Page 664 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

A-24. A-24. ...
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PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS

RECTANGLE EQUAL RECTANGLES
Axis of moments through A
Axis of moments on base A bd center of gravity b (d - di)
d
I c d c 2
b (d' - d,•)
bd•
l __ .1 s - - 3- s b (d' - d,•) 'O
c
d
12
>
bd 2
6d
- - 3-
,/J - {di-=-if;s '2.
a,·
d
b- .577350 d 12(d - di) a.
.,
"'O
s
0
UNEQUAL RECTANGLES ,,,
RECTANGLE ,,,
A bd Axis of moments through
Axis of moments on diagonal center of gravity A bt + b,t, CJ
bd 1_� ,,,
CD
c 1 r---b-;1 'h bt• + b,t, (d - 'ht,)
vb•+d2 .,.---- -'--r c A ii"
' ----- ·---;:- I
I
b'd' j ·1·--- y I c bt> b,t,• :::,
.,
+ b,t,y,•
6 (bl + di) d d,------i-+- 12 + bty• + -,-2- o'
b 1 d 1 o
s Llt,;-·::F:9 -- s c s, zr
sv b' +d·1 -- -_-J __r� c, CD
._,_,
bd I ., f; 3
,1·;, (bl + di) --bl- � .... �
Ill
:::,
a.
RECTANGLE TRIANGLE
bd "'O
Axis of moments any line Axis of moments through A - 2 !2.
.,
through center of gravity A bd center of gravity
0
b sin a + d cos a 2d 0
c c - 3 �
2 CD
bd (b• sin•a + d 2 cos 2 a) bd' 3
12 - 36 �
2
s bd (b' sin•• + d 2 cos a) s bd2 "'O
6 (b sin a + d cos a) - 24 iii
d
iii
bJ. sinza + di cosza v,s- - :::,
� 12 .235702 d
HOLLOW RECTANGLE TRIANGLE
Axis of moments through center A bd - b1d1 Axis of moments on base A -2-
bd
�[=BIT c - 2 12 c 12
d
d
i
�
--1
bd' - b,d,•
bdl
J_�: --
a
bd' - b,d,•
bd•
s
I
6d
,/ 6- -
d
� -bd' ;;:·d··· s - 12
b .408248 d