# spar calculation

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#### dominique

##### Active Member
Hello
for the calculation of a wood wing spar it is customary to subtract the weight of the wing from the total weight of the aircraft
Some authors (book "stress without tears" articles published in Kitplanes magazine) also propose to subtract everything that is carry by the wing regardless of its location
In the case that interests me the landing gear
But I understand that other people do not agree because they consider that the weight of the landing gear acts at a punctuated place and not linearly on the whole span
Is there an indisputable source as to whether or not it is possible to subtract the weight of a landing gear for the calculations ?
Thank you, kindly
Dominique sorry for the text ... google translate

#### albaz

##### New Member
MR.dominique you have any design for cricri mc 15 propeller

#### wsimpso1

##### Super Moderator
Staff member
Log Member
We are simply talking beam mechanics here. The general case is "what is the loading, and what does that do to the shear and bending moment diagram?" While some designers may argue about how to do all of this, the structures guys know that there is no debate. We figured out beam theory before the Wright's figured out airplanes. If you want to fly no more wing weight than you have to, you need to do the whole job.

Going to a wing, well, it is not just a beam with vertical forces (weight and lift), there is also torsion (from wing pitching moment) and longitudinal forces (thrust and drag). Most of the time, drag induced shear and bending is pretty darned small compared to lift, but torsion from pitching moment is real, and you have to handle it too. Reference I like is Timoshenko and Gere Mechanics of Materials, but there are others.

I have a sticky on this general topic here:
Beam Theory Explained - How Spars Work, scroll down to "Shear, Bending Moments, Curvature, Beam Slope and Deflections are all Related"

For the sake of learning, let's just concentrate on the weight and lift forces:

In the simplest conceivable airplane, it is a cantilever wing, the weight in the wings is insignificant, and weight of the airplane is concentrated at BL00. Let's establish a convention too - lift is positive, weights are negative.

Half of the fuselage weight is carried by the wing on each side of BL00. Shear diagram starts at one tip V=0, and accumulates upward as we move toward BL00 equal to one-half the weight, then there is an step downward from weight of the fuselage and the shear accumulates upward again toward the opposite tip. Bending moment is first integral of that shear diagram, so it too starts at zero at the tips and ramps up rapidly to big bending moment at BL00, and then back down to the other tip.

Real airplanes usually pick up the wing at or near the fuselage wall. So a zero weight wing will look similar, but will only accumulate shear to the close fuselage wall, shear will drop to zero there as half the fuselage weight is applied, with a similar but opposite sense curve accumulating from the other tip.

Now let's say we have some force dropped in at a spot on the wing. Imagine an engine hung on one spot out there. You can do one of two things: You can modify that shear diagram to include the engine 'dropping in' at that point, then integrate the bending moment diagram, or; you can do the shear and bending diagram for just the engine and superimpose that upon the existing diagram. They both work, and depending upon your computational methods, one or the other might be easier.

Let's try the independent curve. Shear at the tip is zero, running along towards the root, big negative when you get to the weight of the engine, then that negative carries to the root fitting where that load comes back out. Moment diagram is zero also from tip to engine. From engine to root, moment is engine weight times distance you are inboard of engine until you get to the root fitting. Now you add the shear curves together and add the bending moments together to get the result curves....

Now let's think about distributed loads. Let's say the wing weighs as much as the engine. and we do just the wing weight. Shear again starts at zero at the tip, and accumulates as you go inboard by the amount of wing weight outboard of any spot you are calculating. Moment accumulates from all those little weights times the distance to any spot you are calculating. And given that weights are negative, these are negatives. Then we can add the curves to the others we already have.

Except we have not yet made the lift curve from aerodynamic forces correct yet... The area under the wing's elliptical lift curve must lift not just the fuselage, but must also lift the weight of those point loads and distributed loads along the wing, so the lift curve is higher than just for the fuselage load. The shape is the same, but higher. The total shear and bending diagrams are then decreased by the loads along the wing.

This can also be done by modifying the loading diagram to include lift forces, distributed inertial forces, and concentrated inertial forces, then integrating to get shear and bending moments. But you are not really done yet. You also have fore and aft forces - drag may be almost neglectable, but think about stall at Va. The airplane then has a significant fraction of lift acting from the trailing edge toward the leading edge. Then there is pitching moment accumulating from the tip toward the root. And the wing must carry all of these simultaneously.

Welcome to the Monkey House,

Billski

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
Edit—looks like Billski beat me to it. I’ll go ahead and post this anyway in the hopes it helps.

The best practice when analyzing a spar is to apply the loads onto it where they actually occur. However, it is a little easier to simply apply the whole weight of the airplane (including the wings and wing-mounted gear) at the center of the spar. This results in higher shear and moment than reality—it is a conservative shortcut.

It is closer to reality to apply the loads at their actual location on your load diagram. What should NOT be done is simply to neglect the weight of the wings or the gear attached to them—this might be done as a first pass, but it is not a conservative method of real analysis.

#### Pops

##### Well-Known Member
HBA Supporter
Log Member
Edit—looks like Billski beat me to it. I’ll go ahead and post this anyway in the hopes it helps.

The best practice when analyzing a spar is to apply the loads onto it where they actually occur. However, it is a little easier to simply apply the whole weight of the airplane (including the wings and wing-mounted gear) at the center of the spar. This results in higher shear and moment than reality—it is a conservative shortcut.

It is closer to reality to apply the loads at their actual location on your load diagram. What should NOT be done is simply to neglect the weight of the wings or the gear attached to them—this might be done as a first pass, but it is not a conservative method of real analysis.
I included the weight of the wings on the SSSC and JMR for a conservative result.
Wood wings.

#### Map

##### Well-Known Member
Considering the weight of the wing for loads analysis is not conservative. During a positive load factor, the lift from the wing acts upwards, the weight of the wing acts downwards, reducing the bending moment. So neglecting the influence of the wing weight results in a higher bending moment. This is usually done for airplanes (short wings).
But the wing weight is considered in the loads analysis of gliders because the wing weight there is a much larger proportion of the total weight. The structural weight limitation then becomes the mass of the non-lifting parts: gross weight minus wing weight.

For airplanes where the wing and wing fuel weight was not considered for loads the weight limitation is just the gross weight.

#### Lendo

##### Well-Known Member
To be honest, I have always been confused with Wing Weight included and not included - maybe some day I will understand.
As Jim Marsh's manual is primarily for Gliders I can see the reasons WHY in his approach - thanks Map.
George