Socrates A.Ioannides,Ph.D., S.E.,is Presidentand John L.Ruddy, P. E.,is ChiefOperatingOfficer, ofStructuralAffiliatesInternational,Inc., inNashville.This article isbased on apaper sched-uled to bepresented atthe 2000NorthAmerican

Steel Construction Conference in LasVegas.

In earlier times when computerswere neither available nor essential, oneobjective of the structural design processwas to discover a computational method,which was elegant, simple and appropri-ately accurate. When such a process wasidentified it was recorded as an expedientapproach to solving a recurring structuraldesign problem. Thus, quick “Rules ofThumb” became essential resources forthe structural engineer. As computer soft-ware has proliferated, become very com-prehensive, and been made very userfriendly, the importance of “Rules ofThumb” and approximate methods hasbeen diminished. It has been argued that,with the computational speed and ease ofapplication of computer methods, theneed for approximations and “Rules ofThumb” no longer exists. However,equally imposing arguments can be madefor the value of these quick approachessuch as:

• The structural engineer should havetools to make on-the-spot intelligentdecisions,

• A reasonable solution is often requiredas computer input,

• The validity of the computer outputshould be verified with rationalapproximations.

So, with the objective of fostering con-tinued development, use and enthusiasmfor “Rules of Thumb” and approximatemethods, several steel framing “Rules ofThumb” are presented in this paper. Ingeneral, these rules of thumb are service-load based, which simplifies their applica-tion. Formal checks can then be made

Rules of Thumb for Steel DesignNorth American Steel Construction Conference

with factored loads and LRFD or serviceloads and ASD in the final design.

SSttrruuccttuurraall DDeepptthhss::Inevitably, a question raised in a pro-

ject concept meeting is what will be thestructural depth? Regularly, the partici-pants are impressed by the response ofthe structural engineer and that positiveimpression lasts if the actual depthsdesigned fall within the range of theseearly predictions. Therefore, it is impor-tant to have established rules of thumb,which allow structural depth predictions.The depth of the structural system isinfluenced by the span of the elements aswell as such variables as the spacing ofelements, loads and loading conditions,continuity, etc. Nonetheless, ratios ofspan to depth can often be relied upon toprovide a guide and a starting point fromwhich further refinement can be made.With the caution that variables otherthan span need to be considered, theinformation in Table 1 is presented.

It is convenient to remember that ser-viceable steel section depths are in therange of ½” of depth for each foot ofspan (L/24). Some people might find iteasier to remember the following simpli-fied rule where the length is expressed infeet and the depth of the member ininches:

Depth of Roof Beams, Roof Joists =0.5*Length

Depth of Floor Beams, Floor Joists= 0.6*Length

Depth of Composite Beams =0.55*Length

System L/ds Span RangeSteel Beam 20 to 28 0’ to 75’

Steel Joist

Floor Member 20 8’ to 144’

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’

Table 1: Structural Depths

Modern Steel Construction / February 2000 / 67

and width (b) as:

BBeeaammssThe rapid determination of a steel

section size can be made without refer-ence to a steel manual using a very sim-ple equation. If the moment capacity,depth and foot weight of the economysteel beams listed in the AISCSpecification are tabulated with momentdivided by the depth as the independentvariable and foot weight as the depen-dent variable, a linear regression analysisresults in a rather simple equation forFy=36 ksi.

The closest economy section of thedepth used in the equation that has afoot weight greater than predicted by theequation indicates the beam that will sus-tain the moment. This equation was con-firmed by the author using an alternateapproach, coined “Visual Semi-rigorousCurve Fitting”3. If all the beam sectionsare included, a slope value in the linearequation of 5.2 yields closer approxima-tions for Fy=36 ksi.

Consider a beam spanning 30 feetsupporting a 10 foot width of floor with atotal supported load of 140 psf, resultingin a moment of 157.5 foot-kips. For an18” deep beam, the equation yields 43.75pounds per foot. A W18x50 is the pre-dicted section and the actual momentcapacity is 176 foot-kips. If a beamdepth of 21” is assumed, the equationyields 37.5 suggesting a W21x44, whichhas a moment capacity of 162 foot-kips.

A similar formulation for steel havingFy = 50 ksi produces:

For an 18” deep beam, the equationyields 30.6 pounds per foot, therefore, aW18x35 is predicted. The actual capacityof a W18x35 beam with Fy=50 ksi is 158foot kips.

For common composite beam floorsystems (e.g. 5½” slabs with 3” compositedeck, 4½” slab with 2” composite deck,

Section Properties

Wide flange steel section propertiescan be estimated with reasonable accura-cy when the member depth, width andfoot-weight are known. Recalling thatthe density of steel is 490 pcf, the rela-tionship between cross section area andfoot-weight can readily be derived as:

D45.0rx

≈≈

b26.0ry

≈≈

DM5

Wt ≈≈

The strong axis moment of inertia canbe approximated using:

The radius of gyration is an importantcross section property when consideringcolumn buckling. Both the strong axisand weak axis radius of gyration can beestimated using the member depth (D)

20Wt

DI 2x

≈≈

4.3Wt

A ==

DM3.5

Wt ≈≈

68 / Modern Steel Construction / February 2000

Ple

ase

Cir

cle

# 73

etc.), the simplified equations yield rela-tively accurate foot weights if 70% to75% of the simple span moment is usedfor M. Following are two more “Rules ofThumb” relating to composite construc-tion and Fy=36:

In ASD Number of shear studsrequired for Full Composite Action= 1.1*Wt

In LRFD Number of shear studsrequired for Full Composite Action= 1.25*Wt

CCOOLLUUMMNNSSWhen the column axial capacity is

plotted as a function of Kl/r, an approxi-mate linear relation can be observed.Certainly, the column curve is not linear,however an accurate approximation ofcolumn capacity for Fy=36 ksi can becalculated using:

A similar formulation for steel havingFy = 50 ksi produces:

Thus, using the section propertyapproximations in conjunction with amember foot-weight, width, depth andunsupported length, the capacity of a col-umn can be approximated.

RRooooff SSyysstteemmssA common approach to economy in

steel roof systems of single story buildingsis to cantilever girders over the columns.The ends of the cantilever support areduced span beam. When this system issubjected to a uniform load and multipleequal spans are available, a cantileverlength approximately equal to 15%(0.146) of the span length will result inthe maximum moment in any span beingequal to 1/16 wL2. For end spans, nega-tive and positive moments can be bal-anced using a cantilever length equal to25% of the first interior span.

Another approach to economical roofsystems is the use of plastic analysis.Although not as critical for this system,splice locations in the plastically designedcontinuous beams are usually chosen sothat they are close to the point of zero

moment.

Hinge or splice location for can-tilever or continuous roof systemsis 15% to 25% of span length

TTrruusssseessThe foot weight of trusses utilizing

Fy=36 ksi steel can be calculated byassuming Fa=22 ksi. The Chord Force

−−≈≈

rlK

10.00.22AP

−−≈≈

rlK

15.00.30AP

(Fch) is then equal to the moment (M) infoot-kips divided by de (center of topchord to center of bottom chord) in feet,resulting in a chord area of M/22de. Byrecognizing that Wt = A*3.4, convertingde to inches and assuming that de = 0.9Dand that the total truss weight is equal to3.5 times the chord weight then:

DM6

Wt ≈≈

Modern Steel Construction / February 2000 / 69

Please C

ircle # 122

The same formulation using steel withFy=50 ksi produces the followingapproximation:

These weight approximations includetruss joint connection material weight.

RRiiggiidd FFrraammee AAnnaallyyssiissAApppprrooxxiimmaattiioonnss::

The following “Rules of Thumb” areuseful in determining preliminary sizesfor Rigid Moment Frames resistingLateral loads. They are based on the tra-ditional “Portal Frame” approach modi-fied from the authors’ experiences with“real” frames.

The moments in beams framinginto exterior columns are half of theabove values

SStteeeell WWeeiigghhtt EEssttiimmaatteessCost is generally the basis for confirm-

ing a structural system since safety andfunctions are essential for any optionsconsidered. Economy is related to theweight of the structural steel althoughcosts are influenced by many other para-meters. Yet, weight can be a valuableindicator of cost and Rules of Thumb areuseful in establishing an expectation forsteel weight. A quick assessment ofanticipated weight serves as a check ofthe reliability of the weight determinedby more involved investigations.

Bracing is a cost-effective means ofproviding lateral load resistance for lowto medium rise buildings. As the buildingheight increases, the unit steel weightincreases since columns are subjected tolarger loading at the lower floors and lat-

eral load resisting components are sub-jected to greater loads for greater heights.Thus, one parameter influencing thesteel weight is building height. A roughapproximation for steel weight per squarefoot in a braced building using steel withFy = 50 ksi is:

Wt(psf) = stories/3 + 7

A three-story building would have asteel weight in the range of 8 psf and a27-story building would require 16 psf.Certainly, this relationship is an oversimplification. Yet, it provides a value,which can be used to confirm that theresults of a more detailed analysis arereasonable.

TTaallll BBuuiillddiinngg SSttrruuccttuurraall SSyysstteemmssThe late Fazlur Khan hypothesized

that the appropriate structural system toresist lateral loads was directly related tobuilding height. He predicted that struc-tural economy could be realized usingthe appropriate system shown in Table 2.

DM5.4

Wt ≈≈

col

storycol n

V

2H2.1

M ••≈≈

RoofatColumnsInterior2MM col

beam ≈≈

RoofatNotColumnsInteriorMM colbeam ≈≈

70 / Modern Steel Construction / February 2000 Please Circle # 127

MMiisscceellllaanneeoouussEnd rotation of a simple beam = 0.2radians

Deflection of simple span beam (reduc-tion due to connections) = 80% of calcu-lated

Roof Framing Systems

For Cantilevered or continuous roofbeams :

• Run beams inshort direction

• Optimum bay sizeis 30’ x 40’

For Truss Joist andJoist roof systems:

• Run Girders inLong direction

• Optimum bay sizeis 40’ x 40’

NNoommeennccllaattuurree

A = Area (in2)

b = Nominal member width (inches)

D = Nominal member depth (inches)

ds = System depth (ft)

Fy = Yield strength of steel

H = Story Height

I = Moment of Inertia (in4)

l = Column Length (inches)

L = Length (ft)

M = Bending moment (foot-kips)

Mbeam = Design Moment for Beam

Mcol = Design Moment for Column

ncol = Number of Columns (not bays) inthe story of the Frame

P = Column Axial Capacity

rx = Strong Axis Radius of Gyration(inches)

ry = Weak Axis Radius of Gyration (inch-es)

S = Elastic Section Modulus (in3)

Vstory = Total Story Shear for the Frame

Wt = Foot weight of the steel beam(pounds per foot)

Wt(psf) = Weight of steel structure (psf)

Stories Lateral Load Resisting System

<30 Rigid frame

30 to 40 Frame – shear truss

41 to 60 Belt truss

61 to 80 Framed tube

81 to 100 Truss – tube w/ interior columns

101 to 110 Bundled tube

111 to 140 Truss – tube without interior columns

Table 2: Tall Building Structural Systems

Modern Steel Construction / February 2000 / 71Please Circle # 113