Page 176 - 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]
Š‡ ƒ”‡ƒ ‘ˆ –Š‡ ›Ž‹†”‹ ƒŽ ’ƒ”– ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤ͹͹Ȑ ‹• ‰‹˜‡ „›ǣ

[Fig 1.77: cylinder develops to a rectangle]

Area of the developed cylinder = H ∗ 2πr
2

The sum of the developed cylinder area and that of the cone will give us the total material area.

π r + r ∗ S + H ∗ 2πr
2
2
1

‘S’ is the slant height of the frustum of the cone, as shown in [Fig 1.78], and is given by:

[Fig 1.78: slant length (S) of the frustum of the cone]

We have calculated the area of the sector/frustum of a cone to be: π r + r ∗ S
2
1
Replacing the value of ‘s’ from [Fig 1.78] in the above expression, we get:

π r + r ∗ H + r − r
2
2
2
1
1
2

The total area = π r + r ∗ H + r − r + H ∗ 2πr
2
2
1
2
1
2
2

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 79