Standard forces on a bike frame

What you are asking is engineering. Even if you can calculate the correct thickness for all "reasonable" impacts and forces thrown at a bicycle, you still need to take into account that the bicycle will be used, so the material will undergo hysteresis.

A frame can stand a single impact providing a force of X, but it may fail after one hundred impacts of smaller force X/1000 (yes, you are reading correct, standing a single impact of force X, but failing after a cumulative impact force of 1/10 of X). If you then bring into the picture a material that evolves with time, like wood, you should expect ... a lot of trial and error.

An example: you draw your ideal wood bike, knowing the tensile strength and other parameters of wood you calculate that the top tube should be long 30cm, have a diameter 1.8 cm and a thickness of 2 mm. However, with the use you realize that such a tube will produce some resonance and some vibration, so for some unlucky reasons hysteresis will cause the connection of the seat stays (calculated to be long 22 cm, diameter 1.2 cm, thickness 1.9 mm) to fail on average after 500 km. You try to reinforce the connection, but the solution maybe is just to have a top tube with a larger diameter, or shorter, to dampen the vibrations/resonance.

How to proceed? you have two choices:

[scientific/industrial approach]

• the mechanical engineer way, such as this page hosted on sheldonbrown site https://www.sheldonbrown.com/rinard/fea.htm or you check the latest peer reviewed research: https://journals.sagepub.com/doi/full/10.1177/1687814017739513

[empirical approach]

• you take some frame building courses, where you get the experience of learning by doing, so you have a "feeling" for what is the right thickness/shape/angles etcetc.

It is not that the calculation of forces is complex or there are industrial secret preventing us from its understanding (well, there are industrial secrets on why a certain thing is built a certain way, but physics is not an industrial secret :D ). The fact is that we have a very rough understanding of reality and forces at the microscopic scale, but we can obtain insight on the resulting macroscopic behavior of materials only via:

• engineering/advanced calculus/tests and experiments (use Finite Element software to calculate stresses and plastic behavior of the material and then you obtain the composite tube shapes of a Kestrel road bike https://www.compositesworld.com/articles/ultralight-carbon-fiberepoxy-road-bike-from-kestrel )

Kestrel co-owner Preston Sandusky credits the low weight to the bike's "modular monocoque" frame, fabricated from three individually bladder-molded parts: the triangular front frame, and two two-pronged, U-shaped forks, which form the seat stay section (running from the top of the seat tube to the rear wheel dropouts) and chain stay section (from the bottom of the seat tube to the rear dropouts). Developed by former aerospace engineers at Kestrel's headquarters in Santa Cruz, Calif., U.S.A., using Pro-ENGINEER and RHINO 3-D Solid Modeling software (PTC, Needham, Mass., U.S.A.), the frame structures are fabricated

• via empirical reasoning (Columbus steel tubes works great to build a bicycle with drops, why? because it does! )

I would NOT be surprised if, after doing some calculation based on very simple principle, you would find out that a steel frame with thickness 0.1mm and a weight of 500 grams would be able to stand all the forces related to a standard cycling scenarios.

After reviewing some of the recommended sources above and giving the matter some thought myself, I came up with the following load cases for a hardtail mountain bike. These are by no means definitive but should cover the vast majority of normal use cases. I'll apply a factor of safety (probably 2.0) on top of the resulting calculations:

Normal Use Load Cases:

• Full effort standing start - assume 150% rider weight applied to one pedal, 25% rider weight upwards force applied to other pedal, and remainder of upwards force applied at handlebars
• Steady state pedaling - assume rider weight distributed between pedals and seat, applying say 400 watts of power.
• Climbing force - same as standing effort but with a 20% incline
• Cornering force - assume 1G (2 x rider weight) applied to pedals
• Front braking force - not exactly sure what I'll use here
• Rear braking force - apply maximum force before skid to rear disc caliper mounts based on a reasonable coefficient of friction for the tire and standard weight distribution
• Jump landing force - assume a 3-foot vertical drop onto both wheels, with 80% of rider weight on pedals. (Assume rigid fork) Bike and rider decelerate in a distance equal to tire distance from rim.
• Maximum seat force - 3 x rider weight applied to seat tube, roughly simulates going off a drop and landing on the seat

Frame resilience tests:

• Frontal impact on fork - apply a 200 pound force at the front dropouts in the direction of the back of the bike
• Bottom Bracket Pull Test - essentially hang a 750 lb weight from the bottom bracket
• Rear Stay Stiffness Test - apply a 30 lb force along the axis of the rear axle to one rear stay
• Torsional Test - apply 100% rider weight to one pedal to create a moment while fixing the head tube (to simulate frame torsion between pedal and handlebars)