ANÁLISIS SÍSMICO

ANALISIS Y DISEÑO DE UN PARQUEADERO DE 04 PISOS EN LA CIUDAD DE CHINCHA

CARACTERÍSTICAS DE LA ESTRUCTURA DEL PARQUEADEROLugar CHINCHA f'c Concreto 210 Kg/cm²ZONA 3 Peso Acabados 100 Kgf/m²factor Z 0.3 Peso Muro Perimetrales 500 Kgf/m²Perfil de Suelo Peso Tabiquería 100 Kgf/m²Tp 0.9 Peso Losa Aligerada 300 Kgf/m²S 1.4 S/C Por Nivel 250 Kgf/m²CATEGORÍA EDIFICACIÓN A (CENTRO EDUCATIVO)S/C Azotea 150 Kgf/m²Factor de Uso Edif. Importante C = 2.5*(Tp/T) ; C≤ 2.5

U 1.3 UAP 3.0 m.Cnfiguración Estructural Regular AYACUCHO 8.0 m.Coef. De Reducción 8 ANCHO (Y) 24.0 m.Desplazamiento Lateral ∆= 0.007 LARGO (X) 12.0 m.Nº de pisos 4 TOTAL 288.0 m²

4,200 Kg/cm²

2.4 2.4 2.4 2.4

V5 V6 V6 V5

C1 C2 C2 C2 C1

7.20 7.40 8.0

7.40 V1 V3 V3 V3 V1

V7 V8 V8 V7

C2 C3 C3 C3 C2

8.0

7.40 V2 V4 7.00V4 V4 7.40 V2

V7 V8 V8 V7

C2 C3 C3 C3 C2

2.25 2.1 2.1 2.25 8.0

7.40V1 V3 7.20V3 V3 7.40 V1

C1 C2 C2 C2 C1

V5 V6 V6 V5

2.4 2.4 2.4 2.4

3.0 3.0 3.0 3.0

VIGA PRINCIPAL:D = L/10 ~L/12 b = D/2 ~ D/2.5 DD = 700/10 ~ 700/12 b = 70/2D = 70 ~ 60cm b = 35 ~ 30cm

INERCIA EN Y-YVIGAS: b (m.) h (m.) COLUMNAS: b (m) h (m)

0.60 0.90 0.60 0.60 1,080,000.00

0.80 0.90 0.60 0.60 1,080,000.00

0.90 1.00 7,500,000.003,645,000.00 4,860,000.00

S3

fy Acero

1.- PREDIMENSIONAMIENTO:

Ic (cm4)

TIPO V1= TIPO C1 =

TIPO V2= TIPO C2 =

Iv1 (cm4) Iv2 (cm4) TIPO C3 =

1 2 3 4 5

B

A

D

C

VIGAS b (m.) h (m.) L (m.) A (m²) P (ton.)V1 0.6 0.9 0.03645 7.4 0.54 9.5904V2 0.6 0.9 0.03645 7.4 0.54 9.5904V3 0.6 0.9 0.03645 7.2 0.54 9.3312V4 0.6 0.9 0.03645 7 0.54 9.072V5 0.8 0.9 0.0486 2.4 0.72 4.1472V6 0.8 0.9 0.0486 2.4 0.72 4.1472V7 0.8 0.9 0.0486 2.25 0.72 3.888V8 0.8 0.9 0.0486 2.1 0.72 3.6288

VIGAS EJES V1 (ton) V2 (ton) V3 (ton) V4 (ton) TOTAL

NIVEL1

EJE 1 19.1808 9.590 28.7712 ton.EJE 2 18.662 9.072 27.7344 ton.EJE 3 18.662 9.072 27.7344 ton.EJE 4 18.662 9.072 27.7344 ton.EJE 5 19.1808 9.590 28.7712 ton.

Sub total 38.3616 19.181 55.987 27.216 140.7456 ton.NIVEL2 38.3616 19.181 55.987 27.216 140.7456 ton.NIVEL3 38.3616 19.181 55.987 27.216 140.7456 ton.NIVEL4 38.3616 19.181 55.987 27.216 140.7456 ton.

VIGAS EJES V5 (ton) V6 (ton) V7 (ton) V8 (ton) TOTAL

NIVEL 1

EJE A 8.2944 8.294 16.5888 ton.EJE B 7.776 7.258 15.0336 ton.EJE C 7.776 7.258 15.0336 ton.EJE D 8.2944 8.294 16.5888 ton.

Sub total 16.5888 16.589 15.552 14.515 63.2448 ton.NIVEL 2 16.5888 16.589 15.552 14.515 63.2448 ton.NIVEL 3 16.5888 16.589 15.552 14.515 63.2448 ton.NIVEL 4 16.5888 16.589 15.552 14.515 63.2448 ton.

B).- COLUMNASCOLUMNAS b (m.) h (m.) L (m.) A (m²) P (ton.)

C10.6 0.6 0.0108 3 0.36 2.5920.6 0.6 0.0108 3 0.36 2.5920.6 0.6 0.0108 1.5 0.36 1.296

C20.6 0.6 0.0108 3 0.36 2.5920.6 0.6 0.0108 3 0.36 2.5920.6 0.6 0.0108 1.5 0.36 1.296

C30.9 1 0.075 3 0.9 6.480.9 1 0.075 3 0.9 6.480.9 1 0.075 1.5 0.9 3.24

COLUMNAS EJES C1 (ton) C2 (ton) C3 (ton) TOTAL

NIVEL1

EJE 1 5.184 5.184EJE 2 5.184 12.96EJE 3 5.184 12.96EJE 4 5.184 12.96EJE 5 5.184 5.184

Sub total 10.368 25.92 38.88 75.168NIVEL2 10.368 25.92 38.88 75.168

2.- METRADO DE CARGASA).- VIGAS

I (m4)

I (m4)

NIVEL3 10.368 25.92 38.88 75.168

NIVEL4

EJE 1 2.592 2.592EJE 2 2.592 6.48EJE 3 2.592 6.48EJE 4 2.592 6.48EJE 5 2.592 2.592

Sub total 5.184 12.96 19.44 37.584

7.40

7.40

7.40

7.40 8.00

2.20 2.20 2.20 2.20

7.40

7.40

7.40

7.40 8.00

2.20 2.20 2.20 2.20 24.00

a 7.40

7.40

7.40

7.40 8.00

2.20 2.20 2.20 2.20b

3.00 3.00 3.00 3.0012.00

WD = Wlosa Alig.+Wacabados 400.0 Kg/m²WL = W s/c 250.0 Kg/m² (RNE E-020: Art. 6.1; Tabla 1)WU = 1.4WD + 1.7WL 985.0 Kg/m² (RNE E-020: Cargas Modif.)Carga por c/vigueta = Wu/2.5 394.0 Kg/m²Mu = WL²/8 = (394/1000)x7²/8 0.4433 Tn-m.

NIVELES a (m) b (m) Nro de Paños TOTAL (Tn)

1 -2 - 3 -4 0.3 7.400 2.2000 12 58.608 Tn.t = 0.20 m

L (m) A (m) TOTAL (Tn)

NIVEL 1 0.1 12 24 28.8 Tn.NIVEL 2 28.8 Tn.NIVEL 3 28.8 Tn.

L (m) A (m) TOTAL (Tn)

NIVEL 1 0.1 12 24 28.8 Tn.NIVEL 2 28.8 Tn.NIVEL 3 28.8 Tn.

C) TECHO ALIGERADO:

W losa alig (Tn/m²)

D) TABIQUERIA:

W Tabique (Tn/m²)

E) ACABADOS:

W Acabados (Tn/m²)

L (m) Nro A (m) Nro Total (Tn)

NIVEL 1 0.5 12 2 24 2 36.0 Tn.NIVEL 2 36.0 Tn.NIVEL 3 36.0 Tn.

L (m) A (m) Nro TOTAL (Tn)

NIVEL 4 0.150 12 24 2 10.8 Tn.

RNE: E-020 CARGASSobrecarga para Losa de Pisos o entrepisos = 250.0 Kg/m²Sobrecarga en Azotea = 150.0 Kg/m²

W s/c (Tn/m²) L (m) A (m) REDUCCION PESO (Tn)NIVEL 1 0.250 12 24 0.5 36.0 Tn.NIVEL 2 0.250 12 24 0.5 36.0 Tn.NIVEL 3 0.250 12 24 0.5 36.0 Tn.NIVEL 4 0.150 12 24 0.5 21.6 Tn.

RESUMEN DE METRADO DE CARGAS PARA EL ANALISIS DINAMICO

TIPO DE CARGA NIVEL 1 NIVEL2 NIVEL 3 NIVEL 4 TOTALVIGAS V1 38.362 38.362 38.362 38.362 153.446 VIGAS V2 19.181 19.181 19.181 19.181 76.723 VIGAS V3 55.987 55.987 55.987 55.987 223.949 VIGAS V4 27.216 27.216 27.216 27.216 108.864 VIGAS V5 16.589 16.589 16.589 16.589 66.355 VIGAS V6 16.589 16.589 16.589 16.589 66.355 VIGAS V7 15.552 15.552 15.552 15.552 62.208 VIGAS V8 14.515 14.515 14.515 14.515 58.061

COLUMNAS C1 10.368 10.368 10.368 5.184 36.288 COLUMNAS C2 25.92 25.92 25.92 12.96 90.72 COLUMNAS C3 38.88 38.88 38.88 19.44 136.08

ALIGERADO 58.608 58.608 58.608 58.608 234.432 TABIQUERIA 28.8 28.8 28.8 0.0 86.4 ACABADOS 28.8 28.8 28.8 0.0 86.4

MUROS PERIMÉTRICOS 36.0 36.0 36.0 18.0 126.0 PARAPETOS 0.0 0.0 0.0 10.8 10.8

SOBREGARGA 36.0 36.0 36.0 21.6 129.6 TOTALES (Ton) 467.3664 Tn. 467.3664 Tn. 467.3664 Tn. 350.5824 Tn. 1,752.6816 Tn.

F) MUROS PERIMETRALES:

W muro per (Tn/m)

G) PARAPETOS:

W parapeto (Tn/m)

E) SOBRECARGA:

http://www.tube8.com/latina/luscious-lopez-lex/416681/

http://www.tube8.com/latina/luscious-lopez-lex/416681/

6/63

3). ANÁLISIS DINÁMICO DE LA EDIFICACIÓN

3.1) CÁLCULO DE RIGIDECES: MÉTODO MUTOf´c = 210 Kg/cm2f y = 4200 Kg/cm2

C1 C2 C2 C2 C1

8.00

C2 C3 C3 C3 C2

8.00

C2 C3 C3 C3 C2

8.00

C1 C2 C2 C2 C1

3.00 3.00 3.00 3.00 8.00 8.00 8.00PLANTA ELEVACIÓN

a) EJE X-X: 1080000.00a.1) PÓRTICO: A y D 1080000.00 E = 218819.788867461

Iv = 4860000.00 E = 218.82

16200 16200 16200 16200

Ic1/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 Ic1/L= 3600.0k= 4.5000 k= 9.0000 k= 9.0000 k= 9.0000 k= 4.5a= 0.7 a= 0.8 a= 0.8 a= 0.8 a= 0.7K= 72.7 K= 85.9 K= 85.9 K= 85.9 K= 72.7

16200 16200 16200 16200


16200 16200 16200 16200


16200 16200 16200 16200


Ic1 = cm4

Ic2 = cm4

cm4

1 2 3 4 5

A

B

C

D

1 2 3 4 5

7/63

a.2) PÓRTICO: B y C Ic2 = 1080000 Iv = 4860000Ic3 = 7500000

16200 16200 16200 16200


16200 16200 16200 16200


16200 16200 16200 16200


16200 16200 16200 16200


MODELO DINAMICO DE LA ESTRUCTURA HPDIRECCION X- X 0.357372477 M4= 350.58

K4= 2818.159

0.476418349 M3= 467.37

K3= 2818.159

0.476418349 M2= 467.37

K2= 2818.159

0.476418349 M1= 467.3664

K1= 3575.335

cm4 cm4

1 2 3 4 5

8/63

3). ANÁLISIS DINÁMICO DE LA EDIFICACIÓN b) EJE Y-Y: 1080000

b.1) PÓRTICO: 1 y 5 1080000 7,500,000

Iv = 3645000

4556.25 4556.25 4556.25

Ic1/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 Ic1/L= 3600.03.00 k= 1.266 k= 2.531 k= 2.531 k= 1.3

a= 0.4 a= 0.6 a= 0.6 a= 0.4K= 40.7 K= 58.7 K= 58.7 K= 40.7 198.761

3.00 4556.25 4556.25 4556.25

Ic1/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 Ic1/L= 3600.03.00 k= 1.266 k= 2.531 k= 2.531 k= 1.3

a= 0.4 a= 0.6 a= 0.6 a= 0.4K= 40.7 K= 58.7 K= 58.7 K= 40.7 198.761

3.00 4556.25 4556.25 4556.25

Ic1/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 3600.0k= 1.266 k= 2.531 k= 2.531 1.266a= 0.4 a= 0.6 a= 0.6 0.4K= 40.7 K= 58.7 K= 58.7 40.7 198.761

4556.25 4556.25 4556.25Kg/cm²Tn/cm² Ic1/L= 3600.0 Ic2/L= 3600.0 Ic2/L= 3600.0 Ic1/L= 3600.0

k= 1.266 k= 2.531 k= 2.531 k= 1.266a= 0.5 a= 0.7 a= 0.7 a= 0.5K= 56.8 K= 70.3 K= 70.3 K= 56.8 254.104

b.2) PÓRTICO: 2, 3 y 4403.240 4556.25 4556.25 4556.25

Ic2/L= 3600.0 Ic3/L= 25000.0 Ic3/L= 25000.0 Ic2/L= 3600.0k= 1.266 k= 0.365 k= 0.365 k= 1.266a= 0.4 a= 0.2 a= 0.2 a= 0.4K= 40.7 K= 112.4 K= 112.4 K= 40.7 306.295

403.240 4556.25 4556.25 4556.25


403.240 4556.25 4556.25 4556.25


433.722 4556.25 4556.25 4556.25


Ic2 = cm4

Ic1 = cm4 Ic3 =

cm4

Ktotal(Tn/cm)

Ktotal(Tn/cm)

Ktotal(Tn/cm)

A B C D

A B C D

9/63

MODELO DINAMICO DE LA ESTRUCTURADIRECCION Y- Y HP

0.3573724771 M4= 350.58

K4= 1316.407

0.4764183486 M3= 467.37

1005.839 K3= 1316.407

0.4764183486 M2= 467.37

K2= 1316.407

1005.839 0.4764183486 M1= 467.37

K1= 2449.022

CUADRO DE RESUMEN RIGIDEZ:

EJE X-X1005.839 NIVEL

1 2 3 4PÓRTICO

A 433.722 403.240 403.240 403.240

B 1353.945 1005.839 1005.839 1005.839

1353.945C 1353.945 1005.839 1005.839 1005.839

D 433.722 403.240 403.240 403.240

3575.33529063 2818.159 2818.1588013 2818.1588

EJE Y-YNIVEL

1 2 3 4PÓRTICO

1 254.104 198.761 198.761 198.761

2 646.938 306.295 306.295 306.295

3 646.938 306.295 306.295 306.295

4 646.938 306.295 306.295 306.295

5 254.104 198.761 198.761 198.761

2449.022 1316.407 1316.407 1316.407

cm4

Ktotal(Tn/cm)

K Total(ton/cm)

K Total(ton/cm)

3.2) CALCULO DE "W" Y "T": METODO DE HOLZER3.2.1) DIRECCION X - X:PRIMERA FORMA DE MODO

METODO ITERATIVO

NIVEL 1 2 3 4K (Ton/cm) 3575.3353 2818.1588 2818.1588 2818.1588

M (Ton) 467.366 467.366 467.366 350.582

0.4764183486 0.4764183486 0.4764183486239 0.3573724771

460

X 1.00000 2.19091 3.21145 3.98225 W² = 881.66614985382sX 1.00000 1.19091 1.02054 0.77080 W = 29.692863618281V 3575.33529 3356.18285 2876.03885 2172.24140 1517.59346F 219.15244 480.14400 703.79745 654.64794

Wi+1 = 912.8919842034 T = 2 * PI / WT = 0.2116059059831

912.8919842034

X 1.00000 2.11435 2.90240 3.24253sX 1.00000 1.11435 0.78805 0.34013V 3575.33529 3140.41680 2220.84665 958.53951F 434.91849 919.57015 1262.30714 1057.85068

Wi+1 = 881.85983299298

881.85983299298

X 1.00000 2.11960 2.92320 3.29101sX 1.00000 1.11960 0.80360 0.36781V 3575.33529 3155.20109 2264.68604 1036.54912 -0.6213892 RESIDUOF 420.13421 890.51504 1228.13692 1037.17051 -0.621389

Wi+1 = 881.66614985382 W2= 881.66614985

(Ton-seg²)cm

DIRECCION X - XSEGUNDA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 3575.3352906 2818.1588013 2818.1588013279 2818.1588013M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

460

X 1.00000 2.19091 3.21145 3.98225 W² = 881.66614985382sX 1.00000 1.19091 1.02054 0.77080 W = 29.692863618281V 3575.33529 3356.18285 2876.03885 2172.24140 1517.59346F 219.15244 480.14400 703.79745 654.64794

Wi+1 = 912.8919842034 T = 2 * PI / WT = 0.2116059059831

912.8919842034

X 1.00000 2.11435 2.90240 3.24253sX 1.00000 1.11435 0.78805 0.34013V 3575.33529 3140.41680 2220.84665 958.53951 -99.31118F 434.91849 919.57015 1262.30714 1057.85068

Wi+1 = 881.85983299298

881.85983299298

X 1.00000 2.11960 2.92320 3.29101sX 1.00000 1.11960 0.80360 0.36781V 3575.33529 3155.20109 2264.68604 1036.54912 -0.62138923 RESIDUOF 420.13421 890.51504 1228.13692 1037.17051 -0.621389

Wi+1 = 881.66614985382 W2= 881.66614985

DIRECCION X - XTERCERA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 3575.3352906 2818.1588013 2818.1588013279 2818.1588013M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

3650

X 1.00000 1.65163 1.28414 0.12427 W² = 2586.2700945582sX 1.00000 0.65163 -0.36750 -1.15987 W = 50.85538412556V 3575.33529 1836.40832 -1035.66273 -3268.68468 -3430.78694F 1738.92697 2872.07105 2233.02195 162.10227

Wi+1 = 3483.9215338434 T = 2 * PI / WT = 0.1235500510952

3483.9215338434

X 1.00000 1.67971 1.37013 0.25358sX 1.00000 0.67971 -0.30958 -1.11654V 3575.33529 1915.53115 -872.45872 -3146.59870 -3462.32211F 1659.80414 2787.98987 2274.13998 315.72341

Wi+1 = 3163.2486470531

3163.2486470531

X 1.00000 1.73392 1.54062 0.52346sX 1.00000 0.73392 -0.19331 -1.01716V 3575.33529 2068.30559 -544.76467 -2866.51830 ### RESIDUOF 1507.02970 2613.07026 2321.75363 591.74474 -3458.26304 -3458.263040

Wi+1 = 2586.2700945582 W2= 2586.2700946

DIRECCION X - XCUARTA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 3575.3352906 2818.1588013 2818.1588013279 2818.1588013M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

3650

X 1.00000 1.65163 1.28414 0.12427 W² = 2586.2700945582sX 1.00000 0.65163 -0.36750 -1.15987 W = 50.85538412556V 3575.33529 1836.40832 -1035.66273 -3268.68468 -3430.78694F 1738.92697 2872.07105 2233.02195 162.10227

Wi+1 = 3483.9215338434 T = 2 * PI / WT = 0.1235500510952

3483.9215338434

X 1.00000 1.67971 1.37013 0.25358sX 1.00000 0.67971 -0.30958 -1.11654V 3575.33529 1915.53115 -872.45872 -3146.59870 -3462.32211F 1659.80414 2787.98987 2274.13998 315.72341

Wi+1 = 3163.2486470531

3163.2486470531

X 1.00000 1.73392 1.54062 0.52346sX 1.00000 0.73392 -0.19331 -1.01716V 3575.33529 2068.30559 -544.76467 -2866.51830 ### RESIDUO

3163.2486470531

F 1507.02970 2613.07026 2321.75363 591.74474 -3458.263040Wi+1 = 2586.2700945582 W2= 2586.2700946

350.96980018.734188

0.335386

2774.80311752.676400

0.119279

5935.43324677.041763

8.155556

89.136390

7.048955

3.2.2) DIRECCION Y - Y:PRIMERA FORMA DE MODO

NIVEL 1 2 3 4K (Ton/cm) 2449.0217 1316.4074 1316.4074 1316.4074

M (Ton) 467.366 467.366 467.366 350.582

0.4764183486 0.4764183486 0.4764183486239 0.3573724771

470

X 1.00000 2.69029 3.92296 4.48836 W² = 467.66372832815sX 1.00000 1.69029 1.23268 0.56539 W = 21.6255341744V 2449.02173 2225.10511 1622.70533 744.28864 -9.59855F 223.91662 602.39978 878.41669 753.88719

Wi+1 = 467.66568896303 T = 2 * PI / WT = 0.2905447447683

467.66568896303

X 1.00000 2.69113 3.92678 4.49782sX 1.00000 1.69113 1.23565 0.57104V 2449.02173 2226.21722 1626.62110 751.71619F 222.80452 599.59612 874.90491 751.72426

Wi+1 = 467.66372832953

467.66372832953

X 1.00000 2.69113 3.92679 4.49783sX 1.00000 1.69113 1.23565 0.57104V 2449.02173 2226.21815 1626.62439 751.72244 0.0000000 RESIDUOF 222.80358 599.59376 874.90195 751.72244 0.000000

Wi+1 = 467.66372832815 W2= 467.66372833

(Ton-seg²)cm

DIRECCION Y -Y:SEGUNDA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 2449.0217316 1316.4073893 1316.4073893193 1316.4073893M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

470

X 1.00000 2.69029 3.92296 4.48836 W² = 467.66372832815sX 1.00000 1.69029 1.23268 0.56539 W = 21.6255341744V 2449.02173 2225.10511 1622.70533 744.28864 -9.59855F 223.91662 602.39978 878.41669 753.88719

Wi+1 = 467.66568896303 T = 2 * PI / WT = 0.2905447447683

467.66568896303

X 1.00000 2.69113 3.92678 4.49782sX 1.00000 1.69113 1.23565 0.57104V 2449.02173 2226.21722 1626.62110 751.71619 -0.00807F 222.80452 599.59612 874.90491 751.72426

Wi+1 = 467.66372832953

467.66372832953

X 1.00000 2.69113 3.92679 4.49783sX 1.00000 1.69113 1.23565 0.57104V 2449.02173 2226.21815 1626.62439 751.72244 -0.00000001 RESIDUOF 222.80358 599.59376 874.90195 751.72244 0.000000

Wi+1 = 467.66372832815 W2= 467.66372833

DIRECCION Y - YTERCERA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 2449.0217316 1316.4073893 1316.4073893193 1316.4073893M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

3680

X 1.00000 1.52856 0.02135 -1.51429 W2 = 3698.948691333sX 1.00000 0.52856 -1.50721 -1.53565 W = 60.818982985027V 2449.02173 695.80221 -1984.10158 -2021.53644 -30.04128F 1753.21952 2679.90379 37.43486 -1991.49516

Wi+1 = 3698.8817661557 T = 2 * PI / WT = 0.1033096082637

3698.8817661557

X 1.00000 1.52173 0.00639 -1.51750sX 1.00000 0.52173 -1.51534 -1.52389V 2449.02173 686.80659 -1994.80553 -2006.06154 -0.10596F 1762.21514 2681.61212 11.25601 -2005.95558

Wi+1 = 3698.9486905234

3698.9486905234

X 1.00000 1.52170 0.00633 -1.51751sX 1.00000 0.52170 -1.51537 -1.52385V 2449.02173 686.77470 -1994.84325 -2006.00629 -0.0000013 RESIDUOF 1762.24703 2681.61795 11.16304 -2006.00629 0.00000 -0.000001

Wi+1 = 3698.948691333 W2= 3698.9486913

DIRECCION Y - YCUARTA FORMA DE MODO

K K1 K2 K3 K4Ton/cm 2449.0217316 1316.4073893 1316.4073893193 1316.4073893M (Ton) 467.3664 467.3664 467.3664 350.5824

(Ton-seg2)/cm 0.4764183486 0.4764183486 0.4764183486239 0.3573724771

3680

X 1.00000 1.52856 0.02135 -1.51429 W2 = 3698.948691333sX 1.00000 0.52856 -1.50721 -1.53565 W = 60.818982985027V 2449.02173 695.80221 -1984.10158 -2021.53644 -30.04128F 1753.21952 2679.90379 37.43486 -1991.49516

Wi+1 = 3698.8817661557 T = 2 * PI / WT = 0.1033096082637

3698.8817661557

X 1.00000 1.52173 0.00639 -1.51750sX 1.00000 0.52173 -1.51534 -1.52389V 2449.02173 686.80659 -1994.80553 -2006.06154 -0.10596F 1762.21514 2681.61212 11.25601 -2005.95558

Wi+1 = 3698.9486905234

3698.9486905234

X 1.00000 1.52170 0.00633 -1.51751sX 1.00000 0.52170 -1.51537 -1.52385V 2449.02173 686.77470 -1994.84325 -2006.00629 -0.0000013 RESIDUOF 1762.24703 2681.61795 11.16304 -2006.00629 -0.000001

Wi+1 = 3698.948691333 W2= 3698.9486913

404.84113520.120664

0.312275

3205.97648356.621343

6891.27272783.013690

7.568854

9333.48767796.609977

6.503660

3.3) CÁLCULO DE VALORES CARACTERÍSTICOS (X-X):(K1+k2)-M1*W2 - K 2 0.00000 0.00000 f1

-K 2 (K2+k3)-M2*W2 - K 3 0.00000 * f2 = [0]0.00000 - K 3 (K3+k4) -M3*W2 - K 4 f30.00000 0.00000 - K 4 K4-M4*W2 f4

1 2 3 4K= Ton/cm 3575.33529 2818.15880 2818.15880 2818.15880M= (ton-seg²)/cm 0.47642 0.47642 0.47642 0.35737w= 1 / seg 29.69286 29.69286 50.85538 50.85538

w = 29.69286 881.666155973.45216 -2818.15880 0.00000 0.00000 f1-2818.15880 5216.27567 -2818.15880 0.00000 * f2 = [0]

0.00000 -2818.15880 5216.27567 -2818.15880 f30.00000 0.00000 -2818.15880 2503.07559 f4

1.0 2.0 3.0 4.0 fi = 1.00000 2.11963 2.92333 3.29132

SEGUNDA FORMA DE MODOK= Ton/cm 3575.33529 2818.15880 2818.15880 2818.15880M= (ton-seg2)/cm 0.47642 0.47642 0.47642 0.35737w= 1 / seg 29.69286 29.69286 50.85538 50.85538

w = 29.69286 881.666155973.45216 -2818.15880 0.00000 0.00000 f1-2818.15880 5216.27567 -2818.15880 0.00000 * f2 = [0]

0.00000 -2818.15880 5216.27567 -2818.15880 f30.00000 0.00000 -2818.15880 2503.07559 f4

1.0 2.0 3.0 4.0 fi = 1.00000 2.11963 2.92333 3.29132

TERCERA FORMA DE MODO

K= Ton/cm 3575.33529 2818.15880 2818.15880 2818.15880M= (ton-seg2)/cm 0.47642 0.47642 0.47642 0.35737w= 1 / seg 29.69286 29.69286 50.85538 50.85538

w = 50.85538 2586.27009

5161.34756 -2818.15880 0.00000 0.00000 f1-2818.15880 4404.17108 -2818.15880 0.00000 * f2 = [ 0 ]

0.00000 -2818.15880 4404.17108 -2818.15880 f30.00000 0.00000 -2818.15880 1893.89705 f4

1.0 2.0 3.0 4.0 fi = 1.00000 1.83146 1.86218 2.77096

CUARTA FORMA DE MODO


w = 50.85538 2586.27009

5161.34756 -2818.15880 0.00000 0.00000 f1-2818.15880 4404.17108 -2818.15880 0.00000 * f2 = [ 0 ]

0.00000 -2818.15880 4404.17108 -2818.15880 f30.00000 0.00000 -2818.15880 1893.89705 f4

1.00 2.00 3.00 4.00

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[ fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

fi = 1.00000 1.83146 1.86218 2.77096

FACTORES DE PARTICIPAXION MODAL

1.00000 1.00000 1.00000 1.00000 12.11963 2.11963 1.83146 1.83146 4.4928287

MODOS 2.92333 2.92333 1.86218 1.86218 8.54586693.29132 3.29132 2.77096 2.77096 10.83276

0.47642 0.00000 0.00000 0.00000[M] = 0.00000 0.47642 0.00000 0.00000

0.00000 0.00000 0.47642 0.000000.00000 0.00000 0.00000 0.35737

FPM1 =4.05520

= 0.3840310.55962

FPM2 =4.05520

= 0.3840310.55962

FPM3 =3.22640

= 0.498636.47050

FPM4 =3.22640

= 0.498636.47050

3.4) ESPECTRO DE RESPUESTAS DEL SISMORESPUESTA=263.321 gals. Factor de Reducción= R = 8.0Amoriguamiento b (en CºAº ) = 0.1

MODO PERIODO

(seg) (1/seg) (cm/seg) (cm/seg)1 0.21161 29.69286 68.00000 51.64799 1533.576682 0.21161 29.69286 48.00000 36.45740 1082.524723 0.12355 50.85538 41.00000 31.14070 1583.672214 0.12355 50.85538 38.00000 28.86211 1467.79375

3.4.1) FUERZA CORTANTE EN LA BASE (VB)

CORT.BASAL F.P.M SUNA(M*fi) Sa VBVB1 = 0.38403 4.05520 1533.57668 = 2388.26400VB2 = 0.38403 4.05520 1082.52472 = 1685.83341VB3 = 0.49863 3.22640 1583.67221 = 2547.78973VB4 = 0.49863 3.22640 1467.79375 = 2361.36609

3.4.2) FUERZA DE INERCIA (F) PARA CADA FORMA DE MODO

V.BASAL NIVEL fi MASA (Ton) fi* MASAPRIMER MODO DE VIBRACION

2388.26400

1 1.00000 467.36640 467.36640 280.58096 78725.676022 2.11963 467.36640 990.64355 594.72765 ###3 2.92333 467.36640 1366.26690 820.23115 ###4 3.29132 350.58240 1153.87740 692.72423 ###

3978.15426 2388.26400 ###

SEGUNDO MODO DE VIBRACION

1685.83341

1 1.00000 467.36640 467.36640 198.05715 39226.634422 2.11963 467.36640 990.64355 419.80775 ###3 2.92333 467.36640 1366.26690 578.98670 ###4 3.29132 350.58240 1153.87740 488.98181 ###

3978.15426 1685.83341 ###

FRECUENC. (W)

VELOC. DE ESPECTRO

(S'v)

VELOC, NORMALIZ.

200 (Sv)

ACELERACION NORMALIZADO

(Sa)

(cm/seg2)

Fza INERCIA F (Ton)

R3

NO TOCAR ESTAS CELDAS NI MODIFICRALS

N28

OBTENER S'v DE UN ESPECTRO DE VELOCIDADES CON b= 0.10 INGRESANDOCON UN PERIODO T

Q56

NO CAMBIAR

Q57

NO TOCAR TODA ESTA FILA

TERCER MODO DE VIBRACION

2547.78973

1 1.00000 467.36640 467.36640 376.21319 ###2 1.83146 467.36640 855.96327 689.01974 ###3 1.86218 467.36640 870.31858 700.57525 ###4 2.77096 350.58240 971.44892 781.98155 ###

3165.09717 2547.78973 ###

CUARTO MODO DE VIBRACION

2361.36609

1 1.00000 467.36640 467.36640 348.68540 ###2 1.83146 467.36640 855.96327 638.60366 ###3 1.86218 467.36640 870.31858 649.31364 ###4 2.77096 350.58240 971.44892 724.76338 ###

3165.09717 2361.36609

3.4.3) FUERZA DE DISEÑO POR PISO

RESPUESTA MAXIMA ELASTICA ESPERADA :Factor de Reducción = R= 8.0

NIVEL S1+S2 F diseño (Ton)

1 300.88418 462.98162 763.86579 95.483222 585.53970 891.36557 1476.90527 184.613163 687.27668 1039.34377 1726.62046 215.827564 672.11274 1021.69359 1693.80633 211.72579

3.4.4)DESPLAZAMIENTOS DE PISOS

MODOFRECUENCIA VELOCIDAD DE VELOCIDAD ACELERACION

F.P.M Sd=Sv/W F.P.M *Sd(W) ESPECTRO NORM 200.00 NORMALIZADA

(1/seg) S¨v S v (cm/seg) S a

1.0 29.69286 68.00000 51.64799 1533.57668 0.38403 1.73941 0.667982.0 29.69286 48.00000 36.45740 1082.52472 0.38403 1.22782 0.471523.0 50.85538 41.00000 31.14070 1583.67221 0.49863 0.61234 0.305334.0 50.85538 38.00000 28.86211 1467.79375 0.49863 0.56753 0.28299

MODO NIVEL F.P.M *Sd fi ( X )

1.0

1

0.66798

1.00000 0.66798 0.446202 2.11963 1.41588 2.004713 2.92333 1.95274 3.813184 3.29132 2.19854 4.83359

2.0

1

0.47152

1.00000 0.47152 0.222332 2.11963 0.99944 0.998893 2.92333 1.37840 1.899994 3.29132 1.55191 2.40843

3.0

1

0.30533

1.00000 0.30533 0.093232 1.83146 0.55920 0.312713 1.86218 0.56858 0.323284 2.77096 0.84606 0.71582

4.0

1

0.28299

1.00000 0.28299 0.080082 1.83146 0.51829 0.268623 1.86218 0.52698 0.277714 2.77096 0.78415 0.61490

0.25*(Σ FUERZAS DEL MISMO NIVEL)

= S1

0.75*(RAIZ DE Σ DE CUADRAD. DE

FUERZ. EN EL NIVEL) = S2

Q105

EDIXON: NO TOCAR

NIVELX S1 S2 r

X-1 X-2 X-3 X-4 S1+S24 2.19854 1.55191 0.84606 0.78415 1.34517 2.19594 3.541113 1.95274 1.37840 0.56858 0.52698 1.10667 1.88460 2.991272 1.41588 0.99944 0.55920 0.51829 0.87320 1.42004 2.293241 0.66798 0.47152 0.30533 0.28299 0.43196 0.68814 1.12009

rx1 Di Di/he3.54111 0.54984 0.001832.99127 0.69803 0.002332.29324 1.17315 0.003911.12009 1.12009 0.00373

TOLERANCIA= 7.00000

he (cm) Fdiseño (Ton) Xdiseño (cm) Di/he (Di/he)x1000211.72579 3.5411 0.00183 1.83279

300

215.82756 2.9913 0.00233 2.32677

300

184.61316 2.2932 0.00391 3.91049

300

95.48322 1.1201 0.00373 3.73365

300

707.64973

DISTRIBUCION DE LAS FUERZAS SISMICAS EN CADA PORTICO

PORTICO A FT FNIVEL 4 211.72579 0.14309 30.29510NIVEL 3 215.82756 0.14309 30.88201NIVEL 2 184.61316 0.14309 26.41565NIVEL 1 95.48322 0.12131 11.58303 99.17579

PORTICO D FT FNIVEL 4 211.72579 0.14309 30.29510NIVEL 3 215.82756 0.14309 30.88201NIVEL 2 184.61316 0.14309 26.41565NIVEL 1 95.48322 0.12131 11.58303 99.17579

PORTICO B FT FNIVEL 4 211.72579 0.35691 75.56779NIVEL 3 215.82756 0.35691 77.03177NIVEL 2 184.61316 0.35691 65.89093NIVEL 1 95.48322 0.37869 36.15859 254.64907

PORTICO C FT FNIVEL 4 211.72579 0.35691 75.56779

0.25*Σ|xi| 0.75*√Σ(xi2)

% = (Ki/KT)

% = (Ki/KT)

% = (Ki/KT)

% = (Ki/KT)

NIVEL 3 215.82756 0.35691 77.03177NIVEL 2 184.61316 0.35691 65.89093NIVEL 1 95.48322 0.37869 36.15859 254.64907

TOTAL= 707.64973

1 1 14.49282866043373 3.35424891097883 3.354248910978838.54586687431605 3.46770010868345 3.4677001086834510.8327599164943 7.67820529183037 7.67820529183037

U3

NO TOCAR ESTAS CELDAS NI TOCARLAS

3.5) CONSIDERANDO UN ESPECTRO TEORICO SEGÚN NORMAS E-030

C= FACTOR DE AMPLIFICACION DINAMICO FACTOR CZ*S=ACELERACION MAXIMA QUE RECIBE UNA ESTRUCTURA EN SU CIMENTACIONT= PERIODO FUNDAMENTAL DE VIBRACIONZ*S*C= ACELERACION DE RESPUESTA DE UNA ESTRUCTURA

ESPECTRO ELASTICO DE ACELERACIONES PARA LA ZONA DE MAYOR SISMICIDAD Y SUELO RIGIDOZ*S*C

Z*S*C

0 0.25 0.5 0.75T

Z = 0.3 ZONA SISMICA: 3 (TACNA)U = 1.3 CATEGORIA DE LA EDIF: A (CENTRO EDUCATIVO)S = 1.4 Tp (seg) = 0.9 SUELO TIPO : S3

R = 8.0; C£2.5

MODO C1 C (Z*U*S/R)*g

1 0.211605905983 0.9 15.269802307675 2.5 66.885 167.21252 0.211605905983 0.9 15.269802307675 2.5 66.885 167.21253 0.123550051095 0.9 29.918477123664 2.5 66.885 167.21254 0.123550051095 0.9 29.918477123664 2.5 66.885 167.2125

FUERZA CORTANTE EN LA BASE (VB)Sa: obtenido del reglamento

(No) CORT. BASAL F.P.M suma(M*fi) Sa VB1 VB1 0.3840291788793 4.0552031150531 167.2125 = 260.402755569752 VB2 0.3840291788793 4.0552031150531 167.2125 = 260.402755569753 VB3 0.4986321154312 3.2263987436413 167.2125 = 269.009134169524 VB4 0.4986321154312 3.2263987436413 167.2125 = 269.00913416952

FUERZA DE INERCIA PARA CADA MODO DE VIBRACION

V.BASAL NIVEL fi MASA (Ton) fi*MASA

260.4027555697

1 1.00000 467.36640 467.36640 30.592962 2.11963 467.36640 990.64355 64.845733 2.92333 467.36640 1366.26690 89.433354 3.29132 350.58240 1153.87740 75.53072

3978.15426 260.40276

260.4027555697

1 1.00000 467.36640 467.36640 30.592962 2.11963 467.36640 990.64355 64.845733 2.92333 467.36640 1366.26690 89.433354 3.29132 350.58240 1153.87740 75.53072

3978.15426 260.40276

269.0091341695

1 1.00000 467.36640 467.36640 39.722582 1.83146 467.36640 855.96327 72.750353 1.86218 467.36640 870.31858 73.970454 2.77096 350.58240 971.44892 82.56575

3165.09717 269.00913

269.0091341695

1 1.00000 467.36640 467.36640 46.604292 1.83146 467.36640 855.96327 85.35394

C=2.5*(Tp/T)1.25

T(seg)

Tp(seg)

(Z*U*S/R)*g*CSa (cm/seg2)

Fza INERCIA F (Ton)

269.00913416953 1.86218 467.36640 870.31858 86.785404 2.77096 350.58240 971.44892 96.86980

2697.73077 269.00913

RESPUESTA MAXIMA ELASTICA ESPERADA

NIVEL S1 + S2 F diseño (Ton)

1 36.87820 56.23350 93.11170 93.111702 71.94894 108.65387 180.60280 180.602803 84.90564 127.72036 212.62599 212.625994 82.62425 124.62337 207.24762 207.24762

DESPLAZAMIENTOS DE PISOFactor de Reducción = R = 8.0

MODO F.P.M. F.P.M*Sd

1 29.69286 167.21250 0.38403 0.18966 0.072832 29.69286 167.21250 0.38403 0.18966 0.072833 50.85538 167.21250 0.49863 0.06465 0.032244 50.85538 167.21250 0.49863 0.06465 0.03224


1

1

0.07283

1.00000 0.07283 0.005302 2.11963 0.15438 0.023833 2.92333 0.21292 0.045334 3.29132 0.23972 0.05746

2

1

0.07283

1.00000 0.07283 0.005302 2.11963 0.15438 0.023833 2.92333 0.21292 0.045334 3.29132 0.23972 0.05746

3

1

0.03224

1.00000 0.03224 0.001042 1.83146 0.05904 0.003493 1.86218 0.06003 0.003604 2.77096 0.08933 0.00798

4

1

0.03224

1.00000 0.03224 0.001042 1.83146 0.05904 0.003493 1.86218 0.06003 0.003604 2.77096 0.08933 0.00798

NIVELX S1 S2

X-1 X-2 X-3 X-44 0.23972 0.23972 0.08933 0.08933 0.16452 0.271343 0.21292 0.21292 0.06003 0.06003 0.13647 0.234642 0.15438 0.15438 0.05904 0.05904 0.10671 0.175311 0.07283 0.07283 0.03224 0.03224 0.05254 0.08448

r X diseñoNIVEL S1+S2 r*R Di Di/he

4 0.43586 3.48690 0.51802 0.001733 0.37111 2.96889 0.71271 0.00238

0.25*(Σ FUERZAS DEL

MISMO NIVEL) = S1

0.75*(RAIZ DE Σ DE CUADRAD. DE FUERZ. EN EL NIVEL) = S2

FRECUENCIAW (1/seg)

ACELERACIONSa (cm/seg2) Sd=Sa/W2

0.25*Σ|xi| 0.75*√Σ(xi2)

2 0.28202 2.25618 1.16005 0.003871 0.13702 1.09613 1.09613 0.00365

3.6) ANALISIS SISMICO MEDIANTE EL PROCEDIMIENTO DE ANALISIS POR FUERZAS ESTATICAS EQUIVALENTES

Válido para edificios sin irregularidades y de no mas de 45 m de altura

Valores de los parámetros utilizados para el presente proyecto:

Z= 0.3 Zona sísmica: 3 (TACNA)U= 1.3 Categoría de la Edificac: A (CENTRO EDUCATIVO)S= 1.4 Suelo tipo: S3hn= 12 Altura de la edificación (m)

35 (RNE 030, Art. 7.2)0.343 (Periodo fundamental de vibración)

C= 2.5 (Factor de amplificación dinámica )R= 8

3.6.1) FUERZA CORTANTE TOTAL EN LA BASE DE LA ESTRUCTURA CORRESPONDIENTE A LA DIRECCION CONSIDERADA (VH):

Peso (Ton)NIVEL 1 467.3664NIVEL 2 467.3664NIVEL 3 467.3664NIVEL 4 350.5824

V = TOTAL = 1752.6816V = 299.051298

NIVEL 1 2 3 4K = (Ton/cm) 3575.33529 2818.15880 2818.15880 2818.15880M = (ton-seg)/cm 0.47642 0.47642 0.47642 0.35737

NIVEL 4 12 350.58240 4206.98880 99.69469 2818.15880 0.03538NIVEL 3 9 467.36640 4206.29760 99.67831 2818.15880 0.03537NIVEL 2 6 467.36640 2804.19840 66.45220 2818.15880 0.02358NIVEL 1 3 467.36640 1402.09920 33.22610 3575.33529 0.00929

12619.58400 299.05130

NIVEL 4 0.10362 0.82895 0.00094NIVEL 3 0.06824 0.54595 0.00094NIVEL 2 0.03287 0.26299 0.00063NIVEL 1 0.00929 0.07435 0.00025


PORTICO A FT FNIVEL 4 99.69469 0.143086505506 14.26496420298

CT=T= hn/CT

(Z*U*S*C/R)*P (Ton)

hi

(m)Peso (Pi)

(Ton) (hi)x(Pi) Fi=Pixhi/Σpixhi(Ton)

Ki

(Ton/cm)Fi/Ki

(cm)

Xi

(cm)Xdiseño=Xi*R

(cm) Di/he

% = (Ki/KT)

NIVEL 3 99.67831 0.143086505506 14.26262049737NIVEL 2 66.45220 0.143086505506 9.508413664911NIVEL 1 33.22610 0.121309530211 4.030642829186 42.06664119444

PORTICO D FT % FNIVEL 4 99.69469 0.143086505506 14.26496420298NIVEL 3 99.67831 0.143086505506 14.26262049737NIVEL 2 66.45220 0.143086505506 9.508413664911NIVEL 1 33.22610 0.121309530211 4.030642829186 42.06664119444

PORTICO B FT % FNIVEL 4 99.69469 0.356913494494 35.5823786774NIVEL 3 99.67831 0.356913494494 35.57653256245NIVEL 2 66.45220 0.356913494494 23.71768837496NIVEL 1 33.22610 0.378690469789 12.58240819075 107.45900780556

PORTICO C FT % FNIVEL 4 99.69469 0.356913494494 35.5823786774NIVEL 3 99.67831 0.356913494494 35.57653256245NIVEL 2 66.45220 0.356913494494 23.71768837496NIVEL 1 33.22610 0.378690469789 12.58240819075 107.45900780556

TOTAL= 299.051298

TOLERANCIA = 7.00000


30099.67831 0.5459 0.00094 0.94320

30066.45220 0.2630 0.00063 0.62880

30033.22610 0.0743 0.00025 0.24782

300

299.05130

DISTRIBUCION DE LAS FUERZAS SISMICAS EN CADA PORTICOANALISIS MODAL ESPECTRAL CONSIDERANDO UN ESPECTRO TEORICO SEGÚN NORMA E-030DIRECCION X

PORTICO A FT FNIVEL 4 207.2476 0.1431 29.6543NIVEL 3 212.6260 0.1431 30.4239

935.928961582 NIVEL 2 180.6028 0.1431 25.84184204.96846273 NIVEL 1 93.1117 0.1213 11.2953 97.21547998.3243095

5704.88967894 PORTICO D FT % F67809.5951083 NIVEL 4 207.2476 0.1431 29.6543935.928961582 NIVEL 3 212.6260 0.1431 30.42394204.96846273 NIVEL 2 180.6028 0.1431 25.84187998.3243095 NIVEL 1 93.1117 0.1213 11.2953 97.2154

5704.8896789467809.5951083 PORTICO B FT % F

NIVEL 4 207.2476 0.3569 73.96951577.88349137 NIVEL 3 212.6260 0.3569 75.88915292.61398256 NIVEL 2 180.6028 0.3569 64.45965471.6267545 NIVEL 1 93.1117 0.3787 35.2605 249.5787

6817.10366195PORTICO C FT % F

2171.95996985 NIVEL 4 207.2476 0.3569 73.96957285.29436356 NIVEL 3 212.6260 0.3569 75.88917531.7058235 NIVEL 2 180.6028 0.3569 64.4596

9383.75763806 NIVEL 1 93.1117 0.3787 35.2605 249.5787

TOTAL= 693.5881


he (cm) Fdiseño (Ton) K (Ton/cm) Xdiseño (cm) Di/he

207.24762 3.48690 0.00173

300 2818.15880133

212.62599 2.96889 0.00238

300 2818.15880133

180.60280 2.25618 0.00387

300 2818.15880133

93.11170 1.09613 0.00365

300 3575.33529063TOTAL 693.58812

% = (Ki/KT)

3.7) CÁLCULO DE VALORES CARACTERÍSTICOS (Y-Y):(K1+K2)-M1*W2 - K 2 0 0 f1

-K 2 (K2+k3)-M2*W2 - K 3 0 * f2 = [ 0 ]0 - K 3 (K3+k4) -M3*W2 - K 4 f30 0 - K 4 K4-M4*W2 f41 2 3 4


w = 21.62553 467.663733542.62554 -1316.40739 0.00000 0.00000 f1-1316.40739 2410.01120 -1316.40739 0.00000 * f2 = [ 0 ]

0.00000 -1316.40739 2410.01120 -1316.40739 f30.00000 0.00000 -1316.40739 1149.27724 f4

1.0 2.0 3.0 4.0 fi = 1.00000 2.69113 3.92679 4.49783

SEGUNDA FORMA DE MODOK= Ton/cm 2449.02173 1316.40739 1316.40739 1316.40739M= (ton-seg2)/cm 0.47642 0.47642 0.47642 0.35737w= 1 / seg 21.62553 21.62553 60.81898 60.81898

w = 21.62553 467.663733542.62554 -1316.40739 0.00000 0.00000 f1-1316.40739 2410.01120 -1316.40739 0.00000 * f2 = [ 0 ]

0.00000 -1316.40739 2410.01120 -1316.40739 f30.00000 0.00000 -1316.40739 1149.27724 f4

1.0 2.0 3.0 4.0 fi = 1.00000 2.69113 3.92679 4.49783

TERCERA FORMA DE MODO


w = 60.81898 3698.94869

2003.18209 -1316.40739 0.00000 0.00000 f1-1316.40739 870.56775 -1316.40739 0.00000 * f2 = [ 0 ]

0.00000 -1316.40739 870.56775 -1316.40739 f30.00000 0.00000 -1316.40739 -5.49507 f4

1.0 2.0 3.0 4.0 fi = 1.00000 1.52170 0.00633 -1.51751

CUARTA FORMA DE MODO


w = 60.81898 3698.94869

2003.18209 -1316.40739 0.00000 0.00000 f1-1316.40739 870.56775 -1316.40739 0.00000 * f2 = [ 0 ]

0.00000 -1316.40739 870.56775 -1316.40739 f30.00000 0.00000 -1316.40739 -5.49507 f4

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[ fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

w2 =

[[K]-W2*[M]]*[fi]=[0]=

1.00 2.00 3.00 4.00 fi = 1.00000 1.52170 0.00633 -1.51751

FACTORES DE PARTICIPAXION MODAL

1.00000 1.00000 1.00000 1.00000 12.69113 2.69113 1.52170 1.52170 7.2421894

MODOS 3.92679 3.92679 0.00633 0.00633 15.4196474.49783 4.49783 -1.51751 -1.51751 20.230445

0.47642 0.00000 0.00000 0.00000[M] = 0.00000 0.47642 0.00000 0.00000

0.00000 0.00000 0.47642 0.000000.00000 0.00000 0.00000 0.35737

FPM1 =5.23672

= 0.2830218.50274

FPM2 =5.23672

= 0.2830218.50274

FPM3 =0.66209

= 0.275572.40260

FPM4 =0.66209

= 0.275572.40260

3.8) ESPECTRO DE RESPUESTAS DEL SISMORESPUESTA=263.321 gals. Factor de Reducción= R = 8.0Amoriguamiento b (en CºAº ) = 0.1

MODO PERIODO FRECUENC. (W)

(seg) (1/seg) (cm/seg) (cm/seg)1 0.29054 21.62553 68.00000 51.64799 1116.915342 0.29054 21.62553 43.00000 32.65976 706.284703 0.10331 60.81898 41.00000 31.14070 1893.945644 0.10331 60.81898 39.00000 29.62164 1801.55805

3.8.1) FUERZA CORTANTE EN LA BASE (VB)

CORT.BASAL F.P.M SUNA(M*fi) Sa VBVB1 = 0.28302 5.23672 1116.91534 = 1655.39703VB2 = 0.28302 5.23672 706.28470 = 1046.79518VB3 = 0.27557 0.66209 1893.94564 = 345.55320VB4 = 0.27557 0.66209 1801.55805 = 328.69694

3.8.2) FUERZA DE INERCIA (F) PARA CADA FORMA DE MODO

V.BASAL NIVEL fi MASA (Ton) fi* MASAPRIMER MODO DE VIBRACION

1655.39703

1 1.00000 467.36640 467.36640 150.60233 22681.062672 2.69113 467.36640 1257.74449 405.29070 ###3 3.92679 467.36640 1835.24777 591.38311 ###4 4.49783 350.58240 1576.85890 508.12088 ###

5137.21756 1655.39703 ###

SEGUNDO MODO DE VIBRACION

1046.79518

1 1.00000 467.36640 467.36640 95.23383 9069.482022 2.69113 467.36640 1257.74449 256.28677 65682.906153 3.92679 467.36640 1835.24777 373.96285 ###4 4.49783 350.58240 1576.85890 321.31174 ###

5137.21756 1046.79518 ###

VELOC. DE ESPECTRO (S'v)

VELOC, NORMALIZ. 200

(Sv)ACELERACION

NORMALIZADO (Sa)

(cm/seg2)

Fza INERCIA F (Ton)

R3

NO TOCAR ESTAS CELDAS NI MODIFICRALS

N28

OBTENER S'v DE UN ESPECTRO DE VELOCIDADES CON b= 0.10 INGRESANDOCON UN PERIODO T

Q56

NO CAMBIAR

Q57

NO TOCAR TODA ESTA FILA

TERCER MODO DE VIBRACION

345.55320

1 1.00000 467.36640 467.36640 248.65034 61826.993122 1.52170 467.36640 711.19322 378.37217 ###3 0.00633 467.36640 2.96055 1.57509 2.480904 -1.51751 350.58240 -532.01391 -283.04440 80114.13198

649.50626 345.55320 ###

CUARTO MODO DE VIBRACION

328.69694

1 1.00000 467.36640 467.36640 236.52106 55942.210912 1.52170 467.36640 711.19322 359.91499 ###3 0.00633 467.36640 2.96055 1.49825 2.244764 -1.51751 350.58240 -532.01391 -269.23736 72488.75356

649.50626 328.69694

3.8.3) FUERZA DE DISEÑO POR PISO

RESPUESTA MAXIMA ELASTICA ESPERADA :Factor de Reducción = R= 8.0

NIVEL S1+S2 F diseño (Ton)

1 182.75189 290.00838 472.76027 59.095032 349.96615 531.73241 881.69857 110.212323 242.10483 524.77866 766.88349 95.860444 345.42859 537.71964 883.14823 110.39353

3.8.4)DESPLAZAMIENTOS DE PISOS

MODO

FRECUENCIA VELOCIDAD DE VELOCIDAD ACELERACION

F.P.M Sd=Sv/W F.P.M *Sd(W) ESPECTRO NORM 200.00 NORMALIZADA

(1/seg) S¨v S v (cm/seg) S a

1.0 21.62553 68.00000 51.64799 1116.91534 0.28302 2.38829 0.675942.0 21.62553 43.00000 32.65976 706.28470 0.28302 1.51024 0.427433.0 60.81898 41.00000 31.14070 1893.94564 0.27557 0.51202 0.141104.0 60.81898 39.00000 29.62164 1801.55805 0.27557 0.48705 0.13422


1.0

1

0.67594

1.00000 0.67594 0.456902 2.69113 1.81905 3.308943 3.92679 2.65428 7.045204 4.49783 3.04027 9.24325

2.0

1

0.42743

1.00000 0.42743 0.182702 2.69113 1.15028 1.323153 3.92679 1.67844 2.817174 4.49783 1.92252 3.69610

3.0

1

0.14110

1.00000 0.14110 0.019912 1.52170 0.21471 0.046103 0.00633 0.00089 0.000004 -1.51751 -0.21412 0.04585

4.0

1

0.13422

1.00000 0.13422 0.018012 1.52170 0.20424 0.041713 0.00633 0.00085 0.000004 -1.51751 -0.20367 0.04148

NIVELX S1 S2 r

0.25*(Σ FUERZAS DEL MISMO NIVEL)

= S1

0.75*(RAIZ DE Σ DE CUADRAD. DE

FUERZ. EN EL NIVEL) = S2

Q103

EDIXON: NO TOCAR

NIVELX-1 X-2 X-3 X-4 S1+S2

4 3.04027 1.92252 -0.21412 -0.20367 1.34515 2.70694 4.052083 2.65428 1.67844 0.00089 0.00085 1.08362 2.35533 3.438952 1.81905 1.15028 0.21471 0.20424 0.84707 1.62940 2.476471 0.67594 0.42743 0.14110 0.13422 0.34467 0.61734 0.96201

rx1 Di Di/he4.05208 0.61314 0.002043.43895 0.96248 0.003212.47647 1.51446 0.005050.96201 0.96201 0.00321

TOLERANCIA= 7.00000


300

95.86044 3.4389 0.00321 3.20826

300

110.21232 2.4765 0.00505 5.04820

300

59.09503 0.9620 0.00321 3.20670

300

375.56132


PORTICO 1 FT FNIVEL 4 110.39353 0.15099 16.66806NIVEL 3 95.86044 0.15099 14.47374NIVEL 2 110.21232 0.15099 16.64070NIVEL 1 59.09503 0.10376 6.13156 53.91407




0.25*Σ|xi| 0.75*√Σ(xi2)

% = (Ki/KT)

% = (Ki/KT)

% = (Ki/KT)

% = (Ki/KT)


TOTAL= 375.56132

% = (Ki/KT)

1 1 17.242189 2.31558237887023 2.3155823788702315.41965 4.0126485811E-05 4.0126485811E-0520.23045 2.30285058101259 2.30285058101259

U3

NO TOCAR ESTAS CELDAS NI TOCARLAS

3.9) CONSIDERANDO UN ESPECTRO TEORICO SEGÚN NORMAS E-030

C= FACTOR DE AMPLIFICACION DINAMICO FACTOR CZ*S=ACELERACION MAXIMA QUE RECIBE UNA ESTRUCTURA EN SU CIMENTACIONT= PERIODO FUNDAMENTAL DE VIBRACIONZ*S*C= ACELERACION DE RESPUESTA DE UNA ESTRUCTURA

ESPECTRO ELASTICO DE ACELERACIONES PARA LA ZONA DE MAYOR SISMICIDAD Y SUELO RIGIDOZ*S*C

Z*S*C

0 0.25 0.5 0.75T

Z = 0.3 ZONA SISMICA: 3 (TACNA)U = 1.3 CATEGORIA DE LA EDIF: A (CENTRO EDUCATIVO)S = 1.4 Tp (seg) = 0.9 SUELO TIPO : S3R = 8.0

; C£2.5

MODO C1 C (Z*U*S/R)*g

1 0.29054474477 0.9 10.273699644197 2.5 66.885 167.21252 0.29054474477 0.9 10.27369964 2.5 66.885 167.21253 0.10330960826 0.9 37.416852509106 2.5 66.885 167.21254 0.10330960826 0.9 37.416852509106 2.5 66.885 167.2125

FUERZA CORTANTE EN LA BASE (VB)Sa: obtenido del reglamento

(No) CORT. BASAL F.P.M suma(M*fi) Sa VB1 VB1 0.283023803721 5.236715150818 167.2125 = 247.828161291182 VB2 0.283023803721 5.236715150818 167.2125 = 247.828161291183 VB3 0.2755707214018 0.6620858887182 167.2125 = 30.5081691001054 VB4 0.2755707214018 0.6620858887182 167.2125 = 30.508169100105

FUERZA DE INERCIA PARA CADA MODO DE VIBRACION

V.BASAL NIVEL fi MASA (Ton) fi*MASA

247.828161291

1 1.00000 467.36640 467.36640 22.546552 2.69113 467.36640 1257.74449 60.675753 3.92679 467.36640 1835.24777 88.535494 4.49783 350.58240 1576.85890 76.07037

5137.21756 247.82816

247.828161291

1 1.00000 467.36640 467.36640 22.546552 2.69113 467.36640 1257.74449 60.675753 3.92679 467.36640 1835.24777 88.535494 4.49783 350.58240 1576.85890 76.07037

5137.21756 247.82816

30.5081691001

1 1.00000 467.36640 467.36640 21.952822 1.52170 467.36640 711.19322 33.405693 0.00633 467.36640 2.96055 0.139064 -1.51751 350.58240 -532.01391 -24.98940

649.50626 30.50817

30.5081691001

1 1.00000 467.36640 467.36640 78.283212 1.52170 467.36640 711.19322 119.12386

C=2.5*(Tp/T)1.25

T(seg)

Tp(seg)

(Z*U*S/R)*g*CSa (cm/seg2)

Fza INERCIA F (Ton)

30.50816910013 0.00633 467.36640 2.96055 0.495894 -1.51751 350.58240 -532.01391 -89.11158

182.13986 30.50817

RESPUESTA MAXIMA ELASTICA ESPERADA

NIVEL S1 + S2 F diseño (Ton)

1 36.33229 65.49902 101.83130 101.831302 68.47026 112.92302 181.39328 181.393283 44.42648 93.90686 138.33335 138.333354 66.56043 106.43329 172.99372 172.99372

DESPLAZAMIENTOS DE PISOFactor de Reducción = R = 8.0

MODO F.P.M. F.P.M*Sd

1 21.62553 167.21250 0.28302 0.35755 0.101192 21.62553 167.21250 0.28302 0.35755 0.101193 60.81898 167.21250 0.27557 0.04521 0.012464 60.81898 167.21250 0.27557 0.04521 0.01246


1

1

0.10119

1.00000 0.10119 0.010242 2.69113 0.27233 0.074163 3.92679 0.39737 0.157904 4.49783 0.45516 0.20717

2

1

0.10119

1.00000 0.10119 0.010242 2.69113 0.27233 0.074163 3.92679 0.39737 0.157904 4.49783 0.45516 0.20717

3

1

0.01246

1.00000 0.01246 0.000162 1.52170 0.01896 0.000363 0.00633 0.00008 0.000004 -1.51751 -0.01890 0.00036

4

1

0.01246

1.00000 0.01246 0.000162 1.52170 0.01896 0.000363 0.00633 0.00008 0.000004 -1.51751 -0.01890 0.00036

NIVELX S1 S2

X-1 X-2 X-3 X-44 0.45516 0.45516 -0.01890 -0.01890 0.23703 0.483183 0.39737 0.39737 0.00008 0.00008 0.19872 0.421472 0.27233 0.27233 0.01896 0.01896 0.14564 0.289551 0.10119 0.10119 0.01246 0.01246 0.05683 0.10814

r X diseñoNIVEL S1+S2 r*R Di Di/he

4 0.72021 5.76170 0.80011 0.00267

0.25*(Σ FUERZAS DEL

MISMO NIVEL) = S1

0.75*(RAIZ DE Σ DE CUADRAD. DE FUERZ. EN EL NIVEL) = S2

FRECUENCIAW (1/seg)

ACELERACIONSa (cm/seg2) Sd=Sa/W2

0.25*Σ|xi| 0.75*√Σ(xi2)

3 0.62020 4.96159 1.48008 0.004932 0.43519 3.48151 2.16176 0.007211 0.16497 1.31976 1.31976 0.00440

3.10) ANALISIS SISMICO MEDIANTE EL PROCEDIMIENTO DE ANALISIS POR FUERZAS ESTATICAS EQUIVALENTES

Válido para edificios sin irregularidades y de no mas de 45 m de altura

Valores de los parámetros utilizados para el presente proyecto:

Z= 0.3 Zona sísmica: 3 (TACNA)U= 1.3 Categoría de la Edificac: A (CENTRO EDUCATIVO)S= 1.4 Suelo tipo: S3hn= 12 Altura de la edificación (m)

35 (RNE 030, Art. 7.2)0.3428571428571 (Periodo fundamental de vibración)

C= 2.5 (Factor de amplificación dinámica )R= 8.0

3.6.1) FUERZA CORTANTE TOTAL EN LA BASE DE LA ESTRUCTURA

Peso (Ton)NIVEL 1 467.3664NIVEL 2 467.3664NIVEL 3 467.3664NIVEL 4 350.5824

V = TOTAL = 1752.6816V = 299.051298

NIVEL 1 2 3 4K = (Ton/cm) 2449.02173 1316.40739 1316.40739 1316.40739M = (ton-seg)/cm 0.47642 0.47642 0.47642 0.35737

NIVEL 4 12 350.58240 4206.98880 99.69469 1316.40739 0.07573NIVEL 3 9 467.36640 4206.29760 99.67831 1316.40739 0.07572NIVEL 2 6 467.36640 2804.19840 66.45220 1316.40739 0.05048NIVEL 1 3 467.36640 1402.09920 33.22610 2449.02173 0.01357

12619.58400 299.05130

NIVEL 4 0.21550 1.72400 0.00202NIVEL 3 0.13977 1.11814 0.00202NIVEL 2 0.06405 0.51238 0.00135NIVEL 1 0.01357 0.10854 0.00036

CT=T= hn/CT

CORRESPONDIENTE A LA DIRECCION CONSIDERADA (VH):

(Z*U*S*C/R)*P (Ton)

hi

(m)Peso (Pi)

(Ton) (hi)x(Pi) Fi=Pixhi/Σpixhi(Ton)

Ki

(Ton/cm)Fi/Ki

(cm)

Xi

(cm)Xdiseño=Xi*R

(cm) Di/he



PORTICO 2 FT % FNIVEL 4 99.69469 0.23267488074 23.1964491198NIVEL 3 99.67831 0.23267488074 23.1926379887NIVEL 2 66.45220 0.23267488074 15.4617586592NIVEL 1 33.22610 0.264161639859 8.77706160099 70.627907368695




TOTAL= 299.051298



30099.67831 1.1181 0.00202 2.01920

300

% = (Ki/KT)

66.45220 0.5124 0.00135 1.34613

30033.22610 0.1085 0.00036 0.36179

300

299.05130

DISTRIBUCION DE LAS FUERZAS SISMICAS EN CADA PORTICOANALISIS MODAL ESPECTRAL CONSIDERANDO UN ESPECTRO TEORICO SEGÚN NORMA E-030DIRECCION X

PORTICO 1 FT FNIVEL 4 172.9937 0.1510 26.1199NIVEL 3 138.3333 0.1510 20.8866

508.347118064 NIVEL 2 181.3933 0.1510 27.38823681.54608637 NIVEL 1 101.8313 0.1038 10.5658 84.96057838.533232945786.70119221 PORTICO 2 FT % F

61418.797529 NIVEL 4 172.9937 0.2327 40.2513508.347118064 NIVEL 3 138.3333 0.2327 32.18673681.54608637 NIVEL 2 181.3933 0.2327 42.20577838.53323294 NIVEL 1 101.8313 0.2642 26.8999 141.54365786.70119221

61418.797529 PORTICO 3 FT % F

NIVEL 4 172.9937 0.2327 40.2513481.926253076 NIVEL 3 138.3333 0.2327 32.18671115.93993954 NIVEL 2 181.3933 0.2327 42.20570.01933800696 NIVEL 1 101.8313 0.2642 26.8999 141.5436624.470016983

PORTICO 4 FT % F6128.26139866 NIVEL 4 172.9937 0.2327 40.251314190.4941078 NIVEL 3 138.3333 0.2327 32.18670.24590559406 NIVEL 2 181.3933 0.2327 42.20577940.87368196 NIVEL 1 101.8313 0.2642 26.8999 141.5436


TOTAL= 594.5516


he (cm) Fdiseño (Ton) K (Ton/cm) Xdiseño (cm) Di/he

172.99372 5.76170 0.00267

300 2818.15880133

138.33335 4.96159 0.00493

300 2818.15880133

181.39328 3.48151 0.00721

300 2818.15880133

101.83130 1.31976 0.00440

% = (Ki/KT)

% = (Ki/KT)

300 3575.33529063TOTAL 594.55164

EJE X-X

ESPECTRO DE RESPUESTA SEGÚN NORMA E-030 FUERZAS ESTATICAS EQUIV.

NIVELES X Diseño DESPLAZAMIENTOS X Diseño DESPLAZAMIENTOS X Diseño DESPLAZAMIENTOS

1 1.12009 0.00373 1.09613 0.00365 0.07435 0.000252 2.29324 0.00391 2.25618 0.00387 0.26299 0.000633 2.99127 0.00233 2.96889 0.00238 0.54595 0.000944 3.54111 0.00183 3.48690 0.00173 0.82895 0.00094

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.0080

1

2

3

4

5

1

2

3

4

1

2

3

4

1

2

3

4

ESPECTRO

NORMA E-030

FUERZAS ESTATICAS

DESPLAZAMIENTO

NIVE

LES

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1

2

3

4

1

2

3

4

1

2

3

4

ESPECTRO

NORMA E-030

FUERZAS ESTATICAS

X DISEÑO

NIVE

LES

EJEY-Y

ESPECTRO DE RESPUESTA SEGÚN NORMA E-030 FUERZAS ESTATICAS EQUIV.

NIVELES X Diseño DESPLAZAMIENTOS X Diseño DESPLAZAMIENTOS X Diseño DESPLAZAMIENTOS

1 0.96201 0.00321 1.31976 0.00440 0.10854 0.000362 2.47647 0.00505 3.48151 0.00721 0.51238 0.001353 3.43895 0.00321 4.96159 0.00493 1.11814 0.002024 4.05208 0.00204 5.76170 0.00267 1.72400 0.00202

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.0080

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1

2

3

4

1

2

3

4

1

2

3

4ESPECTRO

NORMA E-030

FUERZA EQUIVALENTE

DESPLAZAMIENTO

NIVE

LES

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000 7.000000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1

2

3

4

1

2

3

4

1

2

3

4

ESPECTRO

HORMA E-0.30

FUERZA EQUIVALENTE

X DISEÑO

NIVE

LES

NOMBRE : WITHMAN GROVER YALLE GUILLÉN EL ANALISIS DINAMICO DE UN PARQUEADERO EN CHINCHA

CORRECCION POR TORSIONf´c: 210 Kg/cm²FY= 4200 Kg/cm²

8.000

8.000

8.000

3.000 3.000 3.000 3.000

SECCION DE COLUMNASINERCIA EN X-X

COLUMNAS b h ITIPO C1 = 0.60 0.60 1080000TIPO C2 = 0.60 0.60 1080000TIPO C3 = 0.90 1.00 6075000

INERCIA EN Y-YCOLUMNAS: b h IC

TIPO C1 = 0.60 0.60 1080000TIPO C2 = 0.60 0.60 1080000TIPO C3 = 0.90 1.00 7500000

K=12EI/(h^3(1+2g))

C3

C1

C3C3

C2 C2 C2 C1

C2

C3 C3 C2C3

C2 C2 C2 C1

C2

C2

C2

A

B

C

D

1 2 3 4 5

donde:

REGIDEZ EN LA DIRECCION ( Kx ) NIVEL COLUMNAS TIPO DE COLUMNAS REGIDEZ POR EJE

EJES 0 C2 C2 C2 C1 A - A 151.893 187.142 187.142 187.142 151.893 865.212

1er D - D 151.893 187.142 187.142 187.142 151.893 865.212 3460.848C2 C3 C3 C3 C2

B - B 151.893 187.142 187.142 187.142 151.893 865.212C --C 151.893 187.142 187.142 187.142 151.893 865.212EJES 0 C2 C2 C2 C1 A - A 64.208 111.207 111.207 111.207 64.208 462.037

2do D - D 64.208 111.207 111.207 111.207 64.208 462.037C2 C3 C3 C3 C2 1848.150

B - B 64.208 111.207 111.207 111.207 64.208 462.037C --C 64.208 111.207 111.207 111.207 64.208 462.037EJES 0 C2 C2 C3 C1 A - A 64.208 111.207 111.207 111.207 64.208 462.037

3er D - D 64.208 111.207 111.207 111.207 64.208 462.037C2 C3 C3 C3 C2 1848.150

B - B 64.208 111.207 111.207 111.207 64.208 462.037C --C 64.208 111.207 111.207 111.207 64.208 462.037EJES 0 C2 C2 C2 C1 A - A 64.208 111.207 111.207 111.207 64.208 462.037

4to D - D 64.208 111.207 111.207 111.207 64.208 462.037C2 C3 C3 C3 C2 1848.150

B - B 64.208 111.207 111.207 111.207 64.208 462.037C --C 64.208 111.207 111.207 111.207 64.208 462.037

=Ʃ 9005.298

REGIDEZ EN LA DIRECCION ( Ky ) NIVEL COLUMNAS TIPO DE COLUMNAS REGIDEZ POR EJE

EJES 0.000 C2 C2 C1EJE - 1 207.303 244.825 244.825 207.303 904.257

1er EJE - 5 207.303 244.825 244.825 207.303 904.257 C2 C3 C3 C2 4521.284

g=6EIf/GAh^2……...(otros)g=0(en columna)

EJE - 2 207.303 244.825 244.825 207.303 904.257EJE - 3 207.303 244.825 244.825 207.303 904.257EJE - 4 207.303 244.825 244.825 207.303 904.257EJES 0.000 C2 C2 0.000

EJE - 1 60.286 110.315 110.315 60.286 341.2022do EJE - 5 60.286 110.315 110.315 60.286 341.202

C2 C3 C3 C2 1706.012EJE - 2 60.286 110.315 110.315 60.286 341.202EJE - 3 60.286 110.315 110.315 60.286 341.202EJE - 4 60.286 110.315 110.315 60.286 341.202EJES 0.000 C2 C2 C1

EJE - 1 60.286 110.315 110.315 60.286 341.2023er EJE - 5 60.286 110.315 110.315 60.286 341.202

C2 C3 C3 C3 1706.012EJE - 2 60.286 110.315 110.315 60.286 341.202EJE - 3 60.286 110.315 110.315 60.286 341.202EJE - 4 60.286 110.315 110.315 60.286 341.202EJES 0.000 C2 C2 C1

EJE - 1 60.286 110.315 110.315 60.286 341.2024to EJE - 5 60.286 110.315 110.315 60.286 341.202

C2 C3 C3 C2 1706.012EJE - 2 60.286 110.315 110.315 60.286 341.202EJE - 3 60.286 110.315 110.315 60.286 341.202EJE - 4 60.286 110.315 110.315 60.286 341.202

=Ʃ 7933.308

CALCULO DE CENTRO DE MASA ( Xcm , Ycm)

valor referencial de : X = 14valor referencial de : Y = 12

peso - x peso - y

NIVEL Fxi Fyi X Y Fxi * X Fxi * Y Xcmi Ycmi

4 183.324 233.661 14 12 2566.5413506 2803.9326545 14 12

3 221.508 325.253 14 12 3101.1163603 3903.0346143 14 12

2 156.130 182.318 14 12 2185.8244566 2187.8170938 14 12

1 130.616 171.466 14 12 1828.6193465 2057.595591 14 12

totalƩ 691.579 912.698 9682.10 10952.38

Xcmi = 14 m

Ycmi = 12 m

CALCULO DE CENTRO DE CARGA ( Xcq , Ycq)

Qx= Fxi=Ʃ 691.579 tonQy= Fyi=Ʃ 912.698 ton

Xcmi= 14.00 m (del primer al cuarto piso)Ycmi= 12.00 m (del primer al cuarto piso)

PISO Fxi(ton) Fyi(ton) Xcmi Ycmi Fyi*Xcmi Fxi*Ycmi Xcq Ycq

4 183.324 233.661 14.00 12.00 3271.255 2199.893 14.000 12.0003 221.508 325.253 14.00 12.00 4553.540 2658.100 14.000 12.0002 156.130 182.318 14.00 12.00 2552.453 1873.564 14.000 12.0001 130.616 171.466 14.00 12.00 2400.528 1567.388 14.000 12.000

totalƩ 691.579 912.698 12777.777 8298.9442

Xcq= (Fyi*Xcmi)/QyƩ

Xcq = 14.000

Ycq= (Fxi*Ycmi)/QxƩ

Ycq 12.000

CALCULO DE CENTRO DE REGIDEZ LATERAL ( CR )

"XCR" PRIMER NIVEL "XCR" SEGUNDO TERCERO Y CUARTO

Xcm= (Fxi*X)/ fxiƩ Ʃ

Ycm= (Fyi*X)/ fyiƩ Ʃ

XCR= (Kyi*Xcg)/ KyiƩ Ʃ XCR= (Kyi*Xcg)/ KyiƩ Ʃ

EJE Kyi(ton/cm) Xcg (Kyi*Xcg) EJE Kyi(ton/cm) Xcg (Kyi*Xcg)K 1 - 1 904.257 0 0 K 1 - 1 341.202 0 0K 2 - 2 904.257 7 6329.797 K 2 - 2 341.202 7 2388.417K 3 - 3 904.257 14 12659.595 K 3 - 3 341.202 14 4776.834K 4 - 4 904.257 21 18989.392 K 4 - 4 341.202 21 7165.252K 5 - 5 904.257 28 25319.190 K 5 - 5 341.202 28 9553.669

=Ʃ 4521.284 63297.974 =Ʃ 1706.012 23884.172

XCR= 14 XCR= 14

"YCR" PRIMER NIVEL "YCR" SEGUNDO TERCERO Y CUARTO

YCR= (Kxi*Xcg)/ KxiƩ Ʃ YCR= (Kxi*Xcg)/ KxiƩ Ʃ

EJE Kxi(ton/cm) Ycg(m) Kxi*Ycg EJE Kxi(ton/cm) Ycg(m) Kxi*YcgK A - A 865.212 0 0.00 K A - A 462.037 0 0.00K B - B 865.212 8 6921.6964173 K B - B 462.037 8 3696.2998206K C - C 865.212 16 13843.392835 K C - C 462.037 16 7392.5996413K D - D 865.212 24 20765.089252 K D - D 462.037 24 11088.899462

=Ʃ 3460.848 41530.179 =Ʃ 1848.150 22177.799

YCR= 12 m YCR= 12 m

ANALISIS EN LA DIRECCION Y-YExentricidad accidental: ea=0.05B (Norma E-030)

B= 28.00 mea= 1.4 m

Exentricidad real(e )

XCR= 14.00Xcq= 14.00

e= 0 me<ea….( hay inversion de momento torsor)Exentricidad reglamentaria(e'1) Exentricidad reglamentaria(e'2)

e'1=e+ea e'2=e-eae'1= 1.4 m e'2= -1.4 m

MOMENTO TORSOR(Mt) MOMENTO TORSOR(Mt)Mt=Qy1*e'1 Mt=Qx1*e'2

e=IXCR-XcqI

Qy1= 912.70 ton Qx1= 912.70 tonMt1= 1277.7776613 ton-m Mt1'= -1277.777661 ton-m

ANALISIS EN LA DIRECCION X-XExentricidad accidental: ea=0.05B (Norma E-030 )

B= 28.00 mea= 1.4 m

Exentricidad real(e )

YCR= 12.00Ycq= 12.000

e= 0.00 me>ea….(hay inversion de momento torsor)Exentricidad reglamentaria(e'1) Exentricidad reglamentaria(e'2)

e'1=e+ea e'2=e-eae'1= 1.4 m e'2= -1.4 m

MOMENTO TORSOR(Mt) MOMENTO TORSOR(Mt)Mt=Qx1*e'1 Mt=Qx1*e'2

Qx1= 233.66 ton Qx1= 233.66 tonMt2= 327.12547636 ton-m Mt2'= -327.1254764 ton-m

CORTANTE DE DISEÑO

CORTANTE DE DISEÑO EN DIRECCION "Y"

XCR= 14 mYCR= 12 m

Ri:Mt1= 1277.778Mt1'= -1277.778

Ky=Ʃ 4521.284 ton/cmQy= 912.698 ton

qi=Ki*Ri*Mt1/ (Ki*Ri^2)Ʃ

Vtras=Qy*Kyi/ kyiƩ

Ri = XCR - Xcg

e=IYcq-YCRI

distancia entre eje y CRton-m(momento torsor en direccion Y)ton-m(momento torsor en direccion Y)

TABLA SISMO EN "Y-Y"

EJE Ri (m) Ki (ton/cm) Ki*Ri^2 (ton-m2/cm) Mt1 (ton-m) Vtras (ton) 0.75Vtrasqi q'i

qi<0.75Vtras qi<0.75Vtras

1 14.000 904.257 12659.595 177234.328 1277.778 -1277.778 182.53966589 136.90474942 22.468 -22.472 7.000 904.257 6329.797 44308.582 1277.778 -1277.778 182.53966589 136.90474942 11.234 -11.233 0.000 904.257 0.000 0.000 1277.778 -1277.778 182.53966589 136.90474942 0.000 0.004 7.000 904.257 6329.797 44308.582 1277.778 -1277.778 182.53966589 136.90474942 11.234 -11.235 14.000 904.257 12659.595 177234.328 1277.778 -1277.778 182.53966589 136.90474942 22.468 -22.47A 12.000 865.212 10382.545 124590.536 1277.778 -1277.778 18.427 -18.43B 4.000 865.212 3460.848 13843.393 1277.778 -1277.778 6.142 -6.14C 4.000 865.212 3460.848 13843.393 1277.778 -1277.778 6.142 -6.14D 12.000 865.212 10382.545 124590.536 1277.778 -1277.778 18.427 -18.43=Ʃ 719953.676 912.69832947 116.544 -116.544

CORTANTE DE DISEÑO EN DIRECCION "X"

XCR= 14 mYCR= 12 m

Ri:Mt2= 327.12547636Mt2'= -327.1254764

Kx=Ʃ 3460.84821 ton/cmQx= 233.66105 ton

qi=Ki*Ri*Mt2/ (Ki*Ri^2)Ʃ q'i=Ki*Ri*Mt2'/ (Ki*Ri^2)Ʃ

Vtras=Qx*Kxi/ KxiƩ

TABLA SISMO EN "X-X"

EJE Ri (m) Ki (ton/cm) Ki*Ri^2 (ton-m2/cm) Mt1 (ton-m) Vtras (ton) 0.75Vtrasqi q'i

qi<0.75Vtras qi<0.75Vtras1 14.000 904.257 12659.595 177234.328 327.125 -327.125 5.7521 -5.7522 7.000 904.257 6329.797 44308.582 327.125 -327.125 2.8761 -2.8763 0.000 904.257 0.000 0.000 327.125 -327.125 0.0000 0.0004 7.000 904.257 6329.797 44308.582 327.125 -327.125 2.8761 -2.8765 14.000 904.257 12659.595 177234.328 327.125 -327.125 5.7521 -5.752

Ki*Ri

(ton-m/cm)Mt1' (ton-

m)

distancia entre eje y CRton-m(momento torsor en direccion X)ton-m(momento torsor en direccion X)

Ki*Ri

(ton-m/cm)Mt1' (ton-

m)

A 12.000 865.212 10382.545 124590.536 327.125 -327.125 58.415263635 43.811447727 4.7175 -4.718B 4.000 865.212 3460.848 13843.393 327.125 -327.125 58.415263635 43.811447727 1.5725 -1.573C 4.000 865.212 3460.848 13843.393 327.125 -327.125 58.415263635 43.811447727 1.5725 -1.573D 12.000 865.212 10382.545 124590.536 327.125 -327.125 58.415263635 43.811447727 4.7175 -4.718=Ʃ 719953.676 233.66105454 29.836 -29.836

5.752 -5.752 22.468 -22.468 205.0082.876 -2.876 11.234 -11.234 193.7740.000 0.000 0.000 0.000 182.5402.876 -2.876 11.234 -11.234 193.7745.752 -5.752 22.468 -22.468 205.0084.718 -4.718 63.1328 18.427 -18.4271.573 -1.573 59.9878 6.142 -6.1421.573 -1.573 59.9878 6.142 -6.1424.718 -4.718 63.1328 18.427 -18.427

qi (sentidos)

q'i (sentidos)

Vdiseño (ton) qi

(sentidos)q'i (sentidos)

Vdiseño (ton)

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