Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

16.2 Shear of Open Section Beams 487

Fig.16.8

Shear center position for type of open section beam shown.

Fig.16.9

Determination of shear center position of channel section of Example 16.2.

TheshearcenterSliesonthehorizontalaxisofsymmetryatsomedistanceξS,say,fromtheweb.
IfweapplyanarbitraryshearloadSythroughtheshearcenter,thentheshearflowdistributionisgiven
byEq.(16.14)andthemomentaboutanypointinthecrosssectionproducedbytheseshearflowsis
equivalenttothemomentoftheappliedshearload.Syappearsonbothsidesoftheresultingequation
andmaythereforebeeliminatedtoleaveξS.
Forthechannelsection,CxisanaxisofsymmetrysothatIxy=0.AlsoSx=0andthereforeEq.(16.14)
simplifiesto

qs=−

Sy

Ixx

∫s

0

tyds (i)

where

Ixx= 2 bt

(

h

2

) 2

+

th^3

12

=

h^3 t

12

(

1 +

6 b

h

)