Relative Strength

Any ham with a tower or who has home brewed yagis will know there are a variety of software tools available to help with mechanical design. There are mast stress calculators to determine wind and ice survival of various grades and sizes of steel masts. Other calculators will determine stress on yagi booms and elements with attention to wind and ice loads. For the experts there are FEA (finite element analysis) engineering packages that handle most complex structures such as towers, both guyed and free standing.

Most of these tools are not used when buying commercial products. Instead we rely on manufacturer specifications and recommendations. Unfortunately some knowledge of various standards may be required since many advertisements attempt to place products in the best light and therefore choose to highlight specifications that may mislead even when accurate. Buying is not always worry free.

Guessing, optimism and hope abound among hams, including myself. I often calculate but other times times I rely on extrapolation from known designs and existing installations. If done carefully it can produce good results.

This is not an article about all those software and web tools for doing the heavy lifting for those mechanical calculations. Instead I want to discuss how I resolved a common question I deal with all the time when doing these calculations:

What happens when I change X?

X is a variable regarding a pipe or tube choice that may include but not limited to:

• Strength: bending, axial or other load limit
• Weight
• Wind load
• Cost

All have a bearing on the choice of boom, mast and yagi element structural members. It is helpful to play the game of What if? to see if the change is helpful or deleterious with respect to those criteria. Sometimes I choose pipes based on what best fits!

The relationship among those values can be complicated since, for example, reducing pipe diameter reduces strength and weight but also reduces wind load and cost. Trying alternatives can be enlightening, just like when using antenna models or electrical circuit simulators. Going by intuition and guesswork is faster but unwise. Using the engineering models spits out results but it is left up to the user to numerically compare among multiple scenarios.

As a design aid I use spreadsheets for calculations that may be inconvenient to do in other ways. Examples include: coils size, Q, wire length and inductance; transmission line impedance for wire diameter and spacing; wire coordinates under rotations for use in antenna models; and much more.

I wrote one for pipes, to calculate the parameters listed above. It compares two pipes to facilitate review and assessment. It makes it easy to discover the trend of pipe strength as diameter and wall thickness are varied. Wind force and pipe weight can change to a surprising degree. It's all excellent data to have in hand.

The first example compares two aluminum tubes of different diameter and the same wall thickness. Notice the better than 60% strength increase for a tube only 25% larger. Since the wind load increases in proportion to diameter the wind speed and ice survival is superior. Cost of large pipes and tubes is approximately in proportion to weight so this, too, is reasonable at 27%.

Notice that the spreadsheet doesn't calculate the actual strength of each pipe or the force for a specific wind speed and ice coating. There are ample tools available to do those calculations and I use them. This spreadsheet is a supplement not a replacement or consolidation. The spreadsheet assumes both pipes are the same alloy with identical strengths.

The spreadsheet works in English units since the large majority of pipes and tubes used in Canada are sized in these units despite this being a metric country. Industry inertia is strong, as is trade with the US. It would not be difficult to convert the spreadsheet to metric. The spreadsheet was calibrated using trade data for steel and aluminum pipe and tubes. Differences among alloys and tempers are negligible and are ignored.

The second example compares nominal 2-½" steel pipes, one schedule 40 and the other schedule 80. The heavier pipe is 26% stronger but weighs 32% more. This is poor economy. However on plus side the wind area is identical so the additional strength comes with no wind load penalty.

These first two examples illustrate the well-known rule that for a similar quantity of material (cross section or weight) it is better to increase diameter than wall thickness.

The final example compares a 2" schedule 80 aluminum pipe to a larger diameter 2-½" schedule 40 pipe. Again the thinner wall pipe of larger diameter is the better choice. Strength is 45% better for an increase of 21% is wind load and 15% in weight and approximate cost.

I don't always use the optimum pipe or tube, choosing to use what I have available or can acquire at a good price. The spreadsheet helps me understand the implications, in particular where I run the risk of poor economy. Ideally I should include alloy and temper in the spreadsheet to broaden the range of experimentation. Perhaps I will do so eventually.

Although I have not included the specific formulas used in the spreadsheet they are straight-forward to derive or look up. I extracted the strength calculation from a public domain beam spreadsheet. Surface area is simply length multiplied by diameter, after which you must apply the widely available wind load calculation for long cylinders. Circular cross section is the area of the outer diameter less the area of the inner diameter. Multiplying that by a constant gives the weight.