Torsional and Flexural-Torsional Buckling of Members without Slender Elements per AISC 360-16 with ideCAD

How does ideCAD calculate Torsional and Flexural-Torsional Buckling of Members limit state for compression strength according to AISC 360-16?

Symbols

A_g : Gross cross-sectional area of member
C_w : Warping constant, in.⁶ (mm⁶)
E : Structural steel modulus of elasticity
F_cr : Critical stress
F_e : Elastic buckling stress determined according to Equation E3-4
F_ex : Elastic buckling stress in buckling limit state with bending around x-axis
F_ey : Elastic buckling stress in buckling limit state with bending around y-axis
F_ez : Elastic buckling stress in torsional buckling limit state z-axis
F_y : Specified minimum yield stress of the type of steel being used
G : shear modulus of elasticity of steel = 11,200 ksi (77 200 MPa)
J : Torsional constant, in.⁴ (mm⁴)
K : Effective length factor
L : Laterally unbraced length of the member
L_cy : Effective length of member for buckling about x-axis
L_cy : Effective length of member for buckling about y-axis
L_cz : Effective length of member around the z-axis (= KL)
P_n : Nominal compressive strength, kips (N)
I_x , I_y : Moment of inertia about the principal axes, in.⁴ (mm⁴)
r : Radius of inertia
r_x : radius of gyration about x-axis
r_y : radius of gyration about y-axis
x_o , y_o : coordinates of the shear center with respect to the centroid

Torsional and Flexural-Torsional Buckling of Members Without Slender Elements §E4

This section applies to singly symmetric and unsymmetric members, certain doubly symmetric members, and doubly symmetric members when the torsional unbraced length exceeds the lateral unbraced length, all without slender elements. The compressive strength of the elements is determined according to the axial force acting from the section center of gravity.

In the torsional buckling boundary case where buckling occurs by the rotation of the element around its longitudinal axis (+ shaped cross-section or open cross-section elements consisting of 4 corners placed back to back), the elastic buckling stress F_e is calculated for doubly symmetric members by Equation E4.2.

The nominal compressive strength, P_n, is determined based on the limit states of torsional and flexural-torsional buckling:

The critical stress, F_cr, is determined as follows:

• When

• When

The torsional or flexural-torsional elastic buckling stress, F_e, for doubly symmetric members twisting about the shear center is determined as follows:

The torsional or flexural-torsional elastic buckling stress, F_e, for singly symmetric members twisting about the shear center where y is the axis of symmetry is determined as follows:

For unsymmetric members twisting about the shear center, F_e is the lowest root of the cubic equation given below.