Fuselage Loads

8/3/2019 Fuselage Loads

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Fuselage Loads

The first step is to identify loads. The particulars come from flying your vehicle throughits mission. But we can identify two load cases that occur in almost every design. These

are pure compression and bending of the fuselage.

To begin our analysis, we will look at the boost phase of a rocket. This case is interesting

because the forces in the fuselage are due to dead-weight loads as well as inertial loads

due to acceleration. The loads are primarily compressive in this situation.

F ma= , or Newtons 2nd Law of Motion, is a vector equation. However, for our

purposes we will treat it as a scalar equation. Newtons 3rd Law of Motion for every

action there is an opposite and equal reaction will also be used in this discussion. The

examples used in these discussions will make use of the Delta rocket shown below.

Lets start off with Newtons 2nd Law. Its obvious that the vehicle

is experiencing forces that are propelling it upwards. Somethinghas to be pushing up on the rocket to make it go up. This is simply

a statement of the vector form ofF = ma (a points up soFhas toalso). But its obvious that the exhaust is going down. So whats

pushing up?

The exhaust exerts a pressure on the surrounding air. Because of

Newtons 2nd Law, this pressure is transmitted back into the exhaust

nozzles. I dont want to go into a rigorous proof of this, but the

force pushing up on the rocket is this pressure applied over the

projected horizontal area of the nozzles. In the solid rocket

boosters, this pressure is applied across the bottom face of the solidfuel and to the top inside surface of the casing. Also note that thepressure applied to the air surrounding the rocket is transmitted to

the ground. Although the pressure increase on the ground is very

weak, it is applied over a wide area. The same is true of wingsproducing lift. So every time we fly an airplane or launch a rocket,

the earth is being pushed out of the way.

Of more immediate concern to us are the compressive stresses

inside the rockets structure. These stresses will determine how

much material we use in the structure to prevent the material from

reaching its crushing strength and to prevent buckling.


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Lets now look at the stresses in an arbitrary location in the rocket.

Lets start by calling the upper section m1 and the lower section m2. As drawn, theupper section has less mass than the lower section. If you write out a free-body

diagram you get the forces as shown to the right. If the forces are summed on the

upper section, the following equation is obtained:

Doing the same for the lower section gives

IfF1 is substituted into the 2nd equation

Examining the equation for each force, the forces in the structure are

clearly largest at the bottom of the rocket. Dont forget thatW = mg.

As the rocket gains altitude the weight becomes less and less because

g decreases.

F1 tells us how the forces in the rocket vary along its length. If wewere to draw the cut lower, both m1and W1 would increase. Although

this expression is exact, the way that this force is distributed at a

given cross section is not known. However, at the early stages it isOK to assume that this force is evenly distributed.

One parameter that always comes up is the loading parameter. It is

defined as the load per length or width. In the case of a circular crosssection, the loading parameter for pure compression can be written as

D

F

N

1=

which is simply the load applied over the circumference.

F m a W 1 1 1

= +

212WFamT ++=

( )ammWWT2121

+++=

F2

W2

T

F1


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The second load case is bending. The bending of a fuselage can be due to the dead

weight of the payload inside, accelerations, or externally applied forces such as the tail

loads necessary for trim or maneuvering. Pure bending almost never occurs in fuselages.The bending moments are usually a result of shear forces acting at some distance from a

support.

Bruhn uses a typical aircraft as an example in Chapter 5 of Analysis & Design of Flight

Vehicle Structures.

Usually the fuselage is broken into stations where the shears and moments are computed.

The weights or other forces must be distributed to these stations in some physicallyconsistent manner. The way to do this is to ensure that the moments about some

reference point are the same before and after. There is another consideration. Thereactions at the front and rear wing spars can not be arbitrarily assigned. They need to becomputed by summing the forces and moments. This gives two equations and two

unknowns, the wing reaction forces. For a wing with more than two spars, the system is

indeterminate and other methods such as Castiglianos theorem must be used.

Note that if you draw in the lift forces due to a hypersonic aerodynamics calculation, the

moments may not balance. This is probably because you are forgetting that the vehicle

needs to be trimmed. You are missing the force due to the control surface that istrimming the vehicle.


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We can make a table to help us remember how to make the shear and bending moment

diagrams.

Station Load w Shear =

w x = V

xMoment

11 -893 0 0 0 0

50 -388 -893 39 34827 -34827

73 1780 -1281 23 29463 -64290

80 -307 499 7 -3493 -60797

116 775 192 36 -6912 -53885

120 -409 967 4 -3868 -50017

170 -311 558 50 -27900 -22117

200 -76 247 30 -7410 -14707

230 -10 171 30 -5130 -9577

260 -21 161 30 -4830 -4747

290 -118 140 30 -4200 -547315 -22 22 25 -550 3

In algorithm form,

=

+=

i

j

ji VV1

1

= VdxdM iiii xVMM +=+1

-1500

-1000

-500

0

500

1000

1500

11 50 73 8011

612

017

020

023

026

029

031

5

Station (in)

Sh

ear(lbs)


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For more information, it is suggested that you consult the references. Several key effectshave been ignored for the launch case. They are probably not important for a vehicle

being carried as payload on top of a launch vehicle. Examples of these effects include

the bending moments due to cross winds, angle-of-attack, and angular accelerations due

to gimbaling. Bruhn gives a good discussion on this.

References

1. Bruhn, Elmer. Analysis and Design of Flight Vehicle Structures.

2. Bruhn, Elmer. Analysis and Design of Missile Structures.

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

11

50

73

80

116

120

170

200

230

260

290

315

Station (in)

Moment(in-lb)

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Fuselage Loads