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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
ͳǤͶ ’’Ž‹‡† ƒŽ —Ž—•

ƒŽ —Ž—• ™ƒ• ˆ—†ƒ‡–ƒŽŽ› †‡˜‡Ž‘’‡† –‘ †‡ƒŽ ™‹–Š ‘-Ž‹‡ƒ” •›•–‡•ǡ ™Š‡”‡‹ǡ Šƒ‰‡• ‘ˆ ƒ
“—ƒ–‹–› ™‹–Š ”‡•’‡ – –‘ ƒ‘–Š‡” “—ƒ–‹–› ‹• ˜ƒ”›‹‰ ‹ ƒ ‘-Ž‹‡ƒ” ˆƒ•Š‹‘Ǥ

‘ ‹ŽŽ—•–”ƒ–‡ –Š‹• Ž‡– —• ‘•‹†‡” ƒ •–”ƒ‹‰Š– Ž‹‡ ƒ† ƒ —”˜‡ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤͳ Ƭ ͳǤʹȐǤ

[Fig 1.1: slope for a straight line] [Fig 1.2: slope for a curve]

 ’”ƒ –‹ ‡ǡ –Š‡”‡ ƒ”‡ ˆ‡™ •›•–‡• –Šƒ– ƒ”‡ Ž‹‡ƒ”ǡ ƒ† ‘–Š‡”• ƒ”‡ ‘-Ž‹‡ƒ”Ǥ

šƒ’Ž‡ǣ Šƒ‰‡ ‹ –Š‡ Ž‡˜‡Ž ‘ˆ ™ƒ–‡” ‹ ƒ –›’‹ ƒŽ ™ƒ–‡” –ƒ ˜• –‹‡ ‹• ƒ ‘-Ž‹‡ƒ” —”˜‡ǡ ƒ• –Š‡
–ƒ’ ‡š‹– ˜‡Ž‘ ‹–› ‹• ƒ ‘-Ž‹‡ƒ” ˆ— –‹‘ ‘ˆ ™ƒ–‡” Ž‡˜‡Ž ‹ –Š‡ –ƒǤ Š‡”‡ƒ• ‹ ”‡ƒ•‡ ‹ †‹•–ƒ ‡
™‹–Š –‹‡ ȋ’”‘˜‹†‡†ǡ ˜‡Ž‘ ‹–› ‹• ‡’– ‘•–ƒ–Ȍ Šƒ• ƒ Ž‹‡ƒ” ”‡Žƒ–‹‘•Š‹’Ǥ

ƒŽ›œ‹‰ Ž‹‡ƒ” •›•–‡• ȏ ‹‰ ͳǤͳȐ ‹• ‡ƒ•›ǡ ƒ•ǡ –Š‡ ”ƒ–‡ ‘ˆ Šƒ‰‡ ‘ˆ †‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ ȋ›Ȍ ™‹–Š
”‡•’‡ – –‘ –Š‡ ‹†‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ ȋšȌ ‹• ‘•–ƒ– ƒŽŽ –Š‡ ™Š‹Ž‡Ǥ Š‡ †‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ ‹• ƒŽŽ‡†
•‘ǡ „‡ ƒ—•‡ǡ ‹– ‹• ƒ ˆ— –‹‘ ‘ˆ –Š‡ ‹†‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ ȏ› α ˆȋšȌȐǤ Š‡”‡ˆ‘”‡ǡ –Š‡ Šƒ‰‡• ‹ –Š‡
†‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ †‡’‡† ‘ –Š‡ Šƒ‰‡• ‹ –Š‡ ‹†‡’‡†‡– ˜ƒ”‹ƒ„Ž‡Ǥ
ƒŽ›œ‹‰ ‘-Ž‹‡ƒ” •›•–‡• ‹• †‹ˆϐ‹ —Ž–ǡ ƒ•ǡ ƒ– ‡ƒ Š ’‘‹– –Š‡ ”ƒ–‡ ‘ˆ Šƒ‰‡ ‘ˆ †‡’‡†‡– ˜ƒ”‹ƒ„Ž‡
™‹–Š ”‡•’‡ – –‘ –Š‡ ‹†‡’‡†‡– ˜ƒ”‹ƒ„Ž‡ ‹• ‹ ”‡ƒ•‹‰ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤʹȐǤ

’Š›•‹ ƒŽ ‹–‡”’”‡–ƒ–‹‘ ‘ˆ ƒ ‘-Ž‹‡ƒ” •›•–‡ǡ •ƒ›ǡ ƒ ƒ” ƒ ‡Ž‡”ƒ–‹‰ ƒ– ƒ ‘•–ƒ– ”ƒ–‡ǡ ‹• ƒ•
ˆ‘ŽŽ‘™•Ǥ

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