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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
Substituting the values of ‘r ’, ‘r ’ and ‘H’ in the above expression we get:
1
2
The total material area = π 12 + 3 ∗ 32 + 12 − 3 + 32 ∗ 2π ∗ 3 = 2169.655 inch
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2
2
šƒ’Ž‡ ͵ǣ ‹ ƒ› ‡‰‹‡‡”‹‰ •‹–—ƒ–‹‘•ǡ ‘™‹‰ –‘ –Š‡ ƒ–—”‡ ‘ˆ ‡‰‹‡‡”‹‰ǡ –Š‡ ’ƒ”ƒ‡–‡”•
Šƒ˜‡ •‹‰‹ϐ‹ ƒ– ˜ƒ”‹ƒ„‹Ž‹–›Ǥ ‘ ‰‡– –Š‡ ƒ˜‡”ƒ‰‡ ˜ƒŽ—‡ ‘ˆ ƒ ’ƒ”ƒ‡–‡”ǡ ‘‡ ‘—Ž† —•‡ –Š‡ ȋ ‘‘–
‡ƒ “—ƒ”‡Ȍ ˜ƒŽ—‡Ǥ

‡– —• ‘•‹†‡” ƒ ‘–‘”ǡ ™Š‘•‡ –‘”“—‡ ”‡“—‹”‡‡– ‹• †‹ˆˆ‡”‡– ˆ‘” †‹ˆˆ‡”‡– ’‡”‹‘†• ‘ˆ –‹‡Ǥ Š‡
‘–‘” —•– „‡ ‘–”‘ŽŽ‡† ‹ •— Š ƒ ™ƒ› –Šƒ– ‹– †‘‡• ‘– •—ˆˆ‡” ‡š ‡••‹˜‡ †ƒƒ‰‡ †—‡ –‘ ‘˜‡” Š‡ƒ–Ǧ
‹‰ ‘” †‡ƒ‰‡–‹œƒ–‹‘ ‡ˆˆ‡ –•Ǥ
Let us say, that, the torque requirements (T , T , T − − − −−, T ) for different time ranges and the
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3
n
1
time intervals be (t , t , t − − − −−, t ).
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1
2
n
The RMS torque value is given by:
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2
2
2
T t + T t + T t + − − − − T t
n n
1 1 2 2 3 3
t + t + t + − − − − −t n
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1
2
‡”‡ǡ ‡ƒ Š –‘”“—‡ ˜ƒŽ—‡ Šƒ• –Š‡ ™‡‹‰Š– ƒ• –‹‡ ‹–‡”˜ƒŽǤ Š‡”‡ˆ‘”‡ǡ –Š‡ •— ‘ˆ –Š‡ ™‡‹‰Š–‡†
•“—ƒ”‡• ‘ˆ –‘”“—‡• ‹• †‹˜‹†‡† „› –Š‡ –‘–ƒŽ ™‡‹‰Š–Ȁ–‹‡ –‘ ‰‡– –Š‡ ™‡‹‰Š–‡† ‡ƒ •“—ƒ”‡ǡ ™Š‘•‡
•“—ƒ”‡ ”‘‘– ‰‹˜‡• –Š‡ ˜ƒŽ—‡ ‡‡†‡†Ǥ
Š‡ ˜ƒŽ—‡ Š‡Ž’• ‹ •‡Ž‡ –‹‰ –Š‡ „‡•– ‘–‘” ˆ‘” ƒ ‰‹˜‡ •‹–—ƒ–‹‘Ǥ
‡– —• ‘•‹†‡” ƒ‘–Š‡” •‹–—ƒ–‹‘Ǥ
ƒ–‡”‹ƒŽ ™‹–Š ”‡Žƒ–‹˜‡ ’”‘’‡”–› ”ƒ ƒ† ™‡‹‰Š–ƒ‰‡ǡ ‰‹˜‡ –‘ ‡ƒ Š ’”‘’‡”–› ƒ• •Š‘™ ‹ –Š‡ –ƒ„Ž‡
„‡Ž‘™Ǥ Š‡ ™‡‹‰Š–‡† ƒ˜‡”ƒ‰‡ ‹• ˆ‘—† •— Š –Šƒ–ǡ –Š‡ ƒ–‡”‹ƒŽ• ‘—Ž† „‡ ‘’ƒ”‡† ˆ‘” ƒ’’Ž‹ ƒ–‹‘Ǥ
Š‡ ƒ–‡”‹ƒŽ ™‹–Š Š‹‰Š‡•– ™‡‹‰Š–‡† ƒ˜‡”ƒ‰‡ ‹• –Š‡ „‡•– •—‹–‡† ƒ–‡”‹ƒŽǤ

‘–‡ǣ ‡”‡ ™‡‹‰Š–• ƒ”‡ ‘”ƒŽ‹œ‡† •— Š –Šƒ– –Š‡‹” •— ‹• ͳ

Material Property Relative Rank Weightage given

Yield strength 9 0.1

Fatigue strength 7 0.4

Young’s Modulus to density ratio 8 0.2

Cost 9 0.3

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,
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