Two weeks ago, we calculated the loads for our longboard frame.
Last week we reviewed the numbers and went with carbon fiber tubes as the building blocks for the frame.
Today we are going to choose the tubes that will do the job.
Strength of Materials 101
The loads that we apply to the structure are balanced by the internal stresses which are created inside.
This happens because everything is in balance - external loads are balanced by internal stresses.
Stress have the units of force divided by area. The higher the applied loads, the higher are the stress, the bigger and beefier the structure, the smaller the stress.
Why is this important?
Stress levels can be calculated. Once we know the stress levels, we can choose the appropriate materials and dimensions for our purposes.
Each material has the stress levels that it can accept - allowable, and the stress level at which it breaks - fracture.
Whatever you choose, make sure that the actual stress levels are lower than the fracture stress.
Is this all?
In real-world problems the final solution is a compromise between several requirements.
We can't make everyone happy, but we can design a solution that will satisfy the requirements, and in the end of the day everyone will be almost happy .
So, what is there besides the stresses?
There are also safety factors, stiffness, and the total weight.
What is a safety factor - the bench example
Imagine you are building a park bench.
You did all your calculations, verification, testing and you've built it.
You chose your structure and materials in a way that the maximum load is 200 kg, so it breaks at around 200.1 kg.
This was your goal and you're happy with the result.
You take your bench to the park, put it in the spot.
Before you leave, you place a big sign that says: “Maximum load – 100 kg”.
Congrats, you have just created a Factor of Safety (FS) of 2.
FS is the ratio between the fracture stress/load and the existing stress/load.
Why would we use these factors?
It accounts for all of the things we don’t know.
Even though we do our best with loads calculations, and choosing correct material properties, there are always things that we don't know.
For all this we put in the safety factor.
What is the down side?
Usually it's the weight of the product. Higher safety factors will need more material and so they'll weight more.
Safety factors are design requirements.
In our everyday life, the lowest safety factors are in aerospace structures, where mass is extremely important.
The highest safety factors are in civil engineering, where you can always use another ton or two of concrete to make the building stronger.
It's basically the “springiness” of the structure.
Remember playing with springs at the science class?
Spring will expand or compress when you apply force on it.
In the case of longboard frame, it's the elastic sinking of the frame (deflection) when we stand on it.
Stiffness is the ratio between the applied load and the deflection.
Why is this important?
If we know the deflection we're comfortable with, we can design the frame to meet this requirement.
We don’t want too flexible frame – it'll be very uncomfortable to ride, on the other hand too stiff is also not that great – we'll feel every bump on the road.
An interesting thing to do is to use the stiffness as our damper, with zero additional cost and no added mass.
We want the lightest frame possible, together with other requirements.
What do we do here?
These are our requirements/guidelines:
- Three parallel tubes as the main deck.
- Standard sizes for the tubes.
- Minimum safety factor of 2 to fracture.
- Deflection in the middle of the frame of no more than 30mm with maximum weight.
- Minimum mass.
A quick note before we dive further.
In general, two “types” of stresses are important: the global stresses and the stresses at interfaces/joints.
Here we will deal with global ones.
When you hear carbon tubes, what comes first to your mind?
Standard tubes are made everywhere, but the fibers themselves (the raw material) are sourced from a handful of manufacturers.
One of the leading world manufacturers is Toray from Japan.
T300 is the fiber type that is manufactured by them, and it is by far the most widespread and known fiber in the world.
There is a high chance that any standard carbon fiber tube that you look at will be produced out of T300 with 3k tow count.
Let's look at the properties of this fiber.
There are two sections in the data sheet: for the fibers themselves and the composite material. We are interested in the latter.
These are lower than the pure fiber because of the added epoxy.
These numbers are the ideal properties, they can't be guaranteed by any manufacturer.
To be on the safe side, we'll knock down these numbers by 30% - this is usually very realistic.
Two numbers which are the most interesting for us:
Tensile Strength, which is the fracture stress.
Tensile Modulus, which is the elasticity property of the material.
Rest of the numbers will be relevant later.
Let's consider Case 1 for the loads with the longest frame, we'll be on the safe side with any variation of loads and frame length.
These are the numbers to do the calculations with:
L=86cm=860mm – length of the frame
M=25.9 kg.m – Max. bending moment
V=60 kg – Max. shear force
The cross-section of the tube is simply the area of the ring once we "cut" the tube.
In our case, it's a ring with inside diameter (ID) and outside diameter (OD).
With known diameters we can calculate two important values: the area of the cross-section:
and the moment of inertia:
Area is simple, but what's the moment of inertia?
It tells us how resistant the cross-section to bending.
Or, what is the structure stiffness to bending.
Think of a simple metal ruler: it's very easy to bend it in one direction (thickness), and almost impossible in the second one (width).
The moment of inertia is much larger in the width direction.
Now it's time to calculate some stresses.
Bending stress can be calculated by:
Shear stress is simply:
The deflection is calculated with formula from "Roark's Formulas for Stress and Strain":
Not forgetting the 3 tubes in parallel and units, this is what we have:
Last week I mentioned the shear is less significant than bending. Now you can see the numbers.
Anything special with the diameters?
These are simply standard sizes which can be found anywhere. It's readily available, so no additional development costs.
Looking top to bottom, the first two won't satisfy the requirements for safety factor or stiffness or both.
The smallest diameter tube which makes sense for us is the third one:
Obviously, bigger tubes will work, but they're bigger and heavier.
They are also stiffer and we don’t want that.
The three tubes together will weight less than 400 gr, which is cool.
Congrats, we've chosen the carbon tubes that we'll use!
Next time we'll see what can be done with the end units of the frame.