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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
Š‡ •ƒ‡ ‘—Ž† „‡ ˆ‡† –‘ ƒ ‘Ž‹‡ ƒŽ —Žƒ–‘”Ǥ Š‡ ƒŽ —Žƒ–‘” ™‘—Ž† ‘’—–‡ •‹‰‹ϐ‹ ƒ–
”‡•’‘•‡• ƒ– ˜ƒ”‹‘—• ˆ”‡“—‡ ‹‡•ǡ ™Š‹ Š ‹-–—” ™‘—Ž† Š‡Ž’ Ž‘ ƒ–‡ –Š‡ ”‡•‘ƒ– ˆ”‡“—‡ ‹‡• ƒ–
™Š‹ Š –Š‡ ”‡•’‘•‡ ‹• ”‡Žƒ–‹˜‡Ž› ƒš‹—Ǥ

ͳǤͳ͸ ‘—–‹‡ ‰‹‡‡”‹‰ ƒŽ —Žƒ–‹‘•

 ƒ› ‡‰‹‡‡”‹‰ •‹–—ƒ–‹‘•ǡ –Š‡ ƒŽ —Žƒ–‹‘ ‘ˆ –Š‡ ‡Ž‡˜ƒ–‹‘ ‘ˆ ƒ ‰‡‘‰”ƒ’Š‹ ƒŽ Ž‘ ƒ–‹‘ ™‹–Š ”‡Ǧ
•’‡ – –‘ ƒ‘–Š‡” Ž‘ ƒ–‹‘ǡ ˆ‘” ϐŽ‘™ ƒƒŽ›•‹• ‘ˆ ‰ƒ•‡• ‘” †‹•–ƒ ‡ ƒŽ —Žƒ–‹‘•ǡ ‡ ‡••‹–ƒ–‡ –Š‡ ƒŽ —Ǧ
Žƒ–‹‘ ‘ˆ ȋšǡ › ƒ† œȌ ‘‘”†‹ƒ–‡•ǡ ˆ”‘ –Š‡ ƒ˜ƒ‹Žƒ„Ž‡ ˜ƒŽ—‡• ‘ˆ Žƒ–‹–—†‡ ƒ† Ž‘‰‹–—†‡ ‘ˆ –Š‡ ‰‡‘Ǧ
‰”ƒ’Š‹ ƒŽ Ž‘ ƒ–‹‘Ǥ
šƒ’Ž‡ ͳǣ ƒŽ —Žƒ–‡ –Š‡ •Š‘”–‡•– –—‡Ž †‹•–ƒ ‡ „‡–™‡‡ ƒ‰ƒŽ‘”‡ ƒ† ‘‹„ƒ–‘”‡Ǥ Ž•‘ ƒŽǦ
—Žƒ–‡ –Š‡ †‹•–ƒ ‡ ƒŽ‘‰ –Š‡ ‡ƒ”–Šǯ• •—”ˆƒ ‡ ȋ–Š‡ ‰”‡ƒ– ‹” Ž‡Ȍǡ ƒ••—‹‰ –Š‡ ‡ƒ”–Š –‘ „‡ ƒ ’‡”ˆ‡ –
•’Š‡”‡ ‘ˆ ”ƒ†‹—• Ǯ ǯǤ Ž•‘ ‡•–‹ƒ–‡ –Š‡ ‡ƒ”–Šǯ• •—”ˆƒ ‡ ˜‡Ž‘ ‹–› ƒ† ‡–”‹ˆ—‰ƒŽ ˆ‘” ‡ ƒ– ƒ‰ƒŽ‘”‡Ǥ
Š‡ ‰‡‘‰”ƒ’Š‹ ‘‘”†‹ƒ–‡• ‘ˆ ƒ‰ƒŽ‘”‡ ƒ† ‘‹„ƒ–‘”‡ ‹• ƒ• –ƒ„—Žƒ–‡†ǣ

‹–› ƒ–‹–—†‡ ȋȽȌ ‘‰‹–—†‡ ȋȾȌ
ƒ‰ƒŽ‘”‡ ͳ͵-†‡‰”‡‡ ‘”–Š ͹ͺ-†‡‰”‡‡ ƒ•–
‘‹„ƒ–‘”‡ ͳͳ-†‡‰”‡‡ ‘”–Š ͹͹-†‡‰”‡‡ ƒ•–

Š‡ Žƒ–‹–—†‡ ƒ† Ž‘‰‹–—†‡ ƒ‰Ž‡• –Šƒ– ƒ”‡ ȋȽ ƒ† ȾȌ ”‡•’‡ –‹˜‡Ž› ƒ”‡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤ͹ʹȐǤ

[Fig 1.72: A location on the surface of the earth with geographic coordinates]

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