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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
ˆ –Š‡ • ”‡™ ‹• ‰‹˜‡ ƒ Ž‘ ™‹•‡ ”‘–ƒ–‹‘ǡ –Š‡ǡ –Š‡ • ”‡™ ƒ†˜ƒ ‡• ‹ –Š‡ ‡‰ƒ–‹˜‡ †‹”‡ –‹‘Ǥ
‡ ‡ ‰‘‹‰ „› –Š‡ ”—Ž‡ǡ –Š‡ Ǯwǯ ˆ‘” –Š‡ • ”‡™ •Š‘™ ‹ –Š‡ ȏ ‹‰ „Ȑ ‹• ˜‡ –‘”‹ƒŽŽ› ”‡’”‡•‡–‡† ƒ•ǣ

w = w −k , indicating that the direction is along negative Z axis (clock wise)
w = w k , indicating that the direction is along positive Z axis (anti - clock wise)

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

[Fig b: Right Handed Screw]

ͳǤͷǤ͵ ƒ”–‡•‹ƒ ˜‡ –‘”

‡– —• ‘•‹†‡” ƒ ˜‡ –‘” ‘‡ –‹‰ –Š‡ ‘”‹‰‹ ȋͲǡͲǡͲȌ ƒ† ƒ ƒ”„‹–”ƒ”› ’‘‹– ‹ •’ƒ ‡ ȋšǡ ›ǡ œȌǤ

˜‡ –‘” ‹ ƒ ͵ ƒ”–‡•‹ƒ •’ƒ ‡ ‹• ”‡’”‡•‡–‡† ƒ• ˆ‘ŽŽ‘™•ǣ

Vector V = [(magnitude along ‘x’ ∗ unit vector along ‘x’) + (magnitude along ‘y’
∗ unit vector along ‘y’) + (magnitude along ‘z’ ∗ unit vector along ‘z’)

That is: [V = x − x i + y − y j + (z − z )k]
1
2
1
2
1
2
Š‡”‡ǡšͳǡ ›ͳ ƒ† œͳ ƒ”‡ ‘‘”†‹ƒ–‡• ‘ˆ –Š‡ ‘”‹‰‹Ǥ Š‡”‡ˆ‘”‡ǡ
™‡ Šƒ˜‡ǣ

[V = x − 0 i + y − 0 j + (z − 0)k]
2
2
2
Let us analyze a vector V in a 3D space as shown in [ . ].
,

[Fig 1.19: Vector in a 3D space]

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