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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
šƒ’Ž‡ ͳǣ ϐ‹† –Š‡ ƒ”‡ƒ —†‡” –Š‡ —”˜‡ •Š‘™ ‹ ȏ ‹‰ ͳǤͳͶȐǤ

2
[Fig 1.14: area under a parabola [y = x ] ]

b 2 2
x 3 8 8
2
The area under the curve is given by: f x dx = x dx = = − 0 =
3 3 3
a 0 0

šƒ’Ž‡ ʹǣ ϐ‹† –Š‡ •—”ˆƒ ‡ ƒ”‡ƒ ƒ† ˜‘Ž—‡ ‘ˆ ƒ •’Š‡”‹ ƒŽ ƒ’ ™Š‹ Š •—„–‡†• ƒ ƒ‰Ž‡ ǮʹɅͳǯ ƒ–
–Š‡ ‡–‡” ‘ˆ –Š‡ •’Š‡”‡ ƒ† ‹ –Š‡ ’Žƒ‡ ‘ˆ –Š‡ ‹ƒ‰‡ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤͳͷȐǤ

[Fig 1.15: a spherical cap]

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