EngineeringHiranyagarbha · Class 11-12
Gravity dam ki stability: overturning, sliding aur uplift
Kabhi socha hai ki ek concrete ki deewar, jo kahin bandhi nahi, sirf apne wazan se lakhon tonne paani kaise rokti hai? Woh khisakti kyun nahi, ulatti kyun nahi?
Socho pehle… phir dekho jawab
Kyunki engineer teen jaanch karte hain: overturning (toe ke ird-gird ulatna), sliding (neev par khisakna) aur stress (concrete ya chattan par zyada dabaav). Har jaanch mein rokne wala bal ya moment, dhakelne wale se ek tay guna (factor of safety) zyada rakha jaata hai — jaise building ke column mein.
Bal: (1) Paani ka horizontal bal P = ½γH² (γ = ρg), tali se H/3 par. (2) Deewar ka wazan W, katav ke kendra par. (3) Uplift U — neev ke neeche risa paani upar dhakelta hai; drain na ho toh heel par lagbhag γH se toe par lagbhag shoonya, trikon jaisa.
Overturning: FoS = rokne wala moment (W ka) ÷ ulatane wala moment (P aur U ke) toe ke ird-gird. Sliding: FoS = μ(W − U) ÷ P (sirf ghirshan; asal design mein neev ki shear taakat bhi). Uplift W ko ghatata hai, isliye drainage gallery aur grout curtain uplift kam karte hain — sasta upaay, bada faayda.
Middle-third niyam: parinaami bal (resultant) neev ke beech ke tihaai hisse mein gire, taaki heel par tension na aaye — concrete tension mein kamzor hai. Isliye tikona katav: neeche chaudai se resultant beech mein rehta hai.
Trade-off aur kadi: star badha, phir P ∝ H² badha, phir uplift bhi badha, isliye dono FoS ek saath girte hain. Isliye spillway ki kshamata, star ki nigraani aur drain ki safai design jitni hi zaroori hain — 'chalta hua' baandh bina margin ke ho sakta hai.
Humne kya kiya :- Gravity dam par lagne wale teen bal (paani, wazan, uplift) se overturning aur sliding ki jaanch ki aur middle-third niyam samjha.
Isse kya hua :- Samjhe ki baandh ki suraksha ek sankhya (FoS) hai jo star, drain aur rakh-rakhaav ke saath badalti hai.
Ghar pe try karo
Moti gatte ki ek tikona deewar (neeche 10 cm, oonchai 15 cm) aur ek aayataakaar deewar (5 cm × 15 cm) kaato. Mez par khadi karke peeche se ek hi pencil se dheere dhakelo — kaun pehle ulti? Phir kaagaz par H = 30 m, base 24 m ki deewar ke liye P = ½γH² aur uska moment nikalo (γ = 9.8 kN/m³).
Wow!
Kai baandhon mein deewar ke andar ek surang (drainage/inspection gallery) hoti hai, jahan se engineer andar ghoom kar risaav aur uplift naapte hain!
3 sawaal
- Gravity dam par paani ka horizontal bal (per metre) aur uski jagah kya hai?
Jawab dekho
½γH², tali se H/3 par. Dabaav trikon jaisa; kul bal ½γH², kendra tali se H/3 par.
- Uplift dam ki sthirta ko kaise prabhavit karta hai?
Jawab dekho
Prabhavi wazan (W − U) ghatata hai, sliding aur overturning FoS girte hain. Uplift neeche se upar dhakelta hai, isliye prabhavi wazan ghatta hai; drainage gallery ise kam karti hai.
- Middle-third niyam kis liye hai?
Jawab dekho
Resultant beech ke tihaai mein rahe taaki heel par tension na aaye. Concrete tension mein kamzor hai; resultant middle third mein ho toh poori neev compression mein rehti hai.
NCERT se jodo: NCERT Class 11 Physics — fluids aur torque ka santulan; Class 12 ke liye civil engineering ka parichay (idea in words)