Semimonocoque4_2011

8/13/2019 Semimonocoque4_2011

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SPACE STRUCTURESProf. Alessandro Airoldi

Semimonocoque 4 Ribs, symmetry, frames


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2Space Structures - Prof. Alessandro Airoldi

SemiSemiSemiSemi----monocoquemonocoquemonocoquemonocoque [4][4][4][4] Ribs, symmetry and framesRibs, symmetry and framesRibs, symmetry and framesRibs, symmetry and frames

1. Load introduction in stressed-skin structures (I)Ribs (in wings/areodynamic surfaces) and frames (in fuselages/integrated tanks of aircraftor launchers) are transverse elements that are idealized with infinite in-plane stiffness andnegligible out-of-plane stiffness. They have three basic and well-defined functions is semi-monocoque structures:

i. Maintaining the shape of thin-walled beam

ii. Introduce forces in the beam structure

iii. Stabilize panels and stringers

One of the consequencesis the rigid rotation ofsection in twisting

Will be addressed in a subsequent part of

the course

All components that transmit largeconcentrated force are directly attachedto Frames (never to thin-walled skin)

Moreover, panels also introduce theaerodynamic or distributed forces, suchas aerodynamic pressures in wings ordistributed inertial forces in fuselages(due to payload or fuel)


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In panels constrained to frames, the application of external loadinduces a stress state that can be considered superimposed to theone deriving from internal actions in the beam

In semi-monocoquescheme is attributed toidealized stringers

Nz Nz

The effects of pressure application can be considered a short-range effect. Thin panels bendand can also react with membrane stress for equilibrating the vertical load (non-linear effectthat can not be considered in small strain-rotation assumption).

Overall, panels are compliant intransverse bending and wouldnot resist without the support offrames, which exert the reaction

forces.

As far as this aspect is concerned, thin idealized

panels of wings do not behave very differently afabric cover in a non-stressed skin construction,which collect loads and transmit them to the frame(but in stressed skin construction panels also haveother structural roles, if long-range effects whichare quantified by internal forces - are considered)

1. Load introduction in stressed-skin structures (II)


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2. Internal forces in thin-walled framed beams

According to the previous considerations,distributed loads are introduced in the beamstructure by frames, even if they act on panels

that belong to the semi-monocoque structure

This means that a continuous load distribution isactually introduced as discrete, concentratedforces, at frame locations

Influence length of a frame

Ma

Ta

Mb

Tb

Element of fuselage subjected to payload weight

Ty

Mx

The actual course of internal forces is influencedby the mechanism of load introduction:

Shear internal force is constant between

two adjacent frames

Bending moment is piecewise linear alongthe beam axis


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3. Equilibrium of ribs and frames

q

q+q

q+q

q

T

T+T

T+T

TFe

q+q

q

Fe

Generalized forces applied topanels and internal shear force

along the beam

Generalized forces appliedto the rib

q Fe

The rib/frame is in equilibrium under the action of theexternal forces, which are introduced by the rib, and

the shear flows that are transmitted through the rib-panel junctions.

Such shear flows are equivalent to T, which equilibratesthe external force Fe.

Hence, the shear flows acting on the rib are the

equilibrant of Fe



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4. Analysis of ribs

q Fe The knowledge of the semi-monocoque scheme of thesection, which is reinforced by the rib/frame, allows theevaluation of the equilibrating shear flow distribution

A self-equilibrating system acting on the rib/frame canbe evaluated

PROCEDURE FOR THE ANALYSIS OF RIBS (approximated by variable-section beams)

Consider the semi-monocoque section that is reinforced by the rib and apply the system

of external forces (in this phase the system can be reduced to the resultant forces andmoments)

Solve the semi-monocoque section and invert the shear flow to obtain the flowdistribution that equilibrates the external force system

Apply the self-equilibrating force system along the beam axis and evaluate the internalactions (in this phase, the external force system must be applied with its actual distribution)

Flows applied through longitudinal panelsare equivalent to distributed moments

( ) ddMT

Coordinate along abeam axis



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5. Symmetry in plane structures (II)

X

v

y

uFor a symmetrically loaded symmetrical structure

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )000

0000

0000

vTRUEvvxvxv

xx

uuuxuxu

==

===

===

vu

The introduction of a slider allows studying half of the structure. On thesymmetric side, axial force and bending moment will be symmetric,whereas shear will be anti-symmetric

X

v

y

u v

u

For a anti-symmetrically loaded symmetrical structure

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) 0000

000

000

===

==

==

vvvxvxv

vTRUExx

uTRUEuuxuxu

The introduction of a support allows studying half of the structure. Onthe symmetric side, axial force and bending moment will be anti-symmetric, whereas shear will be symmetric



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6. Analysis of Frames (I)Symmetry considerations can simplify the studies offrames. In fact ,such a type of structures can be oftenschematized as closed rings of beams with a givensection.

The frames introduces in the semi-monocoque structurethe external load. Accordingly they are in equilibriumunder the system constituted by the external loads andthe correspondent equilibrating flows

q+qq

F


z

Accordingly, the evaluationof the stress state in theframes can be carried outby first solving the semi-monocoque section to findthe equilibrating flow

system


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6. Analysis of Frames (III)The equivalent flows in the semimonocoque sections can be evaluated in the two loadconditions, namely the symmetric and the antisymmetric one.

Once that the sections have been solved, the flows can be inverted to find the equilibrating

flows and the two system can be separately studied by considering half of the frame, with theadequate symmetry constraints:

(FA+FB)/2

q1

q2

q3

q4

X

W

The symmetric problem is twofold staticallyundetermined. W and X can be consideredthe undetermined unknown forces, whereas

the slider at the opposite end represent aconstraint.

(FA-FB)/2

q1

q2

q3

q4

Y

The anti-symmetric problem is one time staticallyundetermined. Y is the undetermined unknownforces, whereas the support at the opposite end

represents the constraint.


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7. Ribs and frame under distributed loads

The practical examples that have been provided in thislecture always considered concentrated external loads.

Actually, ribs and frames also introduce distributed loads:aerodynamic forces, inertia forces due to the distributedpayload, fuel in internal or integrated tanks.

Such distributed loads are collected by the panels of thesemimonocoque scheme and then transmitted to the rib orthe frame by means of transversal junctions. Then the load

is re-distributed in the semi-monocoque section andintroduced in the beam.

The evaluation of the equilibrating flow can be doneconsidering the resultant of such external force systems:this can be done because the transversal element (rib orframe) is considered infinitely rigid in its plane and load re-

distribution only depend on semimonocoque sectionproperties.

On the other end, the evaluation of internal force in thetransversal element must take into account the realdistribution of the external load.

Semimonocoque4_2011

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