Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

21.2 Shear 579

Table 21.1

Stringer/boom y(mm) σz(N/mm^2 )

1 381.0 302.4

2,16 352.0 279.4

3,15 269.5 213.9

4,14 145.8 115.7

5,13 0 0

6,12 −145.8 −115.7

7,11 −269.5 −213.9

8,10 −352.0 −279.4

9 −381.0 −302.4

closedsectionbeam.TheshearflowdistributionisthereforegivenbyEq.(19.11),inwhichthedirect
stress-carryingcapacityoftheskinisassumedtobezero,thatis,tD=0,thus,

qs=−

(

SxIxx−SyIxy

IxxIyy−I^2 xy

) n

∑

r= 1

Bryr−

(

SyIyy−SxIxy

IxxIyy−Ixy^2

) n

∑

r= 1

Brxr+qs,0 (21.1)

Equation (21.1) is applicable to loading cases in which the shear loads are not applied through the
sectionshearcentersothattheeffectsofshearandtorsionareincludedsimultaneously.Alternatively,
ifthepositionoftheshearcenterisknown,theloadingsystemmaybereplacedbyshearloadsacting
through the shear center together with a pure torque, and the corresponding shear flow distributions
maybecalculatedseparatelyandthensuperimposedtoobtainthefinaldistribution.

Example 21.2
ThefuselageofExample21.1issubjectedtoaverticalshearloadof100kNappliedatadistanceof
150mmfromtheverticalaxisofsymmetryasshown,fortheidealizedsection,inFig.21.2.Calculate
thedistributionofshearflowinthesection.

AsinExample21.1,Ixy=0,and,sinceSx=0,Eq.(21.1)reducesto

qs=−

Sy

Ixx

∑n

r= 1

Bryr+qs,0 (i)

inwhichIxx=2.52× 108 mm^4 asbefore.Then,

qs=

− 100 × 103

2.52× 108

∑n

r= 1

Bryr+qs,0

or

qs=−3.97× 10 −^4

∑n

r= 1

Bryr+qs,0 (ii)