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1 North American Steel Construction Conference Rules of Thumb for Steel Design with factored loads and LRFD or service I n earlier times when computers were neither available nor essential, one loads and ASD in the final design. Structural Depths: objective of the structural design process was to discover a computational method, Inevitably, a question raised in a pro- which was elegant, simple and appropri- ject concept meeting is what will be the ately accurate. When such a process was structural depth? Regularly, the partici- identified it was recorded as an expedient pants are impressed by the response of approach to solving a recurring structural the structural engineer and that positive design problem. Thus, quick Rules of impression lasts if the actual depths Thumb became essential resources for designed fall within the range of these the structural engineer.

2 As computer soft- early predictions. Therefore, it is impor- ware has proliferated, become very com- tant to have established Rules of Thumb , prehensive, and been made very user which allow structural depth predictions. friendly, the importance of Rules of The depth of the structural system is Thumb and approximate methods has influenced by the span of the elements as been diminished. It has been argued that, well as such variables as the spacing of with the computational speed and ease of elements, loads and loading conditions, Socrates A. application of computer methods, the continuity, etc. Nonetheless, ratios of Ioannides, need for approximations and Rules of span to depth can often be relied upon to , , Thumb no longer exists.

3 However, provide a guide and a starting point from is President equally imposing arguments can be made which further refinement can be made. for the value of these quick approaches With the caution that variables other and John L. such as: than span need to be considered, the Ruddy, P. E., information in Table 1 is presented. is Chief The structural engineer should have tools to make on-the-spot intelligent It is convenient to remember that ser- Operating decisions, viceable steel section depths are in the Officer, of A reasonable solution is often required range of of depth for each foot of Structural as computer input, span (L/24). Some people might find it Affiliates The validity of the computer output easier to remember the following simpli- International, should be verified with rational fied rule where the length is expressed in approximations.

4 Feet and the depth of the member in Inc., in inches: Nashville. So, with the objective of fostering con- This article is tinued development, use and enthusiasm Depth of Roof Beams, Roof Joists =. for Rules of Thumb and approximate *Length based on a methods, several steel framing Rules of paper sched- Thumb are presented in this paper. In Depth of Floor Beams, Floor Joists uled to be general, these Rules of Thumb are service- = *Length presented at load based, which simplifies their applica- Depth of Composite Beams =. the 2000 tion. Formal checks can then be made *Length North American Steel Construction Conference in Las Table 1: Structural Depths Vegas. System L/ds Span Range Steel Beam 20 to 28 0' to 75'. Steel Joist Floor Member 20 8' to 144'.

5 Roof Member 24. Plate Girder 15 40' to 100'. Joist Girder 12 20 to 100'. Steel Truss 12 40' to 300'. Space Frame 12 to 20 80' to 300'. Modern Steel Construction / February 2000. Section Properties Consider a beam spanning 30 feet Roof Systems supporting a 10 foot width of floor with a A common approach to economy in Wide flange steel section properties total supported load of 140 psf, resulting can be estimated with reasonable accura- steel roof systems of single story buildings in a moment of foot-kips. For an is to cantilever girders over the columns. cy when the member depth, width and 18 deep beam, the equation yields foot-weight are known. Recalling that The ends of the cantilever support a pounds per foot. A W18x50 is the pre- reduced span beam.

6 When this system is the density of steel is 490 pcf, the rela- dicted section and the actual moment tionship between cross section area and subjected to a uniform load and multiple capacity is 176 foot-kips. If a beam equal spans are available, a cantilever foot-weight can readily be derived as: depth of 21 is assumed, the equation length approximately equal to 15%. yields suggesting a W21x44, which Wt ( ) of the span length will result in A= has a moment capacity of 162 foot-kips. the maximum moment in any span being A similar formulation for steel having equal to 1/16 wL2. For end spans, nega- Fy = 50 ksi produces: tive and positive moments can be bal- The strong axis moment of inertia can anced using a cantilever length equal to be approximated using: For an 18 deep beam, the equation 25% of the first interior span.

7 M foot, therefore, a yields . Wtpounds Another approach to economical roof W18x35 is The actual capacity Wt systems is the use of plastic analysis. I x D2. of a W18x35 beam with Fy=50 ksi is 158. foot kips. Although not as critical for this system, 20 splice locations in the plastically designed For common composite beam floor continuous beams are usually chosen so The radius of gyration is an important systems ( 5 slabs with 3 composite that they are close to the point of zero cross section property when considering deck, 4 slab with 2 composite deck, moment. column buckling. Both the strong axis etc.), the simplified equations yield rela- and weak axis radius of gyration can be tively accurate foot weights if 70% to Hinge or splice location for can- estimated using the member depth (D) 75% of the simple span moment is used tilever or continuous roof systems and width (b) as: for M.

8 Following are two more Rules of is 15% to 25% of span length Thumb relating to composite construc- ry b tion and Fy=36: In ASD Number of shear studs required for Full Composite Action Trusses rx D = *Wt The foot weight of trusses utilizing Fy=36 ksi steel can be calculated by In LRFD Number of shear studs assuming Fa=22 ksi. The Chord Force required for Full Composite Action (Fch) is then equal to the moment (M) in = *Wt foot-kips divided by de (center of top chord to center of bottom chord) in feet, Beams resulting in a chord area of M/22de. By The rapid determination of a steel recognizing that Wt = A* , converting section size can be made without refer- COLUMNS de to inches and assuming that de = ence to a steel manual using a very sim- When the column axial capacity is and that the total truss weight is equal to ple equation.

9 If the moment capacity, plotted as a function of Kl/r, an approxi- times the chord weight then: depth and foot weight of the economy mate linear relation can be observed. steel beams listed in the AISC 6M. Specification are tabulated with moment Certainly, the column curve is not linear, however an accurate approximation of Wt . divided by the depth as the independent column capacity for Fy=36 ksi can be D. variable and foot weight as the depen- calculated using: dent variable, a linear regression analysis The same formulation using steel with results in a rather simple equation for Fy=50 ksi produces the following Fy=36 ksi. Kl approximation: P A . Wt . 5M r M. D Wt . A similar formulation for steel having D. Fy = 50 ksi produces: The closest economy section of the These weight approximations include depth used in the equation that has a truss joint connection material weight.

10 Foot weight greater than predicted by the Kl . equation indicates the beam that will sus- P A . tain the moment. This equation was con- r . firmed by the author using an alternate approach, coined Visual Semi-rigorous Thus, using the section property Rigid Frame Analysis Curve Fitting 3. If all the beam sections approximations in conjunction with a Approximations: are included, a slope value in the linear member foot-weight, width, depth and The following Rules of Thumb are equation of yields closer approxima- unsupported length, the capacity of a col- useful in determining preliminary sizes tions for Fy=36 ksi. umn can be approximated. for Rigid Moment Frames resisting Modern Steel Construction / February 2000. Lateral loads. They are based on the tra- ditional Portal Frame approach modi- Table 2: Tall Building Structural Systems fied from the authors' experiences with Stories Lateral Load Resisting System real frames.