3.6.1 · D1Structural loads — axial (thrust), bending (wind shear), dyn
Ek rocket ek patli metal ki tube hai jo toot-ni nahi chahiye jab engine neeche se dhakka de aur hawa side se thappad mare. Is topic mein sab kuch bas force ka area par spread (stress) aur woh force kitni tezi se hilti hai (frequency) ka hisaab-kitaab hai — taaki hum check kar sakein ki tube margin ke saath survive karti hai.
Parent note padhne se pehle, tumhe kuch ideas ki ek choti si kit chahiye. Neeche har ek tumhe deta hai: saada matlab → picture → topic ko isko kyun chahiye. Ye is tarah order kiye gaye hain ki har paaydaan apne pehle wale par khada ho. Koi bhi cheez use hone se pehle build nahi hoti.
F push ya pull . Newtons (N) mein measure hoti hai. Ek newton roughly ek chote seb ka weight hai jo tumhare haath mein rakha ho.
Ek arrow banao. Arrow ki length yeh batati hai ki push kitni hard hai; arrow jis direction mein point karta hai woh batata hai ki woh kis taraf push karta hai. Woh arrow hi force hai.
Engine ki thrust ek aisa arrow hai (upar point karta hua). Hawa ka ek jhatka ek aur arrow hai (side mein point karta hua). Poora topic arrows ke baare mein hai aur woh metal ke saath kya karte hain.
m a Mass m kitna stuff hai (kilograms, kg). Acceleration a speed kitni tezi se change ho rahi hai (metres per second, har second — m/s 2
Intuition Topic ko isko kyun chahiyeEngine poore rocket ko upar accelerate karta hai. Lekin neeche ki metal ko uske upar ki saari mass ko bhi upar push karna hota hai. Mass m a F = ma squeeze karta hai.
Definition Gravitational accelerationg g ≈ 9.81 m/s 2 m g
n akela dimensionless number jo gravity aur engine acceleration ko saath mein bundle karta hai: g + a = n g n
Kursi par baitho: tum n = 1 n = 6 chhe kilogram ki tarah press ho raha feel hota hai. Engineers kehte hain "payload 6 g dekhta hai" — woh "6" hi n
n a n g + a = n g
Yeh page par sabse important idea hai. Figure dekho.
Definition Cross-sectional areaA tube ko seedha cross mein slice karo aur metal-face ki ring dekho jo tumne cut ki, metal-face ka jo amount tum dekhte ho woh area A m 2
σ Force divided by area jo usse carry kar rahi hai : σ = F / A = N/m 2 megapascal (MPa) hai.
Intuition Area se kyun divide karo?Ek moti wall par same push vs. ek patli wall: patli wall tootne ke zyada paas hai. Materials total force ki parwah nahi karte — woh face ke per unit force ki parwah karte hain. Ek thumbtack isliye kaam karta hai kyunki ek tiny point-area ke through chhoti force bahut badi stress banati hai. Stress woh number hai jo decide karta hai "kya metal survive karta hai?"
Ek rubber band lo. Dono ends ko alag kheencho → woh stretch hoti hai → yeh tension hai (positive stretching). Ends ko saath mein push karo → woh chhota hota hai aur buckle karna chahta hai → yeh compression hai.
Thrust rocket ko squeeze karta hai: compression . Jab hum tube ko bend karte hain, ek side stretch hoti hai (tension) aur doosri side bilkul usi moment mein squeeze hoti hai (compression).
Topic ko dono signs chahiye kyunki sabse bura fibre woh hai jahan do compressions add up hoti hain.
Definition Young's modulusE stiffness number : ek given stretch produce karne ke liye kitni stress chahiye. Steel ka bada E E
Topic ko isko kyun chahiye: bending formula derive karne ke liye, hum kehte hain "ek fibre jo zyada stretch hoti hai woh zyada stress mein hai," aur Hooke's law exactly woh rule hai jo stretch ko stress se connect karta hai.
Ek beam ek end par firm pakdi gayi aur doosre par free — jaise ek diving board, ya ek broomstick jise tum ek end par pakad kar beech mein push karo.
Intuition Rocket ek kyun haiRocket lamba aur slender hai. Jab hawa uski side push karti hai, yeh exactly ek diving board ki tarah jhukta hai jiske tip par koi khada ho. Reader ko "bending" samajhne ke liye yeh picture dikhna chahiye.
Definition Bending momentM twisting/bending effort , force times uski lever-arm (distance) ke barabar. Units: newton-metres (N⋅m base bahut bada bending effort feel karta hai kyunki lever arm lamba hai.
Definition Neutral axis, distancey c middle line na stretch hoti hai na squeeze — woh hai neutral axis . Uske upar distance y Sabse door fibre distance c
Definition Second moment of areaI batata hai ki material neutral axis se kitna door hai : I = ∫ y 2 d A y zyada count karta hai (squared!); middle ke paas wala material mushkil se help karta hai.
Intuition Picture — kyun integral sign aata hai∫ … d A d A y 2 shape par sum karna hota hai. Woh bahut-saare-tiny-pieces-ka-summing exactly wahi hai jo ek integral hai.
Isliye ek I-beam top aur bottom flanges mein metal rakhta hai (bahut door) aur isliye ek patla rocket ring efficient hai: uska almost saara metal radius R I ≈ π R 3 t
f ω Frequency f hertz , Hz). Angular frequency ω = 2 π f
k c Stiffness k = ek spring stretch ke har metre per kitna hard push back karta hai (N/m). Damping c = friction jo energy bahar nikalta hai, wiggle ko dheere-dheere khatam karta hai.
Definition Natural frequencyf n ω n khud se wiggle karti hai jab tum usse pluck karo. ω n = k / m
Intuition Resonance — dangerEk bachche ke swing ko bilkul sahi rhythm par push karo aur chhoti pushes ek bada swing banate hain. Yeh hai resonance : jab pushing frequency f n f n door rahe.
ζ Q ζ = c / ( 2 k m ) wiggles kitni jaldi khatam hoti hain . Iska partner Q = 1/ ( 2 ζ ) amplify karta hai. Low damping (tiny ζ Q
Flexure sigma equals Mc over I
Distance y and outer fibre c
Khud test karo — jawab dene ke baad hi reveal karo.
Stress kya hai, words aur units mein? Force divided by area jo usse carry kar rahi hai; pascals (Pa = N/m²), aksar MPa.
Force ko area se divide kyun karo? Materials force per unit face ke basis par tootte hain, total force ke basis par nahi — patli wall wahan fail hoti hai jahan moti survive karti hai.
Load factor n Gravity aur engine acceleration, g + a = n g
Cantilever kya hai, aur rocket ek kyun hai? Ek beam ek end par fixed, doosre par free; ek slender rocket diving board ki tarah jhukta hai jab hawa uski side push karti hai.
Neutral axis kya hai, aur outer fibre c Middle line jo na stretch hoti hai na squeeze; c
I = ∫ y 2 d A Material neutral axis se kitna door hai; squaring matlab door-baahar wala metal bahut zyada count karta hai, toh shape (sirf amount nahi) stiffness decide karta hai.
Hooke's law batao aur har symbol ka naam lo. σ = E ε
Natural frequency kya hai aur kya isse high banata hai? Woh frequency jis par ek part wiggle karta hai jab pluck karo,
ω n = k / m ; stiffer (bada
k ) ya halka (chhota
m ) → zyada.
Low damping ζ Q = 1/ ( 2 ζ ) ζ Q
