# Validation of AISI Design of Cold-Formed Steel Beams Using Non-Linear Finite Element Analysis
## 4 Conclusions
\begin{tabular}{l l}
**Nomenclature** & \\ \(A\) & Full, unreduced cross-sectional area of member \\ \(C_{b}\) & Bending coefficient dependent on moment gradient \\ \(C_{m}\) & Coefficient assuming no lateral translation of frame \\ \(C_{w}\) & Warping constant of torsion \\ \(E\) & Modulus of elasticity of steel \\ \(F_{ccl}\) & Elastic distortional buckling stress \\ \(F_{ccr}\) & Critical elastic flexural, torsional, or flexural-torsional buckling stress \\ \(F_{y}\) & Yield stress \\ \(G\) & Shear modulus of steel \\  & Saint-Venant's torsion constant of the cross-section (for open sections composed \\ \(J\) & of n segments of uniform thickness). \\ \(K_{d}\) & Effective length factor for distortion 0.5 \(<=\) 0.1 (bo. D.Sin\(\theta\)/ho. t)0.7 \(<=\) 8.0 \\ \(K_{t}\) & Effective length factor for twisting \\ \(K_{x}\) & Effective length factor for bending about \(x\)-axis \\ \(K_{y}\) & Effective length factor for bending about \(y\)-axis \\ \(k_{qfe}\) & Elastic rotational stiffness provided the flange \\ \(k_{qave}\) & Elastic rotational stiffness provided by the web to the flange-web juncture \\ \(k_{\phi}\) & Rotational stiffness provided by bracing to the flange-web juncture \\  & Geometric rotational stiffness demanded by the flange from the \\ \(k\)\(\sim\)\(qfe\) & Gaugetic rotational stiffness demanded by the web from the flange-web juncture \\ \(L\) & Span length \\ \(L_{b}\) & Distance between braces on individual concentrically loaded compression \\  & member to be braced \\ \(L_{cr}\) & Critical unhraced length of distortional buckling1.5 \(h_{o}\) (\(b_{o}\)\(DSin\theta\)/\(h_{o}\) t)0.6 \(<=\) 10 \(h_{o}\) \\ \(L_{ccl}\) & Critical unhraced length of distortional buckling \\ \(L_{crl}\) & Critical unhraced length of local buckling \\ \(L_{m}\) & Distance between discrete restraints that restrict distortional or shear buckling \\ \(L_{u}\) & Limit of unhraced length below which lateral-torsional buckling is not considered \\ \(L_{x}\) & Unhraced length of member for bending about \(x\)-axis \\ \(L_{y}\) & Unhraced length of member for bending about \(y\)-axis \\ \(L_{t}\) & Unhraced length of member for torsion \\ \(M_{cr}\) & \(M_{cr}\), global (lateral-torsional); \(M_{crl}\), local; or \(M_{crl}\), distortional elastic buckling \\  & moment about the axis of bending \\ \(M_{crl}\) & Distortional buckling moment \\ \(M_{crc}\) & Global buckling momentLateral-torsional buckling moment \\ \(M_{n}\) & Critical elastic local buckling moment \\ \(M_{n}\) & Nominal flexural moment \\ \(M_{nd}\) & Nominal flexural moment for distortional buckling \\ \(M_{ne}\) & Nominal flexural moment for yielding and global (lateral-torsional) buckling \\ \(M_{nl}\) & Nominal flexural moment for local buckling \\ \(M_{p}\) & Member plastic moment \\ \(M_{y}\) & Member yield moment (=\(S_{y}F_{y}\)) \\ \(M1\), \(M2\) & Smaller and larger end moments in an unhraced segment, respectively, in the \\ \(r_{o}\) & Polar radius of gyration about the shear center \\ \(r_{x}\) & Radius of gyration of full unreduced cross-section about \(x\)-axis \\ \(r_{y}\) & Radius of gyration of full unreduced cross-section about \(y\)-axis \\ \(S_{e}\) & Effective section modulus calculated relative to extreme compression or tension fiber at \(F_{y}\)orEffective section modulus calculated at extreme fiber compressive stress of \(F_{n}\) \\ \(S_{f}\) & Elastic section modulus of full unreduced section relative to extreme compression \\ \(S_{fy}\) & Elastic section modulus of full unreduced cross-section relative to extreme fiber \\ \(t\) & Base steel thickness of any element or section \\ \(Z_{f}\) & Plastic section modulus \\ \end{tabular}