APPLIED MECHANICS 
ie 
106 
Moments of Inertia, etc., of Various Beam Sections (see Art. 111, p. 105). 
"Fe 
_Bips_a te 
L=53(P d*), _ 
__B(D? - d*) it _ BD? 
Utara eat "Ba 
l= *(p_ d4. 
Ga! ) 
_ w (D4-d*\* 
Os ON ae 
y, =0°5756r. 
aie y2=0°4244r. 
I = aqe> —_ bd*), I re 0°1098r4. 
_ 3 (BD - bd? Z,=0°190775. 
=35( D ) Z=0°25867°. 
CRS _D@B+)) —y, D(B+25) —y_(Bt44B) +09? 
a  B(B +0) BB+) B6(B+B) 
4 FL _(BP+4BO4ONDe pT (BP4 4B ON)? 
Y yy, + 122B+5) ~ “y, 12B+2b) ~ 
Rapp ee Woe _ bD?+ Bd? 
1=7,0D'+ Bd’). Z=— 
_ BD? - td? _ BD?~26dD +bd? 
“=o ppoedy =" eBD-bd) 
1. (BD? —bd*)?~ 4BDbd(D - d)? 
" 12(BD — bd) ; 
_ 1 _ (BD? -bd?)? - 4BDbd(D — d)? Ln = I __ (BD? —bd*)? — 4BDbd(D — d)* 
es Bi, 6( BD? — bd?) - “ye 6(BD? — 26dD + bd?) 
a, =area of top flange. d,=area of bottom flange. §a=area of web. 
a bi y, =k2D = be) tanh told + 24) 
; 4 oa 2(a, +244) 
s a yeti 2D = t) + ata + ald + 2a) 
Bee ef 2(a, +a2+a) 
pati tats tad | aya(D+d)?+a,a(t, +d)?+a,a(to+d)? 7 I ae 
= e : ee 
12 4(a, + a+ a) Yi Y2 
Z,=aeh, where h is the total depth of the section. 
In actual practice it is often sufficiently accurate to take Z,—a,h, and 
* If d does not differ much from D, then Z=5,(D3— d*) nearly. 
