Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

556 CHAPTER 19 Structural Idealization

andzismeasuredfromthebuilt-inendofthecantilever.Theactualshearflowdistributionhasbeen
calculatedinExample19.3.Inthiscase,theq 1 shearflowsmaybededucedfromtheactualdistribution
showninFig.19.8,thatis,

q 1 =q 0 /4.8× 103

Evaluatingthebendingdeflection,wehave

(^) M=
(^2000) ∫
0
4.8× 103 ( 2000 −z)^2 dz
70000 × 48 × 106
=3.81mm
Thesheardeflection (^) Sisgivenby
(^) S=
(^2000) ∫
0

1

30000 × 1

[

1

4.8× 103

( 62 × 200 + 122 × 400 + 62 × 200 )

]

dz

=1.0mm

Thetotaldeflection isthen (^) M+ (^) S=4.81mminaverticalupwarddirection.

Problems..............................................................................................

P.19.1 IdealizetheboxsectionshowninFig.P.19.1intoanarrangementofdirectstress-carryingboomspositioned
atthefourcornersandpanelswhichareassumedtocarryonlyshearstresses.Hence,determinethedistanceofthe
shearcenterfromtheleft-handweb.

Ans. 225mm.

Fig. P.19.1

P.19.2 The beam section shown in Fig. P.19.2 has been idealized into an arrangement of direct stress-carrying
booms and shear-stress-only-carrying panels. If the beam section is subjected to a vertical shear load of 1495N
throughitsshearcenter,booms1,4,5,and8eachhaveanareaof200mm^2 ,andbooms2,3,6,and7eachhavean
areaof250mm^2 ,determinetheshearflowdistributionandthepositionoftheshearcenter.