Computers can be used toperform complex cal-culations at incrediblespeeds. Complicated de-sign equations that

would take pages and hours to com-plete can be plugged into a spreadsheetthat yields immediate results. In spiteof myriad technological advancements,there is still a need for “quick anddirty” design methods. After all, isn’tthat what the back of the envelope wasmade for? This practical design aid willprovide reasonable estimates for axialcapacities of common compressionmembers. You won’t need a computer.And you may not even need yourtrusty envelope!

When calculating compressivestrength using the AISC LRFD Specifi-cation, a multitude of variables, equa-tions, and reduction factors must beconsidered. In some cases, flexuralbuckling controls, and the only consid-eration is whether λc is greater or lessthan 1.5. However, with non-symmet-ric shapes flexural-torsional bucklingand its related critical buckling stressFcrft must be considered. In other cases,the effects of local buckling need to bedetermined through the use of reduc-

tion term Q. Each of these calculationstakes a significant amount of time andrequires a solid understanding ofwhich equations to use.

The rules of thumb presented hereuse simple variables. For each calcula-tion, you will need to know the nomi-nal weight per linear foot (Wt), theeffective length of the compressionmember in feet (KL), and one critical di-mension of the section (bf , d, or h).

The presented equations serve asquick, reasonably accurate estimates ofthe capacity of several different typesof compression members. Due to largelocal buckling reduction factors for teesand rectangular hollow structural sec-tions (HSS), rules of thumb were notdeveloped for these shapes. For theshapes that are presented, the rules ofthumb were developed to apply tothose sizes found in the column tablesin the 3rd Edition LRFD Manual.

Each equation is derived from a lin-ear approximation of the standardLRFD column curves and an approxi-mate gross area. The linear approxima-tion is generally within 15% of theactual design strength (for KL/r ≤ 180 ),although this is not always conserva-tive. Unconservative cases are dis-

cussed in the box on the next page. Theequations do apply for slenderness ra-tios greater than 180, but the approxi-mations tend to become less accurate.

The table also includes equationsthat approximate the area of steel sec-tions using the nominal weight per foot(based on a standard steel weight of490 lb/ft3 ). These equations take intoconsideration a 0.93t design thicknessfor hollow structural sections. Also in-cluded are approximate Wt values forthose shapes not generally specifiedwith the Wt values (such as angles, forwhich weight does not appear in thedesignation like L8×8×1/2). Finally, thetable includes approximate r values foruse in quickly approximating slender-ness ratios.

This work was inspired by a 2001NASCC conference paper, “Rules ofThumb for Steel Design,” by JohnRuddy, Chief Operating Officer andPrincipal, Structural Affiliates Interna-tional, Nashville.

Keith Mueller is Senior Engineer andBrian Dekker is an engineering intern withAISC’s Steel Solutions Center in Chicago.Email the Steel Solutions Center at solu-tions@aisc.org or visit them on the AISC website at www.aisc.org.

Keith Mueller and Brian Dekker

Are you still writing equations on the back of envelopes? Try this

timesaving design aid for estimating theaxial capacities of commonly-used

compression members.

ESTIMATING THE AXIAL CAPACITY OF

SteelWise

Modern Steel Construction • July 2002

COMPRESSIONMEMBERS

July 2002 • Modern Steel Construction

Final designs must always be veri-fied to comply with the requirementsin the LRFD Specification. Here’s why:

The linear approximation of theaxial design strength curve is illus-trated in the graph. In the case of eachshape, the equations approximate avalue that is conservative for smallervalues of KL/r. As the effective lengthincreases, the approximation resultsbecome higher than the actual capacity(although it generally stays within15%), and then turn back toward con-servative as KL/r increases further up tothe slenderness limit of KL/r = 180.

There are some particular problemcases that should be noted:• Square HSS. The approximation for

axial capacity is higher (as much as 50%) than the actual value forsome thick walled sections when 120 < (KL/r) < 150 and is lower (asmuch as 20%) than the actual value formany sections when 30 < (KL/r) < 90.

• W-Shapes. The approximation foraxial capacity is higher (as much as30%) than the actual value for thelightest sections for each nominaldepth when 19 ft < KL < 28 ft.

• Double Angles. The approxima-tion for axial capacity is higher (asmuch as 25%) than the actual valuefor thick-legged sections when 140 < (KL/r) < 170.

KL

Axi

al C

apac

ity

Approximation

AISC Column Curve

conservative

conservative

unconservative

Shape yF Approx. A

Approx. Wt Approx. r

Approx. crF

W 50 3 4.Wt N/A .≈ 0 22y fr b −50 12

f

KLb

HP 36 3 4.Wt N/A .≈ 0 24yr d −36 8

f

KLb

Equal leg L 36 3 4.Wt 6.5bt .≈ 0 20zr b −36 10 KL

b

Equal leg 2L, 3/8” separation 36

3 4.Wt 13bt .≈ 0 20yr b .−36 6 5 KL

b

Square HSS 46 3 65.Wt 12ht .≈ 0 37r h −46 7 KL

h

Round HSS 42 3 65.Wt 10dt .≈ 0 33r d −42 7 KL

d

Pipe 35 3 4.Wt 10dt .≈ 0 32r d .−35 5 5 KL

d

A area b leg length, in. bf flange width, in. d depth of member (HP);

outer diameter of member (Round HSS and Pipe), in. h outer dimension of square HSS, in. r, ry, rz radius of gyration, in. KL effective length, ft t thickness Wt weight of member, lb/ft

THE FINE PRINT