1) Exemplu de nivelment prin metoda celor mai mici patrate

Cota punctului APunct Cota (m)HA 82.789

Nr. Crt. De la-la Dist.(Km)

1 dhA_1 3.6453 1.8 3.64533112 dhA_2 -1.8562 1.6 -1.85676643 dhA_3 -3.2456 1.5 -3.24569524 dhA_4 0.5628 1.7 0.56348035 dh1_2 -5.5028 2.4 -5.50209756 dh2_3 -1.3888 2.1 -1.38892887 dh3_4 3.8095 2.6 3.80917558 dh4_1 3.0813 2 3.0818508

1 0 0 00 1 0 00 0 1 0

A= 0 0 0 1-1 1 0 00 -1 1 00 0 -1 11 0 0 -1

0.5555555556 0 0 0 0 00 0.625 0 0 0 00 0 0.6666667 0 0 0

P= 0 0 0 0.588235294 0 00 0 0 0 0.4166667 00 0 0 0 0 0.476190 0 0 0 0 00 0 0 0 0 0

1 0 0 0 -1 0A tr.= 0 1 0 0 1 -1

0 0 1 0 0 10 0 0 1 0 0

0.5555555556 0 0 0 -0.4166667 0M1= 0 0.625 0 0 0.4166667 -0.47619

Dif. de nivel mas.

(m)

Diferente cote

corectate

0 0 0.6666667 0 0 0.476190 0 0 0.588235294 0 0

5.8333333E-05L= 0.000827381

0.0001373626-0.0010230769

1.4722222222 -0.416667 0 -0.5N= -0.4166666667 1.517857 -0.47619 0

0 -0.47619 1.5274725 -0.384615385-0.5 0 -0.384615 1.472850679

0.8813142229 0.298474 0.1802353 0.346252601N-1= 0.2984738001 0.836943 0.3065904 0.181387229

0.1802352928 0.30659 0.8195512 0.2752007660.3462526007 0.181387 0.2752008 0.868365522

3.1123917E-05x= -0.0005664224

-9.520498E-050.000680328

3.1123917E-05-0.0005664224-9.520498E-05

A*x= 0.000680328-0.00059754640.0004712175

0.000775533-0.0006492041

3.1123917E-05 9.686982E-10-0.0005664224 3.208344E-07-9.520498E-05 9.063988E-09

v= 0.000680328 4.628462E-07 pvv=0.0007024536 4.934411E-07

-0.0001287825 1.658494E-08-0.000324467 1.052788E-070.0005507959 3.033761E-07

sumpvv

m mm m mmS0= 0.000470384 0.4703835588 Sx1 0.000441588 0.4415883

vv=

Sx2 0.000430328 0.4303284Sx3 0.000425834 0.4258338Sx4 0.000438332 0.4383322

Cote provizorii Cote finaleh1 86.4343 86.4343311239h2 80.9328 80.9322335776h3 79.5434 79.543304795h4 83.3518 83.352480328

000

l= -4.2188475E-150.0013

-0.0006-0.00110.0012

0 00 00 00 00 00 0

0.384615385 00 0.5

0 10 0

-1 01 -1

0 0.50 0

-0.384615385 00.384615385 -0.5

5.381657E-102.005215E-076.042659E-092.722625E-072.056005E-077.897591E-094.049186E-081.516881E-078.850428E-07

m mmSvA1 0.000631 0.631086

SvA2 0.000595 0.594993SvA3 0.000576 0.576100SvA4 0.000613 0.613305Sv12 0.000729 0.728715Sv23 0.000682 0.681651Sv34 0.000758 0.758471Sv41 0.000665 0.665223

2) Exemplu de nivelment prin metoda celor mai mici patrate - neponderate

Cota punctului APunct Cota (m)HA 82.789

Nr. Crt. De la-la Dist.(Km)

1 dhA_1 3.6453 1 3.64533112 Cote provizorii2 dhA_2 -1.8562 1 -1.8567664 h13 dhA_3 -3.2456 1 -3.2456952 h24 dhA_4 0.5628 1 0.56348033 h35 dh1_2 -5.5028 1 -5.5020975 h46 dh2_3 -1.3888 1 -1.38892887 dh3_4 3.8095 1 3.809175538 dh4_1 3.0813 1 3.0818508

1 0 0 00 1 0 00 0 1 0

A= 0 0 0 1-1 1 0 00 -1 1 00 0 -1 11 0 0 -1

1 0 0 0 0 0 00 1 0 0 0 0 00 0 1 0 0 0 0

P= 0 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 10 0 0 0 0 0 0

1 0 0 0 -1 0 0A tr.= 0 1 0 0 1 -1 0

0 0 1 0 0 1 -10 0 0 1 0 0 1

0.555556 0 0 0 -0.4166667 0 0M1= 0 0.625 0 0 0.41666667 -0.47619 0

0 0 0.666667 0 0 0.47619 -0.38461538460 0 0 0.588235 0 0 0.3846153846

Dif. de nivel mas.

(m)

Diferente cote

corectate

5.833E-05L= 0.000827

0.000137-0.001023

1.472222 -0.416667 0 -0.5N= -0.416667 1.517857 -0.47619 0

0 -0.47619 1.527473 -0.384615-0.5 0 -0.384615 1.472851

0.881314 0.298474 0.180235 0.346253N-1= 0.298474 0.836943 0.30659 0.181387

0.180235 0.30659 0.819551 0.2752010.346253 0.181387 0.275201 0.868366

3.112E-05x= -0.000566

-9.52E-050.00068

3.112E-05-0.000566-9.52E-05

A*x= 0.00068-0.0005980.0004710.000776

-0.000649

3.112E-05 9.687E-10 9.686982E-10-0.000566 3.208E-07 3.2083439E-07-9.52E-05 9.064E-09 9.0639881E-09

v= 0.00068 4.628E-07 pvv= 4.6284621E-070.000702 4.934E-07 4.9344111E-07

-0.000129 1.658E-08 1.658494E-08-0.000324 1.053E-07 1.0527884E-070.000551 3.034E-07 3.0337612E-07

sumpvv 1.7123943E-06

m mm m mmS0= 0.000654 0.654292 Sx1 0.000614 0.61423885 SvA1

Sx2 0.000599 0.59857664 SvA2Sx3 0.000592 0.59232482 SvA3Sx4 0.00061 0.6097098 SvA4

Sv12Sv23Sv34

vv=

Sv41

Cote provizorii Cote finale86.4343 86.4343311280.9328 80.9322335879.5434 79.543304883.3518 83.35248033

000

l= -4.21885E-150.0013

-0.0006-0.00110.0012

00000001

100

-1

0.500

-0.5

m mm0.000654292 0.6542920.000654292 0.6542920.000654292 0.6542920.000654292 0.6542920.000654292 0.6542920.000654292 0.6542920.000654292 0.654292

0.000654292 0.654292

3) Exemplu de nivelment prin metoda celor mai mici patrate - Retele libere

Cota punctului APunct Cota (m)HA 82.789

Nr. Crt. De la-la Dist.(Km)

1 dhA_1 3.6453 1.8 3.64532 dhA_2 -1.8562 1.6 -1.8824050463 dhA_3 -3.2456 1.5 -2.7333360944 dhA_4 0.5628 1.7 0.54471160225 dh1_2 -5.5028 2.4 -5.6460916176 dh2_3 -1.3888 2.1 -1.7134788467 dh3_4 3.8095 2.6 3.80958 dh4_1 3.0813 2 3.0813

dx1 dx2 dx3 dx4 dxA1 0 0 0 -10 1 0 0 -10 0 1 0 -1

A= 0 0 0 1 -1-1 1 0 0 00 -1 1 0 00 0 -1 1 01 0 0 -1 0

0.555556 0 0 0 0 00 0.625 0 0 0 00 0 0.6666666667 0 0 0

P= 0 0 0 0.588235 0 00 0 0 0 0.4166666667 00 0 0 0 0 0.4761904760 0 0 0 0 00 0 0 0 0 0

1 0 0 0 -1 00 1 0 0 1 -1

At= 0 0 1 0 0 10 0 0 1 0 0

-1 -1 -1 -1 0 0

0.555556 0 0 0 -0.416666667 00 0.625 0 0 0.4166666667 -0.476190476

At*P= 0 0 0.6666666667 0 0 0.476190476

Dif. de nivel mas. (m)

Diferente cote corectate

0 0 0 0.588235 0 0-0.555556 -0.625 -0.666666667 -0.588235 0 0

1.472222 -0.416667 0 -0.5 -0.555555556-0.416667 1.517857 -0.476190476 0 -0.625

N= 0 -0.47619 1.5274725275 -0.384615 -0.666666667-0.5 0 -0.384615385 1.472851 -0.588235294

-0.555556 -0.625 -0.666666667 -0.588235 2.4354575163

5.833E-050.000827

L= 0.000137-0.001023-3.39E-15

2.899691 -0.898644 0.761091 -1.145739065 -1.616399-0.898644 3.094884 -1.03349 0.7591305753 -1.92188

N*N= 0.761091 -1.03349 3.152303 -0.761813601 -2.11809-1.145739 0.759131 -0.761814 2.9132388772 -1.764817-1.616399 -1.92188 -2.11809 -1.764816786 7.421185

0.540059 -0.026205 -0.136080 0.012011 0.000000-0.042781 0.512264 -0.009725 -0.152854 0.000000

M2=N*NN-1= -0.161020 -0.018088 0.503236 -0.059040 0.0000000.004997 -0.143292 -0.041115 0.534124 0.000000

-0.341255 -0.324679 -0.316316 -0.334241 0.000000

-2.12E-050.000576

X= 0.000105-0.00067

9.965E-06

0.462102 -0.104162 -0.214037 -0.065945649 -0.077957-0.104162 0.450883 -0.071106 -0.214234683 -0.061381

Qxx= -0.214037 -0.071106 0.450218 -0.112057835 -0.053017-0.065946 -0.214235 -0.112058 0.4631812328 -0.070943-0.077957 -0.061381 -0.053017 -0.070943066 0.263298

-3.11E-05 -3.112392E-05 9.686982E-100.000566 0.0005664224 3.208344E-079.52E-05 9.520498E-05 9.063988E-09

A*X= -0.00068 v=A*x+l= -0.000680328 vv= 4.628462E-070.000598 0.0018975464 3.600682E-06

-0.000471 -0.001071217 1.147507E-06-0.000776 -0.001875533 3.517624E-060.000649 0.0018492041 3.419556E-06

m mm m mmS0= 0.001182 1.182031 Sx1 0.000804 0.8035221879

Sx2 0.000794 0.7937084037Sx3 0.000793 0.7931229091Sx4 0.000804 0.8044599359Sx5 0.000607 0.606530791

Cote provizorii Cote finaleh1 86.4343 86.4342788h2 80.9328 80.9333764h3 79.5434 79.5435052h4 83.3518 83.3511296

dhA_1 5.77316E-15dhA_2 0dhA_3 3.996803E-15dhA_4 l= -4.218847E-15dh1_2 0.0013dh2_3 -0.0006dh3_4 -0.0011dh4_1 0.0012

0 00 00 00 00 00 0

0.384615384615 00 0.5

0 10 0

-1 01 -10 0

0 0.50 0

-0.384615384615 0

0.384615384615 -0.50 0

2.899691358 -0.8986442 0.761091 -1.145739065-0.89864418 3.09488379 -1.03349 0.7591305753

M1= 0.761090761 -1.0334903 3.152303 -0.761813601-1.145739065 0.75913058 -0.761814 2.9132388772

0.435901492 0.07692721 -0.046367 0.139264 00.076927213 0.38937704 0.098074 -0.045563 0

A-1=(N*N)-1= -0.046367411 0.09807382 0.373604 0.053906 00.139263638 -0.0455629 0.053906 0.424000 0

0 0 0 0 0

0.314756506 -0.0268358 -0.142211 0.0249422068 0-0.044217774 0.28561401 0.00223 -0.159884307 0

2N(N*N)-1= -0.167512398 -0.0056892 0.277761 -0.060415392 00.018118652 -0.1493259 -0.041937 0.3096789232 0

-0.121144986 -0.103763 -0.095843 -0.114321431 0

M3=[(N*N)ˉ1]²=

5.381657E-102.005215E-076.042659E-09

pvv= 2.722625E-071.500284E-065.464318E-071.352932E-061.709778E-06

sumpvv 5.588791E-06

m mmSvA1 0.001585861279 1.585861279SvA2 0.001495164353 1.495164353SvA3 0.00144768666 1.44768666SvA4 0.001541180139 1.541180139Sv12 0.001831194873 1.831194873Sv23 0.001712925956 1.712925956Sv34 0.001905968053 1.905968053Sv41 0.001671644565 1.671644565

METODA MASURATORILOR CONDITIONATE

HA 82.789

Ddh A1 3.6453 1.8dh A2 -1.8562 1.6dh A3 -3.2456 1.5dh A4 0.5628 1.7dh 12 -5.5028 2.4dh 23 -1.3888 2.1dh 34 3.8095 2.6dh 41 3.0813 2

TABELUL ECUATIILOR DE CONDITIE

V A1 V A2 V A3 V A4 V 12 V 23 V 34 V 411 -1 0 0 1 0 0 00 1 -1 0 0 1 0 00 0 1 -1 0 0 1 0-1 0 0 1 0 0 0 1

1 -1 0 0 1 0 0 0A = 0 1 -1 0 0 1 0 0

0 0 1 -1 0 0 1 0-1 0 0 1 0 0 0 1

0.55555555556 0 0 0 0 0 0 00 0.625 0 0 0 0 0 00 0 0.666667 0 0 0 0 0

p = 0 0 0 0.588235 0 0 0 00 0 0 0 0.416667 0 0 00 0 0 0 0 0.47619 0 00 0 0 0 0 0 0.384615 00 0 0 0 0 0 0 0.5

1 0 0 -1-1 1 0 0

0 -1 1 0A tr. = 0 0 -1 1

1 0 0 00 1 0 00 0 1 00 0 0 1

5.8 -1.6 0 -1.8N K = -1.6 5.2 -1.5 0

0 -1.5 5.8 -1.7-1.8 0 -1.7 5.5

0.00029268901K = -6.1325015E-05

-0.0001247950.00027539795

APLICAREA CORECTIILOR PE DIFERENTE DE NIVEL CALCULUL COORDONATELOR PROVIZORII

Nr. Tronson Δhij° Vij ΔhijA-1 3.6453 3.112E-05 3.645331 h1° 86.43433A-2 -1.8562 -0.000566 -1.856766 h2° 80.93223A-3 -3.2456 -9.52E-05 -3.245695 h3° 79.5433A-4 0.5628 0.00068 0.56348 h4° 83.352481-2 -5.5028 0.000702 -5.5020982-3 -1.3888 -0.000129 -1.3889293-4 3.8095 -0.000324 3.8091764-1 3.0813 0.000551 3.081851

VERFICAREA NEINCHIDERILOR IN POLIGOANE CALCULUL COORDONATELOR DEFINITIVE

TRIUNGHI 1 0 HA 82.789TRIUNGHI 2 0 H1 86.43433TRIUNGHI 3 0 H2 80.93223TRIUNGHI 4 0 H3 79.5433

H4 83.35248

CALCULUL PRECIZIILOR

W-0.00130.00060.0011-0.0012

-0.0013w = 0.0006

0.0011-0.0012

1.8 0 0 0 0 0 0 00 1.6 0 0 0 0 0 00 0 1.5 0 0 0 0 0

p-1 = 0 0 0 1.7 0 0 0 00 0 0 0 2.4 0 0 00 0 0 0 0 2.1 0 00 0 0 0 0 0 2.6 00 0 0 0 0 0 0 2

1.8 0 0 -1.8-1.6 1.6 0 0

0 -1.5 1.5 0M 1 = 0 0 -1.7 1.7

2.4 0 0 00 2.1 0 00 0 2.6 00 0 0 2

0.221995 0.081769 0.04667 0.087078N-1 = 0.081769 0.239612 0.076767 0.050489

0.04667 0.076767 0.216344 0.0821440.087078 0.050489 0.082144 0.235706

3.112E-05-0.000566-9.52E-05

Vi = 0.000680.000702

-0.000129-0.0003240.000551

CALCULUL COORDONATELOR PROVIZORII

CALCULUL COORDONATELOR DEFINITIVE

08.12.2012 METODA MASURARII INDIRECTE PONDERATE

Punct Cota (m)HA 111.234HB 115.875

Nr. Crt. de la-la dif. de niv Dist. (Km)1 dhA1 2.0016 1.2 Cote provizorii2 dhA3 2.6759 1.4 H1 113.23563 dhB3 -1.9677 1.6 H2 110.35394 dhB2 -5.5211 1.7 H3 113.90995 dh14 2.8512 2 H4 116.08886 dhA4 4.8548 2.17 dh34 2.1776 28 dhB4 0.2134 19 dh24 5.7359 1.7

1 0 0 0 00 0 1 0 00 0 1 0 0.00260 1 0 0 0

A= -1 0 0 1 l= 0.0020 0 0 1 00 0 -1 1 0.00130 0 0 1 0.00040 -1 0 1 -0.001

0.833333 0 0 0 0 0 0 00 0.714286 0 0 0 0 0 00 0 0.625 0 0 0 0 00 0 0 0.588235 0 0 0 0

P= 0 0 0 0 0.5 0 0 00 0 0 0 0 0.47619 0 00 0 0 0 0 0 0.5 00 0 0 0 0 0 0 10 0 0 0 0 0 0 0

1 0 0 0 -1 0 0 0

0 0 0 1 0 0 0 0A tr.= 0 1 1 0 0 0 -1 0

0 0 0 0 1 1 1 1

0.833333 0 0 0 -0.5 0 0 0M1= 0 0 0 0.588235 0 0 0 0

0 0.714286 0.625 0 0 0 -0.5 00 0 0 0 0.5 0.47619 0.5 1

-0.001L= 0.000588

0.0009750.001462

1.333333 0 0 -0.5N= 0 1.176471 0 -0.588235

0 0 1.839286 -0.5-0.5 -0.588235 -0.5 3.064426

0.807471 0.076628 0.041662 0.153256N-1= 0.076628 0.952171 0.055549 0.204341

0.041662 0.055549 0.573891 0.1110980.153256 0.204341 0.111098 0.408683

0.000498x= -0.000836

-0.000713-0.000673

0.000498-0.000713-0.000713-0.000836

A*x= -0.00117-0.0006734.029E-05-0.0006730.000164

0.000498 2.478E-07 2.065E-07-0.000713 5.083E-07 3.631E-070.001887 3.561E-06 2.226E-06

-0.000836 6.995E-07 4.114E-07v= 0.00083 vv= 6.882E-07 pvv= 3.441E-07

-0.000673 4.525E-07 2.155E-070.00134 1.796E-06 8.982E-07

-0.000273 7.435E-08 7.435E-08-0.000836 6.995E-07 4.114E-07

sumpvv= 5.15E-06

m mm m mm mS0= 0.001015 1.014901 Sx1 0.911983 911.9834 SvA1 1.111768

Sx2 0.990332 990.3321 SvA3 1.200846Sx3 0.768844 768.8438 SvB3 1.283759Sx4 0.648809 648.8086 SvB2 1.323268

Sv14 1.435286SvA4 1.470731Sv34 1.435286SvB4 1.014901Sv24 1.323268

Cote finale113.236098110.353064113.909187116.088127

00000000

0.588235

0

-101

0-0.588235

00.588235

mm1111.7681200.8461283.7591323.2681435.2861470.7311435.2861014.9011323.268

08.12.2012 METODA MASURARII INDIRECTE NEPONDERATE

Punct Cota (m)HA 111.234HB 115.875

Nr. Crt. de la-la dif. de niv Dist. (Km)1 dhA1 2.0016 1 Cote provizorii2 dhA3 2.6759 1 H13 dhB3 -1.9677 1 H24 dhB2 -5.5211 1 H35 dh14 2.8512 1 H46 dhA4 4.8548 17 dh34 2.1776 18 dhB4 0.2134 19 dh24 5.7359 1

1 0 0 0 00 0 1 0 00 0 1 0 0.00260 1 0 0 0

A= -1 0 0 1 l= 0.0020 0 0 1 00 0 -1 1 0.00130 0 0 1 0.00040 -1 0 1 -0.001

1 0 0 0 0 0 00 1 0 0 0 0 00 0 1 0 0 0 00 0 0 1 0 0 0

P= 0 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 10 0 0 0 0 0 00 0 0 0 0 0 0

1 0 0 0 -1 0 00 0 0 1 0 0 0

A tr.= 0 1 1 0 0 0 -10 0 0 0 1 1 1

1 0 0 0 -1 0 0M1= 0 0 0 1 0 0 0

0 1 1 0 0 0 -10 0 0 0 1 1 1

-0.002L= 0.001

0.00130.0027

2 0 0 -1N= 0 2 0 -1

0 0 3 -1-1 -1 -1 5

0.568182 0.068182 0.045455 0.136364N-1= 0.068182 0.568182 0.045455 0.136364

0.045455 0.045455 0.363636 0.0909090.136364 0.136364 0.090909 0.272727

0.000641x= -0.000859

-0.000673-0.000718

0.000641-0.000673-0.000673-0.000859

A*x= -0.001359-0.000718-4.55E-05-0.0007180.000141

0.000641 4.108E-07 4.108E-07-0.000673 4.526E-07 4.526E-070.001927 3.714E-06 3.714E-06

-0.000859 7.38E-07 7.38E-07v= 0.000641 vv= 4.108E-07 pvv= 4.108E-07

-0.000718 5.158E-07 5.158E-07

0.001255 1.574E-06 1.574E-06-0.000318 1.012E-07 1.012E-07-0.000859 7.38E-07 7.38E-07

sumpvv= 8.655E-06

m mm m mmS0= 0.001316 1.315709 Sx1 0.991753 991.7532 SvA1

Sx2 0.991753 991.7532 SvA3Sx3 0.793403 793.4025 SvB3Sx4 0.687107 687.1068 SvB2

Sv14SvA4Sv34SvB4Sv24

Cote provizorii Cote finale113.2356 113.236241110.3539 110.353041113.9099 113.909227116.0888 116.088082

0 00 00 00 00 00 00 01 00 1

0 00 -10 01 1

0 00 -10 01 1

m mm1.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.709

15.12.2012 METODA MASURARII CONDITIONATE

Punct Cota (m)HA 111.234HB 115.875

Nr. Crt. de la-la Dist. (Km)

1 dhA1 2.0016 1.2 2.0020978 Cote provizorii2 dhA3 2.6759 1.4 2.675187 H13 dhB3 -1.9677 1.6 -1.965813 H24 dhB2 -5.5211 1.7 -5.5219363 H35 dh14 2.8512 2 2.8520296 H46 dhA4 4.8548 2.1 4.85412737 dh34 2.1776 2 2.17894038 dhB4 0.2134 1 0.21312739 dh24 5.7359 1.7 5.7350637

VA1 VA3 VB3 VB2 V14 VA4 V34-1 0 0 0 -1 1 00 1 0 0 0 -1 1

A= 0 0 -1 0 0 0 -10 0 0 1 0 0 00 -1 1 0 0 0 0

0.833333 0 0 0 0 0 00 0.714286 0 0 0 0 00 0 0.625 0 0 0 00 0 0 0.588235 0 0 0

P= 0 0 0 0 0.5 0 00 0 0 0 0 0.47619 00 0 0 0 0 0 0.50 0 0 0 0 0 00 0 0 0 0 0 0

-1 0 0 0 00 1 0 0 -1

A tr.= 0 0 -1 0 10 0 0 1 0

-1 0 0 0 0

dif. de nivel mas. (m)

dif. de nivel comp. (m)

1 -1 0 0 00 1 -1 0 00 0 1 -1 00 0 0 1 0

1.2 0 0 0 0 0 00 1.4 0 0 0 0 0

Qm= 0 0 1.6 0 0 0 00 0 0 1.7 0 0 00 0 0 0 2 0 00 0 0 0 0 2.1 00 0 0 0 0 0 20 0 0 0 0 0 00 0 0 0 0 0 0

-1.2 0 0 0 00 1.4 0 0 -1.40 0 -1.6 0 1.60 0 0 1.7 0

M1= -2 0 0 0 02.1 -2.1 0 0 0

0 2 -2 0 00 0 1 -1 00 0 0 1.7 0

5.3 -2.1 0 0 0N= -2.1 5.5 -2 0 -1.4

0 -2 4.6 -1 -1.60 0 -1 4.4 00 -1.4 -1.6 0 3

0.27259 0.211774 0.165276 0.037563 0.186975N-1= 0.211774 0.534476 0.417125 0.094801 0.4718892

0.165276 0.417125 0.60968 0.138564 0.51982130.037563 0.094801 0.138564 0.258764 0.11814120.186975 0.471889 0.519821 0.118141 0.8307863

-0.000415-9.45E-05

K= -0.000765-0.0004920.000415

0.000498 2.478E-07 2.065E-07

-0.000713 5.083E-07 3.631E-070.001887 3.561E-06 2.226E-06

-0.000836 6.995E-07 4.114E-07v= 0.00083 vv= 6.882E-07 pvv= 3.441E-07

-0.000673 4.525E-07 2.155E-070.00134 1.796E-06 8.982E-07

-0.000273 7.435E-08 7.435E-08-0.000836 6.995E-07 4.114E-07

sumpvv= 5.15E-06

m mm m mmS0= 0.001015 1.014901 Sx1 0.529881 529.88069 SvA1

Sx2 0.741972 741.97242 SvA3Sx3 0.792455 792.45477 SvB3Sx4 0.516269 516.2687 SvB2

Sv14SvA4Sv34SvB4Sv24

Cote provizorii Cote finale

VB4 V24 W Verificare0 0 0.002 00 0 -0.0013 01 0 0.0035 0

-1 1 0.0014 00 0 -0.0026 0

0 00 00 00 00 00 00 01 00 0.588235

0 00 00 00 00 00 00 01 00 1.7

m mm1.111768 1111.7681.200846 1200.8461.283759 1283.7591.323268 1323.2681.435286 1435.2861.470731 1470.7311.435286 1435.2861.014901 1014.9011.323268 1323.268

15.12.2012 METODA MASURARII CONDITIONATE

Punct Cota (m)HA 111.234HB 115.875

Nr. Crt. de la-la Dist. (Km)

1 dhA1 2.0016 1 2.002241 Cote provizorii2 dhA3 2.6759 1 2.675227 H13 dhB3 -1.9677 1 -1.965773 H24 dhB2 -5.5211 1 -5.521959 H35 dh14 2.8512 1 2.851841 H46 dhA4 4.8548 1 4.8540827 dh34 2.1776 1 2.1788558 dhB4 0.2134 1 0.2130829 dh24 5.7359 1 5.735041

VA1 VA3 VB3 VB2 V14 VA4 V34-1 0 0 0 -1 1 00 1 0 0 0 -1 1

A= 0 0 -1 0 0 0 -10 0 0 1 0 0 00 -1 1 0 0 0 0

1 0 0 0 0 0 00 1 0 0 0 0 00 0 1 0 0 0 00 0 0 1 0 0 0

P= 0 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 10 0 0 0 0 0 00 0 0 0 0 0 0

-1 0 0 0 00 1 0 0 -1

A tr.= 0 0 -1 0 10 0 0 1 0

dif. de nivel

mas. (m)

dif. de nivel

comp. (m)

-1 0 0 0 01 -1 0 0 00 1 -1 0 00 0 1 -1 00 0 0 1 0

1 0 0 0 0 0 00 1 0 0 0 0 0

Qm= 0 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 10 0 0 0 0 0 00 0 0 0 0 0 0

-1 0 0 0 00 1 0 0 -10 0 -1 0 10 0 0 1 0

M1= -1 0 0 0 01 -1 0 0 00 1 -1 0 00 0 1 -1 00 0 0 1 0

3 -1 0 0 0N= -1 3 -1 0 -1

0 -1 3 -1 -10 0 -1 3 00 -1 -1 0 2

0.431818 0.295455 0.204545 0.068182 0.25N-1= 0.295455 0.886364 0.613636 0.204545 0.75

0.204545 0.613636 0.886364 0.295455 0.750.068182 0.204545 0.295455 0.431818 0.25

0.25 0.75 0.75 0.25 1.25

-0.0006417.727E-05

K= -0.001177-0.000859

0.00075

0.000641 4.108E-07 4.108E-07-0.000673 4.526E-07 4.526E-070.001927 3.714E-06 3.714E-06

-0.000859 7.38E-07 7.38E-07v= 0.000641 vv= 4.108E-07 pvv= 4.108E-07

-0.000718 5.158E-07 5.158E-070.001255 1.574E-06 1.574E-06

-0.000318 1.012E-07 1.012E-07-0.000859 7.38E-07 7.38E-07

sumpvv= 8.655E-06

m mm m mmS0= 0.001316 1.315709 Sx1 0.86459 864.5904 SvA1

Sx2 1.238699 1238.699 SvA3Sx3 1.238699 1238.699 SvB3Sx4 0.86459 864.5904 SvB2

Sv14SvA4Sv34SvB4Sv24

Cote provizorii Cote finale

VB4 V24 W Verificare0 0 0.002 00 0 -0.0013 01 0 0.0035 0

-1 1 0.0014 00 0 -0.0026 0

0 00 00 00 00 00 00 01 00 1

0 00 00 00 00 00 00 01 00 1

m mm1.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.7091.315709 1315.709

26.01.2013 METODA MASURARII indirecte pondreate libere

Cota punctului APunct Cota (m)HA 111.234HB 115.875

Nr. Crt. de la-la Dist. (Km)

1 dhA1 2.0016 1.2 2.00221 Cote provizorii2 dhA3 2.6759 1.4 2.675438 H13 dhB3 -1.9677 1.6 -1.966061 H24 dhB2 -5.5211 1.7 -5.522037 H35 dh14 2.8512 2 2.852216 H46 dhA4 4.8548 2.1 4.8544267 dh34 2.1776 2 2.1789888 dhB4 0.2134 1 0.2129279 dh24 5.7359 1.7 5.734963

x1 x2 x3 x4 Xa Xb l1 0 0 0 -1 0 00 0 1 0 -1 0 0

A= 0 0 1 0 0 -1 0.00260 1 0 0 0 -1 0

-1 0 0 1 0 0 0.0020 0 0 1 -1 0 00 0 -1 1 0 0 0.00130 0 0 1 0 -1 0.00040 -1 0 1 0 0 -0.001

0.833333 0 0 0 0 0 00 0.714286 0 0 0 0 00 0 0.625 0 0 0 00 0 0 0.588235 0 0 0

P= 0 0 0 0 0.5 0 00 0 0 0 0 0.47619 00 0 0 0 0 0 0.50 0 0 0 0 0 00 0 0 0 0 0 0

dif. de nivel

mas. (m)

dif. de nivel

comp. (m)

1 0 0 0 -1 0 00 0 0 1 0 0 0

A tr.= 0 1 1 0 0 0 -10 0 0 0 1 1 1

-1 -1 0 0 0 -1 00 0 -1 -1 0 0 0

0.833333 0 0 0 -0.5 0 00 0 0 0.588235 0 0 0

M=A tr.*P 0 0.714286 0.625 0 0 0 -0.50 0 0 0 0.5 0.47619 0.5

-0.833333 -0.714286 0 0 0 -0.47619 00 0 -0.625 -0.588235 0 0 0

-0.0010.000588

L=M*l 0.0009750.001462

0-0.002025

1.333333 0 0 -0.5 -0.833333 00 1.176471 0 -0.588235 0 -0.588235

N=M*A 0 0 1.839286 -0.5 -0.714286 -0.625-0.5 -0.588235 -0.5 3.064426 -0.47619 -1

-0.833333 0 -0.714286 -0.47619 2.02381 00 -0.588235 -0.625 -1 0 2.213235

2.722222 0.294118 0.845238 -1.802054 -2.559524 0.50.294118 2.076125 0.661765 -1.90641 0.280112 -1.405709

N*N= 0.845238 0.661765 4.533801 -1.48672 -2.521259 -2.032826-1.802054 -1.90641 -1.48672 11.46348 -1.64916 -4.61914-2.559524 0.280112 -2.521259 -1.64916 5.527211 0.922619

0.5 -1.405709 -2.032826 -4.61914 0.922619 6.635056

2.722222 0.294118 0.845238 -1.802054 -2.5595240.294118 2.076125 0.661765 -1.90641 0.280112

(N*N)cu4= 0.845238 0.661765 4.533801 -1.48672 -2.521259-1.802054 -1.90641 -1.48672 11.46348 -1.64916-2.559524 0.280112 -2.521259 -1.64916 5.527211

1.461469 -0.101668 0.436897 0.414043 1.004756 0-0.101668 0.595478 -0.114337 0.051826 -0.11395 0

(N*N)-1= 0.436897 -0.114337 0.484254 0.181999 0.483309 00.414043 0.051826 0.181999 0.233725 0.341863 01.004756 -0.11395 0.483309 0.341863 0.974443 0

0 0 0 0 0 0

0.904308 -0.066512 0.088773 0.150309 0.356707 0-0.363165 0.670077 -0.241572 -0.076514 -0.335155 0

M3=N*(N*N)-1 -0.121125 -0.154818 0.454461 -0.026302 0.021981 0-0.09903 -0.0292 -0.065743 0.224933 -0.093408 00.306311 -0.0889 0.181482 0.105534 0.626777 0

-0.627299 -0.330647 -0.417401 -0.37796 -0.576902 0

0.000637-0.00041

-0.000435x=-M3*L -0.000347

2.739E-050.000527

0.925553 -0.15456 0.191544 0.210134 0.556353 0-0.637585 0.542587 -0.35969 -0.152083 -0.562354 0

M3*M3= -0.099019 -0.167228 0.2389 -0.02191 0.034906 0-0.121873 -0.001066 -0.063355 0.029815 -0.10654 0

0.46884 -0.166842 0.237955 0.137954 0.526039 0-0.535916 -0.052891 -0.245354 -0.203909 -0.448404 0

0.665377 -0.305443 -0.150158 -0.088622 0.117777 -0.238931-0.305443 0.727798 -0.183851 -0.018792 -0.277434 0.057721-0.150158 -0.183851 0.425428 -0.055335 -0.007052 -0.029033

Qxx=M3*M3*N -0.088622 -0.018792 -0.055335 0.235341 -0.083 0.0104080.117777 -0.277434 -0.007052 -0.083 0.438243 -0.188534

-0.238931 0.057721 -0.029033 0.010408 -0.188534 0.388368

0.00061-0.000462-0.000961

A*x= -0.000937

-0.000984-0.0003748.815E-05-0.000873

6.34E-05

0.00061 3.718E-07 3.098E-07-0.000462 2.135E-07 1.525E-070.001639 2.685E-06 1.678E-06

v= -0.000937 v*v= 8.772E-07 P*v*v= 5.16E-070.001016 1.033E-06 5.164E-07

-0.000374 1.398E-07 6.659E-080.001388 1.927E-06 9.635E-07

-0.000473 2.239E-07 2.239E-07-0.000937 8.772E-07 5.16E-07

sumpvv= 4.943E-06

m mm mmS0= 0.001112 1.111647 Sx1 0.906777 SvA1

Sx2 0.948358 SvA3Sx3 0.72507 SvB3Sx4 0.539282 SvB2SxA 0.735909 Sv14SxB 0.692769 SvA4

Sv34SvB4Sv24

Cote provizorii Cote finale113.2356 H1 113.2362110.3539 H2 110.3535113.9099 H3 113.9095116.0888 H4 116.0885

0 00 00 00 00 00 00 01 00 0.588235

0 00 -10 01 10 0

-1 0

0 00 -0.5882350 01 0.5882350 0

-1 0

mm1.2177481.3153181.406134

1.449411.5721061.6109291.5721061.111647

1.44941