**By Dr. Frank Melsheimer, President, DFM Engineering, Inc.**

In the last Engineering News article, we discussed the relative stiffness to weight ratios for steel and aluminum and their cost implications. We saw that there was very little difference in performance, but considerable differences in cost. Now we will examine the stiffness effect of the shape or geometry of the structure.

The stiffness of a structure depends upon how the part is loaded. Parts loaded in tension or compression (pull or push along the part) are typically very stiff so this form of loading is not very important. The structure is often loaded in bending. Imagine holding one end of a rod and pushing on the other end perpendicular to the length of the rod. The end translates away from the applied force and the entire rod assumes a curved shape so there is an angular change from one end to the other. The part may also be loaded in torsion or twisting along the length of the part. Often the critical loading is a combination of bending and torsion. We want to minimize the translation and most importantly, the rotations.

The simplest way to minimize the deflection is to add more metal. By doubling the diameter of the rod, the weight increases by a factor of 4 and the stiffness increases by a factor of 16. If we remove the original rod making a hollow tube, the stiffness is 15 times higher but the weight is only 3 times heavier resulting in a stiffness to weight ratio improvement of 5 to 1. The limit to maximizing the diameter and minimizing the wall thickness is set by available space, fabrication costs, and local damage or failure of the thin wall of the tube. A diameter to wall thickness ratio of 40 to 1 is common and produces a stiffness to weight ratio increase of 25 to 1.

We now see how the geometry of the part can make a much larger effect on the stiffness to weight ratio than the selection of the material.

We cannot eliminate deflection of the telescope structure, but we can minimize the effect that the deflections have on the performance of the telescope. We will explore this topic in the next DFM Engineering News article.