How does ideCAD calculate Torsional and Flexural-Torsional Buckling of Single Angles And Members limit state for compression strength according to AISC 360-16?
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Ag : Gross cross-sectional area of member
Cw : Warping constant, in.6 (mm6)
E : Structural steel modulus of elasticity
Fcr : Critical stress
Fe: Elastic buckling stress determined according to Equation E3-4
Fex: Elastic buckling stress in buckling limit state with bending around x-axis
Fey: Elastic buckling stress in buckling limit state with bending around y-axis
Fez : Elastic buckling stress in torsional buckling limit state z-axis
Fy : 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
Lcy : Effective length of member for buckling about x-axis
Lcy : Effective length of member for buckling about y-axis
Lcz : Effective length of member around the z-axis (= KL)
Pn : Nominal compressive strength, kips (N)
Ix , Iy : Moment of inertia about the principal axes, in.4 (mm4)
r : Radius of inertia
rx : radius of gyration about x-axis
ry : radius of gyration about y-axis
xo , yo : coordinates of the shear center with respect to the centroid
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Torsional and Flexural-Torsional Buckling of Single Angles And Members Without Slender Elements §E4
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When
Mathinline body --uriencoded--$$ \normalsize \frac dfrac %7BL_c%7D %7Br%7D \leq 4.71 \sqrt %7B \frac%7BE%7D%7BFdfrac%7BE%7D%7BF_y%7D %7D \; \; \; \; \;\;\;\;\; \; \; \; \; (or \; \frac dfrac %7BF_y%7D %7BF_e%7D \leq 2.25) $$
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When
Mathinline body --uriencoded--$$ \normalsize \frac dfrac %7BL_c%7D %7Br%7D > 4.71 \sqrt %7B \frac%7BE%7D%7BFdfrac%7BE%7D%7BF_y%7D %7D \; \; \; \; \;\;\;\;\; \; \; \; \; (or \; \frac dfrac %7BF_y%7D %7BF_e%7D > 2.25) $$
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For unsymmetric members twisting about the shear center, Fe Fe is the lowest root of the cubic equation given below.
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Single-Angle Compression Members Steel Members with Slender Elements per AISC 360-16 with ideCAD