Trabalho Topografia

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FUNDAMENTOS DE TOPOGRAFIA 
LEVANTAMENTO PLANIMÉTRICO 
 
 
 
Acadêmicos: 
1. ADRIANO CONCEIÇÃO 
2. ALEXANDRE ROGER CAMPOS SILVA 
3. CLAUDIO JOAO DE DEUS NETO PINHEIRO 
4. DOMINGAS ROBERTA P. SANTOS 
5. EMERSON DE ALMEIDA FERREIRA 
6. GENIVALDO PEREIRA CARDOSO 
7. MARCIA ANTONIA PEREIRA MARQUES 
8. MARCOS PEREIRA SANTOS 
9. MARIA DO CARMO SILVA DOS SANTOS 
10. RUBEM MANUEL AMARAL ARAUJO 
 
 
 
 
 
 
 
São Luis/MA 
Maio de 2017 
Acadêmicos: 
1. ADRIANO CONCEIÇÃO 
2. ALEXANDRE ROGER CAMPOS SILVA 
3. CLAUDIO JOAO DE DEUS NETO PINHEIRO 
4. DOMINGAS ROBERTA P. SANTOS 
5. EMERSON DE ALMEIDA FERREIRA 
6. GENIVALDO PEREIRA CARDOSO 
7. MARCIA ANTONIA PEREIRA MARQUES 
8. MARCOS PEREIRA SANTOS 
9. MARIA DO CARMO SILVA DOS SANTOS 
10. RUBEM MANUEL AMARAL ARAUJO 
 
 
 
 
 
FUNDAMENTOS DE TOPOGRAFIA 
LEVANTAMENTO PLANIMÉTRICO 
 
 
 
 
 
Trabalho apresentado ao Professor 
HAYLSON RODRIGUES DE ARAÚJO da 
disciplina de Fundamentos de Topografia, 5º 
Período – Noturno, do curso de Engenharia 
Civil. 
 
 
 
 
 
 
 
São Luis/MA 
Maio de 2017 
 
DADOS COLETADOS: 
 
PONTOS DIST. (m) ANG. (H) AZIMUTE Tolerância 
Linear (TL) 
Coordenadas 
Iniciais 
1 – 2 57,770 331°38’01” 75°24’36” 1:500 X Y 
2 – 3 31,355 270°01’35” Coeficiente K 60 80 
3 – 1 65,725 298°18’14” 1 a 3 
 
𝟎𝟏. 𝑬𝑹𝑹𝑶 𝑨𝑵𝑮𝑼𝑳𝑨𝑹 (𝑬𝑨): 
∑ 𝐴 = (𝑛 + 2) 𝑥 180° 
∑ 𝐴 = (3 + 2) 𝑥 180° 
∑ 𝐴 = 900°00′00" 
 
𝐸𝐴 = ∑ 𝐴 − ∑ 𝐴𝐶𝑜𝑙𝑒𝑡𝑎𝑑𝑜 
𝐸𝐴 = 900°00′00" − 899°57′50" 
𝐸𝐴 = 0°02′10" 
 
𝟎𝟐. 𝑻𝑶𝑳𝑬𝑹Â𝑵𝑪𝑰𝑨 𝑨𝑵𝑮𝑼𝑳𝑨𝑹 (𝑻𝑨): 
𝑇𝐴 = ± (1) 𝑥 (0°02′10") 𝑥 √3 
𝑇𝐴 = ± 0°03′45" 
 
𝟎𝟑. 𝑪𝑶𝑹𝑹𝑬ÇÃ𝑶 𝑨𝑵𝑮𝑼𝑳𝑨𝑹 (𝑪𝑨): 
𝐶𝐴 =
𝐸𝐴
𝑛
 
𝐶𝐴 =
0°02′10"
3
 
𝐶𝐴 = 0°00′43" 
 
𝐶𝐴(1−2) = 0°00′43" 
𝐶𝐴(2−3) = 0°00′43" 
𝐶𝐴(3−1) = 0°00′44" 
 
 
∑ 𝐴𝐶𝑜𝑙𝑒𝑡𝑎𝑑𝑜 = 331°38
′01"+270°01'35" + 298°18′14" 
∑ 𝐴𝐶𝑜𝑙𝑒𝑡𝑎𝑑𝑜 = 899°57′50" 
 
𝟎𝟒. 𝑪𝑶𝑹𝑹𝑬ÇÃ𝑶 𝑨𝑵𝑮𝑼𝑳𝑶𝑺 𝑯𝑶𝑹Á𝑹𝑰𝑶𝑺 (𝑨𝒉𝑪): 
𝐴ℎ𝐶(1−2) = 331°38
′01" +0°00°43" 
𝐴ℎ𝐶(1−2) = 331°38′44" 
 
𝐴ℎ(2−3) = 270°01′35" +0°00°43" 
𝐴ℎ𝐶(2−3) = 270°02′18" 
 
𝐴ℎ(3−1) = 298°18′14" +0°00°44" 
𝐴ℎ𝐶(3−1) = 298°18′58" 
 
𝟎𝟓. 𝑪𝑨𝑳𝑪𝑼𝑳𝑶 𝑫𝑶𝑺 𝑨𝒁𝑰𝑴𝑼𝑻𝑬𝑺: 
𝐴𝑧(1−2) = 75°24′36" 
 
𝐴𝑧(2−3) = 75°24
′36"+270°02'18" 
𝐴𝑧(2−3) = 165°26′54" 
 
𝐴𝑧(3−1) = 165°26′54"+298°18'58" 
𝐴𝑧(3−1) = 283°45′52" 
 
𝐴𝑧(1−2) = 283°45′52"+331°38'44" 
𝐴𝑧(1−2) = 75°24′36" 
 
𝟎𝟔. 𝑪𝑨𝑳𝑪𝑼𝑳𝑶 𝑫𝑨𝑺 𝑷𝑹𝑶𝑱𝑬ÇÕ𝑬𝑺 𝑹𝑬𝑳𝑨𝑻𝑰𝑽𝑨𝑺: 
𝑥1 = 57,770 𝑥 𝑆𝑖𝑛 |75°24′36"| 
𝑥1 = 55,907 𝑚 
 
𝑦1 = 57,770 𝑥 𝐶𝑜𝑠 |75°24′36"| 
𝑦1 = 14,552 𝑚 
𝑥2 = 31,355 𝑥 𝑆𝑖𝑛 |165°26′54"| 
𝑥2 = 7,878 𝑚 
 
𝑦2 = 31,355 𝑥 𝐶𝑜𝑠 |165°26′54"| 
𝑦2 = −30,349 𝑚 
𝑥3 = 65,725 𝑥 𝑆𝑖𝑛 |283°45′52"| 
𝑥3 = −63,837 𝑚 
 
𝑦3 = 65,725 𝑥 𝐶𝑜𝑠 |283°45′52"| 
𝑦3 = 15,637 𝑚 
∑ ∆𝑥 = − 0,052 𝑚 ∑ ∆𝑦 = −0,160𝑚 
𝟎𝟕. 𝑪𝑨𝑳𝑪𝑼𝑳𝑶 𝑫𝑶 𝑬𝑹𝑹𝑶 𝑳𝑰𝑵𝑬𝑨𝑹 (𝑬𝑳): 
𝐸𝐿 = √(−0,052𝑚)2 + (−0,160𝑚)2 
𝐸𝐿 = 0,168 𝑚 
 
𝟎𝟖. 𝑷𝑹𝑬𝑪𝑰𝑺Ã𝑶 𝑳𝑰𝑵𝑬𝑨𝑹 (𝑷𝑳): 
𝑃𝐿 =
0,168 𝑚
154,850 𝑚
 
𝑃𝐿 =
1
921,726
 
 
 
𝟎𝟗. 𝑪𝑶𝑹𝑹𝑬ÇÃ𝑶 𝑫𝑨𝑺 𝑷𝑹𝑶𝑱𝑬ÇÕ𝑬𝑺: 
𝐶𝑥1 = −(−0,000335808 𝑥 57,770) 
𝐶𝑥1 = 0,019 𝑚 
 
𝐶𝑦1 = −(−0,001033257 𝑥 57,770) 
𝐶𝑦1 = 0,059 𝑚 
 
𝐶𝑥2 = −(−0,000335808 𝑥 31,355) 
𝐶𝑥2 = 0,011 𝑚 
 
𝐶𝑦2 = −(−0,001033257 𝑥 31,355) 
𝐶𝑦2 = 0,032 𝑚 
 
𝐶𝑥3 = −(−0,000335808 𝑥 65,725) 
𝐶𝑥3 = 0,022 𝑚 
 
𝐶𝑦3 = −(−0,001033257 𝑥 65,725) 
𝐶𝑦3 = 0,068 𝑚 
 
 
𝟏𝟎. 𝑷𝑹𝑶𝑱𝑬ÇÕ𝑬𝑺 𝑪𝑶𝑹𝑹𝑰𝑮𝑰𝑫𝑨𝑺: 
𝑥𝑐1 = 55,907 + (0,019) 
𝑥𝑐1 = 55,926 𝑚 
 
𝑦𝑐1 = 14,552 + 0,060 
𝑦𝑐1 = 14,612 𝑚 
 
𝑥𝑐2 = 7,878 + (0,011) 
𝑥𝑐2 = 7,889 𝑚 
 
𝑦𝑐2 = −30,349 + 0,032 
𝑦𝑐2 = −30,317 𝑚 
 
𝑥𝑐3 = −63,837 + (0,022) 
𝑥𝑐3 = −63,815 𝑚 
 
 
 
𝑦𝑐3 = 15,637 + 0,068 
𝑦𝑐3 = 15,705 𝑚 
 
𝑃𝐿 ≤ 𝑇𝐿 
1
921,726
 ≤ 
1
500
 
 
𝟏𝟏. 𝑪𝑶𝑶𝑹𝑫𝑬𝑵𝑨𝑫𝑨𝑺 𝑻𝑶𝑻𝑨𝑰𝑺: 
𝑥1 = 60,00 
 
𝑦1 = 80,00 
𝑥2 = 60 + 55,926 
𝑥𝑐2 = 115,926 𝑚 
 
𝑦𝑐2 = 80 + 14,612 
𝑦𝑐2 = 94,612 𝑚 
 
𝑥𝑐3 = 115,926 + 7,889 
𝑥𝑐3 = 123,815 𝑚 
 
𝑦𝑐3 = 94,612 + (−30,317) 
𝑦𝑐3 = 64,295 𝑚 
 
𝟏𝟐. Á𝑹𝑬𝑨 𝑨𝑻𝑹𝑨𝑽É𝑺 𝑫𝑨𝑺 𝑪𝑶𝑶𝑹𝑫𝑬𝑵𝑨𝑫𝑨𝑺: 
NÚMERO DO 
VÉRTICE 
COORDENADAS 
(X) 
COORDENADAS 
(Y) 
1 60,00 80 
2 115,926 94,612 
3 123,815 64,295 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
∑(𝑥 − 𝑦)1 = 60,00 𝑥 94,612 
∑(𝑥 − 𝑦)1 = 5.676,72 𝑚² 
 
∑(𝑥 − 𝑦)2 = 115,926 𝑥 64,295 
∑(𝑥 − 𝑦)2 = 7.453,46 𝑚² 
 
∑(𝑥 − 𝑦)3 = 123,815 𝑥 80,00 
∑(𝑥 − 𝑦)3 = 9.905,20 𝑚² 
 
∑(𝑥 − 𝑦) = 23.035,38 𝑚² 
 
∑(𝑦 − 𝑥)1 = 80,00 𝑥 115,926 
∑(𝑦 − 𝑥)1 = 9.274,08 𝑚² 
 
∑(𝑦 − 𝑥)2 = 94,612 𝑥 123,815 
∑(𝑦 − 𝑥)2 = 11.714,38 𝑚² 
 
∑(𝑦 − 𝑥)3 = 64,295 𝑥 60,00 
∑(𝑦 − 𝑥)3 = 3.857,70𝑚² 
 
∑(𝑦 − 𝑥) = 24.846,16 𝑚² 
 
𝑆 =
24.846,16 − 23.035,38
2
 
𝑆 = 905,39 𝑚² 
𝑆 = 0,090539 ℎ𝑎 
𝑆 = 0ℎ𝑎09𝑎05𝑐𝑎 
𝟏𝟑. 𝑪𝑨𝑳𝑪𝑼𝑳𝑶 𝑫𝑨𝑺 𝑫𝑰𝑺𝑻𝑨𝑵𝑪𝑰𝑨𝑺 𝑪𝑶𝑹𝑹𝑰𝑮𝑰𝑫𝑨𝑺: 
 
𝐷1−2 = √(55,926)2 + (14,612)2 
𝐷1−2 = 57,80 𝑚 
 
𝐷2−3 = √(7,889)2 + (−30,317)2 
𝐷2−3 = 31,326 𝑚 
 
𝐷3−1 = √(−63,815)2 + (15,705)2 
𝐷3−1 = 65,719 𝑚 
 
𝟏𝟒. 𝑪Á𝑳𝑪𝑼𝑳𝑶 𝑫𝑶𝑺 𝑨𝒁𝑰𝑴𝑼𝑻𝑬𝑺 𝑪𝑶𝑹𝑹𝑰𝑮𝑰𝑫𝑶𝑺: 
𝐴𝑧(1−2) = tan
−1
+55,926
+14,612
 
𝐴𝑧(1−2) = 75°21′27′′ 
 
𝐴𝑧(2−3) = tan
−1
+7,889
−30,317
+ 180° 
𝐴𝑧(2−3) = 165°24′51′′ 
 
𝐴𝑧(3−1) = tan
−1
−63,815
+15,705
+ 360° 
𝐴𝑧(3−1) = 283°49′33′′