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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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When
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| 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
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| 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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| body | --uriencoded--$$ \normalsize F_%7Be%7D = \Bigbigg( \frac%7Bdfrac%7B\pi%5e2EC_w%7D%7BL_%7Bcz%7D%5e2%7D +GJ \Bigbigg) \frac%7B1%7D%7BIdfrac%7B1%7D%7BI_x+I_y%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-2) $$ |
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| body | --uriencoded--$$ \normalsize F_%7Be%7D = \Bigbigg( \frac%7BFdfrac%7BF_%7Bey%7D+F_%7Bez%7D%7D %7B2H%7D \Bigbigg) \Bigg[1 - \sqrt %7B1- \frac%7B4Fdfrac%7B4F_%7Bey%7DF_%7Bez%7DH%7D%7B(F_%7Bey%7D+F_%7Bez%7D)%5e2%7D %7D \; \Bigg] \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-3) $$ |
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| body | --uriencoded--$$ \normalsize (F_e-F_%7Bex%7D)(F_e-F_%7Bey%7D)(F_e-F_%7Bez%7D)- F_e%5e2(F_e-F_%7Bey%7D)\Big(\frac%7Bxdfrac%7Bx_o%7D%7B\bar%7Br%7D_o%7D \Big)%5e2 - F_e%5e2(F_e-F_%7Bex%7D)\Big(\frac%7Bydfrac%7By_o%7D%7B\bar%7Br%7D_o%7D \Big)%5e2 =0 \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; (E4-4) $$ |
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| body | --uriencoded--$$ \normalsize F_%7Bex%7D = \frac%7Bdfrac%7B\pi%5e2E%7D%7B \Bigbigg( \frac%7BLdfrac%7BL_%7Bcx%7D%7D%7Br_x%7D \Bigbigg)%5e2 %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-5) $$ |
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| body | --uriencoded--$$ \normalsize F_%7Bey%7D = \frac%7Bdfrac%7B\pi%5e2E%7D%7B \Bigbigg( \frac%7BLdfrac%7BL_%7Bcy%7D%7D%7Br_y%7D \Bigbigg)%5e2 %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-6) $$ |
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| body | --uriencoded--$$ \normalsize F_%7Bez%7D = \Bigbigg( \frac%7Bdfrac%7B\pi%5e2EC_w%7D%7BL_%7Bcz%7D%5e2%7D +GJ \Bigbigg) \frac%7B1%7D%7BAdfrac%7B1%7D%7BA_g \bar%7Br%7D_o%5e2 %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-7) $$ |
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| body | --uriencoded--$$ \normalsize H=1- \frac%7Bxdfrac%7Bx_o%5e2+y_o%5e2%7D %7B\bar%7Br%7D_o%5e2%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-8) $$ |
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| body | --uriencoded--$$ \normalsize \bar%7Br%7D_o%5e2 = x_o%5e2+y_o%5e2 + \frac%7BIdfrac%7BI_x+I_y%7D %7BA_g%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (E4-9) $$ |
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