Structural loads — axial (thrust), bending (wind shear), dynamic (vibration, acoustics, shock): Question bank

3.6.1 · D5 · Physics › Spacecraft Structures & Systems Engineering › Structural loads — axial (thrust), bending (wind shear), dyn

True or false — justify

True or false: axial compression sabse zyada rocket ke bilkul upar, payload ke neeche hoti hai.

False — axial force

F = m (x) (g + a)

hoti hai jahan

m (x)

cut ke upar ka mass hai, isliye yeh base ki taraf badhti hai jahan sabse zyada mass neeche dab raha hota hai.

True or false: load factor

n

bas acceleration ka doosra naam hai, isliye "6 g" aur "6 g of acceleration" ek hi cheez hain.

False —

n g = g + a

gravity aur acceleration dono ko bundle karta hai, isliye

n = 6

ka matlab hai ki actual acceleration sirf

a = (n - 1) g = 5 g

hai.

True or false: bending stress cross-section mein uniform hoti hai, bilkul axial stress ki tarah.

False — bending stress

σ = M y / I

neutral axis se $y$ distance ke saath linearly vary karti hai: ek side stretch hoti hai, doosri side compress hoti hai, aur beech zero dekha jaata hai.

True or false: poore launch ka worst structural moment liftoff par hota hai, jab thrust sabse zyada hoti hai.

False — sizing peak usually max-Q ke aas paas hoti hai, jahan axial compression aur wind-shear bending moment ek hi fiber par stack ho jaate hain

F / A + M c / I

ke saath.

True or false: zyada stiff spacecraft (higher

k

) vibration ke against hamesha safe hoti hai.

False — stiffness sirf

f_{n}

ko raise karti hai; yeh tabhi help karta hai jab yeh tumhe excitation band se door le jaaye. Yeh utni hi aasani se

f_{n}

ko kisi strong PSD peak mein push kar sakta hai. Dekho Modal Analysis & Natural Frequencies.

True or false: zyada damping ratio

ζ

ka matlab zyada resonant amplification hai.

False —

Q = 1/ (2 ζ)

, isliye zyada damping ka matlab kam amplification hai. Low

ζ

(~0.02) dangerous case hai jo

Q \approx 25

deta hai.

True or false: hazaron g ki peak accelerations wale shock loads primary load-bearing shell ke liye sabse badi threat hain.

False — shock high-frequency aur bahut chhoti duration ka hota hai, isliye massive parts ko momentum zyada feel nahi hota; yeh electronics, relays, aur brittle components ko barbad karta hai. Dekho Pyrotechnic Separation Systems.

True or false: acoustic loading sabse zyada thick, heavy propellant tanks ke liye matter karti hai.

False — acoustics bade lightweight panels (solar arrays, antennas) par dominate karti hain jinki badi area aur low mass pressure waves par strongly respond karti hai.

True or false: resonance par ek chhoti driving force kabhi bhi sirf chhota deflection hi produce kar sakti hai.

False — resonance par

x_{m a x} \approx Q x_{static}

hota hai, isliye ek modest force ~10–25× amplify hoti hai; isliye hi hum isse bachte hain.

Spot the error

"Ek cut par axial force

F = m_{total} (g + a)

hai jo rocket ki full mass use karta hai." — kya galat hai?

Galat mass — sirf us station par structure jo mass cut ke upar hai,

m (x)

, woh push ho raha hai; neeche ka mass lower structure se carry hota hai.

"Kyunki

g + a = n g

hai, aur rocket free-fall mein

a = - g

ke saath coast karta hai, load factor

n = 1

hai." — error dhundho.

Free-fall mein

a = - g

deta hai

g + a = 0

, isliye

n = 0

— structure koi axial load carry nahi karta (weightlessness),

n = 1

nahi.

σ = M c / I

, isliye bending stress kam karne ke liye bas

c

(radius) chhota karo." — trap kya hai?

c

chhota karne se

I = π R^{3} t

bhi chhota hota hai (jo

R^{3}

ke saath scale karta hai), isliye ratio

c / I \propto 1/ R^{2}

actually badtar ho jaata hai; ek fatter tube bending mein zyada stiff hoti hai.

"Vibration se bachne ke liye hum design karein ki

f_{n}

excitation frequency ke barabar ho ek clean match ke liye." — error?

Frequencies match karna resonance cause karta hai, exactly wahi cheez jo hum avoid karte hain. Miles' rule demand karta hai ki

f_{n}

LV minimums ke upar rahe, excitation se bahut door.

"Miles' equation

g_{RMS} = \frac{π}{2} f_{n} Q W

dikhati hai ki

Q

badhne se response girta hai, isliye

Q

boost karne ke liye stiffness add karo." — do errors dhundho.

Response badhta hai

Q

ke saath (yeh square root ke andar hai, numerator mein), aur

Q = 1/ (2 ζ)

damping se set hota hai, stiffness se nahi — stiffness

f_{n}

move karti hai,

Q

nahi. Dekho Random Vibration & PSD.

"Humne har component ko uski RMS response tak design kiya, isliye yeh safe hai." — kya missing hai?

RMS 1σ value hai; random peaks routinely isse exceed karte hain, isliye design load ==

3 σ

== use karta hai (peaks ka ~99.7% cover karta hai),

1 σ

nahi.

"Thrust lower skin mein tension create karta hai kyunki engine rocket ko upar khichta hai." — error?

Engine neeche se push karta hai aur upar wale mass ki inertia resist karti hai, isliye lower skin compressed hai, stretched nahi.

Why questions

Engineers max-Q ke paas axial aur bending stresses ko alag cases ki jagah ek hi fiber par kyun add karte hain?

Kyunki dono ek saath windward/leeward outer fiber par act karte hain; superposition ka matlab hai ki ek fiber

F / A + M c / I

carry karti hai, aur sum ko ignore karne se actual worst-case stress underestimate ho jaata hai.

Natural frequency

ω_{n} = k / m

kyun hai aur

m / k

kyun nahi?

F = 0, c = 0

set karne se

m \overset{x}{¨} = - k x

milta hai, yani

\overset{x}{¨} = - (k / m) x

;

\overset{x}{¨} = - ω^{2} x

se match karne par

ω_{n}^{2} = k / m

force hota hai. Stiff ya light → faster oscillation.

Hum random vibration ko ek single peak acceleration ki jagah PSD (g²/Hz) se kyun quantify karte hain?

Random vibration ki energy kai frequencies mein spread hoti hai bina kisi repeating peak ke, isliye hum describe karte hain ki kitना power har frequency par hai; structure ka response depend karta hai ki uska

f_{n}

us spectrum mein kahan land karta hai.

Wind loading rocket ko simply-supported beam ki jagah cantilever beam ki tarah behave kyun karata hai?

Vehicle effectively ek end (engine/base) par held/driven hai aur doosri taraf free hai, isliye ek transverse gust isko exactly aise bend karta hai jaise ek broomstick beech mein push ho jab ek end pakda ho.

Miles' equation mein

π /2

factor kyun aata hai?

Yeh SDOF resonance response ko peak ki effective bandwidth par integrate karne se aata hai — sharp resonance curve ke neeche ka area — ek PSD level ko total RMS mein convert karta hai. Dekho Modal Analysis & Natural Frequencies.

Edge cases

Edge case: ballistic coast (engine off, free-fall) ke dauran structure kitna axial load carry karta hai?

a = - g

ke saath,

g + a = 0

milta hai, isliye

F_{axial} = 0

— vehicle weightless hai aur primary axial compression khatam ho jaati hai.

Edge case: cross-section ke neutral axis par bending stress ka kya hota hai?

Wahan yeh zero hoti hai, kyunki

σ = M y / I

mein neutral axis par

y = 0

hota hai; wahan ka material bending work sirf shear mein karta hai, tension/compression mein nahi.

Edge case: jab damping

ζ \to 0

, amplification

Q

kya karta hai?

Q = 1/ (2 ζ) \to \infty

— ek undamped structure resonance par without bound amplify karega; real damping hi deflection ko finite rakhti hai.

Edge case: kisi component ka

f_{n}

exactly ek LV minimum par hai (jaise 25 Hz axial) — kya yeh acceptable hai?

Nahi — rule require karta hai ki

f_{n}

minimum ke upar margin ke saath ho; boundary par baithe rehne se koi separation nahi hoti aur resonant coupling ka risk rehta hai. Dekho Factor of Safety & Margins of Safety.

Edge case: thin ring ke liye

I = π R^{3} t

kyun hai aur

R^{2} \times

(area) kyun nahi?

Kyunki material ring ke around har angle

θ

par baitha hai, aur

\int y^{2} d A = \int (R sin θ)^{2} (R t d θ) = π R^{3} t

;

sin^{2}

averaging

π

deta hai,

2 π

nahi. Dekho Beam Bending & Second Moment of Area.

Edge case: first-stage burnout par axial load factor

n

liftoff ke comparison mein kya hota hai?

Yeh burnout ke paas peak karta hai kyunki vehicle almost empty hoti hai (low mass) lekin thrust abhi bhi high hoti hai, isliye

a

(aur isliye

n

) shutdown se bilkul pehle sabse bada hota hai. Dekho Rocket Equation & Thrust.

Edge case: still air mein exactly zero angle of attack par, wind se bending moment kitna hota hai?

Essentially zero — koi side force nahi matlab koi cantilever bending nahi; bending tabhi appear hoti hai jab koi gust ya wind-shear layer nonzero angle of attack de. Dekho Max-Q and Dynamic Pressure.

Recall Ek-line self-test

Woh single sentence jo axial, bending, aur dynamic ko sizing point par ek saath tie karta hai? ::: Max-Q ke paas outer fiber $F / A + M c / I$ statically carry karta hai, aur $f_{n}$ ke paas koi bhi dynamic input deflections ko upar se $Q$ se multiply karta hai — isliye worst-case = combined static stress with dynamic amplification aur $3 σ$ margin.