NTS STUDY

NTS STUDY

Nodal Theory of Structure : Every Node Matters, Every Structure Tells A Story.

Surveying Master class part 2: All topic Cover in one Place

Surveying Master class part 2: All topic Cover of Survey Engineering 

Surveying Master class part 2: All topic Cover of Survey Engineering


Levelling ke Mukhya Siddhant

Levelling ka upyog dharti ki satah par vibhinn binduon ki unchai (elevation) janne ke liye kiya jata hai.

  • Level Line: Yeh dharti ki satah (Mean Sea Level) ke samantar (parallel) ek line hoti hai.

  • Horizontal Line: Yeh plumb line ke $90^\circ$ par hoti hai aur level line par tangent hoti hai.

  • Mean Sea Level (MSL): Iska nirdharan samudra ki lahro (sea fluctuations) ke $19$ saalo ke ausat (average) se kiya jata hai.

  • Reduced Level (RL): Kisi bhi bindu ki MSL se unchai ko uska RL kehte hain.

Levelling ki Pramukh Paribhashaye

  • Reduced Level (RL): Kisi bhi point ki woh unchai jo Mean Sea Level (MSL) ke sapeksh (with respect to) mapi jati hai, use RL kehte hain.

  • Absolute Level: Agar kisi point ki unchai dharti ke kendra (centre of the earth) se mapi jaye, toh use Absolute level kaha jata hai.

  • Bench Mark (BM): Yeh dharti par woh sthir bindu hai jiska RL pehle se pata hota hai.           Yeh do prakar ke ho sakte hain: Permanent aur Temporary.

Sights ke Prakar

Levelling ke dauran li jane wali readings ko teen bhago mein banta jata hai:

  • Back Sight (BS): Jab instrument ko set kiya jata hai, toh Bench Mark par li jane wali sabse pehli reading ko Back Sight kehte hain.

  • Fore Sight (FS): Instrument ki kisi ek position se li jane wali sabse aakhri reading ko Fore Sight kaha jata hai.

  • Intermediate Sight (IS): Back sight aur Fore sight ke beech li jane wali sabhi anya readings ko Intermediate sight kehte hain.

RL nikalne ki Vidhiya

Points ka RL nikalne ke liye mukhya roop se do vidhiyo ka upyog hota hai:

  1. Height of Instrument (HI) Method

  2. Rise & Fall Method

Height of Instrument (HI) Method ke Sutra

  • HI nikalne ke liye:

    $$HI = RL_{BM} + BS$$

  • Kisi point ka RL nikalne ke liye:

    $$RL = HI - \text{Staff Reading (IS ya FS)}$$

Rise and Fall Method

Yeh levelling mein Reduced Level (RL) nikalne ki dusri mukhya vidhi hai.

  • Siddhant: Isme pichli reading aur agli reading ke antar se yeh pata lagaya jata hai ki zameen upar uth rahi hai (Rise) ya niche gir rahi hai (Fall).

  • Niyam:

    • Agar antar positive (+ive) aata hai, toh use Rise kehte hain.

    • Agar antar negative (-ive) aata hai, toh use Fall kehte hain.

  • RL ki Ganana: Agle point ka RL pichle RL mein Rise ko jodkar ya Fall ko ghatakar nikala jata hai ($RL_{next} = RL_{previous} \pm \text{Rise/Fall}$).

Arithmetical Check

Levelling ke calculations ki shuddhata janchne ke liye niche diye gaye check ka upyog kiya jata hai:

$$\Sigma BS - \Sigma FS = \text{Last RL} - \text{First RL}$$

(Yahan $\Sigma BS$ sabhi Back Sights ka jod hai aur $\Sigma FS$ sabhi Fore Sights ka jod hai).

Numerical Udaharan

1. Height of Instrument (HI) Method se RL nikalna

  • Sawal: Bench Mark (A) ka RL $100.5\text{ m}$ hai. A par staff reading $2.5\text{ m}$ hai aur B par staff reading $1.1\text{ m}$ hai. B ka RL nikalein.

  • Calculation:

    1. HI nikalna: $HI = RL_{BM} + BS = 100.5 + 2.5 = 103\text{ m}$.

    2. RL of B: $RL = HI - \text{Staff Reading at B} = 103 - 1.1 = \mathbf{101.9\text{ m}}$.

2. Sloping Ground par RL nikalna

  • Sawal: Sloping ground par readings $1.2\text{ m}$, $2.1\text{ m}$, $2.7\text{ m}$, $0.9\text{ m}$, $3.0\text{ m}$ li gayi hain. Agar dusre point ka RL $200\text{ m}$ hai, toh aakhri point ka RL nikalein.

  • Step-by-step Solution:

    1. Point B par HI: $200 + 2.0 = 202\text{ m}$ (yahan $2.0$ reading ko base mana gaya hai).

    2. Next point ka RL: $202 - 2.7 = 199.3\text{ m}$.

    3. Agle station par HI ($HI_2$): $199.3 + 0.9 = 200.2\text{ m}$.

    4. Last point ka RL: $200.2 - 3.0 = \mathbf{197.2\text{ m}}$.


Inverted Staff Levelling

Kabhi-kabhi kisi unchi jagah (jaise chhat ya bridge ka nichla hissa) ka RL nikalne ke liye levelling staff ko ulta (inverted) rakha jata hai.

  • Pehchan: Inverted staff ki reading ko hamesha negative (-ive) sign ke saath darshaya jata hai.

  • Upyog: Iska upyog kisi top point ka RL janne ke liye hota hai.

Earth Curvature aur Refraction Corrections

Jab levelling bahut lambi doori ($d$) ke liye ki jati hai, toh dharti ki golai aur vatavaran (atmosphere) ke karan readings mein galti aati hai, jise theek karne ke liye niche diye gaye corrections lagaye jate hain:

1. Curvature Correction ($C_c$)

Dharti ki golai ke karan staff ki reading asliyat se zyada aati hai.

  • Sutra: $C_c = -0.0785 d^2$.

  • Niyam: Yeh correction hamesha negative hota hai.

  • Note: Yahan $d$ kilometre mein hota hai.

2. Refraction Correction ($C_r$)

Hawa ke ghanaipan ke karan light ki kiran niche ki taraf mud jati hai, jisse reading asliyat se thodi kam aati hai.

  • Sutra: $C_r = +0.0112 d^2$.

  • Rishta: Yeh curvature correction ka $1/7$ bhag hota hai ($C_r = \frac{1}{7} |C_c|$).

  • Niyam: Yeh correction hamesha positive hota hai.

Numerical Udaharan: Inverted Staff

  • Sawal: Ek building ki chhat (top) ka RL $510\text{ m}$ hai. Chhat par inverted staff reading $2.2\text{ m}$ hai aur floor par seedhi staff reading $1.2\text{ m}$ hai. Floor ka RL nikalein.

  • Calculation:

    1. HI nikalna: $RL_{top} - (\text{Inverted Reading}) = 510 - 2.2 = 507.8\text{ m}$.

    2. Floor ka RL: $HI - \text{Floor Reading} = 507.8 - 1.2 = \mathbf{506.6\text{ m}}$.


Visible Horizon ki Doori

Kisi khas unchai ($h$) se jitni adhiktam doori ($d$) dekhi ja sakti hai, use Distance of Visible Horizon kehte hain.

  • Sutra (Formula): $h = 0.0785 d^2$ (Combined correction ka upyog karke iska prabhav $h = 0.0673 d^2$ hota hai).

  • Doori nikalne ke liye: $d = 3.855 \sqrt{h}$.

    • Yahan $h$ metres mein unchai hai aur $d$ kilometres mein doori hai.

Reciprocal Levelling

Yeh vidhi tab upyog ki jati hai jab beech mein koi badi rukavat (jaise nadi, ghati, ya talab) ho jahan survey karna seedhe taur par sambhav nahi hota.

  • Siddhant: Isme do points (A aur B) par instrument bari-bari se rakha jata hai aur dono taraf se readings li jati hain taaki curvature aur refraction ke errors cancel ho jayein.

  • Unchai ka antar ($\Delta H$): Iska formula niche diya gaya hai:

    $$\Delta H = \frac{(h_2 - h_1) + (h'_2 - h'_1)}{2}$$

  • RL nikalna: $RL_A = RL_B \pm \Delta H$.

Numerical Udaharan: Reciprocal Levelling

  • Sawal: Nadi ke do kinaro A aur B ke beech readings li gayi hain. Agar B ka RL $450\text{ m}$ hai, toh A ka RL nikalein.

    • Instrument A par: Staff A ($2.5$), Staff B ($1.3$).

    • Instrument B par: Staff A ($1.8$), Staff B ($0.7$).

  • Solution:

    1. $\Delta H$ nikalna: $\frac{(2.5 - 1.3) + (1.8 - 0.7)}{2} = \frac{1.2 + 1.1}{2} = 1.15\text{ m}$.

    2. RL of A: $450 - 1.15 = \mathbf{448.85\text{ m}}$.

Bubble Tube ki Sensitivity

Bubble tube ki sensitivity ($\alpha$) yeh darshati hai ki bubble ke ek division hilne par staff par kitna badlav aata hai.

  • Mukhya Sutra:

    • $\alpha = \frac{S}{nD}$.

    • $\alpha = \frac{l}{R}$.

  • Seconds mein maan: $\alpha = \frac{S}{nD} \times 206265''$.

  • Yahan:

    • $S$: Staff intercept ($S_2 - S_1$).

    • $n$: Bubble ke divisions ki sankhya.

    • $D$: Instrument aur staff ke beech ki doori.

    • $R$: Bubble tube ka radius.

    • $l$: Ek division ki lambai.



Contour aur Uske Maan

  • Contour Line: Yeh ek aisi line hai jo dharti par saman unchai (equal elevation ya equal RL) wale binduon ko jodi hai.

  • Contour Interval (CI): Do lagatar (adjacent) contour lines ke beech ki vertical unchai ke antar ko Contour Interval kehte hain. 

  • Ek hi nakshe ke liye CI ko hamesha ek saman (constant) rakha jata hai taaki area ki alag-alag visheshthao ko pehchana ja sake.

  • Horizontal Equivalent: Do lagatar contour lines ke beech ki horizontal doori ko Horizontal Equivalent kehte hain.   Yeh doori nakshe par badalti rehti hai.

Dhalan (Slope) ki Pehchan

Contour lines ki doori aur banavat se zameen ki dhalan ka pata chalta hai:

  • Uniform Slope: Agar contour lines ek dusre ke parallel aur barabar doori par hon, toh yeh uniform slope darshata hai.

  • Steep Slope (Khadi Dhalan): Pass-pass (closely spaced) bani contour lines steep slope ko darshati hain.

  • Mild Slope (Halki Dhalan): Door-door (distant) bani contour lines mild slope darshati hain.

Hill aur Valley ki Pehchan

Band (closed) contour lines ya toh pahaad (Hill) darshati hain ya ghati (Valley):

  • Hill: Agar andar wali contour line ka maan bahar wali se zyada ho (jaise 100, 110, 120, 130), toh woh Hill hai.

  • Valley: Agar andar wali contour line ka maan kam ho (jaise 100, 90, 80, 70), toh woh Valley ya depression hai.

Vishesh Sharte aur Apvad (Exceptions)

Aamtaur par alag-alag unchai wali do contour lines na toh ek dusre ko kaatti (cross) hain aur na hi milti (join) hain.   Lekin iske kuch apvad hain:

  • Vertical Cliff: Is sthiti mein contour lines ek dusre ko touch karti hui dikhayi deti hain.

  • Overhanging Cliff ya Cave: Is sthiti mein contour lines ek dusre ko cross (cut) karti hain.

Area Calculation ki Vidhiya

Surveying mein kisi plot ya kshetra ka area nikalne ke liye mukhya roop se teen tariko ka upyog kiya jata hai:

1. Triangulation Method (Method-1)

Is vidhi mein poore area ko chhote-chhote tribhujo (triangles) mein banta jata hai.

  • Sutra (Formula): Agar ek triangle ki bhujaye $a, b, c$ hain, toh pehle semi-perimeter ($s$) nikala jata hai:

    $$s = \frac{a+b+c}{2}$$

  • Iske baad Heron's formula se area nikala jata hai:

    $$A_1 = \sqrt{s(s-a)(s-b)(s-c)}$$

2. Coordinate Method (Method-2)

Isme area ko ek central line (jaise $PQ$) aur us par liye gaye offsets ($x_1, x_2...$) ki madad se banta jata hai.

  • Kul Area ($A_T$): Sabhi chhote bhago ($A_1, A_2, A_3, A_4$) ka jod hota hai.

    $$A_T = A_1 + A_2 + A_3 + A_4$$

3. Regular Offset Method (Method-3)

Jab offsets ek saman doori ($d$) par liye jayein, toh in teen rules ka upyog hota hai:

  • Average Ordinate Rule: Isme sabhi offsets ka ausat nikal kar base length se guna kiya jata hai.

    $$A_T = (n-1)d \times \left[ \frac{h_1 + h_2 + \dots + h_n}{n} \right]$$

  • Trapezoidal Rule: Yeh har do offsets ke beech ke area ko ek trapezoid maanta hai.

    $$A_T = \frac{d}{2} \left[ (h_1 + h_n) + 2(h_2 + h_3 + \dots + h_{n-1}) \right]$$

  • Simpson's Rule: Yeh sabse sateek (accurate) mana jata hai kyunki yeh boundary ko ek curve maanta hai.

    $$A_T = \frac{d}{3} \left[ (h_{first} + h_{last}) + 4(\text{sum of even terms}) + 2(\text{sum of odd terms}) \right]$$


Trigonometric Levelling

Is vidhi mein vertical angles aur horizontal distances ka upyog karke points ka RL nikala jata hai.

1. Jab doori (D) mapi ja sake

  • Sutra (Formula): Vertical unchai $V = D \tan \theta$.

  • RL ki Ganana: $RL_P = BM + BS + V$.

2. Jab doori (D) na mapi ja sake

Is sthiti mein do alag stations se angles ($\theta_1, \theta_2$) liye jate hain.

  • Dono equations ko solve karke $D$ aur $V$ ka maan nikala jata hai.

Numerical Udaharan:

  • Data: $BM = 100\text{ m}$, $BS = 2.2\text{ m}$, angle $= 60^\circ$, doori $= 50\text{ m}$.

  • Solution: $RL_{Top} = 100 + 2.2 + 50 \tan 60^\circ = \mathbf{188.8\text{ m}}$.

Tacheometry

Tacheometer ek vishesh theodolite hota hai jisme teen horizontal cross hairs hote hain.

  • Mukhya Fayda: Isse horizontal doori ($D$) seedhe mapi ja sakti hai.

  • Tacheometric Equation: $D = KS + C$.

    • $K$ (Multiplying Constant): $(\frac{f}{i})$.

    • $C$ (Additive Constant): $(f + d)$.

    • $S$: Staff intercept.

Vishesh Note:

  • Anallactic Telescope ke liye $K = 100$ aur $C = 0$ hota hai.

  • Is sthiti mein doori ka formula seedha $D = 100 \times S$ ho jata hai.



Tacheometry: Vishesh Sthiti

Jab staff ko vertical rakha jata hai aur point kisi unchai par ho, toh horizontal doori ($D$) aur vertical unchai ($V$) nikalne ke liye niche diye gaye sutro ka upyog hota hai:

  • Horizontal Distance ($D$):

    $$D = Ks \cos^{2}\theta + C \cos\theta$$

  • Vertical Height ($V$):

    $$V = \frac{1}{2} Ks \sin 2\theta + C \sin\theta$$

  • RL ki Ganana: Point $P$ ka RL nikalne ke liye formula hai:

    $$RL_{p} = BM + S + V - S_{2}$$

    (Yahan $S$ staff intercept hai aur $\theta$ vertical angle hai).

Curves (Mod) ke Prakar

Surveying mein road ya railway line ki disha badalne ke liye curves ka upyog kiya jata hai. Inke mukhya prakar hain:

  1. Simple Curve: Yeh ek circular arc hota hai jiska radius ($R$) hamesha sthir rehta hai.

  2. Compound Curve: Isme do ya do se zyada circular arcs hote hain jinka radius alag-alag hota hai aur wo ek hi disha mein mudte hain.

  3. Reverse Curve: Yeh do circular arcs se banta hai jo vipreet (opposite) dishaon mein mudte hain.

  4. Transition Curve: Yeh ek aisi line hoti hai jiska radius anant (infinity) se badalkar ek nirdharit radius tak jata hai.

Simple Circular Curve ke Ang

Ek simple circular curve mein kai mukhya points hote hain:

  • Point of Curve ($T_1$): Jahan se curve shuru hota hai.

  • Point of Tangency ($T_2$): Jahan curve khatam hota hai.

  • Deflection Angle ($\Delta$): Woh kon jisse line apni asli disha se mudti hai.

  • Length of Tangent ($VT_1$): Iska sutra hai

    $$R \tan(\frac{\Delta}{2})$$

    .

  • Length of Longest Chord: Iska sutra hai

    $$2R \sin(\frac{\Delta}{2})$$

    .

  • Apex Distance ($VC$): Curve ke sabse unche point ki tangent intersection se doori.


Photogrammetry aur Scale ki Jankari

Vertical photograph ke scale aur relief displacement ke mukhya sutra (formulas) aur concepts niche diye gaye hain:

Vertical Photograph ka Scale

Vertical photograph ka scale, map ki doori aur zameen ki doori ka anupat (ratio) hota hai. Isse nikalne ke liye niche diye gaye sutra ka upyog kiya jata hai:

  • Mukhya Sutra:

    $$Scale = \frac{f}{H - h_{avg}}$$

    • $f$: Camera ki focal length.

    • $H$: Camera ki Mean Sea Level (MSL) se unchai.

    • $h_{avg}$: Zameen ki ausat unchai (average height).

Relief Displacement ($d$)

Relief Displacement ka matlab hai kisi object ke top point aur bottom point ki image ke beech ki doori, jo camera ke axis se mapi jati hai.

  • Sutra:

    $$d = r - r'$$

    • $r$: Camera axis se object ke top point ki image ki doori.

    • $r'$: Camera axis se object ke bottom point ki image ki doori.

  • Alternative Sutra:

    $$d = \frac{r \cdot h}{H}$$

    • $h$: Object ki asli unchai.

Numerical Udaharan: Tower ki Unchai

File mein ek sawal hal (solve) kiya gaya hai jahan ek Radio Tower ki unchai nikalni hai:

  1. Deta: $f = 152.4\text{ mm}$, $h_{avg} = 553\text{ m}$, $r = 8\text{ cm}$, $r' = 7\text{ cm}$, aur $d = 1\text{ cm}$.

  2. Calculation: Pehle camera ki unchai ($H$) nikali gayi ($999.48\text{ m}$).

  3. Result: Sutra ka upyog karke Tower ki unchai $55.8\text{ m}$ nikal kar aayi hai.


  4. .

Plane table surveying

Plane table surveying ek aisa method hai jisme field par observation aur plotting dono kaam ek saath (simultaneously) kiye jate hain. Is method ka mukhya principle parallelism hai, jiska matlab hai ki plotting sheet par draw ki gayi har line zameen (ground) ki uske corresponding line ke parallel honi chahiye

Plane table surveying mein mukhya roop se char (four) methods upyog hote hain:

1. Radiation Method

Is method mein instrument ko ek hi station par set kiya jata hai, aur us station se baki sabhi points ki taraf rays draw ki jati hain.

  • Suitability: Yeh chhote areas (small areas) ke survey ke liye sabse best hai.

  • Process: Zameen par distances ko mapa jata hai aur phir drawing sheet par ek suitable scale ke hisab se unhe cut kar liya jata hai.

2. Traversing Method

Is method mein plane table ko har ek station par bari-bari (in succession) set kiya jata hai.

  • Suitability: Iska upyog lambe aur patle rasto (narrow strips) ke survey ke liye hota hai, jaise roads ya railways.

  • Process: Survey line nirdharit karne ke liye ek station se agle station ki taraf foresight li jati hai.

3. Intersection Method

Isme do aise stations chune jate hain jahan se plotted kiye jane wale baki sabhi points saaf dikhayi dein.

  • Suitability: Yeh pahaadi (hilly/undulated) ilako aur lambi doori (large distance) ke points mapne ke liye bahut upyogi hai.

  • Base Line: Do instrument stations ko jodne wali line ko Base Line kaha jata hai.

4. Resection Method

Resection ka upyog tab kiya jata hai jab hume drawing sheet par plane table ki apni position (location) pata karni ho, jo pehle se plotted nahi hai.

  • Orientation: Is method ka mukhya upyog orientation ke liye hota hai.

  • Techniques: Resection ke liye do mukhya techniques hain:

    1. Two-point problem.

    2. Three-point problem.



Vertical Photograph ka Scale

Vertical photograph ka scale map ki doori aur zameen ki doori ka anupat (ratio) hota hai.  Ise nikalne ke liye niche diye gaye sutra ka upyog kiya jata hai:

  • Sutra:

    $$Scale = \frac{f}{H - h_{avg}}$$

    • $f$: Camera ki focal length.

    • $H$: Camera ki Mean Sea Level (MSL) se unchai.

    • $h_{avg}$: Zameen ki ausat unchai (average height).

Relief Displacement ($d$)

Relief Displacement kisi vastu (object) ke top aur bottom points ki image ke beech ki woh doori hai, jo camera ke axis se mapi jati hai.

  • Mukhya Sutra: $d = r - r'$

    • $r$: Camera axis se object ke top point ki image ki doori.

    • $r'$: Camera axis se object ke bottom point ki image ki doori.

  • Alternative Sutra: $d = \frac{r \cdot h}{H}$

    • Jahan $h$ vastu ki asli unchai hai.

Numerical Udaharan: Tower ki Unchai nikalna

:

  • Deta (Given):

    • Line AB ki lambai $= 300\text{ m}$.

    • Map par mapi gayi lambai $= 102.4\text{ mm}$.

    • $h_{avg} = 553\text{ m}$, $f = 152.4\text{ mm}$.

    • $r = 8\text{ cm}$, $r' = 7\text{ cm}$ ($\therefore d = 1\text{ cm}$).

  • Calculation:

    1. Pehle scale aur di gayi lambai ka upyog karke camera ki unchai ($H$) nikali gayi, jo $999.48\text{ m}$ aayi.

    2. Iske baad Relief Displacement ke sutra ($d = \frac{r \cdot h}{H - h_{avg}}$) ka upyog karke tower ki unchai nikali gayi.

  • Result: Tower ki asli unchai $55.8\text{ m}$ nikal kar aayi hai.


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