# Wings as Beams

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#### BBerson

##### Light Plane Philosopher
HBA Supporter
The way I see it each 3' long diagonal rib is a cantilever beam with end load. Starting at the tip each diagonal hands off the torque load to the next and the loads increase to max at the root. So the root rib needs to transfer the full 300 foot pounds of torque.
I can test a root rib with 100 pounds end load at 3' = 300 foot pounds
Might hold several times that.

#### BBerson

##### Light Plane Philosopher
HBA Supporter
I had forgotten it, but today I re-found an example on page 42 of Aircraft Structures (Peery) that should be close enough to estimate the loads on the diagonal ribs.

#### tdfsks

##### Well-Known Member
Wing tests with sandbags; pick a load case, AOA, lift, moment. Figure out the spanwise lift distribution to get the lift. IF all that weight went on the quarter chord line, you would be simulating zero pitching moment. If it is centered a little aft of that, it will generate a pitching moment. You have to figure out just how far aft gives the right moment.

The usual test case is at Vne and max positive g, which is usually a pretty low AOA, the wing is least resistant to bending that way, and pitching moment of the wing is biggest then too. Some folks will also test at Va and max g, AOA is at stall angle, pitching moment is quite a bit smaller then because Va squared is a lot lower than Vne squared.

Billski
You should be testing both the Va / n1 (PHAA) case and Vd / n3 (PLAA) cases for positive load factors (see the flight envelope in FAR 23 Appendix A for the definition of n1 and n3). Additionally you should test the aileron cases because they may be critical for torsion.

Va / n1 will be critical for bending and forward loading on the drag truss. I have seen the drag truss fail on two wings when testing this case. Drag load is approx. 25% of the lift load and, counter-intuitively to many people, acts forward on the wing hence the wing is tested inverted at the required angle of attack so a component of the vertical loading generates a shear load on the drag truss. The angle should be approx. 15 deg to generate a shear load equal to approx. 25% of lift. In this case the centre of pressure (old but useful concept) is further forward.

The Vd / n3 case will be critical for bending and torsion. The wing is set at a smaller angle of attack and the loading is essentially the same (apart from some small differences due to changing tailplane loading). However in this case the centre of pressure moves aft due to the higher pitching moment and so the test load should be located further aft on the wing chord (assuming an airfoil with a negative pitching moment).

The aileron case is similar. You will need to work out which aileron case is critical (see FAR 23) and then move the test mass further back or forward in the region of the aileron as dictated by the case you are testing (up or down aileron).

If you have a wing with flaps the flap cases also need to be tested by moving the test mass aft to generate the torsion loads due to deflected flaps.

Remember that in most positive flight conditions the tailplane will have a downward load causing the wing to generate lift equal to about 1.05 x the weight of the airplane (this will vary depending on load case and aircraft CG position). This should be accounted for in your load schedules. Also, you may account for wing inertial relief which will reduce the test loading applied. In other words the mass of the wing x the load factor being applied can be subtracted from the test load.

Ribs should be tested separately for the different chordwise loadings loading experienced at the corners of the flight envelope. The FAA's Basic Glider Criteria contains one approach to testing ribs.

You should also consider whether you need to test the negative cases, Va / n2 (NHAA) and Vd / n4 (NLAA).

The VA / n4 case can be critical for the leading edge of the wing in some cases.

For a cantilever wing you may not test the negative cases if the spar is symmetric. However many wing spars are not symmetric (the lower cap maybe smaller and designed for higher tension loads than compression with less consideration for compression buckling whilst the upper cap might by heavier and optimised to prevent buckling) so in this case you should be testing the negative cases to make sure you do not have a buckling issue with the caps. Often spar caps fail by buckling and not rupture so this should be carefully considered.

Also remember that if your wing is strut braced, you MUST test the negative cases. The most likely failure mod of the struts is buckling under negative loads, not due to tension in the positive load cases. So both the Va / n2 and Vd / n4 cases need to be tested for a strutted wing because one case will generate the critical compression load in the forward strut whilst the other case will generate the critical compression load in the aft strut.

Also in the case of a two spar, strut based wing (think J3 Cub), the proportion of bending and shear loading carried by the spars will change significantly between the different cases and it is essential that you test them all, unless you have done a good job of the stress calcs and you clearly understand which are the critical cases.

That is just a quick outline of the considerations for testing ... let me know if you have further more specific questions.

BTW :

PHAA = Positive High Angle of Attack
PLAA = Positive Low Angle of Attack
NHAA = Negative High Angle of Attack
NLAA - Negative Low Angle of Attack