

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traçado e dimensionamento laje protendida

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Page 1: traçado e dimensionamento laje protendida

γ 1.4g (kgf/m²) 950 q (kgf/m²) 1330

lx (m) 11.50ly (m) 24.00ly/lx 2.086957 2

αx 14.2 mx (kgf.m) 12386.8αy 42.5 my (kgf.m) 4138.647βx 8 mbx (kgf.m) 21986.56βy - mby (kgf.m) -

Page 2: traçado e dimensionamento laje protendida
Page 3: traçado e dimensionamento laje protendida

SENTIDO X SENTIDO X (BORDA)Mmáx (kgf.m) = 12387 Mmáx (kgf.m) =fck (kgf/cm²) = 300 fcd (kgf/cm²) = 214.2857 fck (kgf/cm²) =h (m) = 0.26 d (cm) = 23 h (m) =bw (cm) = 100 bw (cm) =cobrimento (m) = 0.03 cobrimento (m) =e (m) = 0.08 e (m) =Pi=Mmáx/e (kgf) = 154837.5 Pi=Mmáx/e (kgf) =Perdas (%) = 20 Perdas (%) =P=Pi(100+Perdas) (kgf) = 185805 P=Pi(100+Perdas) (kgf) =Ap (mm²) = 143.4 Ap (cm²) = 1.434 Ap (mm²) =n = 1 Ap (cm²) = 1.434 n =

Carga de Ruptura do Cabo = 18730 = 13061.37 Carga de Ruptura do Cabo =n = 9.920182 cabos/metro = 10 n =espaçamento = 10 cm espaçamento =

σp (kgf/cm²) = 12957.11 σp (kgf/cm²) =

Page 4: traçado e dimensionamento laje protendida

SENTIDO X (BORDA) SENTIDO Y21987 Mmáx (kgf.m) = 4139300 fcd (kgf/cm²) = 214.2857 fck (kgf/cm²) = 300 fcd (kgf/cm²) =0.26 d (cm) = 23 h (m) = 0.26 d (cm) =100 bw (cm) = 1000.03 cobrimento (m) = 0.030.1 e (m) = 0.1219870 Pi=Mmáx/e (kgf) = 4139020 Perdas (%) = 20263844 P=Pi(100+Perdas) (kgf) = 49668143.4 Ap (cm²) = 1.434 Ap (mm²) = 100.9 Ap (cm²) =1 Ap (cm²) = 1.434 n = 1 Ap (cm²) =

26580 = 18535.56 Carga de Ruptura do Cabo = 18730 =9.926411 cabos/metro = 10 n = 2.651789 cabos/metro =10 cm espaçamento = 33.33333 cm

18399.16 σp (kgf/cm²) = 16408.33

Page 5: traçado e dimensionamento laje protendida

SENTIDO Y

214.285723

1.0091.009

18562.933

Page 6: traçado e dimensionamento laje protendida

SENTIDO X SENTIDO Y

ma 0 M=ax²+bx+c c = 0 ma 0mb 12386.796 b = 6220.33 mb 4138.647mc -21986.563 a = -707.149 mc 0

P 263844 P 49668

x M e x M e0.00 0.00 0.00 0.00 0.00 0.000.25 1,510.89 0.01 0.25 170.65 0.000.50 2,933.38 0.01 0.50 337.70 0.010.75 4,267.48 0.02 0.75 501.16 0.011.00 5,513.18 0.02 1.00 661.03 0.011.25 6,670.49 0.03 1.25 817.31 0.021.50 7,739.41 0.03 1.50 970.00 0.021.75 8,719.93 0.03 1.75 1119.09 0.022.00 9,612.06 0.04 2.00 1264.59 0.032.25 10,415.80 0.04 2.25 1406.49 0.032.50 11,131.14 0.04 2.50 1544.81 0.032.75 11,758.09 0.04 2.75 1679.53 0.033.00 12,296.65 0.05 3.00 1810.66 0.043.25 12,746.81 0.05 3.25 1938.19 0.043.50 13,108.58 0.05 3.50 2062.14 0.043.75 13,381.95 0.05 3.75 2182.49 0.044.00 13,566.94 0.05 4.00 2299.25 0.054.25 13,663.52 0.05 4.25 2412.41 0.054.50 13,671.72 0.05 4.50 2521.99 0.054.75 13,591.52 0.05 4.75 2627.97 0.055.00 13,422.93 0.05 5.00 2730.36 0.055.25 13,165.94 0.05 5.25 2829.15 0.065.50 12,820.56 0.05 5.50 2924.36 0.065.75 12,386.78 0.05 5.75 3015.97 0.066.00 11,864.62 0.04 6.00 3103.99 0.066.25 11,254.05 0.04 6.25 3188.41 0.066.50 10,555.10 0.04 6.50 3269.24 0.076.75 9,767.75 0.04 6.75 3346.48 0.077.00 8,892.01 0.03 7.00 3420.13 0.077.25 7,927.87 0.03 7.25 3490.19 0.077.50 6,875.34 0.03 7.50 3556.65 0.077.75 5,734.42 0.02 7.75 3619.52 0.078.00 4,505.10 0.02 8.00 3678.80 0.07

0 20 40 60 80 100 120

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

e

Page 7: traçado e dimensionamento laje protendida

8.25 3,187.39 0.01 8.25 3734.48 0.088.50 1,781.29 0.01 8.50 3786.57 0.088.75 286.79 0.00 8.75 3835.07 0.089.00 -1,296.10 0.00 9.00 3879.98 0.089.25 -2,967.38 -0.01 9.25 3921.30 0.089.50 -4,727.06 -0.02 9.50 3959.02 0.089.75 -6,575.13 -0.02 9.75 3993.15 0.0810.00 -8,511.60 -0.03 10.00 4023.69 0.0810.25 -10,536.46 -0.04 10.25 4050.63 0.0810.50 -12,649.71 -0.05 10.50 4073.98 0.0810.75 -14,851.36 -0.06 10.75 4093.74 0.0811.00 -17,141.40 -0.06 11.00 4109.91 0.0811.25 -19,519.83 -0.07 11.25 4122.48 0.0811.50 -21,986.66 -0.08 11.50 4131.46 0.08

11.75 4136.85 0.0812.00 4138.65 0.0812.25 4136.85 0.0812.50 4131.46 0.0812.75 4122.48 0.0813.00 4109.91 0.0813.25 4093.74 0.0813.50 4073.98 0.0813.75 4050.63 0.0814.00 4023.69 0.0814.25 3993.15 0.0814.50 3959.02 0.0814.75 3921.30 0.0815.00 3879.98 0.0815.25 3835.08 0.0815.50 3786.58 0.0815.75 3734.48 0.0816.00 3678.80 0.0716.25 3619.52 0.0716.50 3556.65 0.0716.75 3490.19 0.0717.00 3420.13 0.0717.25 3346.49 0.0717.50 3269.24 0.0717.75 3188.41 0.0618.00 3103.99 0.0618.25 3015.97 0.0618.50 2924.36 0.0618.75 2829.15 0.0619.00 2730.36 0.0519.25 2627.97 0.0519.50 2521.99 0.0519.75 2412.42 0.0520.00 2299.25 0.05

Page 8: traçado e dimensionamento laje protendida

20.25 2182.49 0.0420.50 2062.14 0.0420.75 1938.20 0.0421.00 1810.66 0.0421.25 1679.53 0.0321.50 1544.81 0.0321.75 1406.50 0.0322.00 1264.59 0.0322.25 1119.09 0.0222.50 970.00 0.0222.75 817.31 0.0223.00 661.04 0.0123.25 501.17 0.0123.50 337.70 0.0123.75 170.65 0.0024.00 0.00 0.00

Page 9: traçado e dimensionamento laje protendida

SENTIDO Y

M=ax²+bx+c c = 0b = 689.7745a = -28.7406

0 20 40 60 80 100 120

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

e

Page 10: traçado e dimensionamento laje protendida

traçado Horizontal VerticalP MN 2.63844 x1 0 y1 0.13r min (m) 3(P)^0.5 4.9 x2 0.75 y2 0.10∆e1 0.080 x3 1.5 y3 0.08∆e 0.170 x4 2.25 y4 0.07l1 11.500 x5 3 y5 0.06a 4.63 x6 3.75 y6 0.05b 0.240 x7 4.5 y7 0.05f2 0.010 x8 5.25 y8 0.05y1,B 0.180 x9 6 y9 0.05eB -0.100 x10 6.75 y10 0.07f1 0.130 x11 7.5 y11 0.08

x12 8.25 y12 0.10x13 9 y13 0.13x14 9.75 y14 0.16x15 10.5 y15 0.19x16 11.25 y16 0.22x17 11.5 y17 0.23x18 11.75 y18 0.22x19 12.5 y19 0.19x20 13.25 y20 0.16x21 14 y21 0.13x22 14.75 y22 0.10x23 15.5 y23 0.08x24 16.25 y24 0.07x25 17 y25 0.05x26 17.75 y26 0.05x27 18.5 y27 0.05x28 19.25 y28 0.05x29 20 y29 0.06x30 20.75 y30 0.07x31 21.5 y31 0.08x32 22.25 y32 0.10x33 23 y33 0.13

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 28 29 30 31 32 33 340.00

0.05

0.10

0.15

0.20

0.25

Chart Title

Page 11: traçado e dimensionamento laje protendida

a b17 0.2316 0.21715 0.19114 0.15713 0.12712 0.10211 0.08110 0.065

9 0.0548 0.0477 0.0456 0.0485 0.0554 0.0673 0.0832 0.1041 0.13

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 28 29 30 31 32 33 340.00

0.05

0.10

0.15

0.20

0.25

Chart Title

Page 12: traçado e dimensionamento laje protendida

ec 0.1ea 0f 0.1l 24

Horizontal Verticalx1 0 y1 0.13x2 1 y2 0.11x3 2 y3 0.1x4 3 y4 0.09x5 4 y5 0.07x6 5 y6 0.06x7 6 y7 0.05x8 7 y8 0.05x9 8 y9 0.04x10 9 y10 0.04x11 10 y11 0.03 Horizontal Verticalx12 11 y12 0.03 x1 0 y1 0x13 12 y13 0.03 x2 1 y2 0.02x14 13 y14 0.03 x3 2 y3 0.03x15 14 y15 0.03 x4 3 y4 0.04x16 15 y16 0.04 x5 4 y5 0.06x17 16 y17 0.04 x6 5 y6 0.07x18 17 y18 0.05 x7 6 y7 0.08x19 18 y19 0.05 x8 7 y8 0.08x20 19 y20 0.06 x9 8 y9 0.09x21 20 y21 0.07 x10 9 y10 0.09x22 21 y22 0.09 x11 10 y11 0.1x23 22 y23 0.1x24 23 y24 0.11x25 24 y25 0.13

Page 13: traçado e dimensionamento laje protendida

x12 11 y12 0.1x13 12 y13 0.1x14 13 y14 0.1x15 14 y15 0.1x16 15 y16 0.09x17 16 y17 0.09x18 17 y18 0.08x19 18 y19 0.08x20 19 y20 0.07x21 20 y21 0.06x22 21 y22 0.04x23 22 y23 0.03x24 23 y24 0.02x25 24 y25 0