# Max bending moment estimate

Context: I study aerodynamics and want to design and build an RC wing to put the theory I learned into practice. The essence of the theory I learned is: Given some mass of wing building material, how do we build the most efficient wing? To actually do this in practice and apply the theory, I need an estimate of the strength of my wing building material (more specifically the spar).

Question: I do not know structural mechanics but I need an estimate of the max bending moment a rod can withstand. Is there any convenient "bending strength coefficient" which I can look up for the rod material, then plug into some relatively simple equation to find the max bending moment of a given rod? If not what would be the easiest way to get this estimation without fully diving into structural mechanics.

The formula for bending stress of

1. Circular rod, $$\sigma = \pm \dfrac{32M}{\pi d^3}$$, $$d$$ is rod diameter.

2. Rectangular rod, $$\sigma = \pm \dfrac{6M}{bh^2}$$, $$b$$ is width, $$h$$ is height.

The resulting stress shall be checked against the allowable stress of the material. Once the limiting stress is known, you can plug it into the respective equation and obtain the maximum allowable bending for the rod.

• Thanks for the response. At what location on the rod is the stress equal to the value obtained from the formula? Is it the location about which we take the moment? Also do these equations have names so I can read more about them? May 5 at 4:24
• Since you are thinking of aircraft wings, I suggest assuming it is a cantilever with the fixed end that subjects to the maximum bending moment, M = PL (P = point load, L = beam length), or M = wL^2/2 (w = uniform load in plf = pressurebeam width).
– r13
May 5 at 20:48
• For articles discussing bending stresses, google "bending/normal stress in beams". For how to obtain bending moment, you should google "analysis of elastic beams". There is a long way ahead though. Good luck.
– r13
May 5 at 20:52

The wing design is the art of designing for strength in the most efficient way to make the plane as light as possible, while not sacrificing the strength.

The part of the wing that carries the bending moment is called spar, basically acting like a cantilever beam, and it is never a simple rod or other simple uniform cross-section.

This is for example the figure of the spar of a Cessna 210, a small single-engine plane. The bigger the plane gets the more complex the spar and its attachments get.

As we see it is a complex assembly of formed sheets of aluminum/ titanium that grows wider and adds layers to get stronger as it nears the haul of the airplane.

It has many openings at places where cutting a hole could save weight but not impede strength.

This same philosophy runs through the rest of the structure of the plane like the fuselage, the rudder, and elevators. The entire structure is light and perforated but strong to take the eventual storm and high G loads.

# Edit

After OP's comment, I add this link to a book on airframe structure.

Airfram Structural Design book.

' • Thanks for the response, do you have any resources on wing design? May 5 at 4:25
• I edit my answer to add a link. even though I encourage you to follow up on your project, I caution you that airframe design is a matter of 3-4 years of the graduate course, after a BS in engineering. May 5 at 4:41