dragonfly wrote:lllazar wrote:I was wondering - since the base legs take more force, would it be a good idea to make them large than the columns in the upper portion of the tower - say, 3/16 in^2?
.... they don't really take MORE force, since obviously the same amount of force is being applied at the top, it's just that they're under more
strain (if you do a sketch of the force components, you'll easily see why). In answer to your question then, SIZE really isn't the main matter, because you could have a bigger piece that's less massive and have those legs break just as easily, so: getting down to the question you
want to be asking, YES it might very well be a good idea to have stronger base legs than your top ones.
If the upper part of a tower is vertical, the base (legs) are inclined, and the applied load (at the top of the tower) is vertical, then the legs do carry more force than the vertical members. Here is an illustration/explanation: Let's say our (very simplified) tower looks something like this:
Basically, the top part of the tower is a rectangular prism and the legs are inclined (the angle between the legs and the horizontal plane is denoted by "a"). Here, it is not difficult to see that the vertical member (labeled 1) carries a compressive force of P, since a vertical force of P is directly applied to it at the top. But, what about the inclined member (labeled 2)? Is the force in member 2 greater than P? To determine this, let's isolate the joint that connects members 1, 2 and 3 and show the forces acting at that joint. We end up with three forces (see image above). Since the algebraic sum of these force vectors must be zero, we can write:
F1 - F2 sin(a) = 0 and
F3 - F2 cos(a) = 0
where F1 is the axial force in member 1, F2 is the axial force in member 2 and F3 is the axial force in member 3.
From the first equation above, we get F2 = F1/sin(a). Since F1 = P, then F2 = P/sin(a). If a = 30 degrees, then F2 = 2 P. That is, the force in member 2 is two times greater than the force in member 1. Clearly, in this example, regardless of angle a, F2 is always greater than F1.
In engineering, the word "strain" is related to displacement not force. For example, if a tension member has a length of 10 feet and it elongates 1 inch, then its axial strain equals to 1/120. The term "strain" should not be used interchangeably with the term "force."
