Exercício - Cartografia e Topografia 2022 1

INSTITUTO DE CIENCIAS Y ESTUDIOS SUPERIORES DE TAMAULIPAS A.C. COORDINACIÓN DE LICENCIATURA EN INGENIERÍA CIVIL Actividad No. 8 Alumno: ________ Fecha: 18/03/2023 Profesor: IBQ. M. en T.I. Francisco Javier Torres González TEMA: ALGEBRA DE MATRICES /EQUILIBRIO ESTRUCTURAL Formula: ∑Fx=0∑ix-∑Tx=0 ∑Fy=0∑iy-∑Ty=0 ∑M=0∑dm IN 0 30 37.5 ..... PG 70 25 70 10 0 0 0 3 11 10 10 0 0 P P1 P2 P2 P4 H2 M1 Grado de Hiperestaticidad: N= -2 N>0 (Estructura Isostatica) N<0 (Estructura Hiperestatic) N=0 Ângulos convertidos para grau decimal para facilitar no excel PONTO ESTAÇÃO PONTO VISADO DIREÇÃO(°) DH(m) º ' " DECIMAL(º) M1 35,1976500 - 35 11 51,54 35,19765 A 119,6767000 65,622 119 40 36,12 119,67670 P1 138,4092500 180,451 138 24 33,30 138,40925 M2 270,6499194 - 270 38 59,71 270,64992 B 318,4035556 54,149 318 24 12,80 318,40356 C 330,5830583 84,721 330 34 59,01 330,58306 D 352,8950833 80,469 352 53 42,30 352,89508 E 3,3746694 35,371 3 22 28,81 3,37467 F 53,5882528 93,065 53 35 17,71 53,58825 P2 96,4472361 144,039 96 26 50,05 96,44724 P1 306,1680083 - 306 10 4,83 306,16801 P3 6,0239861 259,980 6 1 26,35 6,02399 P2 25,2693667 - 25 16 9,72 25,26937 G 68,9732583 29,254 68 58 23,73 68,97326 P4 131,7543750 204,331 131 45 15,75 131,75438 P3 3,9915694 - 3 59 29,65 3,99157 H 33,8663333 83,230 33 51 58,80 33,86633 I 55,2136028 119,871 55 12 48,97 55,21360 J 87,0278972 100,981 87 1 40,43 87,02790 M1 116,0796389 126,330 116 4 46,70 116,07964 P4 46,9448972 - 46 56 41,63 46,94490 M2 199,5094250 - 199 30 33,93 199,50943 COORDENADAS CONHECIDAS DECIMAL = graus + miunto/60 + segundos/3600 X Y M1 606557,197 7777734,327 M2 606615,751 7777689,314 FIGURA A CALCULAR ÁREA: M2 P1 M1 P4 P3 P2 1. DADOS DO LEVANTAMENTO X Y M1 606557,197 7777734,327 DX= 58,55 M2 606615,751 7777689,314 DY= -45,01 arctan(°)= -52,45 azp=azm1m2(°)= 127,55104 PONTO ESTAÇÃO PONTO VISADO DIREÇÃO(°) DH(m) H(º) Azimute(°) M1 35,1976500 - 0,000 307,5510 A 119,6767000 65,622 84,479 32,03009 P1 138,4092500 180,451 103,212 50,7626 M2 270,6499194 - 0,000 230,7626 B 318,4035556 54,149 47,754 278,5163 C 330,5830583 84,721 59,933 290,6958 D 352,8950833 80,469 82,245 313,0078 E 3,3746694 35,371 92,725 323,4874 F 53,5882528 93,065 142,938 13,7010 P2 96,4472361 144,039 185,797 56,5600 P1 306,1680083 - 0,000 236,5600 P3 6,0239861 259,980 59,856 296,4159 P2 25,2693667 - 0,000 116,4159 G 68,9732583 29,254 43,704 160,1198 P4 131,7543750 204,331 106,485 222,9009 P3 3,9915694 - 0,000 42,90095 H 33,8663333 83,230 29,875 72,7757 I 55,2136028 119,871 51,222 94,1230 J 87,0278972 100,981 83,036 125,9373 M1 116,0796389 126,330 112,088 154,9890 P4 46,9448972 - 0,000 334,9890 M2 199,5094250 - 152,565 127,5535 ERRO ANGULAR azp=azm1m2(°)= 127,5510438 azm1m2,calculado(°)= 127,5535438 menor medida(")= 1 erro(°)= 0,0025 pontos= 21 erro(")= 9,0000 erro(")= 9,17 >> erro encontrado está abaixo = ok! 2. CÁLCULO AZIMUTES P1 M2 M1 P4 P3 P2 ITEM PONTO ESTAÇÃO PONTO VISADO Azimute(°) Cazi(°) Azi,corrig(°) 0 M1 307,55104 0,000000 307,55104 1 A 32,03009 -0,000119 32,02997 2 P1 50,76264 -0,000238 50,76241 3 M2 230,76264 -0,000357 230,76229 4 B 278,51628 -0,000476 278,51580 5 C 290,69578 -0,000595 290,69519 6 D 313,00781 -0,000714 313,00709 7 E 323,48739 -0,000833 323,48656 8 F 13,70098 -0,000952 13,70002 9 P2 56,55996 -0,001071 56,55889 10 P1 236,55996 -0,001190 236,55877 11 P3 296,41594 -0,001310 296,41463 12 P2 116,41594 -0,001429 116,41451 13 G 160,11983 -0,001548 160,11828 14 P4 222,90095 -0,001667 222,89928 15 P3 42,90095 -0,001786 42,89916 16 H 72,77571 -0,001905 72,77381 17 I 94,12298 -0,002024 94,12096 18 J 125,93727 -0,002143 125,93513 19 M1 154,98902 -0,002262 154,98675 20 P4 334,98902 -0,002381 334,98664 21 M2 127,55354 -0,002500 127,55104 faz(°)= 0,0025 Azimute inicial= 127,55104 OK -faz/n= -0,000119 Azimute chegada= 127,55104 OK PONTO ESTAÇÃO PONTO VISADO Azi,corrig(°) DH(m) X Y M1 307,55104 - 606557,197 7777734,327 A 32,02997 65,622 606650,554 7777744,946 P1 50,76241 180,451 606755,516 7777803,456 M2 230,76229 - 606615,751 7777689,314 B 278,51580 54,149 606701,964 7777811,475 C 290,69519 84,721 606676,261 7777833,396 D 313,00709 80,469 606696,671 7777858,343 E 323,48656 35,371 606734,469 7777831,884 F 13,70002 93,065 606777,557 7777893,873 P2 56,55889 144,039 606875,709 7777882,833 P1 236,55877 - 606755,516 7777803,456 P3 296,41463 259,980 606642,872 7777998,489 P2 116,41451 - 606875,709 7777882,833 G 160,11828 29,254 606652,820 7777970,978 P4 222,89928 204,331 606503,781 7777848,806 P3 42,89916 - 606642,872 7777998,489 H 72,77381 83,230 606583,278 7777873,454 I 94,12096 119,871 606623,342 7777840,192 J 125,93513 100,981 606585,544 7777789,543 M1 154,98675 126,330 606557,197 7777734,324 P4 334,98664 - M2 127,55104 - P3 P4 M1 3. CORREÇÃO AZIMUTES 4.CÁLCULO DAS CORDENADAS M2 P1 P2 M2 P1 P2 P3 P4 M1 PONTO X Y yi.xi+1 xi.yi+1 A 606650,554 7777744,946 4718773131633,140 4718413643610,680 B 606701,964 7777811,475 4718613587065,730 4718826794253,980 C 606676,261 7777833,396 4718785630102,040 4718642021077,190 D 606696,671 7777858,343 4719094755613,880 4718784712897,850 E 606734,469 7777831,884 4719413829731,860 4719116313009,550 F 606777,557 7777893,873 4718481255263,220 4719498228857,300 G 606652,820 7777970,978 4717987130783,040 4718468867782,700 H 606583,278 7777873,454 4718239590859,410 4717907797693,000 I 606623,342 7777840,192 4717925421772,920 4718188688646,360 J 606585,544 7777789,543 4718400338900,750 4717867647454,420 A 606650,554 7777744,946 0,000 0,000 SOMA= 47185714671726,000 47185714715283,000 Área(m²)= 21778,52 Área(hectares)= 2,178 DESENHO FEITO NO AUTOCAD PARA VERIFICAÇÃO Área (m²)= 21778,5 >> OK 5. CÁLCULO DA ÁREA