When designing a structure, one has to understand the conditions at which this structure will operate. Let’s take our case for example, we want to design a skateboard frame. This frame, or deck, is attached to the wheels and a person is standing on top of it. The whole thing is moving and occasionally meets various bumps on the road. It will see dirt and rain and some kind of abuse during its life span.
What should we do with this information? To begin with, let’s assume that anything, which is not made of paper or glass, will handle rain and dirt and moderate abuse just fine. This leaves us with the weight of the person and the actual riding and meeting various stuff during this ride. Now it is just a matter of translating this to the loads that the frame sees.
Let us make further assumptions: the maximum weight of this person is 120 kg (264 lb) and he/she can stand on this skateboard in two ways – in the middle of the board on one leg (I know, not very realistic) and on two legs, when each leg is at one third of the board. The picture below describes this much clearer. In the first case the entire weight will be applied in the middle, in the second case the weight will be equally divided between two points. L will be the length of the frame between the two wheel trucks.
In nature everything is in balance, just look around you. What does it mean in our case? It simply means that when we apply the loads on the frame, there will be an equal and opposite forces that will balance these loads, these are called reactions. It is easy to understand that these reactions will occur at the point where the wheels meet the ground. For start, and because we are dealing with the frame for now, let’s not be concerned with the trucks and the wheels, they will be considered later.
How is the frame held by the wheels? If we stand on it or push it to the ground, the wheels will support us without any problem. But, if we take it from either side and try to flip it either way, we can easily do so. This kind of support is called “simple support”. We can of course meet it in other places in our life, consider for example this railroad bridge that I came across in Hillsborough, NC:
Note the pivot and the massive pin on the left bottom of the upper picture, another one exists on the other side. Consider what this bridge can experience during its life: ground movement, uneven sinking of the ground, all these trains passing on it… Now, look at this from the perspective of these hinges: they will always support it vertically, but will take all this relative motion without any trouble – it will simply adjust its rotational position. The same happens with our skateboard frame. Now let’s draw it again in a much simpler manner.
Now we are less concerned with the actual shape of our frame but rather the loads and the reactions which act on it. It is easy to see that in our case the reaction at each wheel truck will be 60 kg for both cases – just consider symmetry and the total applied load. So, what will be the difference between these two load cases? To answer this we need to go deeper and understand what are the local loads at each point on the frame are.
The local loads in our case are of two types – shear forces and bending moments. Both of them result due to the loads and the reactions on the frame. Shear forces are simply the vertical loads that act on the frame, and bending moments can be regarded as “forces multiplied by a distance”. Bending moments are more significant to the structure. The calculation in both cases is very simple, we start from left to right and sum up all the loads that come by. See the pictures for the actual numbers. x-axis is the location on the frame, it changes between 0 and the length of the board.
For this project I bought a longboard for myself to practice riding (I never rode before) and to have a reference structure for everything that we are doing here. My longboard is 42” (105 cm) long with 34” (86 cm) distance between the wheels. During my riding practice I didn’t see the need to go further than around 27” (69 cm) between the wheels, my legs are distanced less apart. In order to consider both cases, I ran the calculations twice for each length.
Congratulations! We have just calculated the loads for our frame. What does it mean? What’s next? You will have to wait for the next week to find out.