Trabalho de Infraestrutura de Estradas e Rodovias -

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1 
Trabalho de Infraestrutura de Estradas e Rodovias 
Wilian 
 
 
Dados do Projeto 
Distância Inicial = 188 m 
Distância Final = 180 m (*) 
Velocidade de Projeto = 100 Km/h 
Valor de Ft (Tabelado) = 0,28 
 
PC= 19+5,50m (*) 
PT= 30+5,50m (*) 
TS= 48+15,70m (*) 
SC= 58+15,70m (*) 
CS= 72+12,80m (*) 
ST= 79+12,80m (*) 
(*) Valores alterados para resolver o exercício. 
 
 Calculo da Distância “L”: 
 
L1= PT – PC= (30+5,50) – (19+5,50)= 605,50 – 385,50= 220m 
L2= TS – PT= (48+15,70) – (30+5,50)= 975,70 – 605,50= 370,20m 
L3= SC – TS= (58+15,70) – (48+15,70)= 1215,70 – 975,70= 200,00m 
L4= CS – SC= (72+12,80) – (60+15,70)= 1452,80 – 1215,70= 277,10m 
L5= ST – CS= (79+12,80) – (72+12,80)= 1592,80 – 1452,80= 140,00m 
 
∑= 188m – 180m = 8m 
 
 
 Cálculo da Inclinação “i” 
 
188 + (i1 * L1) – (i 2 * L2) + (i 3 * L3) – (i 4 * L4) + (i 5 * L5) = 180 
188–180+[(1,5/100)*220]–[(1,9/100)*370,20]+[(1,5/100)*200]–[(1,0/100)*277,10]+ 
[(i 5*140)=0 
8 + 3,3 – 7,0 + 3,0 – 2,8 + 4,5 + (i5*140) = 0 
i 5= 4,5/140 
i 5= 0,032 * 100 
i 5= 3,2% 
 
 Cálculo do Delta “𝜕” 
𝜕i1= i2 – i1 = (-1,9%) – 1,5%= –3,4% 
𝜕i2= i3 – i2 = 1,5% – (-1,9%)= 3,4% 
𝜕i3= i4 – i3 = (-1,0%) – 1,5%= –2,5% 
𝜕i4= i5 – i4 = 3,2% – (-1,0%)= 4,2% 
 2 
 Determinação do “dp”: 
 
𝑑𝑝 = 0,7 ∗ 𝑉 +
V2
255 ∗ (𝑓𝑡 + 𝑖)
 𝑑𝑝 = 0,7 ∗ 100 +
1002
255 ∗ (0,28 + 0)
 
 
𝑑𝑝 = 210,06 
 
 
 Orientação das Curvas do Projeto: 
- Curvas 1 e 3: Convexa 
- Curvas 2 e 4: Côncava 
 
 
 Cálculo do “LCmín” para Cada Curva: 
 
LCmín Para a Curva 1 (CONVEXA) 
 Supondo que LC > dp = 210,06m 
(*) Na fórmula, considere delta minúsculo “𝜕" 
 
𝐿𝐶𝑚í𝑛 =
𝜕𝑖 ∗ 𝑑𝑝2
4,12
 𝐿𝐶𝑚í𝑛 =
(3,4/100) ∗ 100²
4,12
 
 
𝐿𝐶𝑚𝑖𝑛 =
0,034 ∗ 100²
4,12
 
 
 
 𝐿𝐶𝑚í𝑛 = 364,13  LCmin > dp – OK. 
 
Adotado: LCmín= 380,00m 
 
 
LCmín para a Curva 2 (CÔNCAVA) 
 Supondo que LC < dp = 210,06m 
(*) Na fórmula, considere delta minúsculo “𝜕” 
 
 𝐿𝐶𝑚í𝑛 = 2 ∗ 𝑑𝑝 −
1,22 + 0,335 ∗ (𝑓𝑡 + 𝑖)
𝜕𝑖
 
 𝐿𝐶𝑚í𝑛 = 2 ∗ 210,06 −
1,22 + 0,335 ∗ (0,28 + 0)
(
3,4
100)
 
 
 
𝐿𝐶𝑚í𝑛 = 168,00𝑚  LCmin > dp – OK. 
 
Adotado: LCmín= 180,00m 
 
 3 
 
LCmín Para a Curva 3 (CONVEXA) 
 Supondo que LC > dp = 210,06m 
(*) Na fórmula, considere delta minúsculo “𝜕”. 
𝐿𝐶𝑚í𝑛 =
𝜕𝑖 ∗ 𝑑𝑝2
4,12
 𝐿𝐶𝑚í𝑛 =
(2,5/100) ∗ 100²
4,12
 
 
𝐿𝐶𝑚í𝑛 = 267,74  LCmin > dp – OK. 
 
Adotado: LCmín= 280,00m 
 
 
LCmín para a Curva 4 (CÔNCAVA) 
 Supondo que LC > dp = 210,06m 
(*) Na fórmula, considere delta minúsculo “𝜕” 
𝐿𝐶𝑚í𝑛 =
𝜕𝑖 ∗ 𝑑𝑝²
1,22 + 0,335 ∗ (𝑓𝑡 + 𝑖)
 
 
𝐿𝐶𝑚í𝑛 =
(4,2/100) ∗ 100²
1,22 + 0,335 ∗ (0,28 + 0)
 
 
𝐿𝐶𝑚í𝑛 = 216,57𝑚  LCmin > dp – OK. 
 
Adotado: LCmín= 260,00m 
 
 
 Cálculo da Razão de Mudança de Rampa (rmr) 
(*) Na fórmula, considere delta minúsculo “𝜕” 
 
𝑟𝑚𝑟 =
𝜕𝑖
𝐿𝐶
 
 rmr= (3,4/100)/380 = 0,00009°/m 
rmr= (3,4/100)/180 = 0,00019°/m 
rmr= (2,5/100)/280 = 0,00009°/m 
rmr= (4,9/100)/260 = 0,00019°/m 
 
 
 Cálculo do Raio de Curvatura das Rampas (Rv) 
(*) Na fórmula, considere delta minúsculo “𝜕” 
 
𝑅𝑣 =
𝐿𝐶
𝜕𝑖
 
 
Rv= 380/ (3,4/100) = 11.176,47m 
Rv= 180/ (3,4/100) = 5.294,12m 
Rv= 280/ (2,5/100) = 11,200,00m 
Rv= 260/ (4,9/100) = 5.224,59m 
 
 4 
 
 Locação da Curva 1 
 
PIV= ? 
PIV=PT 
PIV= 30+5,50m 
LC/2= ? 
LC= 380 380/2 = 190 
LC/2= 9+10,00m 
 
 
 
PCV= ? 
PCV=PIV – LC/2 
PCV= (30+5,50) – (9+10,00) 
PCV= 21-4,50m 
PTV= ? 
PTV=PIV + LC/2 
PTV= (30+5,50) + (9+10,00) 
PTV= 39+15,50m 
 
 
Cota PCV= 188+(1,5/100)*30 
Cota PCV= 188,45m 
 
 
 
d’= PCV – PC 
d’= (21-4,50) – (19+5,50) 
d’= 30m 
Cota PTV= 188+(1,5/100)*220,0-(1,9/100)*190 
Cota PTV= 187,69m 
 
d’’= PTV – PT 
d’’= (39+15,50) – (30+5,50) 
d’’= 190m 
 
 
 𝐿𝑜 =
𝑖1∗𝐿𝐶
𝜕𝑖
 
 
𝐿𝑜 =
(1,5/100) ∗ 380
(3,4/100)
 
 
𝐿𝑜 = 7 + 18,77𝑚 
E(V)= PCV + Lo 
E(V)= (21-4,50) + (7+18,77) 
E(V)= 29-5,73m 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 Locação da Curva 2 
 
PIV= ? 
PIV=TS 
PIV= 46+15,70m 
LC/2= ? 
LC= 180 180/2 = 90 
LC/2= 4+10,00m 
 
 
 
PCV= ? 
PCV=PIV – LC/2 
PCV= (46+15,70) – (4+10,00) 
PCV= 42+5,70m 
PTV= ? 
PTV=PIV + LC/2 
PTV= (46+15,70) + (4+10,00) 
PTV= 51+5,70m 
 
 
Cota PCV= 188+(1,5/100)* 220,0-(1,9/100)*240,2 
Cota PCV= 186,74m 
 
 d’= PCV – PT 
d’= (42+5,70) – (30+5,50) 
d’= 240,20m 
 
Cota PTV= 188+(1,5/100)*220,0-(1,9/100)*370,20+(1,5/100)*50 
Cota PTV= 186,38m 
 d’’= PTV – TS 
d’’= (51+5,70) – (48+15,70) 
d’’= 50m 
 
 
 
𝐿𝑜 =
𝑖1 ∗ 𝐿𝐶
𝜕𝑖
 
 
𝐿𝑜 =
(1,9/100) ∗ 180
(3,4/100)
 
 
𝐿𝑜 = 5 + 10,00𝑚 
E(V)= PCV + Lo 
E(V)= (42+5,70) + (5+10,00) 
E(V)= 48-7,28m 
 
 
 
 
 
 
 
 
 
 
 6 
 Locação da Curva 3 
 
PIV= ? 
PIV=SC 
PIV= 58+15,70m 
LC/2= ? 
LC= 280 280/2 = 140 
LC/2= 7+0,00m 
 
 
 
PCV= ? 
PCV=PIV – LC/2 
PCV= (58+15,70) – (7+0,00) 
PCV= 51+15,70m 
PTV= ? 
PTV=PIV + LC/2 
PTV= (58+15,70) + (7+0,00) 
PTV= 66-4,30m 
 
 
Cota PCV= 188+(1,5/100)* 220,0-(1,9/100)*370,20+(1,5/100)*60 
Cota PCV= 185,17m 
 
 d’= PCV – TS 
d’= (51+15,70) – (48+15,70) 
d’= 60m 
 
Cota PTV= 188+(1,5/100)*220,0-(1,9/100)*370,20+(1,5/100)*200-(1/100)*140 
Cota PTV= 185,87m 
 d’’= PTV – SC 
d’’= (66-4,30) – (58+15,70) 
d’’= 140m 
 
 
 
𝐿𝑜 =
𝑖1 ∗ 𝐿𝐶
𝜕𝑖
 
 
𝐿𝑜 =
(1,5/100) ∗ 280
(2,5/100)
 
 
𝐿𝑜 = 8 + 5,00𝑚 
E(V)= PCV + Lo 
E(V)= (51+15,70) + (8+5,00) 
E(V)= 60+0,70m 
 
 
 
 
 
 
 
 
 
 
 7 
 Locação da Curva 4 
 
PIV= ? 
PIV=CS 
PIV= 72+12,80m 
LC/2= ? 
LC= 220 220/2 = 110 
LC/2= 5+10,00m 
 
 
 
PCV= ? 
PCV=PIV – LC/2 
PCV= (72+12,80) – (5+10,00) 
PCV= 67+2,80m 
PTV= ? 
PTV=PIV + LC/2 
PTV= (72+12,80) + (5+10,00) 
PTV= 78+2,80m 
 
 
Cota PCV= 188+(1,5/100)* 220,0-(1,9/100)*370,20+(1,5/100)*200-
(1/100)*167,10 
Cota PCV= 185,60m 
 
 
 
d’= PCV – SC 
d’= (67+2,80) – (58+15,70) 
d’= 167,10m 
 
Cota PTV= 188+(1,5/100)*220,0-(1,9/100)*370,20+(1,5/100)*200-
(1/100)*277,10+(3,2/100)*110 
Cota PTV= 188,03m 
 d’’= PTV – CS 
d’’= (78+2,80) – (72+2,80) 
d’’= 110,00m 
 
 
 
𝐿𝑜 =
𝑖1 ∗ 𝐿𝐶
𝜕𝑖
 
 
𝐿𝑜 =
(1,0/100) ∗ 220
(4,2/100)
 
 
𝐿𝑜 = 2 + 14,78𝑚 
E(V)= PCV + Lo 
E(V)= (67+2,80) + (2+14,78) 
E(V)= 70-2,42m 
 
 
 
 
 
 
 
 
 
 8 
 Equação da Parábola 
 
𝑦 =
𝜕𝑖
2 ∗ 𝐿𝐶
 ∗ 𝑋2 + X 
 
 
 
Para a Curva 1: 
 
𝑦 =
(−3,4/100)
2 ∗ 380
 ∗ 𝑋2 + X 
 
𝑦 = −0,00004 ∗ 𝑋2 + 0,015 ∗ 𝑋 
 
 
 
Para a Curva 2: 
 
𝑦 =
(3,4/100)
2 ∗ 180
 ∗ 𝑋2 + X 
 
𝑦 = −0,00009 ∗ 𝑋2 − 0,019 ∗ 𝑋 
 
Para a Curva 3: 
 
𝑦 =
(−2,5/100)
2 ∗ 280
 ∗ 𝑋2 + X 
 
𝑦 = −0,00004 ∗ 𝑋2 + 0,015 ∗ 𝑋 
 
Para a Curva 4: 
 
𝑦 =
(4,2/100)
2 ∗ 220
 ∗ 𝑋2 + X 
 
𝑦 = −0,00010 ∗ 𝑋2 − 0,010 ∗ 𝑋 
 
 
 
 
 LOCAÇÃO DA CURVA 1: 
 
 Cálculo das Distâncias entre pontos”: 
 
d1= (21+0,00)-(21-34,5)= 4,50m 
d2= (22+0,00)-(21+0,00)=20,00m 
d3= (23+0,00)-(22+0,00)= 20,00m 
d4= (24+0,00)-(23+0,00)= 20,00m 
d5= (25+0,00)-(24+0,00)= 20,00m 
d6= (26+0,00)-(25+0,00)= 20,00m 
d7= (27+0,00)-(26+0,00)= 20,00m 
d8= (28+0,00)-(27+0,00)= 20,00m 
d9= (29-5,73)-(28+0,00)= 14,27m 
d10= (29+0,00)-(29-5,73)= 5,73m 
d11= (30+0,00)-(29+0,00)= 20,00m 
d12= (30+5,50)-(30+0,00)= 5,50m 
d13= (31+0,00)-(30+5,50)= 14,50m 
d14= (32+0,00)-(31+0,00)= 20,00m 
d15= (33+0,00)-(32+0,00)= 20,00m 
d16= (34+0,00)-(33+0,00)= 20,00m 
d17= (35+0,00)-(34+0,00)= 20,00m 
d18= (36+0,00)-(35+0,00)= 20,00m 
d19= (37+0,00)-(36+0,00)= 20,00m 
d20= (38+0,00)-(37+0,00)= 20,00m 
d21= (39+0,00)-(38+0,00)= 20,00m 
d22= (39+15,50)-(39+0,00)= 15,50m 
 
 
 Cálculo do “CR”: 
 
 9 
SUBINDO: 
PCV-1= 188,45m 
E21= (1,5/100) * 4,50= 0,007 
E21= 188,75+0,07= 188,52m 
E22= (1,5/100) * 20= 0,30 
E22= 188,52+0,30= 188,82m 
E23= (1,5/100) * 20= 0,30 
E23= 188,82+0,30= 189,12m 
E24= (1,5/100) * 20= 0,30 
E24= 189,12+0,30= 189,42m 
E25= (1,5/100) * 20= 0,30 
E25= 189,42+0,30= 189,72m 
E26= (1,5/100) * 20= 0,30 
E26= 189,72+0,30= 190,02m 
E27= (1,5/100) * 20= 0,30 
E27= 190,02+0,30= 190,32m 
E28= (1,5/100) * 20= 0,30 
E28= 190,32+0,30= 190,62m 
E(V)-1= (1,5/100) * 14,27= 0,21 
E(V)-1= 190,62+0,21= 190,83m 
E29= (1,5/100) * 5,73= 0,09 
E29= 190,83+0,09= 190,92m 
E30= (1,5/100) * 20= 0,30 
E30= 190,92+0,30= 191,22m 
PIV-1= (1,5/100) * 5,5= 0,08 
PIV-1= 191,22+0,08= 191,30m 
DESCENDO: 
E31= (1,9/100) * 14,50= 0,28 
E31= 191,30 - 0,28= 191,02m 
E32= (1,9/100) * 20= 0,38 
E32=191,02 – 0,38 = 190,64m 
E33= (1,9/100) * 20= 0,38 
E33=190,64 – 0,38= 190,26m 
E34= (1,9/100) * 20= 0,38 
E34= 190,26 – 0,38= 189,88m 
E35= (1,9/100) * 20= 0,38 
E35= 189,88 – 0,38= 189,50m 
E36= (1,9/100) * 20= 0,38 
E36= 189,50 – 0,38= 189,12m 
E37= (1,9/100) * 20= 0,38 
E37= 189,12 – 0,38= 188,74m 
E38= (1,9/100) * 20= 0,38 
E38= 188,74 – 0,38= 188,36m 
E39= (1,9/100) * 20= 0,38 
E39= 188,36 – 0,38= 187,98m 
PIV-1= (1,9/100) * 15,50= 0,29 
PIV-1= 187,98 – 0,29= 187,69m 
 
 
 Cálculo de “X” 
 
PCV-1= 0,0m 
E21= (21+0,0)–(21-4,50)= 4,50m 
E22= (22+0,0)–(21-4,50)= 24,50m 
E23= (23+0,0)–(21-4,50)= 44,50m 
E24= (24+0,0)–(21-4,50)= 64,50m 
E25= (25+0,0)–(21-4,50)= 84,50m 
E26= (26+0,0)–(21-4,50)= 104,50m 
E27= (27+0,0)–(21-4,50)= 124,50m 
E28= (28+0,0)–(21-4,50)= 144,50m 
E(V)-1= (29-5,73)–(21-4,5)= 158,77m 
E29= (29+0,0)–(21-4,50)= 164,50m 
E30= (30+0,0)–(21-4,50)= 184,50m 
PIV-1= (30+5,50)–(21-4,50)= 190,00m 
E31= (39+15,5)–(30+5,5)= 175,5m 
E32= (39+15,5)–(31+0,0)= 155,5m 
E33= (39+15,5)–(32+0,0)= 135,5m 
E34= (39+15,5)–(33+0,0)= 115,5m 
E35= (39+15,5)–(34+0,0)= 95,5m 
E36= (39+15,5)–(35+0,0)= 75,5m 
E37= (39+15,5)–(36+0,0)= 55,5m 
E38= (39+15,5)–(37+0,0)= 35.5m 
E39= (39+15,5)–(38+0,0)= 15,5m 
PIV-1= 0,0m 
 
 
 10 
 Cálculo das Flechas: 
 
𝑓 =
𝜕𝑖
2 ∗ 𝐿𝐶
 ∗ 𝑋2 
 
𝑓 (𝑃𝐶𝑉) =
(−3,4/100)
2 ∗ 380
 ∗ 0,002 = 0,00 
 
𝑓 (𝐸21) =
(−3,4/100)
2 ∗ 380
 ∗ 4,502 = −0,001 
 
𝑓 (𝐸22) =
(−3,4/100)
2 ∗ 380
 ∗ 24,502 = −0,027 
 
𝑓 (𝐸23) =
(−3,4/100)
2 ∗ 380
 ∗ 44,502 = −0,089 
 
𝑓 (𝐸24) =
(−3,4/100)
2 ∗ 380
 ∗ 64,502 = −0,186 
 
𝑓 (𝐸25) =
(−3,4/100)
2 ∗ 380
 ∗ 84,502 = −0,319 
 
𝑓 (𝐸26) =
(−3,4/100)
2 ∗ 380
 ∗ 104,502 = −0,489 
 
𝑓 (𝐸27) =
(−3,4/100)
2 ∗ 380
 ∗ 124,502 = −0,693 
 
𝑓 (𝐸28) =
(−3,4/100)
2 ∗ 380
 ∗ 144,502 = −0,934 
 
𝑓 (𝐸𝑉) =
(−3,4/100)
2 ∗ 380
 ∗ 158,772 = −1,128 
 
𝑓 (𝐸29) =
(−3,4/100)
2 ∗ 380
 ∗ 164,502 = −1,211 
 
𝑓 (𝐸30) =
(−3,4/100)
2 ∗ 380
 ∗ 184,502 = −1,523 
 
𝑓 (𝑃𝐼𝑉) =
(−3,4/100)
2 ∗ 380
 ∗ 1902 = −1,615 
 
𝑓 (𝐸31) =
(−3,4/100)
2 ∗ 380
 ∗ 175,502 = −1,378 
 
𝑓 (𝐸32) =
(−3,4/100)
2 ∗ 380
 ∗ 155,502 = −1,082 
 
𝑓 (𝐸33) =
(−3,4/100)
2 ∗ 380
 ∗ 135,502 = −0,821 
 
𝑓 (𝐸34) =
(−3,4/100)
2 ∗ 380
 ∗ 115,502 = −0,597 
 
𝑓 (𝐸35) =
(−3,4/100)
2 ∗ 380
 ∗ 95,502 = −0,408 
 
𝑓 (𝐸36) =
(−3,4/100)
2 ∗ 380
 ∗ 75,502 = −0,255 
 
𝑓 (𝐸37) =
(−3,4/100)
2 ∗ 380
 ∗ 55,502 = −0,138 
 
𝑓 (𝐸38) =
(−3,4/100)
2 ∗ 380
 ∗ 35,502 = −0,056 
 
𝑓 (𝐸39) =
(−3,4/100)
2 ∗ 380
 ∗ 15,502 = −0,011 
 
𝑓 (𝑃𝑇𝑉) =
(−3,4/100)
2 ∗ 380
 ∗ 0,002 = 0,00 
 
 
 
 Flecha no PIV: 
 
𝐹 =
𝜕𝑖 ∗ 𝐿𝐶
8
 
 
𝐹 =
(−3,4/100) ∗ 380
8
 
 
𝐹 = −1,62 
 
 
 
 
 
 
 11 
 Cálculo do CR + f 
 
 
(𝑃𝐶𝑉) = 188,45 + 0,00 = 188,45 
 
(𝐸21) = 188,52 + (−0,0010) = 188,52 
 
(𝐸22) = 188,82 + (−0,027) = 188,79 
 
(𝐸23) = 189,12 + (−0,089) = 189,03 
 
(𝐸24) = 189,42 + (−0,186) = 189,23 
 
(𝐸25) = 189,72 + (−0,319) = 189,40 
 
(𝐸26) = 190,02 + (−0,489) = 189,53 
 
(𝐸27) = 190,32 + (−0,693) = 189,62 
 
(𝐸28) = 190,62 + (−0,934) = 189,68 
 
(𝐸𝑉) = 190,83 + (−1,128) = 189,70 
 
(𝐸29) = 190,92 + (−1,211) = 189,71 
 
(𝐸30) = 191,22 + (−1,523) = 189,69 
 
(𝑃𝐼𝑉) = 191,30 + (−1,615) = 189,69 
 
(𝐸31) = 191,02 + (−1,378) = 189,65 
 
(𝐸32) = 190,64 + (−1,082) = 189,56 
 
(𝐸33) = 190,26 + (−0,821) = 189,44 
 
(𝐸34) = 189,88 + (−0,597) = 189,29 
 
(𝐸35) = 189,50 + (−0,408) = 189,10 
 
(𝐸36) = 189,12 + (−0,255) = 188,87 
 
(𝐸37) = 188,74 + (−0,138) = 188,61 
 
(𝐸38) = 188,36 + (−0,056) = 188,31 
 
(𝐸39) = 187,98 + (−0,011) = 187,97 
 
(𝑃𝑇𝑉) = 187,69 + 0,00 = 0,00 
 
 
 
 
 
 LOCAÇÃO DA CURVA 2: 
 
 Cálculo das Distâncias entre pontos”: 
 
d1= (43+0,00)-(42-5,70)= 25,70m 
d2= (44+0,00)-(43+0,00)= 20,00m 
d3= (45+0,00)-(44+0,00)= 20,00m 
d4= (46+0,00)-(45+0,00)= 20,00m 
d5= (46+15,70)-(46+0,00)= 15,70m 
d6= (47+0,00)-(46+15,70)= 4,30m 
d7= (48-7,28)-(47+0,00)= 12,72m 
d8= (48+0,00)-( 48-7,28)= 7,28m 
d9= (49+0,00)-(48+0,00)= 20,00m 
d10= (50+0,00)-(49+0,00)= 20,00m 
d11= (51+0,00)-(50+0,00)= 20,00m 
d12= (51+5,70)-(51+0,00)= 5,70m 
 
 Cálculo do “CR”: 
 
 12 
DESCENDO: 
PCV-2= 186,74m 
E43= (1,9/100) * 14,30= 0,27 
E43= 186,74 - 0,27= 186,46m 
E44= (1,9/100) * 20,00= 0,38 
E44= 186,46 - 0,38= 186,08m 
E45= (1,9/100) * 20,00= 0,38 
E45= 186,08 - 0,38= 185,70m 
E46= (1,9/100) * 20,00= 0,38 
E46= 185,70 - 0,38= 185,32m 
PIV-2= (1,9/100) * 15,70= 0,30 
PIV-2= 185,32 – 0,30= 185,03m 
 
SUBINDO: 
E47= (1,5/100) * 4,30= 0,06 
E47= 185,03 + 0,06= 185,09m 
EV-2= (1,5/100) * 12,72= 0,19 
EV-2= 185,09 + 0,19= 185,28m 
E48= (1,5/100) * 7,28= 0,11 
E48= 185,28 + 0,11= 185,39m 
E49= (1,5/100) * 20= 0,30 
E49= 185,39 + 0,30= 185,69m 
E50= (1,5/100) * 20= 0,30 
E50= 185,69 + 0,30= 185,99m 
E51= (1,5/100) * 20= 0,30 
E51= 185,99 + 0,30= 186,29m 
PTV-2= (1,5/100) * 5,70= 0,09 
PTV-2= 186,29 + 0,09= 186,38m 
 
 
 
 
 Cálculo de “X” 
 
PCV-2= 0,0m 
E43= (43+0,0)–(42+5,70)= 14,30m 
E44= (44+0,0)–(42+5,70)= 34,30m 
E45= (45+0,0)–(42+5,70)= 54,30m 
E46= (46+0,0)–(42+5,70)= 74,30m 
PIV-2= (46+15,70)–(42+5,70)= 90,00m 
E47= (51+5,70)–(47+0,00)= 85,70m 
EV-2= (51+5,70)–(48-7,28)= 72,98m 
E48= (51+5,70)–(48+0,00)= 65,70m 
E49= (51+5,70)–(49+0,00)= 45,70m 
E50= (51+5,70)–(50+0,00)= 25,70m 
E51= (51+5,70)–(51+0,00)= 5,70m 
PTV-2= 0,00m 
 
 
 Cálculo das Flechas: 
 
 
𝑓 =
𝜕𝑖
2 ∗ 𝐿𝐶
 ∗ 𝑋2 
 13 
 
𝑓 (𝑃𝐶𝑉) =
(3,4/100)
2 ∗ 180
 ∗ 0,002 = 𝟎, 𝟎𝟎 
 
𝑓 (𝐸43) =
(3,4/100)
2 ∗ 180
 ∗ 14,302 = 𝟎, 𝟎𝟏𝟗 
 
𝑓 (𝐸44) =
(3,4/100)
2 ∗ 180
 ∗ 34,302 = 𝟎, 𝟏𝟏𝟏 
 
𝑓 (𝐸45) =
(3,4/100)
2 ∗ 180∗ 54,302 = 𝟎, 𝟐𝟕𝟖 
 
𝑓 (𝐸46) =
(3,4/100)
2 ∗ 180
 ∗ 74,302 = 𝟎, 𝟓𝟐𝟏 
 
𝑓 (𝑃𝐼𝑉) =
(3,4/100)
2 ∗ 180
 ∗ 90,02 = 𝟎, 𝟕𝟔𝟓 
 
𝑓 (𝐸47) =
(3,4/100)
2 ∗ 180
 ∗ 85,702 = 𝟎, 𝟔𝟗𝟕 
 
 
𝑓 (𝐸𝑉) =
(3,4/100)
2 ∗ 180
 ∗ 72,982 = 𝟎, 𝟓𝟎𝟑 
 
𝑓 (𝐸48) =
(3,4/100)
2 ∗ 180
 ∗ 65,702 = 𝟎, 𝟒𝟎𝟖 
 
𝑓 (𝐸49) =
(3,4/100)
2 ∗ 180
 ∗ 45,702 = 𝟎, 𝟏𝟗𝟕 
 
𝑓 (𝐸50) =
(3,4/100)
2 ∗ 180
 ∗ 25,702 = 𝟎, 𝟎𝟔𝟐 
 
𝑓 (𝐸51) =
(3,4/100)
2 ∗ 180
 ∗ 5,702 = 𝟎, 𝟎𝟎𝟑 
 
𝑓 (𝑃𝑇𝑉) =
(3,4/100)
2 ∗ 180
 ∗ 0,00² = 𝟎, 𝟎𝟎 
 
 
 
 
 
 
 
 Flecha no PIV: 
 
𝐹 =
𝜕𝑖 ∗ 𝐿𝐶
8
 𝐹 =
(3,4/100) ∗ 180
8
 𝐹 = 0,77 
 
 
 
 
 Cálculo do CR + f 
 
(𝑃𝐶𝑉) = 186,74 + 0,00 = 186,74 
 
(𝐸43) = 186,46 + 0,019 = 186,48 
 
(𝐸44) = 186,08 + 0,111 = 186,20 
 
(𝐸45) = 185,70 + 0,278 = 185,98 
 
(𝐸46) = 185,32 + 0,521 = 185,85 
 
(𝑃𝐼𝑉) = 185,03 + 0,765 = 185,79 
 
(𝐸47) = 185,09 + 0,694 = 185,78 
 
(𝐸𝑉) = 185,28 + 0,503 = 185,78 
 
(𝐸48) = 185,39 + 0,408 = 185,80 
 
(𝐸49) = 185,69 + 0,197 = 185,89 
 
(𝐸50) = 185,99 + 0,062 = 186,05 
 
(𝐸51) = 186,29 + 0,003 = 186,29 
 
(𝑃𝑇𝑉) = 186,38 + 0,00 = 186,38 
 
 
 
 
 
 14 
 LOCAÇÃO DA CURVA 3: 
 
 Cálculo das Distâncias entre pontos”: 
 
d1= (52+0,00)-(51+15,7)= 4,3m 
d2= (53+0,00)-(52+0,00)= 20,00m 
d3= (54+0,00)-(53+0,00)= 20,00m 
d4= (55+0,00)-(54+0,00)= 20,00m 
d5= (56+0,00)-(55+0,00)= 20,00m 
d6= (57+0,00)-(56+0,00)= 20,00m 
d7= (58+0,00)-(57+0,00)= 20,00m 
d8= (58+15,70)-(58+0,00)= 15,70m 
d9= (59+0,00)-(58+15,70)= 4,3m 
 
d10= (60+0,00)-(59+0,00)= 20,00m 
d11= (60+0,70)-(60+0,00)= 0,70m 
d12= (61+0,00)-(60+0,70)= 19,30m 
d13= (62+0,00)-(61+0,00)= 20,00m 
d14= (63+0,00)-(62+0,00)= 20,00m 
d15= (64+0,00)-(63+0,00)= 20,00m 
d16= (65+0,00)-(64+0,00)= 20,00m 
d17= (66-4,30)-(65+0,00)= 15,70m 
 
 Cálculo do “CR”: 
 
SUBINDO: 
PCV-3= 185,17m 
E52= (1,5/100) * 4,30= 0,06 
E52= 185,17 + 0,06= 185,23m 
E53= (1,5/100) * 20,00= 0,30 
E53= 185,23 + 0,30= 185,53m 
E54= (1,5/100) * 20,00= 0,30 
E54= 185,53 + 0,30= 185,83m 
E55= (1,5/100) * 20,00= 0,30 
E55= 185,83 + 0,30= 186,13m 
E56= (1,5/100) * 20,00= 0,30 
E56= 186,13 + 0,30= 186,43m 
E57= (1,5/100) * 20,00= 0,30 
E57= 186,43 + 0,30= 186,73m 
E58= (1,5/100) * 20,00= 0,30 
E58= 186,73 + 0,30= 187,03m 
PIV-3= (1,5/100) * 15,70= 0,24 
PIV-3= 187,03 + 0,24= 187,27m 
DESCENDO: 
E59= (1/100) * 4,30= 0,04 
E59= 187,27,03 - 0,04= 187,23m 
E60= (1/100) * 20= 0,20 
E60= 187,23 - 0,20= 187,03m 
EV-3= (1/100) * 0,70= 0,01 
EV-3= 187,03 - 0,01= 187,02m 
E61= (1/100) * 19,03= 0,19 
E61= 187,02 + 0,19= 186,83m 
E62= (1/100) * 20= 0,20 
E62= 186,83 + 0,20= 186,63m 
E63= (1/100) * 20= 0,20 
E63= 186,63 + 0,20= 186,43m 
E64= (1/100) * 20= 0,20 
E64= 186,43 + 0,20= 186,23m 
E65= (1/100) * 20= 0,20 
E65= 186,23 + 0,20= 186,03m 
PTV-3= (1/100) * 15,70= 0,16 
PTV-3= 186,03 + 0,16= 185,87m 
 
 15 
 Cálculo de “X” 
 
PCV-3= 0,0m 
E52= (52+0,0)–(51+15,70)= 4,30m 
E53= (53+0,0)–( 51+15,70)= 24,30m 
E54= (54+0,0)–( 51+15,70)= 44,30m 
E55= (55+0,0)–( 51+15,70)= 64,30m 
E56= (56+0,0)–( 51+15,70)= 84,30m 
E57= (57+0,0)–( 51+15,70)= 104,30m 
E58= (58+0,0)–( 51+15,70)= 124,30m 
PIV-3= (59+0,0)–(51+15,70)= 140,0m 
E59= (66-4,30)–(59+0,00)= 135,70m 
E60= (66-4,30)–(60+0,00)= 115,70m 
EV-3= (66-4,30)–(60+0,70)= 115,00m 
E61= (66-4,30)–(61+0,00)= 95,70m 
E62= (66-4,30)–(62+0,00)= 75,70m 
E63= (66-4,30)–(63+0,00)= 55,70m 
E64= (66-4,30)–(64+0,00)= 35,70m 
E65= (66-4,30)–(65+0,00)= 15,70m 
PTV-2= 0,00m 
 
 
 Cálculo das Flechas: 
 
 
𝑓 =
𝜕𝑖
2 ∗ 𝐿𝐶
 ∗ 𝑋2 
 
𝑓 (𝑃𝐶𝑉) =
(−2,5/100)
2 ∗ 280
 ∗ 0,002 = 𝟎, 𝟎𝟎 
 
𝑓 (𝐸52) =
(−2,5/100)
2 ∗ 280
 ∗ 4,302 = −𝟎, 𝟎𝟎𝟏 
 
𝑓 (𝐸53) =
(−2,5/100)
2 ∗ 280
 ∗ 24,302 = −𝟎, 𝟎𝟐𝟔 
 
𝑓 (𝐸54) =
(−2,5/100)
2 ∗ 280
 ∗ 44,302 = −𝟎, 𝟎𝟖𝟖 
 
𝑓 (𝐸55) =
(−2,5/100)
2 ∗ 280
 ∗ 64,302 = −𝟎, 𝟏𝟖𝟓 
 
𝑓 (𝐸56) =
(−2,5/100)
2 ∗ 280
 ∗ 84,302 = −𝟎, 𝟑𝟏𝟕 
 
 𝑓 (𝐸57) =
(−2,5/100)
2 ∗ 280
 ∗ 104,302 = −𝟎, 𝟒𝟖𝟔 
 
𝑓 (𝐸58) =
(−2,5/100)
2 ∗ 280
 ∗ 124,302 = −𝟎, 𝟔𝟗𝟎 
 
𝑓 (𝑃𝐼𝑉) =
(−2,5/100)
2 ∗ 280
 ∗ 140,02 = −𝟎, 𝟖𝟕𝟓 
 
 
𝑓 (𝐸59) =
(−2,5/100)
2 ∗ 280
 ∗ 135,72 = −𝟎, 𝟖𝟐𝟐 
 
𝑓 (𝐸60) =
(−2,5/100)
2 ∗ 280
 ∗ 115,72 = −𝟎, 𝟓𝟗𝟖 
 
𝑓 (𝐸𝑉) =
(−2,5/100)
2 ∗ 280
 ∗ 115,02 = −𝟎, 𝟓𝟗𝟎 
 
𝑓 (𝐸61) =
(−2,5/100)
2 ∗ 280
 ∗ 95,702 = −𝟎, 𝟒𝟎𝟗 
 
𝑓 (𝐸62) =
(−2,5/100)
2 ∗ 280
 ∗ 75,702 = −𝟎, 𝟐𝟓𝟔 
 
𝑓 (𝐸63) =
(−
2,5
100)
2 ∗ 280
 ∗ 55,702 = −𝟎, 𝟏𝟑𝟗 
 
𝑓 (𝐸64) =
(−2,5/100)
2 ∗ 280
 ∗ 35,702 = −𝟎, 𝟎𝟓𝟕 
 
𝑓 (𝐸65) =
(−2,5/100)
2 ∗ 280
 ∗ 15,702 = −𝟎, 𝟎𝟏𝟏 
 
𝑓 (𝑃𝑇𝑉) = 0,00 
 
 
 16 
 
 Flecha no PIV: 
 
𝐹 =
𝜕𝑖 ∗ 𝐿𝐶
8
 𝐹 =
(2,5/100) ∗ 280
8
 𝐹 = 0,77 
 
 
 
 
 Cálculo do CR + f 
 
(𝑃𝐶𝑉) = 185,17 + 0,00 = 185,17 
 
(𝐸52) = 185,23 + (−0,001) = 185,23 
 
(𝐸53) = 185,53 + (−0,026) = 185,51 
 
(𝐸54) = 185,83 + (−0,088) = 185,75 
 
(𝐸55) = 186,13 + (−0,185) = 185,95 
 
(𝐸56) = 186,43 + (−0,317) = 186,12 
 
(𝐸57) = 186,73 + (−0,486) = 186,25 
 
(𝐸58) = 187,03 + (−0,690) = 186,34 
 
(𝑃𝐼𝑉) = 187,27 + (−0,875) = 186,40 
 
 
(𝐸59) = 187,23 + (−0,822) = 186,40 
 
(𝐸60) = 187,03 + (−0,598) = 186,43 
 
(𝐸𝑉) = 187,02 + (−0,590) = 186,43 
 
(𝐸61) = 186,83 + (−0,409) = 186,42 
 
(𝐸62) = 186,63 + (−0,256) = 186,37 
 
(𝐸63) = 186,43 + (−0,139) = 186,29 
 
(𝐸64) = 186,23 + (−0,057) = 186,17 
 
(𝐸65) = 186,03 + (−0,011) = 186,02 
 
(𝑃𝑇𝑉) = 185,87 + (−0,598) = 185,27 
 
 
 
 LOCAÇÃO DA CURVA 4: 
 
 Cálculo das Distâncias entre pontos”: 
 
d1= (68+0,00)-( 67+2,28)= 4,3m 
d2= (69+0,00)-(68+0,00)= 20,00m 
d3= (70-2,42)-(69+0,00)= 17,58m 
d4= (70+0,00)-(70-2,42)= 2,42m 
d5= (71+0,00)-(70+0,00)= 20,00m 
d6= (72+0,00)-(71+0,00)= 20,00m 
d7= (72+12,8)-(72+0,00)= 12,80m 
 
d8= (73+0,00)-(72+12,8)= 7,20m 
d9= (74+0,00)-(73+0,00)= 20,00m 
d10= (75+0,00)-(74+0,00)= 20,00m 
d11= (76+0,00)-(75+0,00)= 20,00m 
d12= (77+0,00)-(76+0,00)= 20,00m 
d13= (78+0,00)-(77+0,00)= 20,00m 
d14= (78+2,80)-(78+0,00)= 2,80m 
 
 
 Cálculo do “CR”: 
 17 
 
DESCENDO: 
PCV-4= 185,60m 
E68= (1/100) * 17,2= 0,17 
E68= 185,60 - 0,17= 185,43m 
E69= (1/100) * 20,00= 0,20 
E69= 185,43 - 0,20= 185,23m 
EV-4= (1/100) * 17,58= 0,18 
EV-4= 185,23 - 0,18= 185,05m 
E70= (1/100) * 2,42= 0,02 
E70= 185,05 - 0,02= 185,03m 
E71= (1/100) * 20,00= 0,20 
E71= 185,03 - 0,20= 184,83m 
E72= (1/100) * 20,00= 0,20 
E72= 184,83 - 0,20= 184,63m 
PIV-4= (1/100) * 12,80= 0,13 
PIV-4= 184,63 - 0,13= 184,50m 
 
SUBINDO: 
E73= (3,2/100) * 7,20= 0,23 
E73= 184,50 + 0,23= 184,73m 
E74= (3,2/100) * 20= 0,64 
E74= 184,73 + 0,64= 185,37m 
E75= (3,2/100) * 20= 0,64 
E75= 185,37 + 0,64= 186,01m 
E76= (3,2/100) * 20= 0,64 
E76= 186,01 +0,64= 186,65m 
E77= (3,2/100) * 20= 0,64 
E77= 186,65 + 0,64= 187,29m 
E78= (3,2/100) * 20= 0,64 
E78= 187,29 + 0,64= 187,93m 
PTV-4= (3,2/100) * 2,8= 0,09 
PTV-4= 187,93 + 0,09= 188,02m 
 
 Cálculo de “X” 
 
PCV-4= 0,0m 
E68= (68+0,00)–(67+2,80)= 17,20m 
E69= (69+0,00)–(67+2,80)= 37,20m 
EV= (70-2,42)-(67+2,80)= 54,78m 
E70= (70+0,00)–(67+2,80)= 57,20m 
E71= (71+0,00)–(67+2,80)= 77,72m 
E72= (72+0,00)–(67+2,80)= 97,20m 
PIV= (72+12,80)–(67+2,80)= 110,00mE73= (78+2,80)–(73+0,00)= 102,80m 
E74= (78+2,80)–(74+0,00)= 82,80m 
E75= (78+2,80)–(75+0,00)= 62,80m 
E76= (78+2,80)–(76+0,00)= 42,80m 
E77= (78+2,80)–(77+0,00)= 22,80m 
E78= (78+2,80)–(78+0,00)= 2,80m 
PTV-2= 0,00m 
 
 
 Cálculo das Flechas: 
 
 
𝑓 =
𝜕𝑖
2 ∗ 𝐿𝐶
 ∗ 𝑋2 
 
 18 
𝑓 (𝑃𝐶𝑉) =
(3,2/100)
2 ∗ 220
 ∗ 0,002 = 𝟎, 𝟎𝟎 
 
𝑓 (𝐸68) =
(3,2/100)
2 ∗ 220
 ∗ 17,202 = 𝟎, 𝟎𝟐𝟖 
 
𝑓 (𝐸68) =
(3,2/100)
2 ∗ 220
 ∗ 37,202 = 𝟎, 𝟏𝟑𝟐 
 
𝑓 (𝐸𝑉) =
(3,2/100)
2 ∗ 220
 ∗ 54,782 = 𝟎, 𝟐𝟖𝟔 
 
𝑓 (𝐸70) =
(3,2/100)
2 ∗ 220
 ∗ 57,202 = 𝟎, 𝟑𝟏𝟐 
 
𝑓 (𝐸71) =
(3,2/100)
2 ∗ 220
 ∗ 77,202 = 𝟎, 𝟓𝟔𝟗 
 
 𝑓 (𝐸72) =
(
3,2
100)
2 ∗ 220
 ∗ 97,202 = 𝟎, 𝟗𝟎𝟐 
 
𝑓 (𝑃𝐼𝑉) =
(3,2/100)
2 ∗ 220
 ∗ 1102 = 𝟏, 𝟏𝟓𝟓 
 
 
𝑓 (𝐸73) =
(3,2/100)
2 ∗ 220
 ∗ 102,802 = 𝟏, 𝟎𝟎𝟗 
 
𝑓 (𝐸74) =
(
3,2
100)
2 ∗ 220
 ∗ 82,802 = 𝟎, 𝟔𝟓𝟒 
 
𝑓 (𝐸75) =
(3,2/100)
2 ∗ 220
 ∗ 62,802 = 𝟎, 𝟑𝟕𝟔 
 
𝑓 (𝐸76) =
(3,2/100)
2 ∗ 220
 ∗ 42,802 = 𝟎, 𝟏𝟕𝟓 
 
𝑓 (𝐸77) =
(
3,2
100)
2 ∗ 220
 ∗ 22,802 = 𝟎, 𝟎𝟓𝟎 
 
𝑓 (𝐸78) =
(3,2/100)
2 ∗ 220
 ∗ 2,802 = 𝟎, 𝟎𝟎𝟏 
 
 
𝑓 (𝑃𝑇𝑉) = 0,00 
 
 
 
 
 Flecha no PIV: 
 
𝐹 =
𝜕𝑖 ∗ 𝐿𝐶
8
 𝐹 =
(2,5/100) ∗ 280
8
 𝐹 = 0,77 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 19 
 
 
 Cálculo do CR + f 
 
(𝑃𝐶𝑉) = 185,60 + 0,000 = 185,60 
 
(𝐸68) = 185,43 + 0,028 = 185,46 
 
(𝐸69) = 185,23 + 0,132 = 185,36 
 
(𝐸𝑉) = 185,05 + 0,286 = 185,34 
 
(𝐸70) = 185,03 + 0,312 = 185,34 
 
(𝐸71) = 184,83 + 0,569 = 185,40 
 
(𝐸72) = 184,63 + 0,902 = 185,53 
 
(𝑃𝐼𝑉) = 184,50 + 1,155 = 185,66 
 
 
 
(𝐸73) = 184,73 + 1,009 = 185,74 
 
(𝐸74) = 185,37 + 0,654 = 186,02 
 
(E75)= 186,01 + 0,376 = 186,39 
 
(𝐸76) = 186,65 + 0,175 = 186,83 
 
(𝐸77) = 187,29 + 0,050 = 187,34 
 
(𝐸78) = 187,93 + 0,001 = 187,93 
 
(𝑃𝑇𝑉) = 188,02 + 0,000 = 188,02