PROJETO EXECUTIVO DE ENGENHARIA

GOVERNO DO ESTADO DE MATO GROSSO

SECRETARIA DE ESTADO DE INFRAESTRUTURA E LOGÍSTICA

SUPERINTENDÊNCIA DE ENGENHARIA

PROJETO EXECUTIVO DE ENGENHARIA

RODOVIA: MT-160

TRECHO: Ponte e Encabeçamento sobre o Rio Sem Informação I

SEGMENTO: Estaca 0+0,000 a 50+0,000

EXTÊNSÃO: 1,00 Km

DIMENSÕES DA PONTE: 38,74m x 8,80m

CÓDIGO SRE: 160EMT0380

ANEXO 3B – RELATÓRIO DE PROJETO OAE

JANEIRO / 2019

GOVERNO DO ESTADO DE MATO GROSSO

SECRETARIA DE ESTADO DE INFRAESTRUTURA E LOGÍSTICA

SUPERINTENDÊNCIA DE ENGENHARIA

PROJETO EXECUTIVO DE ENGENHARIA

RODOVIA: MT-160

TRECHO: Ponte e Encabeçamento sobre o Rio Sem Informação I

SEGMENTO: Estaca 0+0,000 a 50+0,000

EXTÊNSÃO: 1,00 Km

DIMENSÕES DA PONTE: 38,74m x 8,80m

CÓDIGO SRE: 160EMT0380

Direção : SECRETARIA ADJUNTA DE OBRAS RODOVIÁRIAS– SAOR

Coordenação : SUPERINTENDÊNCIA DE PROJETOS - SUPR

Elaboração : CONSÓRCIO VIA MT

Contratante : SECRETARIA DE ESTADO DE INFRAESTRUTURA E LOGÍSTICA - SINFRA

Resp. Técnico : ALEX TADEU COSTA IANNOTTI - CREA: 1408113872

Contrato : 070/2016/00/00-5

Processo : 233120/2016

Edital : Concorrência – Edital Nº 005/2016

ANEXO 3B – RELATÓRIO DE PROJETO OAE

JANEIRO / 2019

Anexo 3B Volume Único Relatório do Projeto

Projeto Executivo de Ponte e Encabeçamento sobre o Rio Sem Informação I

1. APRESENTAÇÃO O Consórcio ENECON-EPC-RSI (Consórcio Via MT) apresenta o Volume 4 –

Orçamento do Projeto e Documentos para Concorrências referente a

elaboração do PROJETO EXECUTIVO DE IMPLANTAÇÃO E

PAVIMENTAÇÃO DA RODOVIA MT 160, TRECHO: PONTE E

ENCABEÇAMENTO SOBRE O RIO SEM INFORMAÇÃO I, com extensão de

1,00 km, em atendimento ao contrato assinado com a SECRETARIA DE

ESTADO DE INFRAESTRUTURA E LOGÍSTICA – SINFRA no Estado de Mato

Grosso.

Os principais dados contratuais são:

EDITAL: Concorrência – Edital Nº

005/2016

Nº DO PROCESSO: 233120/2016

DATA DA LICITAÇÃO: 17 de agosto de 2016

DATA DA ASSINATURA DO CONTRATO: 22 de dezembro de 2016

CONTRATO Nº: 070/2016/00/00-5

PRAZO CONTRATUAL: 720 dias

O presente documento contém as memórias de cálculos e quantidades da

ponte ser utilizada no projeto em questão. O projeto do trecho é composto

pelos seguintes volumes:

• Volume 1 – Relatório do Projeto e Documentos para Concorrências –

formato A4;

• Volume 2 – Projeto de Execução– formato A3;

• Volume 2c – Projeto de Exceção OAE

• Volume 3A – Estudos Geotécnicos;

• Anexo 3B – Relatório de Projeto OAE

• Anexo 3C- Notas de Serviço e Cálculo de Volume – formato A4;

• Volume 4 – Orçamentos – formato A4.

1



2. MAPA DE SITUAÇÃO

2



3. MEMÓRIA DE CÁLCULO 3.1.1. Objetivo

Esta Memória de Cálculo tem por objetivo apresentar o

dimensionamento estrutural da Ponte Rio Sem Informação 1, localizada na

rodovia MT-160, nas coordenadas 09°56'48.55"S / 57° 05'16.23"O.

Os esforços foram obtidos com o auxílio do software SAP-2000, que

utiliza em sua base de cálculo o Método dos Elementos Finitos e para

dimensionamento das estruturas foram utilizadas tabelas de cálculo do Excel.

3.1.2. SISTEMA DE UNIDADES

Nesta memória foi adotado o Sistema Internacional de Unidades. Todas

as elevações são dadas em metros.

3.1.3. PARÂMETROS ADOTADOS

Apresentam-se a seguir os parâmetros adotados para o Concreto e Aço:

CONCRETO DA SUPERESTRUTURA Resistência à Compressão ............. ........................ ............... fck = 30MPa Módulo de Elasticidade ............. ......................... ............... Ec = 26,07GPa

Coeficiente de Poisson ............. ....................................... ............... = 0,2

Peso Específico ............. ......................................... ............... = 25 kN/m³ CONCRETO DAS LONGARINAS PREMOLDADAS Resistência à Compressão ............. ........................ ............... fck = 40MPa Módulo de Elasticidade ............. ......................... ............... Ec = 30,10GPa


Peso Específico ............. ......................................... ............... = 25 kN/m³ CONCRETO DA MESOESTRUTURA Resistência à Compressão ............. ........................ ............... fck = 25MPa Módulo de Elasticidade ............. ......................... ............... Ec = 23,80GPa


Peso Específico ............. ......................................... ............... = 25 kN/m³

3



CONCRETO DA INFRAESTRUTURA Resistência à Compressão ............. ........................ ............... fck = 20MPa Módulo de Elasticidade ............. ......................... ............... Ec = 21,29GPa


Peso Específico ............. ......................................... ............... = 25 kN/m³ Sendo o módulo de elasticidade calculado conforme o item 8.2.8 da NBR-6118/14:

ckCIfE = 600.585,0 , onde ECI e fck são dados em MPa.

AÇO CA-50 Módulo de Elasticidade ……………………………...………………Ec = 210 GPa

Módulo de Poisson……………………………………………….............….. = 0,3 fy ......................................................................................................... 500 MPa

4



3.2. MODELO ESTRUTURAL

5



6



3.3. METODOLOGIA

Para o cálculo dos esforços foi utilizado o software SAP2000 e para o

dimensionamento das armaduras foram utilizadas planilhas de cálculo do

Excel. Inicialmente foi criado um modelo tridimensional conforme apresentado

a seguir:

7



3.4. CARREGAMENTOS

3.4.1. PESO PRÓPRIO (DEAD) PPLONG = peso próprio das longarinas pré-moldadas PPTAB = peso próprio do tabuleiro DEAD = PPLONG + PPTAB + peso próprio da meso e infraestrutura

Considerou-se o peso próprio em toda estrutura, na direção vertical (Z). 3.4.2. CARGA DE REVESTIMENTO (REV) Considerou-se a carga de revestimento no valor de 2,0kN/m² em todo tabuleiro.

REV – Vão de 30m

8



3.4.3. CARGA DE RECAPEAMENTO (REC) Considerou-se a carga de recapeamento no valor de 2,0kN/m² em todo tabuleiro.

REC – Vão de 30m

9



3.4.4. SOBRECARGA – 1 (SC1) Considerou-se a carga de multidão no valor de 5kN/m² em todo tabuleiro.

SC1 – Vão de 30m

10



3.4.5. SOBRECARGA – 2 (SC2) Considerou-se a carga de multidão no valor de 5kN/m² em metade do tabuleiro.

SC2 – Vão de 30m

11



3.4.6. SOBRECARGA – 3 (SC3) Considerou-se a carga de multidão no valor de 5kN/m² nos vão das vigas centrais.

SC3 – Vão de 30m

12



3.4.7. SOBRECARGA – 4 (SC4) Considerou-se a carga de multidão no valor de 5kN/m² no vão de uma viga central.

SC4 – Vão de 30m

13



3.4.8. SOBRECARGA – 5 (SC5) Considerou-se a carga de multidão no valor de 5kN/m² nos balanços.

SC5 – Vão de 30m

14



3.4.9. SOBRECARGA – 6 (SC6) Considerou-se a carga de multidão no valor de 5kN/m².

SC6 – Vão de 30m

15



3.4.10. PESO PRÓPRIO DO NEW JERSEY (PPNJ) Considerou-se a carga do New Jersey distribuída nas laterais da ponte no valor de 5,8 kN/m.

Figura 4.9–PPNJ 3.4.11. MOVE 1

Foi utilizado o Trem Tipo TB-450 kN conforme a NBR 7188:2013, que admite que a região em que o trem tipo está presente não há necessidade de considerar a sobrecarga, deste modo houve a redução do TB-450 kN para cargas de 60 kN para a simulação de tráfego. Neste caso o Trem Tipo foi aplicado no centro da ponte de forma a se deslocar longitudinalmente.

MOVE 1

16



MOVE 1

3.4.12. MOVE 2

Foi utilizado o Trem Tipo TB-450 kN conforme a NBR 7188:2013, que admite que a região em que o trem tipo está presente não há necessidade de considerar a sobrecarga, deste modo houve a redução do TB-450 kN para cargas de 60 kN para a simulação de tráfego. Neste caso o Trem Tipo foi aplicado a 0,6m do eixo da ponte de forma a se deslocar longitudinalmente.

MOVE 2

17



MOVE 2

3.4.13. MOVE 3


MOVE 3

18



MOVE 3

3.4.14. MOVE 4


MOVE 4

19



MOVE 4

3.4.15. MOVE 5


MOVE 5

20



MOVE 5

3.4.16. MOVE 6


MOVE 6

21



MOVE 6

3.4.17. VENTO (VT)

Foram lançadas cargas de vento no valor de 3,7kN/m em toda a extensão longitudinal da ponte.

H T

OT

AL 200

h

V 1 kN/m2

h 1,7 m

H(total) 3,7 m

F(resultante) 3,7 kN/m

VENTO

22



VT

3.4.18. FRENAGEM (FREN)

Foram lançadas cargas de frenagem no valor de 0,256kN/m² em toda a extensão da ponte.

FREN

LARGURA (B) 8.8 m

CNF 1 adm

COMP. TOTAL 60 m

135 kN

0.255682 kN/m²

FRENAGEM

ADOTADO

23



3.4.19. TEMPERATURA (TEMP1)

Foi lançado um gradiente de temperatura no valor de 5°C/m em todo o tabuleiro da ponte.

TEMP1

3.4.20. TEMPERATURA (TEMP2)

Foi lançada variação de temperatura homogênea no valor de 15ºC em toda a seção da ponte.

TEMP2

24



3.4.21. COEFICIENTE DE IMPACTO

Vão de 30m - Foi considerado coeficiente de impacto no valor de 1,581 nas regiões onde existem juntas e 1,265 para as demais regiões.

COEFICIENTE DE IMPACTO – Vão de 30m

VÃO L(m) N° DE FAIXAS

30 2

CIV 1.265 1.265

CNF 1 1

CIA 1 1.25

COEF. ADOTADO 1.265 1.581

25



3.4.22. EMPUXO DE SOLO SATURADO + EMPUXO DEVIDO À SOBRECARGA (EMP)

Foram lançados esforços de empuxo de solo saturado e empuxo devido à

sobrecarga, considerou-se ka=0,33, s=18kN/m³ e q=10kN/m².

EMP(força)

EMP(momento)

26



3.4.23. REAÇÃO DA LAJE DE TRANSIÇÃO (LT)

Foi lançada a reação da somatória dos carregamentos acidentais e permanentes sobre a cortina da travessa.

LT

27



3.5. PROTENSÃO (PROT) – VÃO DE 30m 3.5.1. SEÇÕES E DADOS DE ENTRADA

3.5.2. DEFORMAÇÃO INSTANTÂNEA DO CONCRETO

V S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16

x(m) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 14.50

h(m) 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40

Ix(m4) 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085

Iy(m4) 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005

yg inf(m) (base) 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651

ygsup(m) (topo) 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749

Wsup(m³) 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114

Winf(m³) 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131 0.131

A(m²) 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336

SEÇÕES DA PONTE

Dados

Nº de cabos 26

Cordoalha 1f15,2

Pi(tf) 19.80

Pi+acom(tf) 19.24

As(cm²) 1.40

Ep(tf/m²) 1.95E+07

(atrito) 0.00

Comp. Cabo(m) 29.50

acom(mm) 6.0

Perda acom(tf) 0.56

fck(MPa) 35

k 0

kL 0

Area seção (cm²) 3363.00

Aço CP190RB

fptk(t/m²) 190000

0,6 fptk (%) 1.5

0,7 fptk (%) 2.5

0,8 fptk (%) 3.5

Ec(kN/m²) 28160540

Ep(kN/m²) 1.95E+08

ap 6.924583

DsP0(tf/cm²) 0.515136

DP0(tf) 18.75097

Perda DI (%) 3.74747

28



3.5.3. PESO PRÓPRIO DA ESTRUTURA

Vão 29

Peso(tf/m) 0.84075

x(m) V M Topo Base

S1 0.00 12.19088 0 0 0

S2 1.00 11.35013 11.7705 -103.475 89.93657

S3 2.00 10.50938 22.70025 -199.56 173.4491

S4 3.00 9.668625 32.78925 -288.253 250.5376

S5 4.00 8.827875 42.0375 -369.555 321.202

S6 5.00 7.987125 50.445 -443.466 385.4424

S7 6.00 7.146375 58.01175 -509.986 443.2588

S8 7.00 6.305625 64.73775 -569.115 494.6511

S9 8.00 5.464875 70.623 -620.852 539.6194

S10 9.00 4.624125 75.6675 -665.199 578.1636

S11 10.00 3.783375 79.87125 -702.155 610.2838

S12 11.00 2.942625 83.23425 -731.719 635.98

S13 12.00 2.101875 85.7565 -753.892 655.2521

S14 13.00 1.261125 87.438 -768.674 668.1002

S15 14.00 0.420375 88.27875 -776.066 674.5243

S16 14.50 0 88.38384 -776.989 675.3273

PARA VIGA BI-APOIADA - PPLONG

Vão 29

Peso(tf/m) 0.9

x(m) V M Topo Base

S1 0.00 13.05 0 0 0

S2 1.00 12.15 12.6 -110.768 96.27465

S3 2.00 11.25 24.3 -213.623 185.6725

S4 3.00 10.35 35.1 -308.567 268.1937

S5 4.00 9.45 45 -395.599 343.838

S6 5.00 8.55 54 -474.718 412.6056

S7 6.00 7.65 62.1 -545.926 474.4965

S8 7.00 6.75 69.3 -609.222 529.5106

S9 8.00 5.85 75.6 -664.606 577.6479

S10 9.00 4.95 81 -712.077 618.9085

S11 10.00 4.05 85.5 -751.637 653.2923

S12 11.00 3.15 89.1 -783.285 680.7993

S13 12.00 2.25 91.8 -807.021 701.4296

S14 13.00 1.35 93.6 -822.845 715.1831

S15 14.00 0.45 94.5 -830.757 722.0599

S16 14.50 0 94.6125 -831.746 722.9195

PARA VIGA BI-APOIADA - PPTAB

29



tf/m²

X Topo Base

0.00 0.00 0.00

1.00 -214.24 186.21

2.00 -413.18 359.12

3.00 -596.82 518.73

4.00 -765.15 665.04

5.00 -918.18 798.05

6.00 -1055.91 917.76

7.00 -1178.34 1024.16

8.00 -1285.46 1117.27

9.00 -1377.28 1197.07

10.00 -1453.79 1263.58

11.00 -1515.00 1316.78

12.00 -1560.91 1356.68

13.00 -1591.52 1383.28

14.00 -1606.82 1396.58

14.50 -1608.74 1398.25

PP

30



3.5.4. ALONGAMENTOS, PERDAS DE ATRITO E ACOMODAÇÃO DOS CABOS

CABO C1

X Y a(rad) Da(rad) Comp.Real(m) Scomp.Real(m) sP0/sPi P0 Panc(tf) Acomod.(mm) P Pfinal

0.00 0.04 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 0.04 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

2.00 0.04 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

3.00 0.04 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

4.00 0.04 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 0.04 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 0.04 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 0.04 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 0.04 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 0.04 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 0.04 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 0.04 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 0.04 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 0.04 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 0.04 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 0.04 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 1

Normal (tf) Cortante (tf) M (tf.m) Área (m²) Wsup (m³) Winf (m³) yg,topo(m) scsup scinf h x (cm) sP0,cabo sPg,cabo

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 1.106328 -8.9E-08 0

9.90 0.00 7.02 0.34 0.11 0.13 0.75 -91.14 24.19 1.40 1.106328 -87.8481 -202.801461

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -391.117104

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -564.946928

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -724.290933

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -869.14912

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -999.521488

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -1115.40804

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -1216.80877

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -202.801461

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -391.117104

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -564.946928

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -724.290933

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -869.14912

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -999.521488

19.24 0.00 13.64 0.34 0.11 0.13 0.75 -177.18 47.03 1.40 1.106328 -170.769 -1115.40804

31



CABO C2

X Y a(rad) Da(rad) Comp.Real(m) Scomp.Real(m) sP0/sPi P0 Panc(tf) Acomodação(mm) P Pfinal

0.00 0.09 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 0.09 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

2.00 0.09 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

3.00 0.09 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

4.00 0.09 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 0.09 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 0.09 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 0.09 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 0.09 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 0.09 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 0.09 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 0.09 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 0.09 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 0.09 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 0.09 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 0.09 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 2


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 1.133439 -8.1E-08 0

9.90 0.00 6.52 0.34 0.11 0.13 0.75 -86.79 20.41 1.40 1.133439 -79.9002 -188.5

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -363.535

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -525.106

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -673.213

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -807.855

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -929.033

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1036.75

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1131

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1211.78

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1279.1

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1332.96

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1373.35

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1400.28

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1413.75

19.24 0.00 12.68 0.34 0.11 0.13 0.75 -168.72 39.68 1.40 1.133439 -155.319 -1415.43

32



CABO C3


0.00 1.25 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.25 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

2.00 1.25 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

3.00 1.25 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

4.00 1.25 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 1.25 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 1.25 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 1.25 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 1.25 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 1.25 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 1.25 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 1.25 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.25 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.25 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.25 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.25 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 3

Normal (tf) Cortante (tf)M (tf.m) Área (m²) Wsup (m³) Winf (m³)yg,topo(m) scsup scinf h x (cm) sP0,cabo sPg,cabo

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.243321 -5.9E-07 0

9.90 0.00 -4.96 0.34 0.11 0.13 0.75 14.16 -67.34 1.40 0.243321 -58.6036 143.3054

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 276.3747

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 399.2079

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 511.805

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 614.166

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 706.2909

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 788.1797

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 859.8324

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 921.249

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 972.4295

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 1013.374

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 1044.082

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 1064.554

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 1074.791

19.24 0.00 -9.64 0.34 0.11 0.13 0.75 27.54 -130.90 1.40 0.243321 -113.92 1076.07

33



CABO C4

CABO C5


0.00 1.30 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.30 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

2.00 1.30 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

3.00 1.30 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

4.00 1.30 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 1.30 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 1.30 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 1.30 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 1.30 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 1.30 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 1.30 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 1.30 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.30 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.30 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.30 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.30 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 4


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.289208 -6.5E-08 0

9.90 0.00 -5.45 0.34 0.11 0.13 0.75 18.52 -71.12 1.40 0.289208 -64.7156 157.6073

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 303.957

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 439.049

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 562.8834

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 675.46

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 776.779

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 866.8404

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 945.644

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1013.19

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1069.478

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1114.509

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1148.282

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1170.797

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1182.055

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1183.462


0.00 1.35 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.35 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

2.00 1.35 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

3.00 1.35 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

4.00 1.35 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 1.35 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 1.35 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 1.35 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 1.35 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 1.35 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 1.35 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 1.35 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.35 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.35 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.35 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.35 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 5

34



CABO C6


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 0

9.90 0.00 -5.95 0.34 0.11 0.13 0.75 22.87 -74.90 1.40 0.327461 -71.4085 171.9093

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 331.5393

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 478.8901

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 613.9617

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 736.754

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 847.2672

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 945.501

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1031.456

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1105.131

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1166.527

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1215.644

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1252.482

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1277.04

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1289.32

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1290.854


0.00 1.30 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.30 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

2.00 1.30 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

3.00 1.30 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

4.00 1.30 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

5.00 1.30 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

6.00 1.30 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 1.30 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 1.30 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 1.30 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 1.30 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 1.30 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.30 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.30 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.30 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.30 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 6


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.289208 -6.5E-09 0

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.289208 -6.5E-09 157.6073

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.289208 -6.5E-09 303.957

9.90 0.00 -5.45 0.34 0.11 0.13 0.75 18.52 -71.12 1.40 0.289208 -64.7156 439.049

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 562.8834

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 675.46

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 776.779

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 866.8404

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 945.644

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1013.19

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1069.478

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1114.509

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1148.282

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1170.797

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1182.055

19.24 0.00 -10.60 0.34 0.11 0.13 0.75 35.99 -138.25 1.40 0.289208 -125.802 1183.462

35



CABO C7

CABO C8


0.00 1.35 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.35 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

2.00 1.35 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

3.00 1.35 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

4.00 1.35 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

5.00 1.35 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

6.00 1.35 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

7.00 1.35 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

8.00 1.35 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

9.00 1.35 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

10.00 1.35 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

11.00 1.35 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.35 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.35 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.35 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.35 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 7


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 0

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 171.9093

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 331.5393

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 478.8901

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-08 613.9617

9.90 0.00 -5.95 0.34 0.11 0.13 0.75 22.87 -74.90 1.40 0.327461 -71.4085 736.754

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 847.2672

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 945.501

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1031.456

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1105.131

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1166.527

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1215.644

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1252.482

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1277.04

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1289.32

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1290.854


0.00 1.35 0 0 0.00 0.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

1.00 1.35 0 0 1.00 1.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

2.00 1.35 0 0 1.00 2.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

3.00 1.35 0 0 1.00 3.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

4.00 1.35 0 0 1.00 4.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

5.00 1.35 0 0 1.00 5.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

6.00 1.35 0 0 1.00 6.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

7.00 1.35 0 0 1.00 7.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

8.00 1.35 0 0 1.00 8.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

9.00 1.35 0 0 1.00 9.00 1.00 19.24 19.24 0.00 CORRIGIR 0.00

10.00 1.35 0 0 1.00 10.00 1.00 19.24 19.24 0.00 CORRIGIR 9.90

11.00 1.35 0 0 1.00 11.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

12.00 1.35 0 0 1.00 12.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

13.00 1.35 0 0 1.00 13.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.00 1.35 0 0 1.00 14.00 1.00 19.24 19.24 0.00 CORRIGIR 19.24

14.50 1.35 0 0 0.50 14.50 1.00 19.24 19.24 0.00 CORRIGIR 19.24

Cabo 8

36



3.5.5. RESUMO DAS PERDAS INICIAIS


0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 0

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 171.9093

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 331.5393

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 478.8901

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 613.9617

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 736.754

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 847.2672

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 945.501

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 1031.456

0.00 0.00 0.00 0.34 0.11 0.13 0.75 0.00 0.00 1.40 0.327461 -7.2E-07 1105.131

9.90 0.00 -5.95 0.34 0.11 0.13 0.75 22.87 -74.90 1.40 0.327461 -71.4085 1166.527

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1215.644

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1252.482

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1277.04

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1289.32

19.24 0.00 -11.57 0.34 0.11 0.13 0.75 44.45 -145.60 1.40 0.327461 -138.812 1290.854

n 2 2 2 4 6 6 2 2

X(m) Cabo1 Cabo2 Cabo3 Cabo4 Cabo5 Cabo6 Cabo7 Cabo8 Po,at+ac (t) % restante(at.+ac) %perda retr.inic % restante inicial,total Po (t)

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.75 -3.75 -19.29

1 9.90 9.90 9.90 9.90 9.90 0.00 0.00 0.00 158.40 30.77 3.75 27.02 139.11

2 19.24 19.24 19.24 19.24 19.24 0.00 0.00 0.00 307.92 59.81 3.75 56.07 288.62

3 19.24 19.24 19.24 19.24 19.24 9.90 0.00 0.00 367.32 71.35 3.75 67.60 348.02

4 19.24 19.24 19.24 19.24 19.24 19.24 0.00 0.00 423.38 82.24 3.75 78.50 404.09

5 19.24 19.24 19.24 19.24 19.24 19.24 9.90 0.00 443.18 86.09 3.75 82.34 423.89

6 19.24 19.24 19.24 19.24 19.24 19.24 19.24 0.00 461.87 89.72 3.75 85.97 442.58

7 19.24 19.24 19.24 19.24 19.24 19.24 19.24 0.00 461.87 89.72 3.75 85.97 442.58

8 19.24 19.24 19.24 19.24 19.24 19.24 19.24 0.00 461.87 89.72 3.75 85.97 442.58

9 19.24 19.24 19.24 19.24 19.24 19.24 19.24 0.00 461.87 89.72 3.75 85.97 442.58

10 19.24 19.24 19.24 19.24 19.24 19.24 19.24 9.90 481.67 93.57 3.75 89.82 462.38

11 19.24 19.24 19.24 19.24 19.24 19.24 19.24 19.24 500.36 97.20 3.75 93.45 481.07

12 19.24 19.24 19.24 19.24 19.24 19.24 19.24 19.24 500.36 97.20 3.75 93.45 481.07

13 19.24 19.24 19.24 19.24 19.24 19.24 19.24 19.24 500.36 97.20 3.75 93.45 481.07

14 19.24 19.24 19.24 19.24 19.24 19.24 19.24 19.24 500.36 97.20 3.75 93.45 481.07

14.5 19.24 19.24 19.24 19.24 19.24 19.24 19.24 19.24 500.36 97.20 3.75 93.45 481.07

PROTENSÃO

37



3.5.6. PERDAS PROGRESSIVAS CÁLCULO DA FLUÊNCIA E RETRAÇÃO

CABO C1

Ac (cm²) 3363

u (cm) 464.24

h0 (cm) 14.4882

e (tabela) -0.00033

j (tabela) 2.2

Retração e Fluência

n 4 tf,m

X(m)

sP0,cabo sPg,cabo DsP,c+s+r sPg0 sP % fptk Relax (%) DsPrel,∞ DsP,c+s+r sP % fptk Relax (%) DsPrel,∞ DsP,c+s+r sP % fptk Relax (%) sP final P final

0 0.00 0.00 -5985.64 6.88E-05 -1795.69 -0.01 -4.6 288.761259 -6254.23 -1876.27 -0.01 -4.6 301.9975 -6266.55 -1879.96 -0.01 -4.6 -6266.55 -0.87732

1 -351.39 -202.80 -13838.72 69468.6 65316.99 0.34 -1.1 -2428.4354 -11579.9 65994.65 0.35 -1.0 -2371.25 -11633.1 65978.69 0.35 -1.0 56431.23 7.900373

2 -683.08 -391.12 -21207.26 135019.4 128657.3 0.68 2.3 10228.2771 -30721.3 125803 0.66 2.1 9339.926 -29895 126050.9 0.66 2.1 102416.1 14.33826

3 -683.08 -564.95 -23670.47 136223.1 129122 0.68 2.3 10375.7636 -33321.7 126226.6 0.66 2.1 9469.865 -32479 126479.4 0.67 2.2 99832.06 13.97649

4 -683.08 -724.29 -25928.42 137326.5 129548 0.68 2.3 10511.6585 -35706 126614.7 0.67 2.2 9589.496 -34848.3 126872 0.67 2.2 97462.83 13.6448

5 -683.08 -869.15 -27981.10 138329.6 129935.3 0.68 2.3 10635.7795 -37874.2 126967.3 0.67 2.2 9698.683 -37002.5 127228.8 0.67 2.2 95308.59 13.3432

6 -683.08 -999.52 -29828.51 139232.4 130283.8 0.69 2.4 10747.9609 -39825.9 127284.6 0.67 2.2 9797.302 -38941.7 127549.9 0.67 2.2 93369.45 13.07172

7 -683.08 -1115.41 -31470.66 140034.8 130593.6 0.69 2.4 10848.0534 -41561.2 127566.5 0.67 2.2 9885.241 -40665.6 127835.2 0.67 2.2 91645.5 12.83037

8 -683.08 -1216.81 -32907.53 140737 130864.7 0.69 2.4 10935.9245 -43079.8 127813.1 0.67 2.2 9962.404 -42174.3 128084.7 0.67 2.2 90136.85 12.61916

9 -683.08 -202.80 -18538.77 133715.4 128153.8 0.67 2.2 10069.3981 -27905 125343.9 0.66 2.1 9199.828 -27096.2 125586.6 0.66 2.1 105214.9 14.73009

10 -683.08 -391.12 -21207.26 135019.4 128657.3 0.68 2.3 10228.2771 -30721.3 125803 0.66 2.1 9339.926 -29895 126050.9 0.66 2.1 102416.1 14.33826

11 -683.08 -564.95 -23670.47 136223.1 129122 0.68 2.3 10375.7636 -33321.7 126226.6 0.66 2.1 9469.865 -32479 126479.4 0.67 2.2 99832.06 13.97649

12 -683.08 -724.29 -25928.42 137326.5 129548 0.68 2.3 10511.6585 -35706 126614.7 0.67 2.2 9589.496 -34848.3 126872 0.67 2.2 97462.83 13.6448

13 -683.08 -869.15 -27981.10 138329.6 129935.3 0.68 2.3 10635.7795 -37874.2 126967.3 0.67 2.2 9698.683 -37002.5 127228.8 0.67 2.2 95308.59 13.3432

14 -683.08 -999.52 -29828.51 139232.4 130283.8 0.69 2.4 10747.9609 -39825.9 127284.6 0.67 2.2 9797.302 -38941.7 127549.9 0.67 2.2 93369.45 13.07172

14.5 -683.08 -1115.41 -31470.66 140034.8 130593.6 0.69 2.4 10848.0534 -41561.2 127566.5 0.67 2.2 9885.241 -40665.6 127835.2 0.67 2.2 91645.5 12.83037

Relaxação, Retração e Fluência

Cabo1

38



CABO C2

CABO C3

CABO C4

CABO C5

n 4 tf,m

X(m)


0 0.00 0.00 -6023.69 6.87518E-05 -1807.11 -0.01 -4.6 290.6352 -6295.75 -1888.73 -0.01 -4.6 304.0456 -6308.31 -1892.49 -0.01 -4.6 -6308.31 -0.88316

1 -319.60 -188.50 -13269.39 69369.56976 65388.75 0.34 -1.1 -2422.46 -11001.8 66069.04 0.35 -1.0 -2364.87 -11055.7 66052.87 0.35 -1.0 57008.61 7.981205

2 -621.28 -363.53 -20067.47 134828.432 128808.2 0.68 2.3 10276.09 -29686.7 125922.4 0.66 2.1 9376.476 -28844.6 126175 0.66 2.1 103466.5 14.48531

3 -621.28 -525.11 -22371.53 135947.2439 129235.8 0.68 2.3 10412 -32118 126311.8 0.66 2.1 9496.086 -31260.7 126569 0.67 2.2 101050.5 14.14706

4 -621.28 -673.21 -24483.59 136972.8216 129627.7 0.68 2.3 10537.17 -34347.3 126668.6 0.67 2.2 9606.167 -33475.8 126930.1 0.67 2.2 98835.35 13.83695

5 -621.28 -807.86 -26403.64 137905.1649 129984.1 0.68 2.3 10651.46 -36374.3 126992.9 0.67 2.2 9706.605 -35489.8 127258.2 0.67 2.2 96821.28 13.55498

6 -621.28 -929.03 -28131.68 138744.2739 130304.8 0.69 2.4 10754.72 -38199 127284.6 0.67 2.2 9797.296 -37302.8 127553.4 0.67 2.2 95008.34 13.30117

7 -621.28 -1036.75 -29667.73 139490.1485 130589.8 0.69 2.4 10846.82 -39821.2 127543.8 0.67 2.2 9878.145 -38914.5 127815.8 0.67 2.2 93396.62 13.07553

8 -621.28 -1131.00 -31011.76 140142.7888 130839.3 0.69 2.4 10927.65 -41241 127770.5 0.67 2.2 9949.069 -40324.9 128045.3 0.67 2.2 91986.19 12.87807

9 -621.28 -1211.78 -32163.79 140702.1948 131053.1 0.69 2.4 10997.12 -42458 127964.8 0.67 2.2 10010 -41534 128242 0.67 2.2 90777.12 12.7088

10 -621.28 -1279.10 -33123.82 141168.3665 131231.2 0.69 2.4 11055.14 -43472.4 128126.7 0.67 2.2 10060.86 -42541.6 128405.9 0.68 2.3 89769.48 12.56773

11 -621.28 -1332.96 -33891.84 141541.3038 131373.8 0.69 2.4 11101.64 -44283.9 128256.1 0.68 2.3 10101.62 -43347.8 128537 0.68 2.3 88963.31 12.45486

12 -621.28 -1373.35 -34467.85 141821.0068 131480.7 0.69 2.4 11136.57 -44892.6 128353.2 0.68 2.3 10132.22 -43952.5 128635.3 0.68 2.3 88358.65 12.37021

13 -621.28 -1400.28 -34851.86 142007.4755 131551.9 0.69 2.4 11159.87 -45298.4 128417.9 0.68 2.3 10152.64 -44355.6 128700.8 0.68 2.3 87955.52 12.31377

14 -621.28 -1413.75 -35043.87 142100.7098 131587.5 0.69 2.4 11171.54 -45501.4 128450.3 0.68 2.3 10162.86 -44557.1 128733.6 0.68 2.3 87753.96 12.28555

14.5 -621.28 -1415.43 -35067.87 142112.3641 131592 0.69 2.4 11172.99 -45526.7 128454.3 0.68 2.3 10164.13 -44582.3 128737.7 0.68 2.3 87728.76 12.28203


Cabo2

n 22 tf,m

X(m)


0 0.00 0.00 -5045.28 0.000688 -1513.58 -0.01 -4.6 242.6097 -5235.5 -1570.65 -0.01 -4.6 251.9216 -5242.8 -1572.84 -0.01 -4.6 -5242.8 -0.73399

1 -1289.28 143.31 -18732.91 67071.96 61452.09 0.32 -1.3 -2722.25 -16598.6 62092.39 0.33 -1.2 -2677.38 -16633.7 62081.84 0.33 -1.2 51430.55 7.200277

2 -2506.25 276.37 -31679.11 130397.3 120893.6 0.64 1.9 7882.108 -37859 119039.6 0.63 1.8 7354.689 -37445.5 119163.7 0.63 1.8 94865.64 13.28119

3 -2506.25 399.21 -30211.98 129546.8 120483.2 0.63 1.8 7764.257 -36299.4 118656.9 0.62 1.7 7247.392 -35894.2 118778.5 0.63 1.8 96416.9 13.49837

4 -2506.25 511.81 -28867.10 128767.1 120106.9 0.63 1.8 7656.772 -34870.3 118306 0.62 1.7 7149.474 -34472.6 118425.3 0.62 1.7 97838.54 13.6974

5 -2506.25 614.17 -27644.49 128058.3 119764.9 0.63 1.8 7559.511 -33571.4 117986.8 0.62 1.7 7060.823 -33180.4 118104.1 0.62 1.7 99130.66 13.87829

6 -2506.25 706.29 -26544.15 127420.3 119457.1 0.63 1.8 7472.344 -32402.7 117699.5 0.62 1.7 6981.333 -32017.8 117815 0.62 1.7 100293.3 14.04107

7 -2506.25 788.18 -25566.06 126853.3 119183.5 0.63 1.8 7395.156 -31364.1 117444 0.62 1.7 6910.912 -30984.5 117557.9 0.62 1.7 101326.6 14.18573

8 -2506.25 859.83 -24710.23 126357.1 118944.1 0.63 1.8 7327.842 -30455.5 117220.5 0.62 1.7 6849.477 -30080.5 117333 0.62 1.7 102230.6 14.31229

9 -2506.25 921.25 -23976.67 125931.8 118738.8 0.62 1.7 7270.313 -29676.9 117028.8 0.62 1.7 6796.953 -29305.7 117140.1 0.62 1.7 103005.4 14.42075

10 -2506.25 972.43 -23365.36 125577.4 118567.8 0.62 1.7 7222.49 -29028.1 116869 0.62 1.7 6753.28 -28660.2 116979.4 0.62 1.7 103650.9 14.51113

11 -2506.25 1013.37 -22876.32 125293.9 118431 0.62 1.7 7184.31 -28509.1 116741.2 0.61 1.6 6718.403 -28143.8 116850.8 0.62 1.7 104167.3 14.58342

12 -2506.25 1044.08 -22509.53 125081.3 118328.4 0.62 1.7 7155.72 -28119.9 116645.3 0.61 1.6 6692.283 -27756.5 116754.3 0.61 1.6 104554.6 14.63764

13 -2506.25 1064.55 -22265.01 124939.5 118260 0.62 1.7 7136.681 -27860.4 116581.4 0.61 1.6 6674.886 -27498.4 116690 0.61 1.6 104812.7 14.67378

14 -2506.25 1074.79 -22142.75 124868.6 118225.8 0.62 1.7 7127.169 -27730.7 116549.4 0.61 1.6 6666.194 -27369.3 116657.8 0.61 1.6 104941.8 14.69185

14.5 -2506.25 1076.07 -22127.47 124859.8 118221.5 0.62 1.7 7125.98 -27714.5 116545.4 0.61 1.6 6665.107 -27353.2 116653.8 0.61 1.6 104957.9 14.69411


Cabo3

n 22 tf,m

X(m)


0 0.00 0.00 -4934.15 6.87518E-05 -1480.24 -0.01 -4.6 237.1748 -5116.01 -1534.8 -0.01 -4.6 246.0706 -5122.83 -1536.85 -0.01 -4.6 -5122.83 -0.7172

1 -1423.74 157.61 -19723.88 66972.92397 61055.76 0.32 -1.3 -2749.27 -17615.8 61688.18 0.32 -1.3 -2705.88 -17649.1 61678.2 0.32 -1.3 50415.19 7.058127

2 -2767.63 303.96 -33712.35 130206.3294 120092.6 0.63 1.8 7652.693 -39580.2 118332.3 0.62 1.7 7156.795 -39200 118446.3 0.62 1.7 93111.15 13.03556

3 -2767.63 439.05 -32134.34 129270.8735 119630.6 0.63 1.8 7521.426 -37901.5 117900.4 0.62 1.7 7036.883 -37530 118011.9 0.62 1.7 94781.11 13.26936

4 -2767.63 562.88 -30687.83 128413.3723 119207 0.63 1.8 7401.788 -36363.3 117504.4 0.62 1.7 6927.524 -35999.6 117613.5 0.62 1.7 96311.47 13.48361

5 -2767.63 675.46 -29372.83 127633.8258 118822 0.63 1.8 7293.601 -34965.3 117144.2 0.62 1.7 6828.571 -34608.8 117251.2 0.62 1.7 97702.35 13.67833

6 -2767.63 776.78 -28189.32 126932.2339 118475.4 0.62 1.7 7196.699 -33707.5 116820 0.61 1.6 6739.894 -33357.3 116925.1 0.62 1.7 98953.85 13.85354

7 -2767.63 866.84 -27137.31 126308.5967 118167.4 0.62 1.7 7110.936 -32589.7 116531.7 0.61 1.6 6661.371 -32245 116635.1 0.61 1.6 100066.1 14.00925

8 -2767.63 945.64 -26216.81 125762.9141 117897.9 0.62 1.7 7036.179 -31611.9 116279.3 0.61 1.6 6592.897 -31272 116381.3 0.61 1.6 101039.1 14.14547

9 -2767.63 1013.19 -25427.80 125295.1862 117666.8 0.62 1.7 6972.316 -30773.9 116063 0.61 1.6 6534.378 -30438.2 116163.7 0.61 1.6 101873 14.26221

10 -2767.63 1069.48 -24770.30 124905.4129 117474.3 0.62 1.7 6919.246 -30075.8 115882.7 0.61 1.6 6485.735 -29743.3 115982.4 0.61 1.6 102567.8 14.35949

11 -2767.63 1114.51 -24244.29 124593.5943 117320.3 0.62 1.7 6876.889 -29517.3 115738.4 0.61 1.6 6446.901 -29187.6 115837.3 0.61 1.6 103123.5 14.4373

12 -2767.63 1148.28 -23849.79 124359.7304 117204.8 0.62 1.7 6845.178 -29098.5 115630.2 0.61 1.6 6417.822 -28770.8 115728.5 0.61 1.6 103540.3 14.49565

13 -2767.63 1170.80 -23586.79 124203.8211 117127.8 0.62 1.7 6824.065 -28819.3 115558 0.61 1.6 6398.458 -28492.9 115655.9 0.61 1.6 103818.2 14.53455

14 -2767.63 1182.06 -23455.29 124125.8664 117089.3 0.62 1.7 6813.516 -28679.7 115522 0.61 1.6 6388.783 -28354 115619.7 0.61 1.6 103957.1 14.55399

14.5 -2767.63 1183.46 -23438.85 124116.1221 117084.5 0.62 1.7 6812.198 -28662.2 115517.5 0.61 1.6 6387.574 -28336.6 115615.1 0.61 1.6 103974.5 14.55643


Cabo4

n 22 tf,m

X(m)


0 0.00 0.00 -4817.94 6.87518E-05 -1445.38 -0.01 -4.6 231.4958 -4991.26 -1497.38 -0.01 -4.6 239.9672 -4997.6 -1499.28 -0.01 -4.6 -4997.6 -0.69966

1 -1570.99 171.91 -20775.66 66873.88902 60641.19 0.32 -1.3 -2776.91 -18696.6 61264.92 0.32 -1.3 -2735.08 -18727.9 61255.53 0.32 -1.3 49336.41 6.907098

2 -3053.86 331.54 -35868.45 130015.3334 119254.8 0.63 1.8 7415.251 -41420.3 117589.2 0.62 1.7 6950.907 -41072.6 117693.5 0.62 1.7 91238.46 12.77338

3 -3053.86 478.89 -34187.78 128994.9905 118738.7 0.62 1.7 7270.261 -39631.1 117105.7 0.62 1.7 6818.004 -39292.5 117207.2 0.62 1.7 93018.63 13.02261

4 -3053.86 613.96 -32647.17 128059.6761 118265.5 0.62 1.7 7138.217 -37991.6 116662.2 0.61 1.6 6696.881 -37661.2 116761.3 0.61 1.6 94649.92 13.25099

5 -3053.86 736.75 -31246.62 127209.3903 117835.4 0.62 1.7 7018.892 -36501.7 116258.9 0.61 1.6 6587.354 -36178.6 116355.8 0.61 1.6 96132.48 13.45855

6 -3053.86 847.27 -29986.12 126444.1331 117448.3 0.62 1.7 6912.082 -35161.3 115895.8 0.61 1.6 6489.257 -34844.7 115990.7 0.61 1.6 97466.43 13.6453

7 -3053.86 945.50 -28865.68 125763.9045 117104.2 0.62 1.7 6817.604 -33970.1 115572.9 0.61 1.6 6402.439 -33659.2 115666.1 0.61 1.6 98651.87 13.81126

8 -3053.86 1031.46 -27885.29 125168.7044 116803.1 0.61 1.6 6735.293 -32928.1 115290.3 0.61 1.6 6326.767 -32622.2 115382 0.61 1.6 99688.92 13.95645

9 -3053.86 1105.13 -27044.96 124658.533 116545 0.61 1.6 6665.006 -32035.1 115048 0.61 1.6 6262.124 -31733.5 115138.5 0.61 1.6 100577.6 14.08087

10 -3053.86 1166.53 -26344.68 124233.3901 116330 0.61 1.6 6606.622 -31291.1 114846.1 0.60 1.5 6208.409 -30993 114935.5 0.60 1.5 101318.1 14.18454

11 -3053.86 1215.64 -25784.46 123893.2758 116157.9 0.61 1.6 6560.037 -30696 114684.5 0.60 1.5 6165.537 -30400.6 114773.1 0.60 1.5 101910.5 14.26746

12 -3053.86 1252.48 -25364.29 123638.19 116028.9 0.61 1.6 6525.17 -30249.7 114563.3 0.60 1.5 6133.443 -29956.4 114651.3 0.60 1.5 102354.7 14.32965

13 -3053.86 1277.04 -25084.18 123468.1329 115942.9 0.61 1.6 6501.959 -29952.2 114482.5 0.60 1.5 6112.074 -29660.3 114570 0.60 1.5 102650.8 14.37111

14 -3053.86 1289.32 -24944.12 123383.1043 115899.9 0.61 1.6 6490.364 -29803.5 114442.1 0.60 1.5 6101.398 -29512.3 114529.4 0.60 1.5 102798.8 14.39183

14.5 -3053.86 1290.85 -24926.62 123372.4757 115894.5 0.61 1.6 6488.915 -29784.9 114437 0.60 1.5 6100.064 -29493.8 114524.3 0.60 1.5 102817.3 14.39443


Cabo5

39



CABO C6

CABO C7

CABO C8

3.5.7. FORÇA DE PROTENSÃO FINAL

n 22 tf,m

X(m)


0 0.00 0.00 -6245.04 6.87518E-06 -1873.51 -0.01 -4.6 301.5441 -6537.68 -1961.3 -0.01 -4.6 315.9916 -6551.7 -1965.51 -0.01 -4.6 -6551.7 -0.91724

1 0.00 157.61 -4034.00 -1091.36514 -2301.56 -0.01 -4.6 372.2543 -4406.25 -2413.24 -0.01 -4.6 390.8133 -4424.81 -2418.81 -0.01 -4.6 -4424.81 -0.61947

2 0.00 303.96 -1804.49 -2104.77563 -2646.12 -0.01 -4.6 429.6629 -2234.16 -2775.02 -0.01 -4.6 451.2516 -2255.75 -2781.5 -0.01 -4.6 -2255.75 -0.3158

3 -1423.74 439.05 -18535.54 65024.05764 59463.4 0.31 -1.4 -2851.99 -16069.4 60203.23 0.32 -1.3 -2805.43 -16109.7 60191.15 0.32 -1.3 51954.59 7.273643

4 -2767.63 562.88 -30687.83 128413.3723 119207 0.63 1.8 7401.788 -36363.3 117504.4 0.62 1.7 6927.524 -35999.6 117613.5 0.62 1.7 96311.47 13.48361

5 -2767.63 675.46 -29372.83 127633.8258 118822 0.63 1.8 7293.601 -34965.3 117144.2 0.62 1.7 6828.571 -34608.8 117251.2 0.62 1.7 97702.35 13.67833

6 -2767.63 776.78 -28189.32 126932.2339 118475.4 0.62 1.7 7196.699 -33707.5 116820 0.61 1.6 6739.894 -33357.3 116925.1 0.62 1.7 98953.85 13.85354

7 -2767.63 866.84 -27137.31 126308.5967 118167.4 0.62 1.7 7110.936 -32589.7 116531.7 0.61 1.6 6661.371 -32245 116635.1 0.61 1.6 100066.1 14.00925

8 -2767.63 945.64 -26216.81 125762.9141 117897.9 0.62 1.7 7036.179 -31611.9 116279.3 0.61 1.6 6592.897 -31272 116381.3 0.61 1.6 101039.1 14.14547

9 -2767.63 1013.19 -25427.80 125295.1862 117666.8 0.62 1.7 6972.316 -30773.9 116063 0.61 1.6 6534.378 -30438.2 116163.7 0.61 1.6 101873 14.26221

10 -2767.63 1069.48 -24770.30 124905.4129 117474.3 0.62 1.7 6919.246 -30075.8 115882.7 0.61 1.6 6485.735 -29743.3 115982.4 0.61 1.6 102567.8 14.35949

11 -2767.63 1114.51 -24244.29 124593.5943 117320.3 0.62 1.7 6876.889 -29517.3 115738.4 0.61 1.6 6446.901 -29187.6 115837.3 0.61 1.6 103123.5 14.4373

12 -2767.63 1148.28 -23849.79 124359.7304 117204.8 0.62 1.7 6845.178 -29098.5 115630.2 0.61 1.6 6417.822 -28770.8 115728.5 0.61 1.6 103540.3 14.49565

13 -2767.63 1170.80 -23586.79 124203.8211 117127.8 0.62 1.7 6824.065 -28819.3 115558 0.61 1.6 6398.458 -28492.9 115655.9 0.61 1.6 103818.2 14.53455

14 -2767.63 1182.06 -23455.29 124125.8664 117089.3 0.62 1.7 6813.516 -28679.7 115522 0.61 1.6 6388.783 -28354 115619.7 0.61 1.6 103957.1 14.55399

14.5 -2767.63 1183.46 -23438.85 124116.1221 117084.5 0.62 1.7 6812.198 -28662.2 115517.5 0.61 1.6 6387.574 -28336.6 115615.1 0.61 1.6 103974.5 14.55643


Cabo6

n 22 tf,m

X(m)


0 0.00 0.00 -4817.94 6.87518E-05 -1445.38 -0.01 -4.6 231.4958 -4991.26 -1497.38 -0.01 -4.6 239.9672 -4997.6 -1499.28 -0.01 -4.6 -4997.6 -0.69966

1 0.00 171.91 -3816.12 -1190.40003 -2335.24 -0.01 -4.6 377.8453 -4193.97 -2448.59 -0.01 -4.6 396.6974 -4212.82 -2454.25 -0.01 -4.6 -4212.82 -0.58979

2 0.00 331.54 -1384.30 -2295.77154 -2711.06 -0.01 -4.6 440.5315 -1824.83 -2843.22 -0.01 -4.6 462.6988 -1847 -2849.87 -0.01 -4.6 -1847 -0.25858

3 0.00 478.89 860.45 -3316.11448 -3574.25 -0.02 -4.7 586.4778 273.9742 -3398.31 -0.02 -4.7 556.5068 303.9451 -3407.3 -0.02 -4.7 303.9452 0.042552

4 0.00 613.96 2918.14 -4251.42885 -5126.87 -0.03 -4.8 855.9017 2062.242 -4870.1 -0.03 -4.8 810.7318 2107.412 -4883.65 -0.03 -4.8 2107.412 0.295038

5 -1570.99 736.75 -16325.11 62962.57442 58065.04 0.31 -1.4 -2934.5 -13822.7 58815.77 0.31 -1.4 -2891.1 -13859.7 58804.67 0.31 -1.4 54204.6 7.588644

6 -3053.86 847.27 -29986.12 126444.1331 117448.3 0.62 1.7 6912.082 -35161.3 115895.8 0.61 1.6 6489.257 -34844.7 115990.7 0.61 1.6 97466.43 13.6453

7 -3053.86 945.50 -28865.68 125763.9045 117104.2 0.62 1.7 6817.604 -33970.1 115572.9 0.61 1.6 6402.439 -33659.2 115666.1 0.61 1.6 98651.87 13.81126

8 -3053.86 1031.46 -27885.29 125168.7044 116803.1 0.61 1.6 6735.293 -32928.1 115290.3 0.61 1.6 6326.767 -32622.2 115382 0.61 1.6 99688.92 13.95645

9 -3053.86 1105.13 -27044.96 124658.533 116545 0.61 1.6 6665.006 -32035.1 115048 0.61 1.6 6262.124 -31733.5 115138.5 0.61 1.6 100577.6 14.08087

10 -3053.86 1166.53 -26344.68 124233.3901 116330 0.61 1.6 6606.622 -31291.1 114846.1 0.60 1.5 6208.409 -30993 114935.5 0.60 1.5 101318.1 14.18454

11 -3053.86 1215.64 -25784.46 123893.2758 116157.9 0.61 1.6 6560.037 -30696 114684.5 0.60 1.5 6165.537 -30400.6 114773.1 0.60 1.5 101910.5 14.26746

12 -3053.86 1252.48 -25364.29 123638.19 116028.9 0.61 1.6 6525.17 -30249.7 114563.3 0.60 1.5 6133.443 -29956.4 114651.3 0.60 1.5 102354.7 14.32965

13 -3053.86 1277.04 -25084.18 123468.1329 115942.9 0.61 1.6 6501.959 -29952.2 114482.5 0.60 1.5 6112.074 -29660.3 114570 0.60 1.5 102650.8 14.37111

14 -3053.86 1289.32 -24944.12 123383.1043 115899.9 0.61 1.6 6490.364 -29803.5 114442.1 0.60 1.5 6101.398 -29512.3 114529.4 0.60 1.5 102798.8 14.39183

14.5 -3053.86 1290.85 -24926.62 123372.4757 115894.5 0.61 1.6 6488.915 -29784.9 114437 0.60 1.5 6100.064 -29493.8 114524.3 0.60 1.5 102817.3 14.39443


Cabo7

n 22 tf,m

X(m)


0 0.00 0.00 -1477.16 0.000688 -443.146 0.00 -4.5 70.15727 -1493.26 -447.978 0.00 -4.5 70.92614 -1493.44 -448.03 0.00 -4.5 -1493.44 -0.20908

1 0.00 171.91 -3816.12 -1190.4 -2335.24 -0.01 -4.6 377.8452 -4193.97 -2448.59 -0.01 -4.6 396.6973 -4212.82 -2454.24 -0.01 -4.6 -4212.82 -0.58979

2 0.00 331.54 -1384.30 -2295.77 -2711.06 -0.01 -4.6 440.5314 -1824.83 -2843.22 -0.01 -4.6 462.6987 -1847 -2849.87 -0.01 -4.6 -1847 -0.25858

3 0.00 478.89 860.45 -3316.11 -3574.25 -0.02 -4.7 586.4777 273.9741 -3398.31 -0.02 -4.7 556.5067 303.945 -3407.3 -0.02 -4.7 303.9457 0.042552

4 0.00 613.96 2918.14 -4251.43 -5126.87 -0.03 -4.8 855.9016 2062.242 -4870.1 -0.03 -4.8 810.7317 2107.412 -4883.65 -0.03 -4.8 2107.412 0.295038

5 0.00 736.75 4788.77 -5101.71 -6538.35 -0.03 -4.8 1108.539 3680.233 -6205.78 -0.03 -4.8 1048.354 3740.418 -6223.84 -0.03 -4.8 3740.419 0.523659

6 0.00 847.27 6472.34 -5866.97 -7808.67 -0.04 -4.9 1342.189 5130.149 -7406.02 -0.04 -4.9 1267.485 5204.853 -7428.43 -0.04 -4.9 5204.853 0.728679

7 0.00 945.50 7968.84 -6547.2 -8937.85 -0.05 -5.0 1554.869 6413.972 -8471.39 -0.04 -4.9 1466.442 6502.399 -8497.92 -0.04 -4.9 6502.4 0.910336

8 0.00 1031.46 9278.28 -7142.4 -9925.88 -0.05 -5.0 1744.817 7533.464 -9402.44 -0.05 -5.0 1643.737 7634.544 -9432.76 -0.05 -5.0 7634.545 1.068836

9 0.00 1105.13 10400.66 -7652.57 -10772.8 -0.06 -5.1 1910.492 8490.166 -10199.6 -0.05 -5.0 1798.079 8602.58 -10233.3 -0.05 -5.0 8602.58 1.204361

10 -1570.99 1166.53 -10741.90 59986.57 56764 0.30 -1.5 -3004.79 -8179.53 57532.72 0.30 -1.5 -2964.01 -8214.3 57522.28 0.30 -1.5 59849.99 8.378998

11 -3053.86 1215.64 -25784.46 123893.3 116157.9 0.61 1.6 6560.037 -30696 114684.5 0.60 1.5 6165.537 -30400.6 114773.1 0.60 1.5 101910.5 14.26746

12 -3053.86 1252.48 -25364.29 123638.2 116028.9 0.61 1.6 6525.17 -30249.7 114563.3 0.60 1.5 6133.443 -29956.4 114651.3 0.60 1.5 102354.7 14.32965

13 -3053.86 1277.04 -25084.18 123468.1 115942.9 0.61 1.6 6501.959 -29952.2 114482.5 0.60 1.5 6112.074 -29660.3 114570 0.60 1.5 102650.8 14.37111

14 -3053.86 1289.32 -24944.12 123383.1 115899.9 0.61 1.6 6490.364 -29803.5 114442.1 0.60 1.5 6101.398 -29512.3 114529.4 0.60 1.5 102798.8 14.39183

14.5 -3053.86 1290.85 -24926.62 123372.5 115894.5 0.61 1.6 6488.915 -29784.9 114437 0.60 1.5 6100.064 -29493.8 114524.3 0.60 1.5 102817.3 14.39443


Cabo8

n 2 2 2 4 6 6 2 2

X(m) Cabo1 Cabo2 Cabo3 Cabo4 Cabo5 Cabo6 Cabo7 Cabo8 P final,total (t) % perda inicial % perda prog % perda total

0 -0.88 -0.88 -0.73 -0.72 -0.70 -0.92 -0.70 -0.21 -19.38 103.75 0.02 103.76

1 7.90 7.98 7.20 7.06 6.91 -0.62 -0.59 -0.59 109.76 72.98 5.70 78.68

2 14.34 14.49 13.28 13.04 12.77 -0.32 -0.26 -0.26 210.06 43.93 15.26 59.20

3 13.98 14.15 13.50 13.27 13.02 7.27 0.04 0.04 258.27 32.40 17.43 49.83

4 13.64 13.84 13.70 13.48 13.25 13.48 0.30 0.30 297.88 21.50 20.63 42.14

5 13.34 13.55 13.88 13.68 13.46 13.68 7.59 0.52 315.31 17.66 21.09 38.75

6 13.07 13.30 14.04 13.85 13.65 13.85 13.65 0.73 329.98 14.03 21.87 35.90

7 12.83 13.08 14.19 14.01 13.81 14.01 13.81 0.91 332.59 14.03 21.37 35.40

8 12.62 12.88 14.31 14.15 13.96 14.15 13.96 1.07 334.86 14.03 20.92 34.95

9 14.73 12.71 14.42 14.26 14.08 14.26 14.08 1.20 341.40 14.03 19.66 33.68

10 14.34 12.57 14.51 14.36 14.18 14.36 14.18 8.38 356.66 10.18 20.54 30.72

11 13.98 12.45 14.58 14.44 14.27 14.44 14.27 14.27 369.08 6.55 21.75 28.31

12 13.64 12.37 14.64 14.50 14.33 14.50 14.33 14.33 369.56 6.55 21.66 28.21

13 13.34 12.31 14.67 14.53 14.37 14.53 14.37 14.37 369.72 6.55 21.63 28.18

14 13.07 12.29 14.69 14.55 14.39 14.55 14.39 14.39 369.56 6.55 21.66 28.21

14.5 12.83 12.28 14.69 14.56 14.39 14.56 14.39 14.39 369.12 6.55 21.75 28.30

PROTENSÃO

40



3.6. FASES DE CONSTRUÇÃO 3.6.1. FASE 1A PESO PRÓPRIO DA LONGARINA (PPLONG) + PROTENSÃO (PROT) 3.6.2. FASE 1B PESO PRÓPRIO DA LONGARINA (PPLONG) + PROTENSÃO (PROT) + PESO PRÓPRIO DO TABULEIRO (PPTAB) 3.6.3. FASE 2 PESO PRÓPRIO DA LONGARINA (PPLONG) + PROTENSÃO (PROT) + PESO PRÓPRIO DO TABULEIRO (PPTAB) + PESO PRÓPRIO DO NEW JERSEY (PPNJ) + REVESTIMENTO (REV) + SOBRECARGA + CARGA MÓVEL

41



3.7. COMBINAÇÕES – VÃO DE 30m 3.7.1. COMBINAÇÕES ÚLTIMAS

✓ COMB PERM = 1,35 x DEAD + 1,35 x PPNJ + 1,35 x REV+1,35 x REC ✓ COMB PERM PROT = 1,00 x COMB PERM + 1,00 x PROT ✓ COMB VERT = 1,00 x COMB PERM PROT + 1,5 x ENV MOVE + 1,5 x

ENV SC ✓ COMB VT = 1,00 x COMB VERT + 1,5 x 0,6 x VT + 1,5 x FREN ✓ COMB VT TEMP = 1,00 x COMB VT + 1,5 x 0,6 x ENV TEMP + 1,4 x LT ✓ COMB VT TEMP EMP = 1,00 x COMB VT TEMP + 1,4 X EMP

3.7.2. ENVOLTÓRIA GERAL DE COMBINAÇÕES ÚLTIMAS

✓ ENV MOVE = 1,265 x MOVE 1 + 1,265 x MOVE 2 + 1,265 x MOVE 3 + 1,265 x MOVE 4 + 1,265 x MOVE 5 + 1,265 x MOVE 6

✓ ENV SC = 1,265 x SC1 + 1,265 x SC2 + 1,265 x SC3 + 1,265 x SC4 + 1,265 x SC5 + 1,265 x SC6

✓ ENV TEMP = 1,00 x TEMP1 + 1,00 x TEMP2 ✓ ENV TOTAL PROT = COMB PERM PROT + COMB VERT + COMB VT

+ COMB VT TEMP + COMB VT TEMP EMP 3.7.3. COMBINAÇÕES DE UTILIZAÇÃO

✓ Verificação da tensão de compressão (TENSÃO 7) TENSÃO 7 (FASE 1A) = 1,0 x PPLONG + 1,1 x PROT

✓ Verificação da tensão de tração, sem cargas acidentais (TENSÃO 8) TENSÃO 8A (FASE 1B) = 1,0 x DEAD + 0,9 x PROT + 1,0 x PPNJ TENSÃO 8B (FASE 2) = 1,0 x DEAD + 0,9 x PROT + 1,0 x REV + 1,0 x PPNJ

✓ Verificação da tensão de tração, cargas acidentais quase permanentes (TENSÃO 9)

TENSÃO 9 (FASE 2) = 1,0 x DEAD + 0,9 x PROT + 1,0 x REV + 1,0 x PPNJ + 0,3 x ENV MOVE (Mmax) + 0,3 x ENV SC (Mmax)

✓ Verificação da tensão de tração, cargas acidentais quase permanentes (TENSÃO 10)

TENSÃO 10 (FASE 2) = 1,0 x DEAD + 0,9 x PROT + 1,0 x REV + 1,0 x PPNJ + 0,3 x ENV MOVE (Mmin) + 0,3 x ENV SC (Mmin)

✓ Verificação da tensão de tração, cargas acidentais frequentes (TENSÃO 11)

TENSÃO 11 (FASE 2) = 1,0 x DEAD + 0,9 x PROT + 1,0 x REV + 1,0 x PPNJ + 0,5 x ENV MOVE (Mmax) + 0,5 x ENV SC (Mmax)

✓ Verificação da tensão de tração, cargas acidentais frequentes (TENSÃO 12)

TENSÃO 12 (FASE 2) = 1,0 x DEAD + 0,9 x PROT + 1,0 x REV + 1,0 x PPNJ + 0,5 x ENV MOVE (Mmin) + 0,5 x ENV SC (Mmin)

42



3.8. VERIFICAÇÃO DA DEFORMAÇÃO

A máxima deformação admissível para os vãos extremos é de350

L ,ou seja,

3500,29 =0,0829m.

0,0827 < 0,0829m OK! Todas as deformações encontradas são inferiores às estabelecidas.

43



3.10. VERIFICAÇÃO DAS COMBINAÇÕES DE UTILIZAÇÃO – VÃO DE 30m

3.10.1. TENSÃO 7

3.10.2. TENSÃO 8A

3.10.3. TENSÃO 8B

PROPRIEDADES

0 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16

h(m) 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

Ix(m4) 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852

cg(m) (base) 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651

cg(m) (topo) 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749

x(m) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 14.50

Wsup(m³) 0.1137517 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.1137517 0.113752 0.113752 0.113752 0.113752

Winf(m³) 0.1308756 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.1308756 0.130876 0.130876 0.130876 0.130876

A(m²) 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363

N (kN) -206.2606 1487.277 3085.83 3720.907 4320.365 4532.057 4731.876 4731.876 4731.876 4731.876 4943.568 5143.3873 5143.387 5143.387 5143.387 5143.387

M (kNm) -2.93E-06 -326.171 -635.855 -894.988 -1142.34 -1189.16 -1237.05 -1169.79 -1110.94 -1060.49 -1149.35 -1239.277 -1214.05 -1197.24 -1188.83 -1187.78

s sup (kN/m²) 613.32336 -1555.07 -3585.97 -3196.34 -2804.38 -3022.23 -3195.41 -3786.7 -4304.08 -4747.54 -4595.84 -4399.458 -4621.19 -4769.01 -4842.92 -4852.16

s inf (kN/m²) 613.32331 -6914.7 -14034.3 -17902.7 -21575.2 -22562.4 -23522.5 -23008.6 -22558.9 -22173.4 -23481.9 -24763.17 -24570.5 -24442 -24377.7 -24369.7

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

VERIF. DA TRAÇÃO OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

VERIF. DA COMPRESSÃO OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

SEÇÕES DA PONTE

TENSÃO 7

PROPRIEDADES


h(m) 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

Ix(m4) 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852 0.0852

cg(m) (base) 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651 0.651

cg(m) (topo) 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749 0.749

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.113752 0.1137517 0.113752 0.113752 0.113752 0.113752

Winf(m³) 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.130876 0.1308756 0.130876 0.130876 0.130876 0.130876

A(m²) 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363 0.3363

N (kN) -174.39 987.8651 1890.566 2324.421 2680.924 2837.809 2969.848 2993.279 3013.767 3072.574 3209.971 3321.6943 3326.025 3327.462 3326.009 3322.094

M (kNm) 56.2953 58.88269 80.93528 35.39499 16.34635 91.15889 163.5345 279.6259 381.2123 497.5415 496.9955 494.46769 534.9865 560.9724 572.4253 571.2098

s sup (kN/m²) 23.65745 -3455.09 -6333.17 -7222.91 -8115.52 -9239.71 -10268.6 -11358.8 -12312.8 -13510.3 -13914.1 -14224.081 -14593.2 -14825.9 -14922.2 -14899.9

s inf (kN/m²) 948.6976 -2487.54 -5003.25 -6641.3 -7846.92 -7741.8 -7581.41 -6764.04 -6048.76 -5334.77 -5747.5 -6099.0251 -5802.3 -5608.02 -5516.19 -5513.84

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



SEÇÕES DA PONTE

TENSÃO 8A

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - Rev 0 -83.7905 -161.596 -233.416 -299.252 -359.102 -412.968 -460.848 -502.743 -538.653 -568.579 -592.5187 -610.474 -622.444 -628.429 -629.177

s sup (kN/m²) - Rev 0 -46.6667 -90 -130 -166.667 -200 -230 -256.667 -280 -300 -316.667 -330 -340 -346.667 -350 -350.417

s inf (kN/m²) - Rev 0 170.5584 328.934 475.1269 609.1371 730.9645 840.6091 938.0711 1023.35 1096.447 1157.36 1206.091 1242.64 1267.005 1279.188 1280.711

s sup` (kN/m²) - Fase 8A 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

s sup (kN/m²) - Fase 8A 23.65745 -3455.09 -6333.17 -7222.91 -8115.52 -9239.71 -10268.6 -11358.8 -12312.8 -13510.3 -13914.1 -14224.08 -14593.2 -14825.9 -14922.2 -14899.9

s inf (kN/m²) - Fase 8A 948.6976 -2487.54 -5003.25 -6641.3 -7846.92 -7741.8 -7581.41 -6764.04 -6048.76 -5334.77 -5747.5 -6099.025 -5802.3 -5608.02 -5516.19 -5513.84

s sup´ (kN/m²) 0 -83.7905 -161.596 -233.416 -299.252 -359.102 -412.968 -460.848 -502.743 -538.653 -568.579 -592.5187 -610.474 -622.444 -628.429 -629.177

s sup (kN/m²) 23.65745 -3501.76 -6423.17 -7352.91 -8282.19 -9439.71 -10498.6 -11615.5 -12592.8 -13810.3 -14230.8 -14554.08 -14933.2 -15172.5 -15272.2 -15250.3

s inf (kN/m²) 948.6976 -2316.98 -4674.32 -6166.17 -7237.79 -7010.83 -6740.8 -5825.97 -5025.41 -4238.32 -4590.14 -4892.934 -4559.66 -4341.02 -4237.01 -4233.13

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



SEÇÕES DA PONTE

TENSÃO 8B - TIPO 1

44



3.10.4. TENSÃO 9

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - Rev +NJ 0 -286.284 -552.12 -797.506 -1022.44 -1226.93 -1410.97 -1574.56 -1717.71 -1840.4 -1942.64 -2024.439 -2085.79 -2126.68 -2147.13 -2149.69

s sup (kN/m²) - Rev +NJ 0 -159.444 -307.5 -444.167 -569.444 -683.333 -785.833 -876.944 -956.667 -1025 -1081.94 -1127.5 -1161.67 -1184.44 -1195.83 -1197.26

s inf (kN/m²) - Rev +NJ 0 582.7411 1123.858 1623.35 2081.218 2497.462 2872.081 3205.076 3496.447 3746.193 3954.315 4120.812 4245.685 4328.934 4370.558 4375.761

s sup` (kN/m²) - Fase 8A 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

s sup (kN/m²) - Fase 8A 23.65745 -3455.09 -6333.17 -7222.91 -8115.52 -9239.71 -10268.6 -11358.8 -12312.8 -13510.3 -13914.1 -14224.08 -14593.2 -14825.9 -14922.2 -14899.9

s inf (kN/m²) - Fase 8A 948.6976 -2487.54 -5003.25 -6641.3 -7846.92 -7741.8 -7581.41 -6764.04 -6048.76 -5334.77 -5747.5 -6099.025 -5802.3 -5608.02 -5516.19 -5513.84

s sup´ (kN/m²) 0 -286.284 -552.12 -797.506 -1022.44 -1226.93 -1410.97 -1574.56 -1717.71 -1840.4 -1942.64 -2024.439 -2085.79 -2126.68 -2147.13 -2149.69

s sup (kN/m²) 23.65745 -3614.54 -6640.67 -7667.07 -8684.97 -9923.04 -11054.4 -12235.8 -13269.5 -14535.3 -14996 -15351.58 -15754.8 -16010.3 -16118.1 -16097.2

s inf (kN/m²) 948.6976 -1904.8 -3879.39 -5017.95 -5765.7 -5244.33 -4709.32 -3558.97 -2552.31 -1588.58 -1793.18 -1978.213 -1556.62 -1279.09 -1145.63 -1138.08

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



TENSÃO 8B - TIPO 2

SEÇÕES DA PONTE

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,3CMmax -1.597366 -194.524 -355.052 -496.227 -623.124 -736.074 -835.837 -925.773 -1003.89 -1070.36 -1126.16 -1170.91 -1204.84 -1228.42 -1241.56 -1244.8

s sup (kN/m²) - 0,3CMmax -0.776828 -94.6006 -172.668 -241.324 -303.036 -357.966 -406.483 -450.22 -488.208 -520.535 -547.671 -569.433 -585.935 -597.404 -603.796 -605.367

s inf (kN/m²) - 0,3CMmax 3.0466829 371.0191 677.1969 946.462 1188.494 1403.926 1594.206 1765.742 1914.727 2041.514 2147.941 2233.289 2298.008 2342.99 2368.057 2374.22

s sup` (kN/m²) - Fase 8B-Central 0 -83.7905 -161.596 -233.416 -299.252 -359.102 -412.968 -460.848 -502.743 -538.653 -568.579 -592.519 -610.474 -622.444 -628.429 -629.177

s sup (kN/m²) - Fase-Central 23.657451 -3501.76 -6423.17 -7352.91 -8282.19 -9439.71 -10498.6 -11615.5 -12592.8 -13810.3 -14230.8 -14554.1 -14933.2 -15172.5 -15272.2 -15250.3

s inf (kN/m²) - Fase-Central 948.69765 -2316.98 -4674.32 -6166.17 -7237.79 -7010.83 -6740.8 -5825.97 -5025.41 -4238.32 -4590.14 -4892.93 -4559.66 -4341.02 -4237.01 -4233.13

s sup´ (kN/m²) -1.597366 -278.315 -516.648 -729.643 -922.376 -1095.18 -1248.8 -1386.62 -1506.63 -1609.01 -1694.74 -1763.42 -1815.31 -1850.87 -1869.99 -1873.97

s sup (kN/m²) 22.880623 -3596.36 -6595.84 -7594.23 -8585.23 -9797.68 -10905.1 -12065.7 -13081 -14330.9 -14778.4 -15123.5 -15519.1 -15770 -15876 -15855.7

s inf (kN/m²) 951.74433 -1945.96 -3997.12 -5219.71 -6049.29 -5606.9 -5146.59 -4060.23 -3110.68 -2196.81 -2442.2 -2659.64 -2261.66 -1998.03 -1868.95 -1858.91

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



SEÇÕES DA PONTE

TENSÃO 9-TIPO 1

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,3CMmax -5.834655 -231.617 -421.735 -590.159 -738.281 -867.436 -981.801 -1084.43 -1171.92 -1245.76 -1307.2 -1356.17 -1393.09 -1418.77 -1433.05 -1436.47

s sup (kN/m²) - 0,3CMmax -2.8375 -112.64 -205.098 -287.005 -359.04 -421.85 -477.468 -527.376 -569.926 -605.834 -635.717 -659.53 -677.485 -689.974 -696.919 -698.584

s inf (kN/m²) - 0,3CMmax 11.128537 441.7667 804.383 1125.62 1408.137 1654.475 1872.605 2068.344 2235.222 2376.052 2493.251 2586.643 2657.062 2706.045 2733.281 2739.813

s sup` (kN/m²) - Fase 8B-Lateral 0 -286.284 -552.12 -797.506 -1022.44 -1226.93 -1410.97 -1574.56 -1717.71 -1840.4 -1942.64 -2024.44 -2085.79 -2126.68 -2147.13 -2149.69

s sup (kN/m²) - Fase 8B-Lateral 23.657451 -3614.54 -6640.67 -7667.07 -8684.97 -9923.04 -11054.4 -12235.8 -13269.5 -14535.3 -14996 -15351.6 -15754.8 -16010.3 -16118.1 -16097.2

s inf (kN/m²) - Fase 8B-Lateral 948.69765 -1904.8 -3879.39 -5017.95 -5765.7 -5244.33 -4709.32 -3558.97 -2552.31 -1588.58 -1793.18 -1978.21 -1556.62 -1279.09 -1145.63 -1138.08

s sup´ (kN/m²) -5.834655 -517.901 -973.855 -1387.67 -1760.73 -2094.37 -2392.77 -2658.99 -2889.63 -3086.16 -3249.85 -3380.61 -3478.87 -3545.45 -3580.18 -3586.16

s sup (kN/m²) 20.819951 -3727.18 -6845.77 -7954.08 -9044.01 -10344.9 -11531.9 -12763.2 -13839.4 -15141.2 -15631.8 -16011.1 -16432.3 -16700.3 -16815 -16795.8

s inf (kN/m²) 959.82619 -1463.03 -3075.01 -3892.33 -4357.57 -3589.86 -2836.72 -1490.62 -317.09 787.4746 700.0698 608.4301 1100.444 1426.955 1587.646 1601.737

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

VERIFICAÇÃO DA TRAÇÃO OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

VERIFICAÇÃO DA COMPRESSÃO OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK

TENSÃO 9-TIPO 2

SEÇÕES DA PONTE

45



3.10.5. TENSÃO 10

3.10.6. TENSÃO 11

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.4062731 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.1987365 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,3CMmin 5.7092839 -10.8541 -23.198 -34.9037 -45.6136 -55.2562 -63.9827 -71.5604 -78.4215 -84.3174 -89.2551 -93.24445 -96.2955 -98.4175 -99.6503 -99.9205

s sup (kN/m²) - 0,3CMmin 2.7765299 -5.27854 -11.2816 -16.9743 -22.1827 -26.8721 -31.116 -34.8011 -38.1378 -41.0051 -43.4064 -45.34649 -46.8303 -47.8622 -48.4618 -48.5932

s inf (kN/m²) - 0,3CMmin -10.88941 20.7022 44.2459 66.57234 86.99956 105.391 122.0353 136.4883 149.5747 160.82 170.2377 177.84673 183.6661 187.7134 190.0646 190.58


s sup (kN/m²) - Fase 8B-Central 23.657451 -3501.76 -6423.17 -7352.91 -8282.19 -9439.71 -10498.6 -11615.5 -12592.8 -13810.3 -14230.8 -14554.08 -14933.2 -15172.5 -15272.2 -15250.3

s inf (kN/m²) - Fase 8B-Central 948.69765 -2316.98 -4674.32 -6166.17 -7237.79 -7010.83 -6740.8 -5825.97 -5025.41 -4238.32 -4590.14 -4892.934 -4559.66 -4341.02 -4237.01 -4233.13

s sup´ (kN/m²) 5.7092839 -94.6446 -184.794 -268.32 -344.865 -414.358 -476.95 -532.408 -581.165 -622.971 -657.834 -685.7632 -706.769 -720.861 -728.079 -729.098

s sup (kN/m²) 26.433981 -3507.04 -6434.46 -7369.88 -8304.37 -9466.58 -10529.7 -11650.3 -12630.9 -13851.3 -14274.2 -14599.43 -14980 -15220.4 -15320.7 -15298.9

s inf (kN/m²) 937.80823 -2296.28 -4630.07 -6099.6 -7150.79 -6905.44 -6618.76 -5689.48 -4875.83 -4077.5 -4419.9 -4715.087 -4376 -4153.31 -4046.94 -4042.55

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



SEÇÕES DA PONTE

TENSÃO 10-TIPO 1

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.40627306 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.19873646 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,3CMmin 1.7782097 -9.98601 -21.6833 -32.7381 -43.3342 -53.3148 -62.5517 -71.1531 -78.5396 -84.9786 -90.4379 -94.884015 -98.2993 -100.71 -102.164 -102.521

s sup (kN/m²) - 0,3CMmin 0.8647761 -4.85638 -10.545 -15.9212 -21.0742 -25.928 -30.42 -34.6031 -38.1953 -41.3267 -43.9816 -46.143843 -47.8047 -48.9773 -49.6842 -49.8579

s inf (kN/m²) - 0,3CMmin -3.39161 19.04649 41.35698 62.442 82.65205 101.6883 119.3059 135.7115 149.8 162.0812 172.4937 180.973902 187.4879 192.0865 194.8591 195.5403




s sup´ (kN/m²) 1.7782097 -296.27 -573.803 -830.244 -1065.78 -1280.25 -1473.52 -1645.72 -1796.25 -1925.38 -2033.08 -2119.3229 -2184.08 -2227.39 -2249.3 -2252.21

s sup (kN/m²) 24.522227 -3619.4 -6651.22 -7683 -8706.04 -9948.97 -11084.8 -12270.4 -13307.7 -14576.7 -15040 -15397.725 -15802.6 -16059.3 -16167.8 -16147

s inf (kN/m²) 945.30604 -1885.75 -3838.04 -4955.51 -5683.05 -5142.65 -4590.02 -3423.25 -2402.51 -1426.5 -1620.69 -1797.239 -1369.13 -1087 -950.775 -942.536

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



TENSÃO 10-TIPO 2

SEÇÕES DA PONTE

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.4062731 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.1987365 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,5CMmax -2.662276 -324.207 -591.753 -827.045 -1038.54 -1226.79 -1393.06 -1542.95 -1673.14 -1783.93 -1876.93 -1951.51 -2008.06 -2047.37 -2069.27 -2074.66

s sup (kN/m²) - 0,5CMmax -1.294714 -157.668 -287.781 -402.207 -505.061 -596.611 -677.472 -750.367 -813.68 -867.559 -912.786 -949.0553 -976.558 -995.674 -1006.33 -1008.95

s inf (kN/m²) - 0,5CMmax 5.0778049 618.3651 1128.661 1577.437 1980.824 2339.877 2657.01 2942.904 3191.212 3402.523 3579.901 3722.1488 3830.013 3904.983 3946.761 3957.034




s sup´ (kN/m²) -2.662276 -407.997 -753.349 -1060.46 -1337.79 -1585.89 -1806.03 -2003.8 -2175.88 -2322.58 -2445.51 -2544.029 -2618.54 -2669.81 -2697.7 -2703.84

s sup (kN/m²) 22.362737 -3659.43 -6710.96 -7755.11 -8787.25 -10036.3 -11176.1 -12365.9 -13406.5 -14677.9 -15143.5 -15503.14 -15909.7 -16168.2 -16278.6 -16259.3

s inf (kN/m²) 953.77545 -1698.61 -3545.66 -4588.74 -5256.96 -4670.95 -4083.79 -2883.07 -1834.2 -835.801 -1010.23 -1170.785 -729.65 -436.036 -290.244 -276.093

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



SEÇÕES DA PONTE

TENSÃO 11-TIPO 1

46



3.10.7. TENSÃO 12

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,5CMmax -9.724425 -386.028 -702.892 -983.598 -1230.47 -1445.73 -1636.33 -1807.38 -1953.2 -2076.26 -2178.67 -2260.281 -2321.81 -2364.62 -2388.42 -2394.12

s sup (kN/m²) - 0,5CMmax -4.729167 -187.733 -341.829 -478.342 -598.4 -703.083 -795.78 -878.96 -949.877 -1009.72 -1059.53 -1099.216 -1129.14 -1149.96 -1161.53 -1164.31

s inf (kN/m²) - 0,5CMmax 18.547561 736.2778 1340.638 1876.034 2346.894 2757.459 3121.009 3447.239 3725.37 3960.087 4155.419 4311.072 4428.436 4510.076 4555.468 4566.355




s sup´ (kN/m²) -9.724425 -672.312 -1255.01 -1781.1 -2252.91 -2672.66 -3047.31 -3381.94 -3670.9 -3916.66 -4121.32 -4284.719 -4407.6 -4491.3 -4535.55 -4543.81

s sup (kN/m²) 18.928284 -3802.27 -6982.5 -8145.42 -9283.37 -10626.1 -11850.2 -13114.7 -14219.4 -15545.1 -16055.6 -16450.8 -16884 -17160.3 -17279.6 -17261.5

s inf (kN/m²) 967.24521 -1168.52 -2538.76 -3141.92 -3418.81 -2486.87 -1588.32 -111.727 1173.058 2371.509 2362.237 2332.859 2871.818 3230.985 3409.834 3428.279

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

VERIFICAÇÃO DA TRAÇÃO OK OK OK OK OK OK OK OK OK OK OK OK OK ARMAR! ARMAR! ARMAR!


TENSÃO 11-TIPO 2

SEÇÕES DA PONTE

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,5CMmax 9.5154731 -18.0902 -38.6633 -58.1728 -76.0226 -92.0936 -106.638 -119.267 -130.703 -140.529 -148.758 -155.4074 -160.493 -164.029 -166.084 -166.534

s sup (kN/m²) - 0,5CMmax 4.6275498 -8.79757 -18.8027 -28.2905 -36.9712 -44.7868 -51.86 -58.0019 -63.5631 -68.3419 -72.344 -75.57749 -78.0505 -79.7704 -80.7696 -80.9886

s inf (kN/m²) - 0,5CMmax -18.14902 34.50366 73.74317 110.9539 144.9993 175.6517 203.3922 227.4805 249.2912 268.0334 283.7295 296.4112 306.1102 312.8556 316.7744 317.6334




s sup´ (kN/m²) 9.5154731 -101.881 -200.259 -291.589 -375.275 -451.196 -519.605 -580.115 -633.446 -679.182 -717.337 -747.9261 -770.966 -786.473 -794.513 -795.711

s sup (kN/m²) 28.285001 -3510.56 -6441.98 -7381.2 -8319.16 -9484.5 -10550.5 -11673.5 -12656.4 -13878.7 -14303.1 -14629.66 -15011.2 -15252.3 -15353 -15331.3

s inf (kN/m²) 930.54862 -2282.48 -4600.57 -6055.22 -7092.79 -6835.18 -6537.4 -5598.49 -4776.12 -3970.29 -4306.41 -4596.523 -4253.55 -4028.16 -3920.23 -3915.49

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



TENSÃO 11-TIPO 1

SEÇÕES DA PONTE

PROPRIEDADES


h(m) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

Ix(m4) 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202 0.2202

cg(m) (base) 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108 1.108

cg(m) (topo) 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542

x(m) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14.5

Wsup(m³) 0.4062731 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273 0.406273063 0.406273 0.406273 0.406273 0.406273

Winf(m³) 0.1987365 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736 0.198736462 0.198736 0.198736 0.198736 0.198736

A(m²) 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772 0.772

s sup` (kN/m²) - 0,5CMmin 2.9636829 -16.6434 -36.1389 -54.5636 -72.2237 -88.8581 -104.253 -118.588 -130.899 -141.631 -150.73 -158.1400256 -163.832 -167.851 -170.273 -170.869

s sup (kN/m²) - 0,5CMmin 1.4412935 -8.09397 -17.575 -26.5353 -35.1237 -43.2133 -50.7001 -57.6718 -63.6588 -68.8778 -73.3027 -76.90640547 -79.6746 -81.6288 -82.807 -83.0965

s inf (kN/m²) - 0,5CMmin -5.652683 31.74415 68.92829 104.07 137.7534 169.4805 198.8432 226.1859 249.6666 270.1354 287.4895 301.6231707 312.4798 320.1441 324.7651 325.9005




s sup´ (kN/m²) 2.9636829 -302.928 -588.259 -852.07 -1094.67 -1315.79 -1515.23 -1693.15 -1848.61 -1982.03 -2093.37 -2182.578928 -2249.62 -2294.53 -2317.41 -2320.56

s sup (kN/m²) 25.098744 -3622.63 -6658.25 -7693.61 -8720.09 -9966.26 -11105.1 -12293.5 -13333.1 -14604.2 -15069.3 -15428.48741 -15834.5 -16092 -16200.9 -16180.3

s inf (kN/m²) 943.04497 -1873.05 -3810.47 -4913.88 -5627.95 -5074.85 -4510.48 -3332.78 -2302.65 -1318.44 -1505.69 -1676.58976 -1244.14 -958.946 -820.869 -812.176

Fck (Mpa) 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

fc (kN/cm²) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2



TENSÃO 11-TIPO 2

SEÇÕES DA PONTE

47



3.11. LONGARINAS PREMOLDADAS – VÃO DE 30m 3.11.1. GRÁFICOS DOS ESFORÇOS MAJORADOS E SEM

PROTENSÃO MOMENTO FLETOR

CISALHAMENTO

48



FORÇA AXIAL

TORÇÃO

49



3.11.2. ARMAÇÃO À FLEXÃO-COMPRESSÃO – S3 (2m)

²13,3104 cmAs == f


FCK 30000 Tpinf 1253571.429 x/ds 0.0397

FPyd 1.71E+06 Epre 5.64E-03 x 0.06352

FY 4.35E+05 Rpd 2.50E+03 a 0.050816

Bf 1.2 a 0.114 Rcd 1.11E+03

Bw 0.14 x 0.143 Rsd -1.39E+03

dp 1.596 x/dp 0.090 Mrd 1739

ds 1.6 a<hf e x/dp<,259 OK As(cm2) -31.89

Aps(cm2) 16.8 Mrd 3844 Mrd/Md 1.00

As(cm2) 0 Mrd/Md 2.20 tem que ser maior do que 1

Np 2106 maior do que 1 As= 0

hf 0.25

Ep 2.00E+08

Md 1745.3

UNIDADES: KN e m, exeto onde indicado

50



²13,3104 cmAs == f


²13,3104 cmAs == f

FCK 30000 Tpinf 1182142.857 x/ds 0.0735

FPyd 1.71E+06 Epre 5.32E-03 x 0.1176

FY 4.35E+05 Rpd 3.75E+03 a 0.09408

Bf 1.2 a 0.171 Rcd 2.06E+03

Bw 0.14 x 0.214 Rsd -1.69E+03

dp 1.591 x/dp 0.135 Mrd 3160


Aps(cm2) 25.2 Mrd 5640 Mrd/Md 1.00



hf 0.25

Ep 2.00E+08

Md 3146.5


FCK 30000 Tpinf 1273928.571 x/ds 0.129

FPyd 1.71E+06 Epre 5.73E-03 x 0.2064

FY 4.35E+05 Rpd 4.16E+03 a 0.16512

Bf 1.2 a 0.190 Rcd 3.61E+03

Bw 0.14 x 0.238 Rsd -5.54E+02

dp 1.595 x/dp 0.149 Mrd 5456


Aps(cm2) 28 Mrd 6244 Mrd/Md 1.00



hf 0.25

Ep 2.00E+08

Md 5460.4


51



3.11.5. ARMAÇÃO À FLEXÃO-COMPRESSÃO – S16 (14,75m)

²57,12204 cmAs == f

FCK 30000 Tpinf 1198376.623 x/ds 0.15

FPyd 1.71E+06 Epre 5.39E-03 x 0.24

FY 4.35E+05 Rpd 4.58E+03 a 0.192

Bf 1.2 a 0.210 Rcd 4.20E+03

Bw 0.14 x 0.262 Rsd -3.83E+02

dp 1.598 x/dp 0.164 Mrd 6302


Aps(cm2) 30.8 Mrd 6839 Mrd/Md 1.00



hf 0.25

Ep 2.00E+08

Md 6306.3


52



3.11.6. CISALHAMENTO E TORÇÃO – S1 (0m)

263,195,1282 cmxAsl == f

mcmcAs /27,1210/5,1290 2==f


263,195,1282 cmxAsl == f

mcmcAs /18,815/5,1290 2==f

B(m) 1.20 Vperm 36.60 Protensão infinita d´(m) 0.04

b(m) 0.14 Vmovmax 30.30 Vpo 0.00 diamcab0 0.00

H(m) 1.65 Vmovmin -1.20 Nprot 35.10 bw(m) 0.14

h(m) 0.25 Mtd 25.70 Mo 0.01

fck(Mpa) 40.00 Msd 0.01

gc 1.40

fctd(Mpa) 1.75 Vc(tf) 47.45 retang.A 0.02 Mtda 20.70

alfav2 0.84 Vsw(tf) 47.41 retang.B 0.00 Mtdb 5.00

Vrd2(tf) 146.06 Ase 7.52 soma 0.02 Ae(m2) 0.09

Vc0(tf) 23.73 Asemin 1.96 Mtrd2 9.04 Ue(m) 3.26

M0/Msd 1.00 Vd/Vrd2 0.65 Asb 6.10

Vd(tf) 94.86 nºpernas 2.00 As90/perna 9.86 Asl(total) 19.88

Viga T - Cisalhamento - Torçao Unidades Tf e m

DADOS DE ENTRADA

DADOS DE SAIDA



H(m) 1.65 Vmovmin 0.50 Nprot 346.50 bw(m) 0.14

h(m) 0.25 Mtd 22.70 Mo 268.60

fck(Mpa) 40.00 Msd 248.60

gc 1.40





M0/Msd 1.00 Vd/Vrd2 0.53 Asb 5.39



DADOS DE ENTRADA

DADOS DE SAIDA

53




263,195,1282 cmxAsl == f

mcmcAs /18,815/5,1290 2==f



H(m) 1.65 Vmovmin 1.62 Nprot 402.50 bw(m) 0.14

h(m) 0.25 Mtd 21.40 Mo 323.00

fck(Mpa) 40.00 Msd 314.70

gc 1.40





M0/Msd 1.00 Vd/Vrd2 0.49 Asb 5.08



DADOS DE ENTRADA

DADOS DE SAIDA

54



3.12. TABULEIRO – VÃO DE 30m 3.12.1. ARMAÇÃO POSITIVA PRINCIPAL

Mdmáx = 41,41KNm ARMADURA NECESSÁRIA:

mcmcAs /18,815/5,12 2==f

3.12.2. ARMAÇÃO NEGATIVA PRINCIPAL

Md (kN x cm) b (cm) fck (MPa) h (cm) d (cm) d'

4141 100 30 22 16 6

Flexão Normal Simples

AS mínAS'

0.00

AS

6.24 3.80

55



Mdmín= 28,49KNm ARMADURA NECESSÁRIA:

mcmcAs /24,515/10 2==f


2849 100 30 22 18.5 3.5


AS mínAS'

0.00

AS

3.63 3.80

56



3.12.3. ARMAÇÃO NEGATIVA NO BALANÇO DA JUNTA DO

TABULEIRO

Pd= TB-45 x CI + SC x CI + COMB PERM Pd= 1,5 x 60 x 1,58 + 1,5 x 5 x 1,58 + (2+2+1,38) x 1,35 = 161,22KN

mcmcAs /85,710/10 2==f

Pd (kgf/m) Hd (kgf/m) h (cm)

16122 1421 22

a (cm) b (cm) c (cm)

25 100 10

d (cm) d`(cm) e (cm)

18.50 3.5 9.5

Tipo

fy d (kgf/cm²) fck (MPa) dcalc. (cm)

4348 30 18.5

σd,máx(kgf/cm²) fcdr (kgf/cm²)

34.71 113.14

Rsd (kgf/m) As,tir (cm²) Fc (kgf)

34,745 7.99 37,257

Ash (cm²/m) 4.00

<

Dados de entrada

Consolos

Resultados:

Biela de concreto - OK

VIGA BALANÇO

57



3.12.4. VERIFICAÇÃO DAS PLACAS PREMOLDADAS (FASE DE

CONSTRUÇÃO)

ARMADURA NECESSÁRIA:

mcmcAs /34,315/8 2==f

L 0.6 (m)

q 9.5 (kN/m)

P 0 (kN)

fck 30 (MPa) M 0.4275 kNxm

E 26071594 (kN/m²) Ra 2.85 kN

b 1 (m) Rb 2.85 kN

h 0.05 (m) Flecha 0.01 cm

I 1.04E-05 (m4) Flecha adm

Cobrimento 2.49 (cm) (L/200)

a 0 (m)

Dados

Tipo Adotado

1

0.3 OK!

M (kN x cm) b (cm) fck (MPa) h (cm) d (cm) d'

42.75 100 30 5 2.51 2.49


AS mínAS'

0.00

AS

0.56 0.86

58



3.13. TRANSVERSINAS DA SUPERESTRUTURA (40x140) – VÃO DE 30m

59



3.13.1. VERIFICAÇÃO À FLEXÃO Mdmáx= 310,41kNm ARMADURA NECESSÁRIA:

256,12204 cmAs == f

Mdmín= 369,65kNm ARMADURA NECESSÁRIA:

256,12204 cmAs == f


31041 40 30 140 120 20


AS mínAS'

0.00

AS

6.04 9.68


36965 40 30 140 136.5 3.5


AS mínAS'

0.00

AS

6.32 9.68

60



3.13.2. VERIFICAÇÃO AO CISALHAMENTO E TORÇÃO Vd = 127,47 kN ARMADURA NECESSÁRIA:

Força Cortante Reduzida (V) 127.5 kN

Força de Compressão (Nc) 0.0 kN

Força de Protensão (Np) 0.0 kN

Ns = Nc* f + Np * f p 0.0 kN

M0 0.0 kNm

Msd,max 0.0 kNm

Base da Seção de Concreto (bw ou bf ) 0.400 m

Altura da Seção de Concreto (h) 1.400 m

Cobrimento (d') 0.035 m

Área de armação longitudinal (As) 19.64 cm2

Área de concreto (Ac) 0.560 m2

Seção transversal totalmente tracionada? NÃO

Resistência nominal do concreto (fck) 30.00 MPa

Resistência de cálculo (fy wd)- Item 19.4.2 435 MPa

Coeficiente de minoração da resistência (c) 1.4

Coeficiente de majoração de carga (f ) 1.0

Coeficiente de majoração da força de protensão (f p) 0.9

fctd (0,7 * 0,3 * fck2/3) / c 1.45 MPa

k Valor absoluto de: 1,6 - d 1.00 m

r As / (bw * d) 0.0036

scp Ns / (bw * h) 0.00 MPa

Vd V * f 127.47 kN

av 2 1 - fck / 250 0.880

VRd2 0,27 * aV2 * fcd * bw * d 2779.92 kN

VC0 0,6 * fctd * bw * d 474.44 kN

M0/Msd,max Se Np 0 - Consultar item 17.4.2.2 da NBR 6118/2014 0.00

Vc Vc0(1+M0/Msd,max) ou 0 (para seção totalmente tracionada) 474.44 kN

Vsw Vd - Vc -346.97 kN

As90 VSW / 0,9 * d * fywd 0.00 cm2 / m

As90,min 0,2 * bw * fctm / fy wk 4.63 cm2 / m

smax(entre estribos) Item 18.3.3.2 da NBR 6118/2014 30.00 cm

smax(entre pernas) Item 18.3.3.2 da NBR 6118/2014 80.00 cm

Fases

A seção resiste a compressão da biela Vd < VRd2

Planilha para Dimensionamento de Seções de Viga ao Cisalhamento

Descrição

Geral:

Dados

Modelo I ( NBR 6118/2014: 17.4.2.2 )

61



Td = 0,0kNm

242,920/1062 cmcxAsl == f

mcmcAs /50,220/8 2==f

Tsd(kg.m) h(cm) b(cm) c1 (cm) fck(MPa)

0 140 40 4 30

2C1 A/u τtd (kN/cm2) τtd2 (kN/cm2)

8.0 15.6 0.000 0.471

A90 (cm2/m) Asl (cm2) S Máx (cm) As 90 Mín

(cm2/m)

Asl mín (cm2)

0.00 0.00 24 0.93 3.04

TORÇÃO

Dados de entrada:

Escolha o valor de he (A/u ≥ he ≥ 2c1) e he deve ser menor do que a

espessura real em caso de peças vazadas.

8

Resultados:

Ok

Armaduras:

2 0.046 Ok 2.32 3.04

Nº de pernas

Resumo

Verificação em conjuntoEstribos Totais

Asl (cm2)A90 (cm2/m/nº de pernas)

62



3.14. NEOPRENES – VÃO DE 30m

DADOS DE ENTRADA

Reação - Carga Permanente 39.43 t

Reação Máxima - Carga Móvel 36.23 t

Reação Mínima - Carga Móvel 0.00 t

Carga Horizontal 2.16 t OK

Rotação devido à Carga Permanente 0.005600 rd

Rotação associada a Nmax 0.009300 rd

Aparelho Circular 0 sim = 1 não = 0

Dimensões em planta do Aparelho a = 250 mm b = 400 mm

Altura do Aparelho 50 mm

Espessura da Chapa de Aço(t) 3 mm

Espessura da Cam. de Neoprene (d) 8 mm

Número de camadas de Neoprene 4

1- TENSÕES MÉDIAS DEVIDO ÀS CARGAS NORMAIS APLICADAS

SIGmax = 97.72 kg / cm² OK-< 135 kg/cm²

SIGmin = 53.23 kg / cm² OK - > 20 kg/cm²

TAUmax = 14.23 kg / cm²

2- TENSÕES DEVIDO À ROTAÇÃO

SIGcp = 100.31 kg / cm²

TAUalfa = 0.00 kg / cm²

3- TENSÕES NA CHAPA DE AÇO

SIGs = 260.58 kg / cm²

4- CÁLCULO DO DESLOCAMENTO

DELTA = 0.27 cm

4- TENSÕES FINAIS

SIGTmax = 97.72 kg / cm²

SIGTmin = 153.54 kg / cm²

TAUT = 14.23 kg / cm²

5- VERIFICAÇÕES

TENSÃO CONDIÇÃO ANÁLISE

Altura do Aparelho <= a/5 OK

SIGTmin > 20 kg / cm² OK

SIGs < 1400 kg/cm² OK

TAUT < 5G = 65 kg/cm² OK

Desl. Horizontal Delta/hn<= 0,7 OK

CÁLCULO DE VERIFICAÇÃO - APARELHO DE APOIO DE NEOPRENE FRETADO

63



3.15. ENCONTROS

64



3.15.1. VERIFICAÇÃO À FLEXÃO Mdmáx= 1072,27kNm ARMADURA NECESSÁRIA:

216,321616 cmAs == f


107227 172.5 25 130 117 13


AS mínAS'

0.00

AS

21.40 33.65

65



3.15.2. VERIFICAÇÃO AO CISALHAMENTO E TORÇÃO Vd = 1451,95kN ARMADURA NECESSÁRIA:

Td = 100,11kNm




Ns = Nc* f + Np * f p 0.0 kN

M0 0.0 kNm

Msd,max 0.0 kNm












fctd (0,7 * 0,3 * fck2/3) / c 1.28 MPa


r As / (bw * d) 0.0018


Vd V * f 1452.00 kN

av 2 1 - fck / 250 0.900

VRd2 0,27 * aV2 * fcd * bw * d 8720.34 kN

VC0 0,6 * fctd * bw * d 1546.38 kN




As90 VSW / 0,9 * d * fywd 0.00 cm2 / m


Fases



Descrição

Geral:

Dados

Modelo I ( NBR 6118/2014: 17.4.2.2 )

66



213,1415/1092 cmcxAsl == f

mcmcAs /18,815/5,1290 2==f

Tsd(kg.m) h(cm) b(cm) c1 (cm) fck(MPa)

10011 120 172.5 4 25

2C1 A/u τtd (kN/cm2) τtd2 (kN/cm2)

8.0 35.4 0.034 0.402

A90 (cm2/m) Asl (cm2) S Máx (cm) As 90 Mín

(cm2/m)

Asl mín (cm2)

0.62 3.45 30 0.82 4.54

TORÇÃO

Dados de entrada:

Escolha o valor de he (A/u ≥ he ≥ 2c1) e he deve ser menor do que a

espessura real em caso de peças vazadas.

8

Resultados:

Ok

Armaduras:

2 0.251 Ok 8.85 4.54

Nº de pernas

Resumo

Verificação em conjuntoEstribos Totais

Asl (cm2)A90 (cm2/m/nº de pernas)

67



3.15.3. VERIFICAÇÃO À FLEXÃO TRANSVERSAL

Mdmáx= 753,52kNm ARMADURA NECESSÁRIA:

298,21207 cmAs == f /por linha de estacas


75352 50 25 100 87 13


AS mínAS'

0.00

AS

21.43 7.50

68



3.16. ALAS E CORTINA

3.16.1. ESFORÇOS DEAD – peso próprio da estrutura.

EMP SOLO – empuxo de solo saturado, considerou-se s=18kN/m³ e K=0,33.

69



EMP SC – empuxo de sobrecarga, considerou-se q=10kN/m² e K=0,33.

LT – reação no consolo de apoio da laje de transição.

70



3.16.2. COMBINAÇÕES

71



3.16.3. ARMAÇÃO HORIZONTAL ALAS

ARMAÇÃO LADO SOLO – HORIZONTAL

15/5,12/18,8 2 cmcmAsadot f==

ARMAÇÃO LADO EXTERNO – HORIZONTAL

15/5,12/18,8 2 cmcmAsadot f==


6226 100 25 25 21.5 3.5


AS mínAS'

0.00

AS

6.99 3.75

72



3.16.4. ARMAÇÃO VERTICAL ALAS

ARMAÇÃO LADO SOLO – VERTICAL

20/10/93,3 2 cmcmAsadot f==

ARMAÇÃO LADO EXTERNO – VERTICAL

20/10/93,3 2 cmcmAsadot f==


1608 100 25 25 21.5 3.5


AS mínAS'

0.00

AS

1.74 3.75

73



3.16.5. ARMAÇÃO HORIZONTAL CORTINA

ARMAÇÃO LADO SOLO – HORIZONTAL

15/10/23,5 2 cmcmAs f==

ARMAÇÃO LADO EXTERNO – HORIZONTAL

15/10/23,5 2 cmcmAs f==


5450 100 25 30 26.5 3.5


AS mínAS'

0.00

AS

4.86 4.50

74



3.16.6. ARMAÇÃO VERTICAL CORTINA

ARMAÇÃO LADO SOLO – VERTICAL

15/10/23,5 2 cmcmAs f==

ARMAÇÃO LADO EXTERNO – VERTICAL

15/10/23,5 2 cmcmAs f==


1500 100 25 30 26.5 3.5


AS mínAS'

0.00

AS

1.31 4.50

75



3.17. ESTACAS PERTENCENTES AO ENCONTRO 1

3.17.1. SONDAGEM

76



3.17.2. DETERMINAÇÃO DO COEFICIENTE DE MOLAS

z SPT Kterreno C'R LI CR bCR 3bCR

0.5 3 300 900 2.335 192.7 77.1 231.2367

1.5 9 300 2700 1.774 2282.4 913.0 2738.922

2.5 6 300 1800 1.964 2291.6 916.6 2749.883

3.5 6 300 1800 1.964 3208.2 1283.3 3849.837

4.5 13 300 3900 1.619 10842.9 4337.2 13011.49

5.5 8 500 4000 1.608 13678.5 5471.4 16414.26

6.5 9 500 4500 1.562 18729.7 7491.9 22475.67

7.5 9 500 4500 1.562 21611.2 8644.5 25933.46

8.5 11 500 5500 1.485 31475.6 12590.3 37770.78

9.5 21 500 10500 1.264 78942.8 31577.1 94731.38

10.5 30 500 15000 1.156 136271.7 54508.7 163526.1

11.5 30 500 15000 1.156 149250.0 59700.0 179100

12.5 40 500 20000 1.076 232434.1 92973.6 278920.9

13.5 40 500 20000 1.076 251028.9 100411.5 301234.6

14.5 50 500 25000 1.017 356365.3 142546.1 427638.3

15.5 50 500 25000 1.017 380942.2 152376.9 457130.6

16.5 50 500 25000 1.017 405519.1 162207.6 486622.9

17.5 50 500 25000 1.017 430096.0 172038.4 516115.2

18.5 50 500 25000 1.017 454673.0 181869.2 545607.5

19.5 50 500 25000 1.017 479249.9 191699.9 575099.8

20.5 50 500 25000 1.017 503826.8 201530.7 604592.1

77



3.17.3. VERIFICAÇÃO DA RESISTÊNCIA DO SOLO

m

m

f (cm) 41

PROF. SPT MAT.

(m) P.P.C.V. D. - Q. MILTON A.H.T. U.R.A. ERNANI MÉDIA

1 3 ARGS 0.83 0.00 0.95 0.00 0.00 1.82 1

2 9 ARGS 3.58 3.96 3.78 1.37 0.83 3.53 3

3 6 ARGS 6.06 8.91 5.68 4.46 3.32 6.81 6

4 6 ARGS 8.26 11.88 7.57 6.52 4.99 13.12 9

5 13 ARE 17.13 14.85 11.67 8.58 6.65 16.52 13

6 8 ARE 18.71 17.27 14.19 13.05 10.25 22.38 16

7 9 ARE 22.33 19.76 17.03 15.79 12.46 27.01 19

8 9 ARE 25.73 22.52 19.87 18.88 14.96 28.41 22

9 11 ARE 28.14 25.29 23.34 21.97 17.45 35.79 25

10 21 ARE 37.81 28.57 29.96 25.75 20.50 46.85 32

11 30 ARE 50.98 34.39 39.43 32.96 26.31 60.35 41

12 30 ARE 62.17 42.42 48.89 43.26 34.62 79.24 52

13 40 ARE 79.52 50.39 61.51 53.56 42.93 94.15 64

14 40 ARE 92.45 60.79 74.12 67.29 54.01 107.91 76

15 50 ARE 103.41 71.13 89.89 81.02 65.09 121.68 89

16 50 ARE 114.36 83.87 105.66 94.75 76.17 131.47 101

17 50 ARE 123.12 96.56 121.43 108.48 87.25 141.25 113

18 50 ARE 131.87 109.19 137.20 122.22 98.33 151.03 125

19 50 ARE 140.63 121.78 152.98 135.95 109.41 160.82 137

20 50 ARE 149.38 134.33 168.75 149.68 120.49 170.60 149

SONDAGEM SM-18

CARGA ADMISSÍVEL - (t)

COTA DE CÁLCULO 0.00

LIMITE DA SONDAGEM 20

OBRA PONTE RIO SEM INFORMAÇÃO 1

TRABALHO FUNDAÇÃO

78



3.17.4. CARGA NOMINAL POR ESTACA

As estacas pertencentes ao Encontro 1 deverão possuir 14 metros de comprimento e carga mínima no teste de PDA de 70tf.

79



3.17.5. ARMAÇÃO DAS ESTACAS

80



ARMADURA LONGITUDINAL

260,6min cmAs = 208,16168 cmAs == f

81



ARMADURA TRANSVERSAL

mcmpernamcmcAs /24,6//12,310/3.690 22 ===f




Ns = Nc* f + Np * f p 0.0 kN

M0 0.0 kNm

Msd,max 0.0 kNm

Diâmetro da Viga 0.410 m












fctd (0,7 * 0,3 * fck2/3) / c 1.11 MPa


r As / (bw * d) 0.0184


Vd V * f 27.08 kN

av 2 1 - fck / 250 0.920

VRd2 0,27 * aV2 * fcd * bw * d 310.19 kN

VC0 0,6 * fctd * bw * d 57.97 kN




As90 VSW / 0,9 * d * fywd 0.00 cm2 / m



Modelo I ( NBR 6118/2003: 19.4.1 )

Fases

Dados


Descrição

Geral:

82



3.18. ESTACAS PERTENCENTES AO ENCONTRO 2

3.18.1. SONDAGEM

83



3.18.2. DETERMINAÇÃO DO COEFICIENTE DE MOLAS

z SPT Kterreno C'R LI CR bCR 3bCR

0.5 3 300 900 2.335 192.7 77.1 231.2367

1.5 8 300 2400 1.827 1970.0 788.0 2363.954

2.5 7 300 2100 1.889 2778.5 1111.4 3334.247

3.5 10 300 3000 1.728 6075.4 2430.1 7290.432

4.5 10 300 3000 1.728 7811.2 3124.5 9373.412

5.5 15 500 7500 1.374 30011.8 12004.7 36014.13

6.5 14 500 7000 1.398 32537.8 13015.1 39045.37

7.5 30 500 15000 1.156 97336.9 38934.8 116804.3

8.5 30 500 15000 1.156 110315.2 44126.1 132378.2

9.5 40 500 20000 1.076 176649.9 70660.0 211979.9

10.5 40 500 20000 1.076 195244.7 78097.9 234293.6

11.5 50 500 25000 1.017 282634.5 113053.8 339161.4

12.5 50 500 25000 1.017 307211.5 122884.6 368653.7

13.5 50 500 25000 1.017 331788.4 132715.3 398146

14.5 50 500 25000 1.017 356365.3 142546.1 427638.3

15.5 50 500 25000 1.017 380942.2 152376.9 457130.6

16.5 50 500 25000 1.017 405519.1 162207.6 486622.9

17.5 50 500 25000 1.017 430096.0 172038.4 516115.2

18.5 50 500 25000 1.017 454673.0 181869.2 545607.5

19.5 50 500 25000 1.017 479249.9 191699.9 575099.8

20.5 50 500 25000 1.017 503826.8 201530.7 604592.1

84



3.18.3. VERIFICAÇÃO DA RESISTÊNCIA DO SOLO

m

m

f (cm) 41

PROF. SPT MAT.

(m) P.P.C.V. D. - Q. MILTON A.H.T. U.R.A. ERNANI MÉDIA

1 3 ARGS 0.83 0.00 0.95 0.00 0.00 1.67 1

2 8 ARGS 3.30 3.96 3.47 1.37 0.83 3.53 3

3 7 ARGS 5.97 8.42 5.68 4.12 3.05 7.16 6

4 10 ARGS 9.36 11.88 8.83 6.52 4.99 10.07 9

5 10 ARGS 12.76 16.51 11.99 9.96 7.76 17.47 13

6 15 ARE 22.86 20.99 16.72 13.39 10.53 24.62 18

7 14 ARE 28.14 23.53 21.13 18.54 14.68 38.72 24

8 30 ARE 43.93 27.54 30.60 23.34 18.56 52.58 33

9 30 ARE 56.18 35.69 40.06 33.64 26.87 69.87 44

10 40 ARE 72.65 43.72 52.67 43.94 35.18 87.57 56

11 40 ARE 87.12 54.21 65.29 57.68 46.26 101.34 69

12 50 ARE 98.08 64.60 81.06 71.41 57.34 115.10 81

13 50 ARE 109.03 77.42 96.83 85.14 68.42 124.89 94

14 50 ARE 117.79 90.15 112.60 98.87 79.49 134.67 106

15 50 ARE 126.54 102.82 128.37 112.60 90.57 144.46 118

16 50 ARE 135.29 115.42 144.14 126.34 101.65 154.24 130

17 50 ARE 144.05 127.98 159.91 140.07 112.73 164.02 141

18 50 ARE 152.80 140.51 175.69 153.80 123.81 173.81 153

19 50 ARE 161.56 153.00 191.46 167.53 134.89 183.59 165

20 50 ARE 170.31 165.47 207.23 181.27 145.97 193.38 177

SONDAGEM SM-19

CARGA ADMISSÍVEL - (t)

COTA DE CÁLCULO 0.00

LIMITE DA SONDAGEM 20

OBRA PONTE RIO SEM INFORMAÇÃO 1

TRABALHO FUNDAÇÃO

85



3.18.4. CARGA NOMINAL POR ESTACA

As estacas pertencentes ao Encontro 2 deverão possuir 11,50 metros de comprimento e carga mínima no teste de PDA de 70tf.

86



3.18.5. ARMAÇÃO DAS ESTACAS

87



ARMADURA LONGITUDINAL

260,6min cmAs = 208,16168 cmAs == f

88



ARMADURA TRANSVERSAL

mcmpernamcmcAs /24,6//12,310/3.690 22 ===f




Ns = Nc* f + Np * f p 0.0 kN

M0 0.0 kNm

Msd,max 0.0 kNm

Diâmetro da Viga 0.410 m












fctd (0,7 * 0,3 * fck2/3) / c 1.11 MPa


r As / (bw * d) 0.0184


Vd V * f 27.08 kN

av 2 1 - fck / 250 0.920

VRd2 0,27 * aV2 * fcd * bw * d 310.19 kN

VC0 0,6 * fctd * bw * d 57.97 kN




As90 VSW / 0,9 * d * fywd 0.00 cm2 / m



Modelo I ( NBR 6118/2003: 19.4.1 )

Fases

Dados


Descrição

Geral:

89



MEMÓRIA DE

CÁLCULO DE QUANTITATIVOS

PONTE RIO SEM INFORMAÇÃO 1 (RODOVIA MT-160)

90



1. Introdução

1.1 Descrição da Obra e Trabalho

O presente trabalho apresentará a memória de cálculo dos quantitativos do projeto executivo da Ponte Rio Sem Informação 1.

1.2 Normas Utilizadas

• NBR 6118/2014 – Projetos de Estruturas de Concreto-Procedimento;

• NBR 7187/1987– Projetos e Execução de Pontes em Concreto Armado e Protendido;

• NBR 7188/2013 – Carga móvel em Ponte Rodoviária e Passarela de Pedestre;

• NBR 6122/1996 – Projeto e execução de Fundações;

• NBR 8681/1996 – Ações e segurança nas estruturas;

91



4. SUPER ESTRUTURA 2.1 Vigas perfil I (Longarinas): Concreto 40MPa

75,293363,0 =Volume

³45,69 mVolume=

Forma

3363,02775,29042,4 +=Área

²38,839 mÁrea =

Aço CA-50:

kgPeso 14194=

Cordoalha D15,2mm:

mComp 5915)5,15,15,29(267 =++=

kgmkgPeso 95,6683/13,15915 ==

Cordoalha D12,7mm:

mComp 121=

kgPeso 94=

Protensão:

182

726

=

=

Und

Und

Comprimento de Mangueiras:

)81812(27 ++=Comp

mComp 532=

Lançamento

tPeso

mtmPeso

63,173

³/5,2³45,69

=

=

92



2.2 Pré-lajes: Concreto 30MPa

5205,0)6,08,0(09,15205,019,28,0 ++=Volume

³52,8 mVolume=

Forma

5205,04)09,1(5205,02)6,08,0(5205,02)19,28,0( ++++=Área

²17,34 mÁrea =

Aço CA-50 – Pré Laje

kgPeso 1214=

Aço CA-25 – Pré Laje

kgPeso 98=

Lançamento

tPeso

mtmPeso

3,21

³/5,2³52,8

=

=

2.3 Laje 2ª Etapa: Concreto 30MPa

301941,1)( =TOTALVolume

³23,58)( mVolumeTOTAL =

Forma

30134,0 =Área

²20,10)( mÁrea TOTAL =

Aço CA-50 – Laje 2ª Etapa:

kgPeso 5260=

Escoramento

605,15,1 =Volume

³135mVolume=

93



2.4 Tranversinas: Concreto 30MPa

2)4,025,123,024,025,106,16()( +=TOTALVolume

³82,6)( mVolumeTOTAL =

Forma

2))4,025,12(23,02)4,025,12(06,16( +++=Área

²56,39)( mÁrea TOTAL =

Aço CA-50- Transversinas:

kgPeso 641=

2.5. Lajes de Transição Concreto das Lajes de Transição 25 MPa

40,4525,040,4507,0 +=LajestrVolume

³51,16 mVolumelajestr =

Forma das Lajes de Transição

)225,01,2225,00,4(8 +=EncontroForma

²40,24 mFormaEncontro =

Concreto Magro Fck 9Mpa

230,805,00,4 =LajestrVolume

³32,3 mVolumelajestr =

Aço CA-50 :

kgPeso 1269=

Cordoalha D12,7mm:

mComp 32=

kgPeso 28=

3. MESO ESTRUTURA

94



3.1. Encontros Concreto dos Encontros 25 MPa

)8,878,2(2 =EncontroVolume

³93,48 mVolumeEncontro =

Forma dos Encontros

478,228,830,6 +=EncontroForma

²0,122 mFormaEncontro =

Aço CA-50 :

kgPeso 2420=

3.2.Alas Concreto 25 MPa

44,04,002,4425,0854,6 +=AlasVolume

³43,9 mVolumeAlas =

Forma

846,8416,925,0 +=AlasForma

²84,76 mFormaAlas =

Aço CA-50 :

kgPeso 968=

3.3. Neoprene

³80,721452,05,20,4 dm=

Peso = 0,39kg/dm³ Peso = 187kg 3.4. Grout

³15,1071438,08,33,5 dm=

3.5 Escoramento E1 = E2 - Laje = 0,25m x 1,45m x 8,8m x 2und = 6,38m³

95



- Alas e parede = 2,5m x 10,80m x 1,45/2 x 2uns = 39,15 Ponte Branca

Volume = 61,88m² x 4m = 247,52m³

96



4. INFRA-ESTRUTURA 4.1. Estacas Raiz Ø41mm Comprimento em solo

=+ 34,131000,1610

moCompriment 40,273=

Aço CA-50 :

kgPeso 4413=

4.2. Demolição concreto armado Altura = 1,0m Diâmentro = 0,41m Estacas = 20und Volume = 2,64m³ 4.3. Bloco de apoio Altura = 1,0m Largura = 2,50m Comprimento = 8,80m Blocos = 2und Volume de concreto 25MPa = 1,0m x 2,5m x 8,80m = 44,0m³ Forma = (2,50 + 2,50 + 8,80 + 8,80) x 1,0m x 2 = 45,2m² Concreto magro = 8,80m x 2,5m x 0,05 x 2und = 2,2m³ Aço CA-50 = 2136kg

97



4.4. Movimentação de terra – Escavação Escavação

Área = 2,5m² Comprimento = 10m Unidades = 2und Volume = 2,5 x 10 x 2 = 50m³ Reaterro Área = 1,25m² Comprimento = 10m Unidades = 2und Volume = 1,25 x 10 x 2 = 25m³

98



5. Acabamentos e Outros 5.1. Guarda-rodas New Jersey - moCompriment 28,77=

- 3

25 85,17 mVolume MPAconcreto =

- 210,139 mArea forma =

- kgCAAço 149750 =−−

5.2. CBUQ

355,18 mcbuq =

5.3.Junta Flex AW-100, Jeene JJ-5070 VV ou similar Comprimento = 8,80 x 2 Comprimento = m60,17

5.4. Limpeza da Ponte

292,340

74,3880,8

mA

A

=

=

5.5. Pintura com nata de cimento

21,139 mA

rodasguardaáreaA

=

−−=

5.6. Dreno D100 Unidade = 12

99

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