Page 106 - C:\Users\trainee\AppData\Local\Temp\msoEAA3.tmp

Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]
šƒ’Ž‡ ʹǣ

‘’—–‡ –Š‡ ‘’–‹— ƒ”‡ƒ ‘ˆ ƒ ‹•‘• ‡Ž‡• –”‹ƒ‰Ž‡ ȋȏ ‹‰ ͳǤͺȐȌ ˆ‘” ƒ ‰‹˜‡ ’‡”‹‡–‡” ȋ ȌǤ

‘Ž—–‹‘ ʹǣ ‘•‹†‡” –Š‡ ‹•‘• ‡Ž‡• –”‹ƒ‰Ž‡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤͺȐǤ

‡– –Š‡ Š‡‹‰Š– ‘ˆ –Š‡ –”‹ƒ‰Ž‡ „‡ ǮŠǯǡ „ƒ•‡ „‡ Ǯšǯ ƒ† –Š‡ ‡“—ƒŽ •‹†‡• „‡ Ǯ›ǯǤ

P − x
The perimeter of the triangle is given by P = x + 2y , therefore y = - - - - (1.4)
2

Š‡ Š‡‹‰Š– ǮŠǯ ‘—Ž† „‡ ‰‘– „› ƒ’’Ž›‹‰ ›–Šƒ‰‘”ƒ• –Š‡‘”‡ǣ

P − x 2 x 2
h = −
2 4

[Fig 1.8: Isosceles triangle of base ‘x’ and height ‘h’]

‘™ǡ –Š‡ ƒ”‡ƒ ‘ˆ –Š‡ –”‹ƒ‰Ž‡ ‹• ‰‹˜‡ „›ǣ

1 1 P − x 2 x 2 1 P 2 x 2 2Px x 2

Area A = ∗ x ∗ h = ∗ x ∗ − = ∗ x ∗ + − −
2 2 2 4 2 4 4 4 4

2 2
1 P x Px 3
Simplifying the above expression, we get: Area A = − - - - - (1.5)
2 4 2

Š‡ ‘’–‹— ˜ƒŽ—‡ ‘ˆ ƒ”‡ƒ ȋ Ȍ ‹• ‰‘– „› †‹ˆˆ‡”‡–‹ƒ–‹‰ ‡“—ƒ–‹‘ ȋͳǤͷȌ ™‹–Š ”‡•’‡ – –‘ ȋšȌ ƒ†
‡“—ƒ–‹‰ –Š‡ †‡”‹˜ƒ–‹˜‡ –‘ œ‡”‘Ǥ Š‹• ‰‹˜‡• –Š‡ ˜ƒŽ—‡ ‘ˆ ȋšȌ ƒ– ™Š‹ Š –Š‡ ˆ— –‹‘ ‹ ‡“—ƒ–‹‘ ȋͳǤͷȌ
ƒ••—‡• –Š‡ ‘’–‹— ˜ƒŽ—‡Ǥ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 9