A MATLAB Code for the Design of Slender Box Columns Subjected to Axial-Bending

A box column supports a 16.5 m-tall signboard (Fig. 1) designed in accordance with AISC 360-16 specifications. An all-in-one MATLAB code for wind load analysis and design is developed and used to investigate the box section as shown in Fig. 2.

Fig. 1 Signboard Structure

Fig. 2 Box column section

Based on AISC 360, this column has a slender element in compression, and a non-compact flange due to Mny. The demand/capacity ratio (DCR) can be computed from the minimum value of

Where Mnx, and Mny are computed from the minimum value of

The notations LTB, FLB and WLB stand for

LTB = Lateral-Torsional Buckling (Mn vs unbraced Length)FLB = Flange local buckling (Mn vs b/t, flange)

WLB = Web local buckling (Mn vs b/t, web)

The bending strength due to non-non compact and slender section, i.e., about x axis, is determined from

The calculation flowchart can be summarized as follows

Wind load integration over height for the base shear (Fw) and moment (Mw)

Fw = ∫ Ce(z) Cp q b dz , Mw = ∫ Ce(z) Cp q z b dz

↓

Required strengths Pr, Mrx, Mry

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Box section properties Ag, I, S, Z

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Slenderness and effective area Q

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Column buckling strength Pc

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Flexural strength candidates:

flange local buckling

web local buckling

lateral-torsional buckling

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Mnx = minimum controlling strength

Mny = minimum controlling strength

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Beam-column interaction DCR

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Print detailed TXT report & plots

A sample graphical plot illustrating the calculation of Mnx, Mny, LTB, and the column interaction chart is shown in Fig. 3. The plots clearly show the design point for the nominal bending moment considering LTB, FLB, and WLB, and the safe region for combined axial-bending action.

Fig. 3 Graphical Plots

Reference:

JC McCormac, SD Csernak, Structural Steel Design, 5th ed., 2017 AISC 360-16