La placa nos queda de la siguiente manera:

El detalle de la cabeza es el siguiente:

Las capas de acero seran vistas de la siguiente forma:

Tendremos 14 capas o niveles de distribucin de refuerzo:

En cada capa tenemos: As capa: 12.97 cm2

DATOS DE GEOMETRIA Y MATERIALES:

f'c 210 kg/cm2

fy 4200 kg/cm2 h = 670 cm

N Capas 14 yo = 335 cm

Recubrimiento 5 cm

b = 25 cm

DIAGRAMA DE INTERACCIN DE LA PLACA

Variaremos "Z" para hallar los distintos puntos del diagrama de interaccin de la placa.

2" + /"

As (cm) N Varillas Varilla N Varillas

1 1 " 2 3/4 " 1 12.97 5

2 1 " 2 3/4 " 1 12.97 15

3 1 " 2 3/4 " 1 12.97 25

4 1 " 2 3/4 " 1 12.97 35

5 1 " 2 3/4 " 1 12.97 45

6 1 " 2 3/4 " 1 12.97 55

7 1 " 2 3/4 " 1 12.97 65

8 1 " 2 3/4 " 1 12.97 605

9 1 " 2 3/4 " 1 12.97 615

10 1 " 2 3/4 " 1 12.97 625

11 1 " 2 3/4 " 1 12.97 635

12 1 " 2 3/4 " 1 12.97 645

13 1 " 2 3/4 " 1 12.97 655

14 1 " 2 3/4 " 1 12.97 665

h = 670 cm

PUNTO 1 Compresin Pura

fs (kg/cm2)

1 0.003 > 0.0021 4200

2 0.003 > 0.0021 4200

3 0.003 > 0.0021 4200

4 0.003 > 0.0021 4200

5 0.003 > 0.0021 4200

6 0.003 > 0.0021 4200

7 0.003 > 0.0021 4200

8 0.003 > 0.0021 4200

9 0.003 > 0.0021 4200

10 0.003 > 0.0021 4200

11 0.003 > 0.0021 4200

12 0.003 > 0.0021 4200

13 0.003 > 0.0021 4200

14 0.003 > 0.0021 4200

1.1.- Calculamos la fuerza de compresion del concreto:

Donde: a = h

Cc 2989875 kg

1.2.- Calculamos la fuerza de compresion del acero:

di (cm)CAPATipo 1 Tipo 2

As (cm2)

= .

=

Capa As (cm2) fs (kg/cm2) Cs (kg)

1 12.97 4200 54474.00

2 12.97 4200 54474.00

3 12.97 4200 54474.00

4 12.97 4200 54474.00

5 12.97 4200 54474.00

6 12.97 4200 54474.00

7 12.97 4200 54474.00

8 12.97 4200 54474.00

9 12.97 4200 54474.00

10 12.97 4200 54474.00

11 12.97 4200 54474.00

12 12.97 4200 54474.00

13 12.97 4200 54474.00

14 12.97 4200 54474.00

1.3.- Calculamos la carga axial nominal:

Pn 3752.51 Tn

1.4.- Calculamos el momento flector nominal:

Mn 0.00 Tn-cm

PUNTO B Falla Balanceada

1.1.- Calculamos Cb:

Cb 391.18 cm

fs (kg/cm2)

1 0.0029617 > 0.0021 4200 Compresin

2 0.0028850 > 0.0021 4200 Compresin

3 0.0028083 > 0.0021 4200 Compresin

4 0.0027316 > 0.0021 4200 Compresin

5 0.0026549 > 0.0021 4200 Compresin

6 0.0025782 > 0.0021 4200 Compresin

7 0.0025015 > 0.0021 4200 Compresin

8 -0.0016398 < 0.0021 -3279.699248 Traccin

9 -0.0017165 < 0.0021 -3433.082707 Traccin

10 -0.0017932 < 0.0021 -3586.466165 Traccin

11 -0.0018699 < 1.0021 -3739.849624 Traccin

12 -0.0019466 < 2.0021 -3893.233083 Traccin

13 -0.0020233 < 3.0021 -4046.616541 Traccin

14 -0.0021000 < 4.0021 -4200 Traccin

1.2.- Calculamos la fuerza de compresion del concreto:

a 332.5 cm

Cc 1483781.25 kg

= +

= .

=

+

= .

1.3.- Calculamos la fuerza de compresion del acero:

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 4200 54474.00 310.00 16886940.0

4 12.97 4200 54474.00 300.00 16342200.0

5 12.97 4200 54474.00 290.00 15797460.0

6 12.97 4200 54474.00 280.00 15252720.0

7 12.97 4200 54474.00 270.00 14707980.0

8 12.97 -3279.699248 -42537.70 -270.00 11485178.8

9 12.97 -3433.082707 -44527.08 -280.00 12467583.2

10 12.97 -3586.466165 -46516.47 -290.00 13489775.2

11 12.97 -3739.849624 -48505.85 -300.00 14551754.9

12 12.97 -3893.233083 -50495.23 -310.00 15653522.3

13 12.97 -4046.616541 -52484.62 -320.00 16795077.3

14 12.97 -4200 -54474.00 -330.00 17976420.0

1.4.- Calculamos la carga axial nominal:

Pn 1525.56 Tn

1.5.- Calculamos el momento flector nominal:

Mn 467202.80 Tn-cm

PUNTO 2 "Z" entre Cb y L total

Z 670.00 cm

fs (kg/cm2)

1 0.0029776 > 0.0021 4200 Compresin

2 0.0029328 > 0.0021 4200 Compresin

3 0.0028881 > 0.0021 4200 Compresin

4 0.0028433 > 0.0021 4200 Compresin

5 0.0027985 > 0.0021 4200 Compresin

6 0.0027537 > 0.0021 4200 Compresin

7 0.0027090 > 0.0021 4200 Compresin

8 0.0002910 < 0.0021 582.0895522 Compresin

9 0.0002463 < 0.0021 492.5373134 Compresin

10 0.0002015 < 0.0021 402.9850746 Compresin

11 0.0001567 < 0.0021 313.4328358 Compresin

12 0.0001119 < 0.0021 223.880597 Compresin

13 0.0000672 < 0.0021 134.3283582 Compresin

14 0.0000224 < 0.0021 44.7761194 Compresin

1.1.- Calculamos la fuerza de compresion del concreto:

a 569.5 cm

Cc 2541393.75 kg

=

= +

= . = .

1.2.- Calculamos la fuerza de compresion del acero:

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 4200 54474.00 310.00 16886940.0

4 12.97 4200 54474.00 300.00 16342200.0

5 12.97 4200 54474.00 290.00 15797460.0

6 12.97 4200 54474.00 280.00 15252720.0

7 12.97 4200 54474.00 270.00 14707980.0

8 12.97 582.0895522 7549.70 -270.00 -2038419.4

9 12.97 492.5373134 6388.21 -280.00 -1788698.5

10 12.97 402.9850746 5226.72 -290.00 -1515747.8

11 12.97 313.4328358 4065.22 -300.00 -1219567.2

12 12.97 223.880597 2903.73 -310.00 -900156.7

13 12.97 134.3283582 1742.24 -320.00 -557516.4

14 12.97 44.7761194 580.75 -330.00 -191646.3

1.3.- Calculamos la carga axial nominal:

Pn 2951.17 Tn

1.4.- Calculamos el momento flector nominal:

Mn 233888.68 Tn-cm

PUNTO 3 "Z" entre Cb y L total

Z 450.00 cm

fs (kg/cm2)

1 0.0029667 > 0.0021 4200 Compresin

2 0.0029000 > 0.0021 4200 Compresin

3 0.0028333 > 0.0021 4200 Compresin

4 0.0027667 > 0.0021 4200 Compresin

5 0.0027000 > 0.0021 4200 Compresin

6 0.0026333 > 0.0021 4200 Compresin

7 0.0025667 > 0.0021 4200 Compresin

8 -0.0010333 < 0.0021 -2066.666667 Traccin

9 -0.0011000 < 0.0021 -2200 Traccin

10 -0.0011667 < 0.0021 -2333.333333 Traccin

11 -0.0012333 < 0.0021 -2466.666667 Traccin

12 -0.0013000 < 0.0021 -2600 Traccin

13 -0.0013667 < 0.0021 -2733.333333 Traccin

14 -0.0014333 < 0.0021 -2866.666667 Traccin

1.1.- Calculamos la fuerza de compresion del concreto:

a 382.5 cm

Cc 1706906.25 kg

=

= +

= . = .

1.2.- Calculamos la fuerza de compresion del acero:

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 4200 54474.00 310.00 16886940.0

4 12.97 4200 54474.00 300.00 16342200.0

5 12.97 4200 54474.00 290.00 15797460.0

6 12.97 4200 54474.00 280.00 15252720.0

7 12.97 4200 54474.00 270.00 14707980.0

8 12.97 -2066.666667 -26804.67 -270.00 7237260.0

9 12.97 -2200 -28534.00 -280.00 7989520.0

10 12.97 -2333.333333 -30263.33 -290.00 8776366.7

11 12.97 -2466.666667 -31992.67 -300.00 9597800.0

12 12.97 -2600 -33722.00 -310.00 10453820.0

13 12.97 -2733.333333 -35451.33 -320.00 11344426.7

14 12.97 -2866.666667 -37180.67 -330.00 12269620.0

1.3.- Calculamos la carga axial nominal:

Pn 1864.28 Tn

1.4.- Calculamos el momento flector nominal:

Mn 427431.99 Tn-cm

PUNTO 4 "Z" entre Cb y 0

Z 250.00 cm

fs (kg/cm2)

1 0.00294 > 0.0021 4200 Compresin

2 0.00282 > 0.0021 4200 Compresin

3 0.0027 > 0.0021 4200 Compresin

4 0.00258 > 0.0021 4200 Compresin

5 0.00246 > 0.0021 4200 Compresin

6 0.00234 > 0.0021 4200 Compresin

7 0.00222 > 0.0021 4200 Compresin

8 -0.00426 > 0.0021 -4200 Traccin

9 -0.00438 > 0.0021 -4200 Traccin

10 -0.0045 > 0.0021 -4200 Traccin

11 -0.00462 > 0.0021 -4200 Traccin

12 -0.00474 > 0.0021 -4200 Traccin

13 -0.00486 > 0.0021 -4200 Traccin

14 -0.00498 > 0.0021 -4200 Traccin

1.1.- Calculamos la fuerza de compresion del concreto:

a 212.5 cm

Cc 948281.25 kg

1.2.- Calculamos la fuerza de compresion del acero:

=

= +

= .

=

= .

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 4200 54474.00 310.00 16886940.0

4 12.97 4200 54474.00 300.00 16342200.0

5 12.97 4200 54474.00 290.00 15797460.0

6 12.97 4200 54474.00 280.00 15252720.0

7 12.97 4200 54474.00 270.00 14707980.0

8 12.97 -4200 -54474.00 -270.00 14707980.0

9 12.97 -4200 -54474.00 -280.00 15252720.0

10 12.97 -4200 -54474.00 -290.00 15797460.0

11 12.97 -4200 -54474.00 -300.00 16342200.0

12 12.97 -4200 -54474.00 -310.00 16886940.0

13 12.97 -4200 -54474.00 -320.00 17431680.0

14 12.97 -4200 -54474.00 -330.00 17976420.0

1.3.- Calculamos la carga axial nominal:

Pn 948.28 Tn

1.4.- Calculamos el momento flector nominal:

Mn 445710.14 Tn-cm

PUNTO 5 "Z" entre Cb y 0

Z 100.00 cm

fs (kg/cm2)

1 0.00285 > 0.0021 4200 Compresin

2 0.00255 > 0.0021 4200 Compresin

3 0.00225 > 0.0021 4200 Compresin

4 0.00195 < 0.0021 3900 Compresin

5 0.00165 < 0.0021 3300 Compresin

6 0.00135 < 0.0021 2700 Compresin

7 0.00105 < 0.0021 2100 Compresin

8 -0.01515 > 0.0021 -4200 Traccin

9 -0.01545 > 0.0021 -4200 Traccin

10 -0.01575 > 0.0021 -4200 Traccin

11 -0.01605 > 0.0021 -4200 Traccin

12 -0.01635 > 0.0021 -4200 Traccin

13 -0.01665 > 0.0021 -4200 Traccin

14 -0.01695 > 0.0021 -4200 Traccin

1.1.- Calculamos la fuerza de compresion del concreto:

a 85 cm

Cc 379312.5 kg

= +

= . = .

1.2.- Calculamos la fuerza de compresion del acero:

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 4200 54474.00 310.00 16886940.0

4 12.97 3900 50583.00 300.00 15174900.0

5 12.97 3300 42801.00 290.00 12412290.0

6 12.97 2700 35019.00 280.00 9805320.0

7 12.97 2100 27237.00 270.00 7353990.0

8 12.97 -4200 -54474.00 -270.00 14707980.0

9 12.97 -4200 -54474.00 -280.00 15252720.0

10 12.97 -4200 -54474.00 -290.00 15797460.0

11 12.97 -4200 -54474.00 -300.00 16342200.0

12 12.97 -4200 -54474.00 -310.00 16886940.0

13 12.97 -4200 -54474.00 -320.00 17431680.0

14 12.97 -4200 -54474.00 -330.00 17976420.0

1.3.- Calculamos la carga axial nominal:

Pn 317.06 Tn

1.4.- Calculamos el momento flector nominal:

Mn 322385.85 Tn-cm

PUNTO 6 "Z" entre Cb y 0, para logra Pn=0

Z 54.276 cm Iteramos hasta lograr Pn = 0 Tn

fs (kg/cm2)

1 0.002723635 > 0.0021 4200 Compresin

2 0.002170904 > 0.0021 4200 Compresin

3 0.001618174 < 0.0021 3236.347557 Compresin

4 0.001065443 < 0.0021 2130.88658 Compresin

5 0.000512713 < 0.0021 1025.425602 Compresin

6 -4.00177E-05 < 0.0021 -80.03537475 Traccin

7 -0.000592748 < 0.0021 -1185.496352 Traccin

8 -0.030440195 > 0.0021 -4200 Traccin

9 -0.030992925 > 0.0021 -4200 Traccin

10 -0.031545656 > 0.0021 -4200 Traccin

11 -0.032098386 > 0.0021 -4200 Traccin

12 -0.032651117 > 0.0021 -4200 Traccin

13 -0.033203847 > 0.0021 -4200 Traccin

14 -0.033756577 > 0.0021 -4200 Traccin

1.1.- Calculamos la fuerza de compresion del concreto:

a 46.1346 cm

Cc 205875.6525 kg

=

= +

= . = .

1.2.- Calculamos la fuerza de compresion del acero:

Capa As (cm2) fs (kg/cm2) Cs (kg) (yo-di) Cs*(yo-di)

1 12.97 4200 54474.00 330.00 17976420.0

2 12.97 4200 54474.00 320.00 17431680.0

3 12.97 3236.347557 41975.43 310.00 13012382.6

4 12.97 2130.88658 27637.60 300.00 8291279.7

5 12.97 1025.425602 13299.77 290.00 3856933.3

6 12.97 -80.03537475 -1038.06 280.00 -290656.5

7 12.97 -1185.496352 -15375.89 270.00 -4151489.7

8 12.97 -4200 -54474.00 -270.00 14707980.0

9 12.97 -4200 -54474.00 -280.00 15252720.0

10 12.97 -4200 -54474.00 -290.00 15797460.0

11 12.97 -4200 -54474.00 -300.00 16342200.0

12 12.97 -4200 -54474.00 -310.00 16886940.0

13 12.97 -4200 -54474.00 -320.00 17431680.0

14 12.97 -4200 -54474.00 -330.00 17976420.0

1.3.- Calculamos la carga axial nominal:

Pn 0.00 Tn

1.4.- Calculamos el momento flector nominal:

Mn 234741.30 Tn-cm

PUNTO 7 Traccin Pura, Mn=0

Capa As (cm2)

1 12.97

2 12.97

3 12.97

4 12.97

5 12.97

6 12.97

7 12.97

8 12.97

9 12.97

10 12.97

11 12.97

12 12.97

13 12.97

14 12.97

As 181.58

1.3.- Calculamos la carga axial nominal:

Pn -762.64 Tn

1.4.- Calculamos el momento flector nominal:

Mn 0.00 Tn-cm

=

=

= +

Pn (Tn) Pn (Tn) Mn (Tn-m) Mn (Tn-m)

3752.51 2101.41 0.00 0.00

2951.17 2065.82 2338.89 1637.22

1864.28 1304.99 4274.32 2992.02

1525.56 1067.89 4672.03 3270.42

948.28 663.80 4457.10 3119.97

317.06 245.34 3223.86 2494.65

0.00 0.00 2347.41 2112.67

-762.64 -686.37 0.00 0.00

502.5

Pu (Tn) Mu (Tn-m)

690.00 12.00

650.00 2647.00

471.00 2629.00

441.00 2643.00

262.00 2633.00

Comb. De diseo

Valor de

0.90

0.9 - (0.2*Pn/Ptranc.)

0.7

RESUMEN GENERAL:

4

P de trancision (Tn):

Intervalo

Ptranc.