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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics

ʹǤͶ ‹–• ƒ† ‹‡•‹‘•

‹–• ƒ† †‹‡•‹‘• ‹• ‘‡ ‘ˆ –Š‡ ‘•– ’‘™‡”ˆ—Ž –‘‘Ž• –Šƒ– ‘—Ž† „‡ —•‡† ‹ ƒ› •‹–—ƒ–‹‘ǡ
‹””‡•’‡ –‹˜‡ ‘ˆ –Š‡ ‡‰‹‡‡”‹‰ †‹• ‹’Ž‹‡ǡ –‘ ‡•–ƒ„Ž‹•Š –Š‡ ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ –Š‡ ’Š›•‹ ƒŽ
’ƒ”ƒ‡–‡”• ‹ “—‡•–‹‘Ǥ
šƒ’Ž‡ǣ ‹– ‘—Ž† „‡ ƒ •‹’Ž‡ ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ǣ
· ‹•’Žƒ ‡‡–ǡ ƒ ‡Ž‡”ƒ–‹‘ ƒ† –‹‡Ǥ
· ‘™‡”ǡ ƒ‰—Žƒ” ˜‡Ž‘ ‹–› ƒ† –‘”“—‡ Ǥ

· Š”—•–ǡ †‡•‹–›ǡ ™‹†‹ŽŽ ǡ ”ƒ†‹—• ‘ˆ –Š‡ ƒ‡”‘ ˆ‘‹Ž ƒ† ™‹† ˜‡Ž‘ ‹–›Ǥ
Š‡ ’Š‹Ž‘•‘’Š› ‘ˆ —‹–• ƒ† †‹‡•‹‘• ‹• –‘ ‹†‡–‹ˆ› ƒŽŽ –Š‡ ’Š›•‹ ƒŽ ’ƒ”ƒ‡–‡”• ‹ ƒ ‰‹˜‡
•‹–—ƒ–‹‘ǡ •— Š –Šƒ–ǡ –Š‡ ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ ƒ› –™‘ ’ƒ”ƒ‡–‡”• ‘—Ž† „‡ ‡•–ƒ„Ž‹•Š‡†Ǥ ‘™‡˜‡”ǡ

‘‡ ‘ˆ –Š‡ Ž‹‹–ƒ–‹‘• ‘ˆ —‹–• ƒ† †‹‡•‹‘• ‹• –Šƒ–ǡ ‹– ƒ‘– „‡ —•‡† –‘ ϐ‹† ‘—– –Š‡
‘•–ƒ–• ‘ˆ ’”‘’‘”–‹‘ƒŽ‹–›Ǥ

Example1: Consider the relationship between displacement, acceleration and time. This is
y z
x
mathematically given by: s = a t - - - - (2.1)
Where, (s) is the displacement, (a) is the acceleration and (t) is time, and (x, y and z) are their
respective exponents that need to be computed.

Parameters Units Dimensions

Displacement (s) Meters (m) Length (L)

m Length ∗ Time LT −2
−2
2
Acceleration (a) meter/second
s 2
Time (t) Seconds(t) Time(T)

Writing the dimension of parameters in equation (2.1), we get:

L y
x
z
y
y
x
z
y z
x
x
s = a t = L = T = L = L T −2y T = L = L T −2y+z - - - - (2.2)
T 2
By equating the exponents of the respective dimensions of LHS and RHS from equation (2.2),
we get:
(x = y) : powers of ‘L’ on both sides
(-2y + z = 0) : comparing powers of time (T) on both sides
Therefore, we have, (z = 2y=2x)
Since we seek displacements relation with acceleration and time, let the power of displacement

(x) be 1.

Page 4 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,