ejercicios vigas

1 b 0.25 mh 0.4 mr 3 mq 1000 kg/m

fck 210 kg/cm2Yc 1.5yf 1.6v 0.2a 30 0.5236 rad

Calculo de parametros fisico-geometricos

E 217370.65 kg/cm2

I 0.001333 m4

h/b k (emp) k1.0 0.141 0.1411.2 0.166 0.1661.5 0.196 0.1952.0 0.229 0.2272.5 0.249 0.2443.0 0.263 0.2531.6 0.2032

J 0.00127 m4

G 90571.10 kg/cm2CORTANTE

RC 2.5202 V = 1570,8 - 1000*X

0.04196529

f0 0 377.69 0.00 1570.80

V = 1570,80 - 3000*f

Mo = 0,04167 q r2

Mf = q r2 (1,04167 cosf - 1)

Mt = q r2 (1,04167 senf - f)

f (rad)Mf

kg-mMt

kg-mV

kg

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.01063315 x³ − 0.09094892 x² + 0.28657412 x − 0.06525168

Column CPolynomial (Column C)

0 10 20 30 40 50 60

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

1500.00

2000.00

Mf kg-mMt kg-mV kg

5 0.08727 342.00 31.92 1309.0010 0.17453 235.22 57.62 1047.2015 0.26180 58.15 70.93 785.4020 0.34907 -187.86 65.77 523.6025 0.43633 -500.93 36.19 261.8030 0.52360 -878.68 -23.55 0.00

fi0 -878.68 -23.55 1570.805 -500.93 36.19 1309.00

10 -187.86 65.77 1047.2015 58.15 70.93 785.4020 235.22 57.62 523.6025 342.00 31.92 261.8030 377.69 0.00 0.0035 342.00 -31.92 -261.8040 235.22 -57.62 -523.6045 58.15 -70.93 -785.4050 -187.86 -65.77 -1047.2055 -500.93 -36.19 -1309.0060 -878.68 23.55 -1570.80

Verificacion de seccion

Mtu = 0,18 fcd (2Ao*do)Vu = 0,3 fcd * b * d

he = A/U = 7.69Ao 559.17 cm2Uo 99.23 cm

Mtd 113.487 kg-mMtu 2167.87 kg-cmVd 1256.64 kgVu 37905.00 kg

1.3846

0.026 ≤ 1 OK

Mf kg-m

Mt kg-m

V kg

a=2(1-he/b)=

0 10 20 30 40 50 60

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

1500.00

2000.00

Mf kg-mMt kg-mV kg

1570.80 kgV = 1570,8 - 1000*X

X = r f = 3 fV = 1570,80 - 3000*f

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.01063315 x³ − 0.09094892 x² + 0.28657412 x − 0.06525168


0 10 20 30 40 50 60

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

1500.00

2000.00

Mf kg-mMt kg-mV kg

0 10 20 30 40 50 60

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

1500.00

2000.00

Mf kg-mMt kg-mV kg

2 b 0.25 mh 0.4 mr 3 mq 1000 kg/m



E 217370.65 kg/cm2

I 0.001333 m4

h/b k (emp) k1.0 0.141 0.1411.2 0.166 0.1661.5 0.196 0.1952.0 0.229 0.2272.5 0.249 0.2443.0 0.263 0.2531.6 0.2032

J 0.00127 m4


RC 2.5202 V = 3141,59 - 1000*X

0.14198421

f0 0 1277.86 0.00 3141.59

V = 3141,59 - 3000*f

Mo = 0,142 q r2

Mf = q r2 (1,142 cosf - 1)

Mt = q r2 (1,142 senf - f)

f (rad)Mf

kg-mMt

kg-mV

kg

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


5 0.08727 1238.75 110.38 2879.7910 0.17453 1121.71 213.93 2617.9915 0.26180 927.65 303.91 2356.1920 0.34907 658.03 373.64 2094.4025 0.43633 314.90 416.62 1832.6030 0.52360 -99.11 426.54 1570.8035 0.61087 -580.87 397.35 1309.0040 0.69813 -1126.70 323.29 1047.2045 0.78540 -1732.46 198.96 785.4050 0.87266 -2393.52 19.31 523.6055 0.95993 -3104.86 -220.25 261.8060 1.04720 -3861.07 -523.89 0.00

fi0 -3861.07 -523.89 3141.595 -3104.86 -220.25 2879.79

10 -2393.52 19.31 2617.9915 -1732.46 198.96 2356.1920 -1126.70 323.29 2094.4025 -580.87 397.35 1832.6030 -99.11 426.54 1570.8035 314.90 416.62 1309.0040 658.03 373.64 1047.2045 927.65 303.91 785.4050 1121.71 213.93 523.6055 1238.75 110.38 261.8060 1277.86 0.00 0.0065 1238.75 -110.38 -261.8070 1121.71 -213.93 -523.6075 927.65 -303.91 -785.4080 658.03 -373.64 -1047.2085 314.90 -416.62 -1309.0090 -99.11 -426.54 -1570.8095 -580.87 -397.35 -1832.60

100 -1126.70 -323.29 -2094.40105 -1732.46 -198.96 -2356.19110 -2393.52 -19.31 -2617.99115 -3104.86 220.25 -2879.79120 -3861.07 523.89 -3141.59


Mtu = 0,18 fcd (2Ao*do)

Mf kg-m

Mt kg-m

V kg

0 20 40 60 80 100 120

-5000.00

-4000.00

-3000.00

-2000.00

-1000.00

0.00

1000.00

2000.00

3000.00

4000.00

Mf kg-mMt kg-mV kg

Vu = 0,3 fcd * b * d

he = A/U = 7.69Ao 559.17 cm2Uo 99.23 cm


1.3846

0.268 ≤ 1 OK

a=2(1-he/b)=

3141.59 kgV = 3141,59 - 1000*X

X = r f = 3 fV = 3141,59 - 3000*f

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


0 20 40 60 80 100 120

-5000.00

-4000.00

-3000.00

-2000.00

-1000.00

0.00

1000.00

2000.00

3000.00

4000.00

Mf kg-mMt kg-mV kg

3 b 0.4 mh 1.2 mr 3 mq 1000 kg/m



E 217370.65 kg/cm2

I 0.057600 m4

h/b k (emp) k1.0 0.141 0.1411.2 0.166 0.1661.5 0.196 0.1952.0 0.229 0.2272.5 0.249 0.2443.0 0.263 0.2533.0 0.2530

J 0.01943 m4


RC 7.1146 V = 4712,39 - 1000*X

0.27323954

f0 0 2459.16 0.00 4712.39

V = 4712,39 - 3000*f

Mo = 0,2732 q r2

Mf = q r2 (1,2732 cosf - 1)

Mt = q r2 (1,2732 senf - f)

f (rad)Mf

kg-mMt

kg-mV

kg

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


10 0.17453 2285.07 419.07 4188.7920 0.34907 1768.08 777.67 3665.1930 0.52360 923.92 1017.19 3141.5940 0.69813 -221.78 1082.62 2617.9950 0.87266 -1634.20 924.24 2094.4060 1.04720 -3270.42 499.14 1570.8070 1.22173 -5080.74 -227.49 1047.2080 1.39626 -7010.14 -1281.31 523.6090 1.57080 -9000.00 -2678.01 0.00

fi0 -9000.00 -2678.01 4712.39

10 -7010.14 -1281.31 4188.7920 -5080.74 -227.49 3665.1930 -3270.42 499.14 3141.5940 -1634.20 924.24 2617.9950 -221.78 1082.62 2094.4060 923.92 1017.19 1570.8070 1768.08 777.67 1047.2080 2285.07 419.07 523.6090 2459.16 0.00 0.00

100 2285.07 -419.07 -523.60110 1768.08 -777.67 -1047.20120 923.92 -1017.19 -1570.80130 -221.78 -1082.62 -2094.40140 -1634.20 -924.24 -2617.99150 -3270.42 -499.14 -3141.59160 -5080.74 227.49 -3665.19170 -7010.14 1281.31 -4188.79180 -9000.00 2678.01 -4712.39



he = A/U = 15.00Ao 2625.00 cm2Uo 260.00 cm


Mf kg-m

Mt kg-m

V kg

0 20 40 60 80 100 120 140 160 180

-10000.00

-8000.00

-6000.00

-4000.00

-2000.00

0.00

2000.00

4000.00

6000.00

Mf kg-mMt kg-mV kg

1.2500

0.147 ≤ 1 OK

a=2(1-he/b)=

4712.39 kgV = 4712,39 - 1000*X

X = r f = 3 fV = 4712,39 - 3000*f

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


0 20 40 60 80 100 120 140 160 180

-10000.00

-8000.00

-6000.00

-4000.00

-2000.00

0.00

2000.00

4000.00

6000.00

Mf kg-mMt kg-mV kg

4 b 0.4 mh 2.0 mr 3 mq 1000 kg/m



E 217370.65 kg/cm2

I 0.266667 m4

h/b k (emp) k1.0 0.141 0.1411.2 0.166 0.1661.5 0.196 0.1952.0 0.229 0.2272.5 0.249 0.2443.0 0.263 0.2535.0 0.3650

J 0.04672 m4


RC 13.6986 V = 6283,19 - 1000*X

0.49239342

f0 0 4431.54 0.00 6283.19

V = 6283,19 - 3000*f

Mo = 0,4165 q r2

Mf = q r2 (1,4165 cosf - 1)

Mt = q r2 (1,4165 senf - f)

f (rad)Mf

kg-mMt

kg-mV

kg

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


10 0.17453 4227.49 761.57 5759.5920 0.34907 3621.52 1452.26 5235.9930 0.52360 2632.06 2003.38 4712.3940 0.69813 1289.16 2350.44 4188.7950 0.87266 -366.37 2435.18 3665.1960 1.04720 -2284.23 2207.28 3141.5970 1.22173 -4406.14 1625.95 2617.9980 1.39626 -6667.64 661.11 2094.4090 1.57080 -9000.00 -705.63 1570.80

100 1.74533 -11332.36 -2480.48 1047.20110 1.91986 -13593.86 -4657.24 523.60120 2.09440 -15715.77 -7217.50 0.00

fi0 -15715.77 -7217.50 6283.19

10 -13593.86 -4657.24 5759.5920 -11332.36 -2480.48 5235.9930 -9000.00 -705.63 4712.3940 -6667.64 661.11 4188.7950 -4406.14 1625.95 3665.1960 -2284.23 2207.28 3141.5970 -366.37 2435.18 2617.9980 1289.16 2350.44 2094.4090 2632.06 2003.38 1570.80

100 3621.52 1452.26 1047.20110 4227.49 761.57 523.60120 4431.54 0.00 0.00130 4227.49 -761.57 -523.60140 3621.52 -1452.26 -1047.20150 2632.06 -2003.38 -1570.80160 1289.16 -2350.44 -2094.40170 -366.37 -2435.18 -2617.99180 -2284.23 -2207.28 -3141.59190 -4406.14 -1625.95 -3665.19200 -6667.64 -661.11 -4188.79210 -9000.00 705.63 -4712.39220 -11332.36 2480.48 -5235.99230 -13593.86 4657.24 -5759.59240 -15715.77 7217.50 -6283.19


Mtu = 0,18 fcd (2Ao*do)

Mf kg-m

Mt kg-m

V kg

-60 -10 40 90 140 190 240

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

Mf kg-mMt kg-mV kg

Vu = 0,3 fcd * b * d

he = A/U = 16.67Ao 4277.78 cm2Uo 413.33 cm


1.1667

0.266 ≤ 1 OK

a=2(1-he/b)=

6283.19 kgV = 6283,19 - 1000*X

X = r f = 3 fV = 6283,19 - 3000*f

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.0106331471 x³ − 0.0909489226 x² + 0.2865741155 x − 0.065251676


-60 -10 40 90 140 190 240

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

Mf kg-mMt kg-mV kg

CALCULO A FLEXION Y TORSION LONGITUDINAL210 1.5

4200 1.15

p 0.0033333 1.6

BLOQUE NIVEL VIGA VanoMf Mt b h d

[T-cm] [T-cm] [cm] [cm] [cm]

1

0 37.8 0.0 25 40 36.1 3.33 0.47

5 34.2 3.2 25 40 36.1 3.33 0.43

10 23.5 5.8 25 40 36.1 3.33 0.29

15 5.8 7.1 25 40 36.1 3.33 0.07

20 -18.8 6.6 25 40 36.1 3.33 0.23

25 -50.1 3.6 25 40 36.1 3.33 0.62

30 -87.9 -2.4 25 40 36.1 3.33 1.10

2

0 127.8 0.0 25 40 36.1 3.33 1.61

5 123.9 11.0 25 40 36.1 3.33 1.56

10 112.2 21.4 25 40 36.1 3.33 1.41

15 92.8 30.4 25 40 36.1 3.33 1.16

20 65.8 37.4 25 40 36.1 3.33 0.82

25 31.5 41.7 25 40 36.1 3.33 0.39

30 -9.9 42.7 25 40 36.1 3.33 0.12

35 -58.1 39.7 25 40 36.1 3.33 0.72

40 -112.7 32.3 25 40 36.1 3.33 1.42

45 -173.2 19.9 25 40 36.1 3.33 2.21

50 -239.4 1.9 25 40 36.1 3.33 3.09

55 -310.5 -22.0 25 40 36.1 3.33 4.07

60 -386.1 -52.4 25 40 36.1 3.33 5.16

CALCULO A CORTE Y TORSION TRANSVERSAL

Bloque Nivel Viga vanoV apoyo Mt b altura d

(T) [T-cm] (cm) (m) (cm) (T) (T)

1

0 1.57 0.0 25 40 36.1 2.51 5.34

5 1.31 3.2 25 40 36.1 2.09 5.34

10 1.05 5.8 25 40 36.1 1.68 5.34

15 0.79 7.1 25 40 36.1 1.26 5.34

20 0.52 6.6 25 40 36.1 0.84 5.34

25 0.26 3.6 25 40 36.1 0.42 5.34

30 0.00 -2.4 25 40 36.1 0.00 5.34

2

0 3.14 0.0 25 40 36.1 5.03 5.34

fck Yc

fyk Ys

Yf

AS min AS simple

[cm2] [cm2]

VD Vcu

2

5 2.88 11.0 25 40 36.1 4.61 5.34

10 2.62 21.4 25 40 36.1 4.19 5.34

15 2.36 30.4 25 40 36.1 3.77 5.34

20 2.09 37.4 25 40 36.1 3.35 5.34

25 1.83 41.7 25 40 36.1 2.93 5.34

30 1.57 42.7 25 40 36.1 2.51 5.34

35 1.31 39.7 25 40 36.1 2.09 5.34

40 1.05 32.3 25 40 36.1 1.68 5.34

45 0.79 19.9 25 40 36.1 1.26 5.34

50 0.52 1.9 25 40 36.1 0.84 5.34

55 0.26 -22.0 25 40 36.1 0.42 5.34

60 0.00 -52.4 25 40 36.1 0.00 5.34

CALCULO A FLEXION Y TORSION LONGITUDINAL

As inferior As superior

N N N N

3.33 0.00 3.33 0.00 3 12

3.33 0.12 3.40 0.06 2 16 2 10

3.33 0.22 3.45 0.11 2 16 2 10

3.33 0.28 3.47 0.14 2 16 2 10

3.33 0.26 0.13 3.46 2 10 2 16

3.33 0.14 0.07 3.40 2 10 2 16

3.33 0.09 0.05 3.38 2 10 3 12

3.33 0.00 3.33 0.00 3 12

3.33 0.43 3.55 0.21 2 16 2 10

3.33 0.83 3.75 0.42 2 16 2 10

3.33 1.18 3.92 0.59 2 16 2 10

3.33 1.45 4.06 0.73 4 12 2 16

3.33 1.62 4.14 0.81 4 12 2 16

3.33 1.66 0.83 4.16 2 10 4 12

3.33 1.54 0.77 4.11 2 10 4 12

3.33 1.26 0.63 3.96 2 10 2 16

3.33 0.77 0.39 3.72 2 10 2 16

3.33 0.08 0.04 3.37 2 10 3 12

4.07 0.86 0.43 4.50 2 10 4 12

5.16 2.04 1.02 6.18 2 10 2 16 2


S corte (cm) S torsion (cm)

(T) Nº 6 Nº 8 Nº 10 Nº 6 Nº 8 Nº 10-2.83 1 -24 1 -42 1 -66 1 0 1 0 1 0

-3.24 1 -21 1 -37 1 -57 1 226 1 402 1 628

-3.66 1 -18 1 -33 1 -51 1 125 1 223 1 348

-4.08 1 -16 1 -29 1 -46 1 102 1 181 1 283

-4.50 1 -15 1 -26 1 -41 1 110 1 195 1 305

-4.92 1 -14 1 -24 1 -38 1 199 1 355 1 554

-5.34 1 -13 1 -22 1 -35 1 307 1 545 1 852

-0.31 1 -215 1 -381 1 -596 1 0 1 0 1 0

AS traccion AS compresion AS simple ASL AS INF AS SUP f mm

f mm

f mm[cm2] [cm2] [cm2] [cm2] [cm2] [cm2]

Vsu

-0.73 1 -92 1 -163 1 -255 1 65 1 116 1 182

-1.15 1 -58 1 -104 1 -162 1 34 1 60 1 94

-1.57 1 -43 1 -76 1 -119 1 24 1 42 1 66

-1.99 1 -34 1 -60 1 -94 1 19 1 34 1 54

-2.41 1 -28 1 -50 1 -77 1 17 1 31 1 48

-2.83 1 -24 1 -42 1 -66 1 17 1 30 1 47

-3.24 1 -21 1 -37 1 -57 1 18 1 32 1 50

-3.66 1 -18 1 -33 1 -51 1 22 1 40 1 62

-4.08 1 -16 1 -29 1 -46 1 36 1 64 1 101

-4.50 1 -15 1 -26 1 -41 1 374 1 664 1 1038

-4.92 1 -14 1 -24 1 -38 1 33 1 58 1 91

-5.34 1 -13 1 -22 1 -35 1 14 1 24 1 38

As superior

3.39 0.00

4.02 1.57

4.02 1.57

4.02 1.57

1.57 4.02

1.57 4.02

1.57 3.39

3.39 0.00

4.02 1.57

4.02 1.57

4.02 1.57

4.52 4.02

4.52 4.02

1.57 4.52

1.57 4.52

1.57 4.02

1.57 4.02

1.57 3.39

1.57 4.52

12 1.57 6.28

Nº USAR

(cm) estribos f S

20 1 6 20 5.43

15 1 6 14 6.32

15 1 6 13 6.47

15 1 6 13 6.55

15 1 6 13 6.52

15 1 6 14 6.34

15 1 6 14 6.27

20 1 6 20 5.43

f mm

AsINF(disp) AsSUP(disp)

[cm2] [cm2]

SmaxVresit

15 1 6 12 6.77

15 1 6 10 7.38

15 1 6 9 7.90

15 1 8 10 10.48

15 1 8 10 10.73

15 1 8 10 10.79

15 1 8 10 10.62

15 1 8 11 10.19

15 1 6 11 7.29

15 1 6 14 6.25

15 1 6 10 7.41

15 1 10 11 14.15


5000 1.15

p 0.0028 1.6



3

0 2459.2 0.0 40 120 116.1 13.44 8.09

10 2285.1 419.1 40 120 116.1 13.44 7.51

20 1768.1 777.7 40 120 116.1 13.44 5.78

30 923.9 1017.2 40 120 116.1 13.44 3.01

40 -221.8 1082.6 40 120 116.1 13.44 0.73

50 -1634.2 924.2 40 120 116.1 13.44 5.34

60 -3270.4 499.1 40 120 116.1 13.44 10.83

70 -5080.7 -227.5 40 120 116.1 13.44 17.10

80 -7010.1 -1281.3 40 120 116.1 13.44 24.05

90 -9000.0 -2678.0 40 120 116.1 13.44 31.58

4

0 4431.5 0.0 40 200 196.1 22.40 8.57

10 4227.5 761.6 40 200 196.1 22.40 8.17

20 3621.5 1452.3 40 200 196.1 22.40 6.99

30 2632.1 2003.4 40 200 196.1 22.40 5.07

40 1289.2 2350.4 40 200 196.1 22.40 2.49

50 -366.4 2435.2 40 200 196.1 22.40 0.73

60 -2284.2 2207.3 40 200 196.1 22.40 4.40

70 -4406.1 1625.9 40 200 196.1 22.40 8.52

80 -6667.6 661.1 40 200 196.1 22.40 12.97

90 -9000.0 -705.6 40 200 196.1 22.40 17.63

100 -11332.4 -2480.5 40 200 196.1 22.40 22.36

110 -13593.9 -4657.2 40 200 196.1 22.40 27.01

120 -15715.8 -7217.5 40 200 196.1 22.40 31.44



(T) [T-cm] (cm) (m) (cm) (T) (T)

3

0 4.71 0.0 40 120 116.1 7.54 31.72

10 4.19 419.1 40 120 116.1 6.70 31.72

20 3.67 777.7 40 120 116.1 5.86 31.72

30 3.14 1017.2 40 120 116.1 5.03 31.72

40 2.62 1082.6 40 120 116.1 4.19 31.72

50 2.09 924.2 40 120 116.1 3.35 31.72

60 1.57 499.1 40 120 116.1 2.51 31.72

fck Yc

fyk Ys

Yf

AS min AS simple

[cm2] [cm2]

VD Vcu

3

70 1.05 -227.5 40 120 116.1 1.68 31.72

80 0.52 -1281.3 40 120 116.1 0.84 31.72

90 0.00 -2678.0 40 120 116.1 0.00 31.72

4

0 6.28 0.0 40 200 196.1 10.05 53.58

10 5.76 761.6 40 200 196.1 9.22 53.58

20 5.24 1452.3 40 200 196.1 8.38 53.58

30 4.71 2003.4 40 200 196.1 7.54 53.58

40 4.19 2350.4 40 200 196.1 6.70 53.58

50 3.67 2435.2 40 200 196.1 5.86 53.58

60 3.14 2207.3 40 200 196.1 5.03 53.58

70 2.62 1625.9 40 200 196.1 4.19 53.58

80 2.09 661.1 40 200 196.1 3.35 53.58

90 1.57 -705.6 40 200 196.1 2.51 53.58

100 1.05 -2480.5 40 200 196.1 1.68 53.58

110 0.52 -4657.2 40 200 196.1 0.84 53.58

120 0.00 -7217.5 40 200 196.1 0.00 53.58



N N N N

13.44 0.00 13.44 0.00 3 20 2 16

13.44 7.64 17.26 3.82 3 25 1 20 2 16

13.44 14.17 20.53 7.09 3 25 2 20 4 16

13.44 18.54 22.71 9.27 3 25 3 20 3 20

13.44 19.73 9.87 23.31 2 20 2 16 5 25

13.44 16.84 8.42 21.86 3 20 4 25 1

13.44 9.10 4.55 17.99 3 16 2 25 3

17.10 4.15 2.07 19.17 4 12 2 25 3

24.05 23.35 11.68 35.72 4 20 8 25

31.58 48.81 24.40 55.98 5 25 12 25

22.40 0.00 22.40 0.00 4 25 1 20

22.40 13.54 29.17 6.77 6 25 2 16 1

22.40 25.82 35.31 12.91 8 25 5 20

22.40 35.62 40.21 17.81 9 25 2 25 3

22.40 41.79 43.29 20.89 9 25 3 25 2

22.40 43.29 21.65 44.05 4 25 1 20 9 25

22.40 39.24 19.62 42.02 4 25 9 25

22.40 28.91 14.45 36.85 2 25 2 20 8 25

22.40 11.75 5.88 28.28 3 16 6 25

22.40 12.55 6.27 28.67 2 16 1 20 6 25

22.40 44.10 22.05 44.45 4 25 1 20 10 25

27.01 82.80 41.40 68.41 9 25 14 25

31.44 128.32 64.16 95.60 14 25 20 25



(T) Nº 10 Nº 12 Nº 16 Nº 10 Nº 12 Nº 16-24.18 1 -30 1 -42 1 -76 1 0 1 0 1 0

-25.02 1 -29 1 -41 1 -73 1 27 1 39 1 68

-25.86 2 -55 1 -40 2 -141 2 29 1 21 1 37

-26.70 2 -53 1 -38 2 -137 2 22 1 16 1 28

-27.54 2 -52 1 -37 2 -133 2 21 1 15 1 26

-28.37 2 -50 1 -36 2 -129 2 24 1 17 1 31

-29.21 1 -24 1 -35 1 -63 1 22 1 32 1 57


f mm


Vsu

-30.05 1 -24 1 -34 1 -61 1 49 1 71 1 126

-30.89 1 -23 1 -33 2 -118 1 9 1 13 2 45

-31.72 1 -22 1 -32 2 -115 1 4 1 6 2 21

-43.53 1 -28 1 -40 1 -71 1 0 1 0 1 0

-44.37 1 -27 1 -39 1 -70 1 24 1 35 1 61

-45.21 1 -27 2 -77 1 -68 1 13 2 36 1 32

-46.04 1 -26 2 -75 1 -67 1 9 2 26 1 23

-46.88 1 -26 2 -74 1 -66 1 8 2 22 1 20

-47.72 1 -25 2 -73 1 -65 1 7 2 22 1 19

-48.56 1 -25 2 -71 1 -64 1 8 2 24 1 21

-49.40 1 -24 2 -70 1 -62 1 11 2 32 1 29

-50.23 1 -24 1 -35 1 -61 1 28 1 40 1 71

-51.07 1 -24 1 -34 1 -60 1 26 1 37 1 66

-51.91 1 -23 2 -67 1 -59 1 7 2 21 1 19

-52.75 1 -23 1 -33 2 -117 1 4 1 6 2 20

-53.58 1 -22 1 -32 2 -115 1 3 1 4 2 13

As superior

13.45 0.00

17.87 4.02

21.01 8.04

24.15 9.42

10.30 24.54

20 9.42 22.78

20 6.03 19.24

20 4.52 19.24

12.57 39.27

24.54 58.90

22.78 0.00

20 29.45 7.16

39.27 15.71

20 44.18 19.24

20 44.18 21.01

22.78 44.18

19.63 44.18

16.10 39.27

6.03 29.45

7.16 29.45

22.78 49.09

44.18 68.72

68.72 98.17

Nº USAR

(cm) estribos f S

20 0 6 0 #DIV/0!

20 1 10 11 58.81

20 2 10 12 95.38

20 2 10 10 104.92

20 2 10 10 107.52

20 2 10 11 101.22

20 1 10 11 62.00

f mm


[cm2] [cm2]

SmaxVresit

20 1 10 14 51.18

20 2 16 14 185.01

20 2 16 10 240.61

20 1 10 20 71.16

20 1 10 11 102.58

20 2 12 13 201.89

20 2 12 11 224.63

20 2 12 11 238.94

20 2 12 10 242.44

20 2 12 11 233.04

20 2 12 12 209.05

20 1 10 12 98.43

20 1 10 11 100.27

20 2 12 10 244.31

20 2 16 10 418.49

20 2 16 8 524.12

5 Calcular la viga circular de la siguiente estructura

1 b 0.30 mh 0.50 mr 3 m

fck 210 kg/cm2fyk 4200 kg/cm2Yc 1.5Ys 1.15Yf 1.6PE 2400 kg/m3v 0.2a 45 0.7854 rad

GEOMETRIA Y CARGASespezor losa cubierta 0.10 mespezor losa base 0.15 mespezos elevaciones 0.15 maltura tanque 3.00 mpeso capa impermeable 80 kg/m2peso revoques 50 kg/m2PE_H2O 1000 kg/m3CARGADOpeso losa cubierta 6785.84 kgpeso losa base 10178.76 kgpeso elevaciones 20357.52 kgpeso viga 6785.84 kgpeso capa impermeable 2261.95 kg

peso revoques 5654.87 kgpeso agua 84823.00 kgPESO TOTAL 136847.78 kgLongutud de viga 18.85 m

q 7260.00 kg/m

CALCULOCalculo de parametros fisico-geometricos

E 217370.65 kg/cm2 3.92699082

I 0.003125 m4

h/b k (emp) k1.0 0.141 0.1411.2 0.166 0.1661.5 0.196 0.1952.0 0.229 0.2272.5 0.249 0.2443.0 0.263 0.2531.7 0.2080

J 0.00281 m4


R 17105.97C 2.6714 V = R - q*X

0.08651

f0.0 0 5652.48 0.00 17105.977.5 0.13090 5045.13 713.39 14254.98

15.0 0.26180 3233.47 1268.23 11403.98

X = r fV = R - q*r*f

Mo = 0,08405 q r2

Mf = q r2 (1,08405 cosf - 1)

Mt = q r2 (1,08405 senf - f)

f (rad)Mf

kg-mMt

kg-mV

kg

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.01063315 x³ − 0.09094892 x² + 0.28657412 x − 0.06525168


0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

15000.00

20000.00

Mf kg-mMt kg-mV kg

22.5 0.39270 248.50 1508.69 8552.9930.0 0.52360 -3858.71 1284.29 5701.9937.5 0.65450 -9017.88 452.55 2851.0045.0 0.78540 -15140.74 -1118.65 0.00

fi0.0 -15140.74 -1118.65 17105.977.5 -9017.88 452.55 14254.98

15.0 -3858.71 1284.29 11403.9822.5 248.50 1508.69 8552.9930.0 3233.47 1268.23 5701.9937.5 5045.13 713.39 2851.0045.0 5652.48 0.00 0.0052.5 5045.13 -713.39 -2851.0060.0 3233.47 -1268.23 -5701.9967.5 248.50 -1508.69 -8552.9975.0 -3858.71 -1284.29 -11403.9882.5 -9017.88 -452.55 -14254.9890.0 -15140.74 1118.65 -17105.97



he = A/U = 9.37Ao 837.89 cm2Uo 122.50 cm


1.3750

0.643 ≤ 1 OK

PARA SAP2000altura tanque 3.00 mpeso capa impermeable 80 kg/m2PE_H2O 1000 kg/m3peso agua 3000.00 kg/m2peso revoques 50 kg/m2

Mf kg-m

Mt kg-m

V kg

a=2(1-he/b)=

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

15000.00

20000.00

Mf kg-mMt kg-mV kg

PESO EN LOSA 3080.00 kg/m2PESO EN ELEVACIONES 50.00 kg/m2

EMPUJE DE AGUAP = 7000 - 1000 Z

Z P4.0 30004.5 25005.0 20005.5 15006.0 10006.5 5007.0 0

0 500 1000 1500 2000 2500 30000.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

f(x) = − 0.001 x + 7

Column BLinear (Column B)

kg

V = R - q*r*f

0.5 1.0 1.5 2.0 2.5 3.0 3.50

0.05

0.1

0.15

0.2

0.25

0.3

f(x) = 0.01063315 x³ − 0.09094892 x² + 0.28657412 x − 0.06525168


0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

15000.00

20000.00

Mf kg-mMt kg-mV kg

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

15000.00

20000.00

Mf kg-mMt kg-mV kg

0 500 1000 1500 2000 2500 30000.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

f(x) = − 0.001 x + 7

Column BLinear (Column B)

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

-20000.00

-15000.00

-10000.00

-5000.00

0.00

5000.00

10000.00

15000.00

20000.00

Mf kg-mMt kg-mV kg


4200 1.15

p 0.0033333 1.6



1

0.0 565.2 0.0 30 50 46.1 5.00 5.78

7.5 504.5 71.3 30 50 46.1 5.00 5.12

15.0 323.3 126.8 30 50 46.1 5.00 3.22

22.5 24.8 150.9 30 50 46.1 5.00 0.24

30.0 -385.9 128.4 30 50 46.1 5.00 3.87

37.5 -901.8 45.3 30 50 46.1 5.00 9.63

45.0 -1514.1 -111.9 30 50 46.1 5.00 18.14



(T) [T-cm] (cm) (m) (cm) (T) (T)

1

0.0 17.11 0.0 30 50 46.1 27.37 8.18

7.5 14.25 71.3 30 50 46.1 22.81 8.18

15.0 11.40 126.8 30 50 46.1 18.25 8.18

22.5 8.55 150.9 30 50 46.1 13.68 8.18

30.0 5.70 128.4 30 50 46.1 9.12 8.18

37.5 2.85 45.3 30 50 46.1 4.56 8.18

45.0 0.00 -111.9 30 50 46.1 0.00 8.18

fck Yc

fyk Ys

Yf

AS min AS simple

[cm2] [cm2]

VD Vcu



N N N N

5.78 0.00 5.78 0.00 3 16

5.12 2.28 6.26 1.14 2 16 2 12 2 10

5.00 4.06 7.03 2.03 4 16 2 12

5.00 4.83 7.42 2.42 4 16 3 12

5.00 4.11 2.06 7.06 2 12 4 16

9.63 1.45 0.72 10.35 2 10 4 20

18.14 3.58 1.79 19.93 2 12 3 25 2



(T) Nº 6 Nº 8 Nº 10 Nº 6 Nº 8 Nº 1019.19 1 4 1 8 1 12 1 0 1 0 1 0

14.63 1 6 1 10 1 16 1 15 1 27 1 42

10.06 1 9 1 15 1 24 1 9 1 15 1 24

5.50 1 16 1 28 1 43 1 7 1 13 1 20

0.94 1 91 1 162 1 253 1 8 1 15 1 23

-3.62 1 -24 1 -42 1 -66 1 24 1 42 1 66

-8.18 1 -10 1 -19 1 -29 1 10 1 17 1 27


f mm


Vsu

As superior

6.03 0.00

6.28 1.57

8.04 2.26

8.04 3.39

2.26 8.04

1.57 12.57

20 2.26 21.01

Nº USAR

(cm) estribos f S

20 1 10 12 17.11

18 1 10 12 17.79

18 1 10 10 19.66

18 1 10 9 20.85

18 1 10 10 19.74

18 1 10 14 15.62

18 1 10 11 18.92

f mm


[cm2] [cm2]

SmaxVresit

ejercicios vigas

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Transcript of ejercicios vigas