Page 668 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

A-24. A-24. .....
0)
(Continued). (Concluded). 0)

PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS

n Nu m her of sides
REGULAR POLYGON 180°
*
Tffi A 2 uh
HALF ELLIPSE
AKis of moments
n
through center
1
2
4a
-3;
m
(
>
8
9<
�
1
�ab•
.J..3
la
3 11-- ---!--- --;;,• 11 - a•b � - _!__) "O
---
cii'
8
�-bj 1 a.
"tJ
2 Ii - 8 r.a•b A(6R• - a•) _ � A(l2R,• + a•) ...
--·24
--48-�-
0
r1 = ra = � 6R•;;�-a•. s
u,
u,
----------·- -- 0
CD
u,
ANGLE 2K
1 tan 20 .-;=-r;-
:::,
• QUARTER ELLIPSE A 4 r.ab Axis of moments through '°
0
center of gravity b' +ct d• + at ...
2 4 4a A t(b + C) X - (b + C) y - 2(b + C)
2
� ·n ,I m 1-; I. ---b- � K Product of Inertia about X-X &. Y-Y o
J
T n 4b 1-- r r · - a J I \ • - + 4fi,-+cf CD
abcdt
3
3r.
\
o'
•
a•bc � -...i..)
3-"---- -b�-r·Ja 11 ab' -- 9r. . y I I Ix 1° (t(d-yJ'+byl-a(y-tJ•) !!?.
16
a,
I-·· ---t--- --,.-I
I
:::,
n,
•
a.
(
4 )
I,
r. - -·--
� -(t(b-x)•+dx•-c(x-t)•)
9r.
16
Iv
...
!!.
1, .L �alb 'r �; --e;_J J 11 • Ix sin•o + Iv cos•o + K sin26 "tJ
,. 1 • lw • Ix cog19 + Iv ain•e- K sin28 0
4 16 0
16 r.ab J
CD
-�·r-\ 3
K Is negative when heel of angle, with respect
y 1- to c. g., 11 In 1et or 3rd quadrant, positive ff
when In 2nd or 4th quadrant. !!?.
Z·Z is axis of minimum I
• ELLIPTIC COMPLEMENT ·----------------- "tJ
iii
:::,
2 BEAMS AND CHANNELS ii,
Transverse force obllq ue
through center of gravity
� I
-- � I
b
I � 1 14 • lxcosz4i+lvainZ�
_:,: ----- ----- __ y__
(
M t. •in.to + ,: eose )
--b--· 3 .
-,./
where M is bending moment due to force F.
Extreme flber assumed same as for case
<to•O. If not, locate extreme fiber and find
f by usual method.
4 4
• To obtain properties of half circle, quarter circle and circular complement substitute a � b • R.