If I know the tensile strength of a pin, how do I compute the total strength of multiple pins? That is, 2 objects are connected by multiple pins, evenly distributed, each with a height of $2mm$ and a cross sectional area of $3.33mm^2$. For some reason the answer of just multiplying the tensile strength of each pin by the number of pins, doesn't make 100% sense to me.
The short answer is yes, it is that simple.
Think about it this way. The pins are connected to end plates of a given area. If all we're worried about is the tensile strength, we can place a one dimensional force on each end plate to put the system in pure tension. Now, split the system into a couple parts and do a force balance.
If we split it right down the middle, so that we're seeing the actual force on the top plate, and the internal force along each of the pins. These two forces have to be equal, otherwise the system would be in motion, meaning the pins have yielded or fractured.
Now, to calculate the stress in the pins, we simply divide the force applied across all the pins by the total area. Because in this case, the pins are all of even cross sectional area, the stress will be divided evenly between them. The implication of this is that none of the pins should fail before the others, and any difference in their tensile strength is due to manufacturing defects or variations, so we can just multiple the tensile strength of a single pin by the number of pins to get the overall tensile strength.
There is an important assumption here that the pins are distributed evenly on the plates. If the pins are lopsided, they're going to end up under some amount of bending, which complicates the stress calculations in them and adds to the stress that they see under the same applied load.
If we make the pins of variable cross-sectional area, then the load begins to concentrate in the larger pins, but it should still end up with the same stress in each pin because the load will distribute proportionally to the area, which is how we calculate stress anyway.
Where this gets more complex is if the pins are made of different materials or treated differently to change the tensile strength. This is essentially creating a composite material, and there we have to take into account volume fractions to calculate new yield and tensile strength numbers, but also consider which material fails first. For further reading I'd suggest chapter 3 in this MIT book (that is a 128 page pdf, beware if you're on mobile).