New Rules of Thumb for Flat Steel Trusses

To view the figures and tables associated with this article, please refer to the flipbook above.

In the January 2024 issue of STRUCTURE Magazine, structural engineer Ciro Cuono praised the skills, intuition, and expertise of the individual engineer that result from years of relating calculations to real-world situations, specifically using rules of thumb. As Cuono explained, the value of these abilities have diminished over time as technological innovations and digital tools have continued to put astonishing analytical and design capabilities at our fingertips. This is, of course, a decades-long phenomenon, the kind of historical trend that Cuono points out has put the slide ruler and the slope deflection method in the proverbial junk drawer. Nevertheless, Cuono warns us that continuing to concede more of the hard engineering work to emerging technologies (such as artificial intelligence) without adequate human know-how and supervision can have unintended and unwanted effects. It can dull an engineer’s abilities at interpreting an equation’s results and making informed, evidence-based decisions in the process of structural design. What is there to interpret or explain to the client other than to say, “This is what the computer came up with”?

Previously, rules of thumb for flat steel trusses led only to the height of these trusses. A new set of rules for flat steel trusses (also known as parallel chord trusses) allow an engineer to determine preliminary sizes for a truss’s diagonals, verticals, and top and bottom chords. As such, they fill a valuable gap in our mental toolkit whenever we are working with these lightweight and efficient long-span structures.

The rules of thumb are as follows:

s = l/32 – l/48
h = l/12 – l/ 24
b ≥ s

The first rule of thumb is for a truss diagonal, which yields the sides of a steel square tube, that is, a square hollow structural section (HSS). The side s (in inches) ranges between a maximum size of l/32 and a minimum size of l/48, where l is the nominal length in inches, from node-to-node, of the longest truss diagonal.

The second rule of thumb is for the top chord of a truss, which yields the height or long side of a rectangular steel tube, that is again, a rectangular HSS. The height h (also in inches) ranges between a maximum size of l/12 and a minimum size of l/24. As in the previous case, l is the nominal length in inches of a segment of a top chord in between two successive nodes. Lastly, the side b of our rectangular HSS must be at least as long as the side of our previously chosen square HSS for our struts and ties. An example will help to explain the uses of these rules.

Let us begin with an arbitrary truss span L of 175 feet. A long-standing, well-know, and widely published rule of thumb tells us that the height H of a flat steel truss is often equal to one tenth of the span,

H = L/10 = 175 ft/10 = 17.5 ft

Dividing the span into10 equal segments conveniently leads to 10 square panels. Put another way, a flat truss spanning 175 feet can be divided into 10 identical panels, each measuring (nominally) 17.5 feet x 17.5 feet. The truss diagonal is at an angle of 45 degrees and is both nominally and approximately 24.75 feet in length. To apply the two rules of thumb listed previously, it is important to begin with the longest diagonal. This is to safeguard against long compression members, which pose a buckling danger if improperly sized.

Rules of thumb may be formula based, or chart or graph based. The charts in Figure 1 simplify the process described previously by relating the rules of thumb in this article directly to a truss’s span. The first chart enables the preliminary sizing of a truss’s diagonal, and the second chart facilitates the preliminary sizing of a truss’s top chord. For each chart, read up from the truss span to the blue line for the minimum size of the desired HSS, and up to the red line for the maximum size of the same HSS.

These rules of thumb emerged out of a need in a structures classroom in an undergraduate architecture program. An instructor teaching rules of thumb would be fortunate to have on hand an exhaustive set of rules of thumb. Oftentimes, however, instructors find themselves cobbling together rules from various sources— their times as students, on-the-job training, or from this or that textbook. Inevitably, students will ask their instructors, “How do I size [ ]?” So, an instructor is compelled to dig further into the books looking for even more rules of thumb. Surprisingly, the instructor comes to find that nothing is published for the individual components of a truss … at least not in any of the textbooks used to teach architecture students. So then, do you size them like beams? That would seem to be nothing more than an unsubstantiated guess. Thus, one structures professor set upon an engineering analysis in search of these elusive truss rules of thumb.

The engineering analysis centered upon a theoretical roof structure comprised of a simple built-up roof, wide-flange steel beams, and Warren trusses with verticals. The study’s author ran dozens of trials relying on randomly selected truss spans between 100 and 200 feet, and locations across the United States with differing snow and wind loads. The roof dead load was a constant. Factored dead, snow, and wind loads were applied to the steel beams, which then transferred their reactions as point loads onto the steel trusses. A full analysis followed for each truss in our theoretical roof structure, which in each case led to a calculated cross-sectional area for each chord, diagonal, and vertical in our notional trusses. The size of every compression member was further tested and bolstered to guarantee against buckling. Following these calculations, the study’s author compared the length of the worst-case diagonal for each truss (i.e., the diagonal carrying the largest compression force) to the sides of its corresponding square HSS. A similar process followed for the worst-case top chord segment. After relating the sides of the square HSSs and the top chord heights for rectangular HSSs to their respective lengths, the results were the rules of thumb

s = l/32 – l/48, h = l/12 – l/24, and b ≥ s.

The study’s author also conducted test trials on Pratt and Howe trusses with square panels similar to the Warren trusses described previously. Owing to very close geometries across these three types of trusses, the rules of thumb derived from the Howe and Pratt trusses varied slightly from those derived for the Warren truss with verticals. Thus, the rules of thumb listed here worked out best across all of the truss types under consideration.

There are three key considerations related to the study’s boundary conditions, as well as some useful advice in the applications of these rules. The first key consideration is the geometries of the trusses in the study. Each truss consisted of a square panel with diagonals at 45 degrees. So, the study that led to these rules of thumb did not include any rectangular panels, or diagonals at 30 or 60 degrees, or any other angles. Second, the study focused on one truss type—the flat steel truss. Thus, the study did not look at triangular, bowstring, scissors, or other novel truss shapes. And third, the study concentrated on two specific cross sections—square HSSs for diagonals and verticals, and rectangular HSSs for top and bottom chords. Clearly, many other cross sections are useful and plentiful in steel truss designs.

The suggested advice for the rules of thumb presented here serve in part to alleviate any concerns behind the study’s boundary conditions mentioned here. To begin with, rules of thumb are suitable for general and preliminary (not final) sizing purposes, and are meant to be flexible in their application. Accordingly, though these rules of thumb were derived for flat steel trusses, they may be applied to truss members in other steel trusses—for example, triangular, bowstring, or sloped trusses in a shed-style roof—with minimal concerns. This is possible because these rules of thumb are not used to approximate truss heights, but rather the cross sections of their individual components. And in that sense, a strut, tie, or chord is an axially loaded part of a truss, whether that truss is flat, triangular, etc. To be sure, further research is called for to generate additional rules of thumb for various steel truss shapes. But for the time being and in the absence of any other guidance, these rules will suffice.

In a similar vein, though these rules of thumb are meant to generate dimensions for square and rectangular HSSs, the dimensions are not strictly limited to those cross sections. The dimensions may be applied towards other cross sections used in similar circumstances, for example, towards wide-flange or round HSS sections used as axially-loaded truss members. If a designer chooses to take this approach, they should do so with one caveat. If translating from a recommended square or rectangular HSS to a different type of cross section, the designer should use the larger dimensions derived from the rule of thumb formulas or charts. This follows from a comparison of recommended cross sections for wide-flange and square HSSs columns contained in the most comprehensive treatment of rules of thumb used by architects (and architecture students), in Edward Allen’s and Joseph Iano’s The Architecture Studio Companion. In that exhaustive reference book, recommended cross sections for wide-flange columns track closely or slightly larger than their recommended square HSSs.

Remember also to use your engineering judgement. To that end, consider the loads and spans for your steel trusses. Settle upon larger sizes for longer spans and/or heavier roof loads, and smaller sizes for shorter spans and/or lighter roof loads. However, if unsure which size to select for a particular strut, tie, or chord, do as one instructor advises his students, “When in doubt, size up” (that is, select the larger option).

The simplicity of rules of thumb belies their utility to anyone working in structural design. The rules presented here narrow an important gap in terms of steel truss design, and hopefully it is a step in the right direction. Further work of this kind would address, for example, the component sizing of space trusses or multistory diagrids. But for now, the rules of thumb in this article are ready for use by engineers, architects, and student designers. ■

About the Author

Cesar Cruz is an Assistant Professor of Architecture at Ball State University, in Muncie, Indiana, where he teaches architectural building structures, design, and architectural history. He may be reached at cacruz@bsu.edu.

References

Cruz, Cesar. “Rules of Thumb for Sizing Horizontal, Diagonal, and Vertical Components of Parallel-Chord Trusses.” In Haq, Saif, and Adil Sharag-Eldin (eds). ARCC 2023 Conference Proceedings: The Research-Design Interface, 543-550. Dallas, Texas: The Architectural Research Centers Consortium, 2023.

https://www.arcc-arch.org/wp-content/uploads/2023/09/ARCC2023ProceedingsFINAL-PW.pdf