Chapter F - Design of Members for Flexure

module F2

This section applies to doubly symmetric I-shaped members and channels bent about their major axis, having compact webs and compact flanges as defined in Section B4.1 for flexure.

calc_Fcr(C_b, E, L_b, r_ts, J, c, S_x, h_0)

Calculates the critical stress of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• C_b: lateral torsional buckling modification factor
• E: modulous of elasticity (ksi)
• L_b: unbraced length (inch)
• r_ts:
• J: torsional constant (inch^4)
• c:
• S_x: elastic section modulous (inch^3)
• h_0: distance between the flange centroids (inch)

Returns

• F_cr: critical stress (ksi)

Reference

• AISC Section F2 (F2-4)

calc_Lp(E, F_y, r_y)

Calculates the limiting laterally unbraced length for the limit state of yielding of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• r_y: radius of gyration about the y-axis (inch)

Returns

• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)

Reference

• AISC Section F2 (F2-5)

calc_Lr(r_ts, E, F_y, J, c, S_x, h_0)

Calculates the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• r_ts:
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• r_y: radius of gyration about the y-axis (inch)
• J: torsional constant (inch^4)
• c:
• S_x: elastic section modulous (inch^3)
• h_0: distance between the flange centroids (inch)

Returns

• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)

Reference

• AISC Section F2 (F2-6)

calc_Mn(E, F_y, Z_x, S_x, r_y, h_0, J, c, r_ts, L_b, C_b=1)

Calculates the moment capacity of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• r_y: radius of gyration about the y-axis (inch)
• h_0: distance between the flange centroids (inch)
• J: torsional constant (inch^4)
• c:
• r_ts:
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F2

calc_MnFY(M_p)

Calculates the moment capacity of the applicable section for yielding.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)

Returns

• M_nFY: moment capacity of the section for yielding. (kip-in)

Reference

• AISC Section F2.1

calc_MnLTB(M_p, F_y, S_x, F_cr, L_b, L_p, L_r, C_b=1)

Calculates the moment capacity of the applicable section for lateral torsional buckling.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• F_cr: critical stress (ksi)
• L_b: unbraced length (inch)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F2.2

calc_Mp(F_y, Z_x)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)

Returns

• M_p: plastic moment of the section (kip-in)

Reference

• AISC Section F2 (F2-1)

calc_variables(E, F_y, Z_x, S_x, r_y, h_0, J, c, r_ts, L_b, C_b=1)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: Doubly symmetric compact I-shaped members and channels bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• r_y: radius of gyration about the y-axis (inch)
• h_0: distance between the flange centroids (inch)
• J: torsional constant (inch^4)
• c:
• r_ts:
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

(;M_p, L_p, L_r, F_cr)

• M_p: plastic moment of the section (kip-in)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• F_cr: critical stress (ksi)

Reference

• AISC Section F2

module F3

This section applies to doubly symmetric I-shaped members bent about their major axis having compact webs and noncompact or slender flanges as defined in Section B4.1 for flexure.

calc_Mn(E, F_y, Z_x, S_x, r_y, h_0, J, c, r_ts, L_b, h, t_w, λ_f, λ_pf, λ_rf, λ_fclass, C_b=1)

Calculates the moment capacity of the applicable section.

Description of applicable member: Doubly symmetric I-shaped members with compact webs and noncompact or slender flanges bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• r_y: radius of gyration about the y-axis (inch)
• h_0: distance between the flange centroids (inch)
• J: torsional constant (inch^4)
• c:
• r_ts:
• L_b: unbraced length (inch)
• h: clear distance between flanges less the fillets (inch)
• t_w: thickness of the web (inch)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F3

calc_MnCFLB(M_p, E, F_y, S_x, k_c, λ_f, λ_pf, λ_rf, λ_fclass)

Calculates the moment capacity of the applicable section for compression flange local buckling.

Description of applicable member: Doubly symmetric I-shaped members with compact webs and noncompact or slender flanges bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• k_c:
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange

Returns

• M_nCFLB: moment capacity of the section for compression flange local buckling. (kip-in)

Reference

• AISC Section F3.2

calc_MnLTB(M_p, F_y, S_x, F_cr, L_b, L_p, L_r, C_b=1)

Calculates the moment capacity of the applicable section for yielding.

Description of applicable member: Doubly symmetric I-shaped members with compact webs and noncompact or slender flanges bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• F_cr: critical stress (ksi)
• L_b: unbraced length (inch)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F3.1

calc_variables(E, F_y, Z_x, S_x, r_y, h_0, J, c, r_ts, L_b, h, t_w, C_b=1)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: Doubly symmetric I-shaped members with compact webs and noncompact or slender flanges bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• r_y: radius of gyration about the y-axis (inch)
• h_0: distance between the flange centroids (inch)
• J: torsional constant (inch^4)
• c:
• r_ts:
• L_b: unbraced length (inch)
• h: clear distance between flanges less the fillets (inch)
• t_w: thickness of the web (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

(;M_p, L_p, L_r, F_cr, k_c)

• M_p: plastic moment of the section (kip-in)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• F_cr: critical stress (ksi)
• k_c:

Reference

• AISC Section F3

module F4

This section applies to doubly symmetric I-shaped members bent about their major axis with noncompact webs and singly symmetric I-shaped members with webs attached to the mid-width of the flanges, bent about their major axis, with compact or noncompact webs, as defined in Section B4.1 for flexure.

calc_FL(S_xt, S_xc, F_y)

Calculates the nominal compression flange stress above which the inelastic buckling limit states apply for the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• S_xt: elastic section modulous referred to tension flange (inch^3)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• F_y: yield strength of steel (ksi)

Returns

• F_L: nominal compression flange stress above which the inelastic buckling limit states apply (ksi)

Reference

• AISC Section F4 (F4-6a through F4-6b)

calc_Fcr(C_b, E, L_b, r_t, J, S_xc, h_0)

Calculates the critical stress of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• C_b: lateral torsional buckling modification factor (default = 1)
• E: modulous of elasticity (ksi)
• L_b: unbraced length (inch)
• r_t: radius of gyration of the flange components in flexural compression plus 1/3 of the web area (inch)
• J: torsional constant (inch^4)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• h_0: distance between the flange centroids (inch)

Returns

• F_cr: critical stress (ksi)

Reference

• AISC Section F4 (F4-5)

calc_Lp(r_t, E, F_y)

Calculates the limiting laterally unbraced length for the limit state of yielding of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• r_t: radius of gyration of the flange components in flexural compression plus 1/3 of the web area (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)

Returns

• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)

Reference

• AISC Section F4 (F4-7)

calc_Lr(r_t, E, F_L, J, S_xc, h_0)

Calculates the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• r_t: radius of gyration of the flange components in flexural compression plus 1/3 of the web area (inch)
• E: modulous of elasticity (ksi)
• F_L: nominal compression flange stress above which the inelastic buckling limit states apply (ksi)
• J: torsional constant (inch^4)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• h_0: distance between the flange centroids (inch)

Returns

• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)

Reference

• AISC Section F4 (F4-8)

calc_Mn(E, F_y, Z_x, S_x, S_xc, S_xt, b_fc, t_fc, h, h_c, t_w, J, h_0, I_y, I_yc, λ_w, λ_pw, λ_rw, λ_f, λ_pf, λ_rf, λ_fclass, L_b, C_b=1)

Calculates the moment capacity of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• S_xt: elastic section modulous referred to tension flange (inch^3)
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)
• h: clear distance between flanges less the fillets (inch)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• J: torsional constant (inch^4)
• h_0: distance between the flange centroids (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• I_yc: second moment of inertia about the y-axis for the compression flange (inch^4)
• λ_w: slenderness ratio of the flange
• λ_pw: compact slenderness ratio limit of the web
• λ_rw: noncompact slenderness ratio limit of the web
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F4

calc_MnCFLB(M_p, R_pc, M_yc, F_L, S_xc, E, k_c, λ_f, λ_pf, λ_rf, λ_fclass)

Calculates the moment capacity of the applicable section for compression flange local buckling.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• R_pc: web plastification factor
• M_yc: yield moment in the compression flange
• F_L: nominal compression flange stress above which the inelastic buckling limit states apply (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• E: modulous of elasticity (ksi)
• k_c:
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange

Returns

• M_nCFLB: moment capacity of the section for compression flange local buckling. (kip-in)

Reference

• AISC Section F4.3

calc_MnCFY(R_pc, M_yc)

Calculates the moment capacity of the applicable section for compression flange yielding.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• R_pc: web plastification factor
• M_yc: yield moment in the compression flange

Returns

• M_nCFY: moment capacity of the section for compression flange yielding. (kip-in)

Reference

• AISC Section F4.1

calc_MnLTB(M_p, R_pc, M_yc, F_L, S_xc, F_cr, L_b, L_p, L_r, C_b=1)

Calculates the moment capacity of the applicable section for lateral torsional buckling.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• R_pc: web plastification factor
• M_yc: yield moment in the compression flange
• F_L: nominal compression flange stress above which the inelastic buckling limit states apply (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• F_cr: critical stress (ksi)
• L_b: unbraced length (inch)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F4.2

calc_MnTFY(M_p, R_pt, M_yt, S_xc, S_xt)

Calculates the moment capacity of the applicable section for tension flange yielding.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• R_pt: web plastification factor corresponding to the tension flange yielding limit state
• M_yt: yield moment in the tension flange
• S_xc: elastic section modulous referred to compression flange (inch^3)
• S_xt: elastic section modulous referred to tension flange (inch^3)

Returns

• M_nTFY: moment capacity of the section for tension flange yielding. (kip-in)

Reference

• AISC Section F4.4

calc_Myc(F_y, S_xc)

Calculates the yield moment in the compression flange of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• F_y: yield strength of steel (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)

Returns

• M_yc: yield moment in the compression flange (kip-in)

Reference

• AISC Section F4

calc_Myt(F_y, S_xt)

Calculates the yield moment in the tension flange of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• F_y: yield strength of steel (ksi)
• S_xt: elastic section modulous referred to tension flange (inch^3)

Returns

• M_yt: yield moment in the tension flange (kip-in)

Reference

• AISC Section F4

calc_Rpc(I_yc, I_y, h_c, t_w, λ_w, λ_pw, λ_rw, M_p, M_yc)

Calculates the web plastification factor of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• I_yc: second moment of inertia about the y-axis for the compression flange (inch^4)
• I_y: second moment of inertia about the y-axis (inch^4)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• λ_w: slenderness ratio of the flange
• λ_pw: compact slenderness ratio limit of the web
• λ_rw: noncompact slenderness ratio limit of the web
• M_p: plastic moment of the section (kip-in)
• M_yc: yield moment in the compression flange (kip-in)

Returns

• R_pc: web plastification factor

Reference

• AISC Section F4 (F4-9a through F4-9b)

calc_Rpt(I_yc, I_y, h_c, t_w, λ_w, λ_pw, λ_rw, M_p, M_yt)

Calculates the web plastification factor corresponding to the tension flange yielding limit state of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• I_yc: second moment of inertia about the y-axis for the compression flange (inch^4)
• I_y: second moment of inertia about the y-axis (inch^4)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• λ_w: slenderness ratio of the flange
• λ_pw: compact slenderness ratio limit of the web
• λ_rw: noncompact slenderness ratio limit of the web
• M_p: plastic moment of the section (kip-inch)
• M_yt: yield moment in the tension flange (kip-inch)

Returns

• R_pt: web plastification factor corresponding to the tension flange yielding limit state

Reference

• AISC Section F4 (F4-9a through F4-9b)

calc_aw(h_c, t_w, b_fc, t_fc)

Calculates a_w of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)

Returns

• a_w: see AISC F4-12

Reference

• AISC Section F4 (F4-12)

calc_rt(b_fc, a_w)

Calculates r_t of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• b_fc: width of compression flange (inch)
• a_w: see AISC F4-12

Returns

• r_t: radius of gyration of the flange components in flexural compression plus 1/3 of the web area (inch)

Reference

• AISC Section F4 (F4-11)

calc_variables(E, F_y, Z_x, S_x, S_xc, S_xt, b_fc, t_fc, h, h_c, t_w, J, h_0, I_y, I_yc, λ_w, λ_pw, λ_rw, L_b, C_b)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: Other I-shaped members with compact webs or noncompact webs bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• S_x: elastic section modulous (inch^3)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• S_xt: elastic section modulous referred to tension flange (inch^3)
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)
• h: clear distance between flanges less the fillets (inch)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• J: torsional constant (inch^4)
• h_0: distance between the flange centroids (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• I_yc: second moment of inertia about the y-axis for the compression flange (inch^4)
• λ_w: slenderness ratio of the flange
• λ_pw: compact slenderness ratio limit of the web
• λ_rw: noncompact slenderness ratio limit of the web
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor

Returns

(;M_p, M_yc, M_yt, k_c, F_cr, F_L, L_p, L_r, R_pc, R_pt)

• M_p: plastic moment of the section (kip-in)
• M_yc: yield moment in the compression flange (kip-in)
• M_yt: yield moment in the tension flange (kip-inch)
• k_c:
• F_cr: critical stress (ksi)
• F_L: nominal compression flange stress above which the inelastic buckling limit states apply (ksi)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• R_pc: web plastification factor
• R_pt: web plastification factor corresponding to the tension flange yielding limit state

Reference

• AISC Section F4

module F5

This section applies to doubly symmetric and singly symmetric I-shaped members with slender webs attached to the mid-width of the flanges and bent about their major axis as defined in Section B4.1 for flexure.

calc_FcrCFLB(E, F_y, k_c, b_fc, t_fc, λ_f, λ_pf, λ_rf, λ_fclass)

Calculates the critical stress relating to compression flange lateral buckling of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• k_c:
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange

Returns

• F_crCFLB: critical stress relating to compression flange lateral buckling (ksi)

Reference

• AISC Section F5 (F5-8 through F5-9)

calc_FcrLTB(E, F_y, C_b, L_b, L_p, L_r, r_t)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• R_pg: bending strength reduction factor
• F_y: yield strength of steel (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)

Returns

• F_crLTB: critical stress relating to lateral torsional buckling (ksi)

Reference

• AISC Section F5 (F5-3 through F5-4)

calc_Lr(r_t, E, F_y)

Calculates the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• r_t: radius of gyration of the flange components in flexural compression plus 1/3 of the web area (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)

Returns

• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)

Reference

• AISC Section F5 (F5-5)

calc_Mn(E, F_y, S_xc, S_xt, b_fc, t_fc, h, h_c, t_w, λ_f, λ_pf, λ_rf, λ_fclass, L_b, C_b=1)

Calculates the moment capacity of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• S_xt: elastic section modulous referred to tension flange (inch^3)
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)
• h: clear distance between flanges less the fillets (inch)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F5

calc_MnCFLB(R_pg, F_crCFLB, S_xc)

Calculates the moment capacity of the applicable section for compression flange lateral buckling.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• R_pg: bending strength reduction factor
• F_crCFLB: critical stress relating to compression flange lateral buckling (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)

Returns

• M_nCFLB: moment capacity of the section for compression flange lateral buckling. (kip-in)

Reference

• AISC Section F5.3

calc_MnCFY(M_p)

Calculates the moment capacity of the applicable section for compression flange yielding.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• M_p: plastic moment of the section (kip-in)

Returns

• M_nCFY: moment capacity of the section for compression flange yielding. (kip-in)

Reference

• AISC Section F5.1

calc_MnLTB(R_pg, F_crLTB, S_xc)

Calculates the moment capacity of the applicable section for lateral torsional buckling.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• R_pg: bending strength reduction factor
• F_crLTB: critical stress relating to lateral torsional buckling (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F5.2

calc_MnTFY(F_y, S_xt)

Calculates the moment capacity of the applicable section for tension flange yielding.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• F_y: yield strength of steel (ksi)
• S_xt: elastic section modulous referred to tension flange (inch^3)

Returns

• M_nTFY: moment capacity of the section for tension flange yielding. (kip-in)

Reference

• AISC Section F5.4

calc_Mp(R_pg, F_y, S_xc)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• R_pg: bending strength reduction factor
• F_y: yield strength of steel (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)

Returns

• M_p: plastic moment of the section (kip-in)

Reference

• AISC Section F5 (F5-1)

calc_Rpg(a_w, h_c, t_w, E, F_y)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• a_w: see AISC F4-12
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)

Returns

• R_pg: bending strength reduction factor

Reference

• AISC Section F5 (F5-6)

calc_variables(E, F_y, S_xc, b_fc, t_fc, h, h_c, t_w, λ_f, λ_pf, λ_rf, λ_fclass, L_b, C_b=1)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: I-shaped members with slender webs bent about their major axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• b_fc: width of compression flange (inch)
• t_fc: thickness of compression flange (inch)
• h: clear distance between flanges less the fillets (inch)
• h_c: twice the distance from the centroid to the following: (inch)
  • the inside face of the compression flange less the fillet or corner radius for rolled shapes
  • the nearest line of fasteners at the compression flange or inside face of the compression flange when welds are used for built-up sections
• t_w: thickness of the web (inch)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor

Returns

(;M_p, R_pg, F_crLTB, F_crCFLB)

• M_p: plastic moment of the section (kip-in)
• R_pg: bending strength reduction factor
• F_crLTB: critical stress relating to lateral torsional buckling (ksi)
• F_crCFLB: critical stress relating to compression flange lateral buckling (ksi)

Reference

• AISC Section F5

module F6

This section applies to I-shaped members and channels bent about ther minor axis.

calc_Fcr(E, b, t_f)

Calculates the critical stress of the applicable section.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• E: modulous of elasticity (ksi)
• b:
  • I-Shapes: half full flange width
  • C-Shapes: full nominal dimension of flange
• t_f: thickness of flange (inch)

Returns

• F_cr: critical stress (ksi)

Reference

• AISC Section F6 (F6-4)

calc_Mn(E, F_y, Z_y, S_y, b, t_f, λ_f, λ_pf, λ_rf, λ_fclass)

Calculates the moment capacity of the applicable section.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• S_y: elastic section modulous about y-axis (inch^3)
• b:
  • I-Shapes: half full flange width
  • C-Shapes: full nominal dimension of flange
• t_f: thickness of flange (inch)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F6

calc_MnFLB(M_p, F_y, S_y, λ_f, λ_pf, λ_rf, λ_fclass, F_cr)

Calculates the moment capacity of the applicable section for flange lateral buckling.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• M_p: plastic moment of the section (kip-in)
• F_y: yield strength of steel (ksi)
• S_y: elastic section modulous about y-axis (inch^3)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• F_cr: critical stress (ksi)

Returns

• M_nFLB: moment capacity of the section for flange lateral buckling. (kip-in)

Reference

• AISC Section F6.2

calc_MnFY(M_p)

Calculates the moment capacity of the applicable section for flange yielding.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• M_p: plastic moment of the section (kip-in)

Returns

• M_nFY: moment capacity of the section for compression flange yielding. (kip-in)

Reference

• AISC Section F6.1

calc_Mp(F_y, Z_y, S_y)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• F_y: yield strength of steel (ksi)
• Z_y: plastic section modulous (inch^4)
• S_y: elastic section modulous about y-axis (inch^3)

Returns

• M_p: plastic moment of the section (kip-in)

Reference

• AISC Section F6 (F6-1)

calc_variables(E, F_y, Z_y, S_y, b, t_f)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: I-shaped members or C-shaped members bent about their minor axis.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• Z_y: plastic section modulous (inch^4)
• S_y: elastic section modulous about y-axis (inch^3)
• b:
  • I-Shapes: half full flange width
  • C-Shapes: full nominal dimension of flange
• t_f: thickness of flange (inch)

Returns

(;M_p, F_cr)

• M_p: plastic moment of the section (kip-in)
• F_cr: critical stress (ksi)

Reference

• AISC Section F6

module F9

This section applies to tees and double angles loaded in the plane of symmetry.

There are two sections:

• WT - for WT shapes (WTShape, STShape, MTShape)
• DoubleAngles - for double angles

calc_Lp(E, F_y, r_y)

Calculates the limiting laterally unbraced length for the limit state of yielding of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• r_y: radius of gyration about the y-axis (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)

Returns

• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)

Reference

• AISC Section F9 (F9-8)

calc_Lr(E, F_y, I_y, J, S_x, d)

Calculates the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• S_x: elastic section modulous (inch^3)
• d: depth of the tee or leg of angle in compression

Returns

• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)

Reference

• AISC Section F2 (F9-9)

calc_Mcr(E, L_b, I_y, J, B)

Calculates M_cr of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• E: modulous of elasticity (ksi)
• L_b: unbraced length (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• B: see AISC F9

Returns

• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Reference

• AISC Section F2 (F9-10)

calc_MnY(M_p)

Calculates M_nY of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• M_p: plastic moment of the section (kip-in)

Returns

• M_nY: moment capacity of the section for yielding. (kip-in)

Reference

• AISC Section F2 (F9-3)

calc_My(F_y, S_x)

Calculates M_y of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)

Returns

• M_y: yield moment of the section bent about the respective axis (kip-in)

Reference

• AISC Section F2 (F9-3)

module WT

This section applies to tees loaded in the plane of symmetry.

There are two sections:

• Negative Bending - when tee stems are in compression
• Positive Bending - when tee stems are in tension

calc_B(d, L_b, I_y, J)

Calculates B of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• d: depth of the tee in compression
• L_b: unbraced length (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)

Returns

• B: see AISC F9

Reference

• AISC Section F9 (9-11)

calc_Mn(r_y, E, F_y, I_y, J, S_x, Z_x, d, L_b, S_xc, λ_f, λ_pf, λ_rf, λ_fclass, b_f, t_f)

Calculates the moment capacity of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• r_y: radius of gyration about the y-axis (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• S_x: elastic section modulous (inch^3)
• Z_x: plastic section modulous (inch^4)
• d: depth of the tee in compression
• L_b: unbraced length (inch)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• b_f: width of flange (inch)
• t_f: thickness of flange (inch)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F9

calc_MnFLB(M_p, F_y, S_xc, λ_f, λ_pf, λ_rf, λ_fclass, M_y, E, b_f, t_f)

Calculates the moment capacity of the applicable section for flange local buckling.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• M_p: plastic moment of the section (kip-in)
• F_y: yield strength of steel (ksi)
• S_xc: elastic section modulous referred to compression flange (inch^3)
• λ_f: slenderness ratio of the flange
• λ_pf: compact slenderness ratio limit of the flange
• λ_rf: noncompact slenderness ratio limit of the flange
• λ_fclass: compact noncompact or slender classification for the flange
• M_y: yield moment of the section bent about the respective axis (kip-in)
• E: modulous of elasticity (ksi)
• b_f: width of flange (inch)
• t_f: thickness of flange (inch)

Returns

• M_nFLB: moment capacity of the section for flange local buckling. (kip-in)

Reference

• AISC Section F9 (F9-14 through F915)

calc_MnLTB(M_p, M_y, M_cr, L_b, L_p, L_r)

Calculates the moment capacity of the applicable section for lateral torsional buckling.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• M_p: plastic moment of the section (kip-in)
• M_y: yield moment of the section bent about the respective axis (kip-in)
• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)
• L_b: unbraced length (inch)
• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F9 (F9-6 through F97)

calc_Mp(M_y)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• F_y: yield strength of steel (ksi)
• Z_x: plastic section modulous (inch^4)
• M_y: yield moment of the section bent about the respective axis (kip-in)

Returns

• M_p: plastic moment of the section (kip-in)

Reference

• AISC Section F9 (9-2)

calc_variables(r_y, E, F_y, I_y, J, S_x, Z_x, d, L_b)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• r_y: radius of gyration about the y-axis (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• S_x: elastic section modulous (inch^3)
• Z_x: plastic section modulous (inch^4)
• d: depth of the tee in compression
• L_b: unbraced length (inch)

Returns

(; Lp, Lr, Mp, My, M_cr)

• L_p: the limiting laterally unbraced length for the limit state of yielding (inch)
• L_r: the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (inch)
• M_p: plastic moment of the section (kip-in)
• M_y: yield moment of the section bent about the respective axis (kip-in)
• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Reference

• AISC Section F9

calc_B(d, L_b, I_y, J)

Calculates B of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• d: depth of the tee in compression
• L_b: unbraced length (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)

Returns

• B: see AISC F9

Reference

• AISC Section F9 (9-12)

calc_Fcr(d, t_w, E, F_y)

Calculates the critical stress of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• d: depth of the tee in compression
• t_w: thickness of the web (inch)
• E: modulous of elasticity (ksi)
• F_y: yield strength of steel (ksi)

Returns

• F_cr: critical stress (ksi)

Reference

• AISC Section F9 (9-12)

calc_Mn(F_y, S_x, d, L_b, I_y, J, t_w, E)

Calculates the moment capacity of the applicable section for local buckling of tee stems.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• d: depth of the tee in compression
• L_b: unbraced length (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• t_w: thickness of the web (inch)
• E: modulous of elasticity (ksi)

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F9

calc_MnLB(F_cr, S_x)

Calculates the moment capacity of the applicable section for local buckling of tee stems.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• F_cr: critical stress (ksi)
• S_x: elastic section modulous (inch^3)

Returns

• M_nLB: moment capacity of the section for local buckling of tee stems. (kip-in)

Reference

• AISC Section F9 (F9-16)

calc_MnLTB(M_cr, M_y)

Calculates the moment capacity of the applicable section for lateral torsional buckling.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)
• M_y: yield moment of the section bent about the respective axis (kip-in)

Returns

• M_nLTB: moment capacity of the section for lateral torsional buckling. (kip-in)

Reference

• AISC Section F9 (F9-13)

calc_Mp(M_y)

Calculates the plastic moment capacity of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• M_y: yield moment of the section bent about the respective axis (kip-in)

Returns

• M_p: plastic moment of the section (kip-in)

Reference

• AISC Section F9 (9-4)

calc_variables(F_y, S_x, d, L_b, I_y, J, t_w, E)

Calculates the intermediate variables needed to then solve for moment capacities of the applicable section.

Description of applicable member: WT-shaped member loaded in the plane of symmetry.

Arguments

• F_y: yield strength of steel (ksi)
• S_x: elastic section modulous (inch^3)
• d: depth of the tee in compression
• L_b: unbraced length (inch)
• I_y: second moment of inertia about the y-axis (inch^4)
• J: torsional constant (inch^4)
• t_w: thickness of the web (inch)
• E: modulous of elasticity (ksi)

Returns

(; Mp, My, Mcr, Fcr)

• M_p: plastic moment of the section (kip-in)
• M_y: yield moment of the section bent about the respective axis (kip-in)
• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)
• F_cr: critical stress (ksi)

Reference

• AISC Section F9

module GeometricAxisBending

LShapes bent about their geometric axis (x-axis, y-axis).

There are two sections:

• Positive Bending - when compression is in the toe of the leg
• Negative Bending - when tension is in the toe of the leg

module PositiveBending

LShapes bent about their geometric axis (x-axis, y-axis) when compression is in the toe of the leg.

calc_Mcr(E, b, t, C_b, L_b)

Calculates the elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Description of applicable member: L-shaped members bent about their geometric axis. For the geometric axis, it is assumed the legs are of equal length.

Arguments

• E: modulous of elasticity (ksi)
• b: length of leg (inch)
• t: thickness of leg (inch)
• C_b: lateral torsional buckling modification factor (default = 1)
• L_b: unbraced length (inch)

Returns

• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Reference

• AISC Section F10 (F10-5aS)

calc_positive_Mn(F_y, S_min, E, b, t, λ_class, L_b, restraint_type, C_b)

Calculates positive moment (when toe of leg is in compression) about geometric axis for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_min: elastic section modulous for desired axis (x or y) (inch^3)
• E: modulous of elasticity (ksi)
• b: length of leg perpendicular to axis of bending (inch)
• t: thickness of leg (inch)
• λ_class: slenderness classification of angle leg
• L_b: unbraced length (inch)
• restraint_type: type of restraint on leg (:fully_restrained, :unrestrained, or :at_max_moment_only)
• C_b: lateral torsional buckling modification factor

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F10

module NegativeBending

LShapes bent about their geometric axis (x-axis, y-axis) when tension is in the toe of the leg.

calc_Mcr(E, b, t, C_b, L_b)

Calculates the elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Description of applicable member: L-shaped members bent about their geometric axis. For the geometric axis, it is assumed the legs are of equal length.

Arguments

• E: modulous of elasticity (ksi)
• b: length of leg (inch)
• t: thickness of leg (inch)
• C_b: lateral torsional buckling modification factor (default = 1)
• L_b: unbraced length (inch)

Returns

• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)

Reference

• AISC Section F10 (F10-5b)

calc_negative_Mn(F_y, S_min, E, b, t, L_b, restraint_type, C_b)

Calculates negative moment (when toe of leg is in tension) about geometric axis for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_min: elastic section modulous for desired axis (x or y) (inch^3)
• E: modulous of elasticity (ksi)
• b: length of leg perpendicular to axis of bending (inch)
• t: thickness of leg (inch)
• L_b: unbraced length (inch)
• restraint_type: type of restraint on leg (:fully_restrained, :unrestrained, or :at_max_moment_only)
• C_b: lateral torsional buckling modification factor

Returns

• M_n: moment capacity of the section. (kip-in)

Reference

• AISC Section F10

module PrincipalAxisBending

LShapes bent about their principal axis (w-axis, z-axis).

There are two sections:

• Major Axis - LShapes bent about their w-axis
• Minor Axis - LShapes bent about their z-axis

calc_Mcr(E, A_g, r_z, t, C_b, L_b, β_w)

Calculates the elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-ft)

Description of applicable member: L-shaped members bent about their principal axis.

Arguments

• E: modulous of elasticity (ksi)
• A_g: gross section area of lshape (inch^2)
• r_z: radius of gyration about the minor principal axis (inch)
• t: thickness of leg (inch)
• C_b: lateral torsional buckling modification factor (default = 1)
• L_b: unbraced length (inch)
• β_w: section property for single angles about major principal axis (inch)

Returns

• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-ft)

Reference

• AISC Section F10 (F10-4)

module MajorAxis

LShapes bent about their principal major axis (w-axis).

There are two sections:

• Positive Bending - when compression is in the short leg
• Negative Bending - when compression is in the long leg

calc_variables(F_y, S_min, E, A_g, r_z, t, β_w, b, L_b, C_b)

Calculates the intermediate variables needed to then solve for moment capacities of the LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_min: elastic section modulous for desired axis (x or y) (inch^3)
• E: modulous of elasticity (ksi)
• A_g: gross section area of lshape (inch^2)
• r_z: radius of gyration about the minor principal axis (inch)
• t: thickness of leg (inch)
• β_w: section property for single angles about major principal axis (inch)
• b: length of leg in compression (long leg) (inch)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

(;M_y, M_cr, F_cr)

• M_y: yield moment of the section bent about the respective axis (kip-in)
• M_cr: elastic lateral-torsional buckling moment of the section bent about the respective axis (kip-in)
• F_cr: critical stress (ksi)

Reference

• AISC Section F10

module PositiveBending

LShapes bent about their principal major axis (w-axis) when compression is in the short leg.

calc_positive_Mnw(F_y, S_wC, E, A_g, r_z, t, β_w , b, S_c, λ_class, L_b, C_b)
calc_positive_Mnw(lshape, λ_class, L_b, C_b)
calc_positive_Mnw(lshape, L_b, C_b)

Calculates positive moment about major principal axis when compression is in the short leg for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_wC: elastic section modulous about w-axis for Point C (see aisc-shapes-database-v16.0) (inch^3)
• E: modulous of elasticity (ksi)
• A_g: gross section area of lshape (inch^2)
• r_z: radius of gyration about the minor principal axis (inch)
• t: thickness of leg (inch)
• β_w: section property for single angles about major principal axis (inch)
• b: length of leg in compression (short leg) (inch)
• S_c: elastic section modulous to the toe in compression relative to the axis of bending (inch^3)
• λ_class: slenderness classification of angle leg
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nw: moment capacity of the section about the w-axis. (kip-in)

Reference

• AISC Section F10

module NegativeBending

LShapes bent about their principal major axis (w-axis) when compression is in the long leg.

calc_negative_Mnw(F_y, S_wC, E, A_g, r_z, t, β_w , b, S_c, λ_class, L_b, C_b)
calc_negative_Mnw(lshape, λ_class, L_b, C_b)
calc_negative_Mnw(lshape, L_b, C_b)

Calculates negative moment about major principal axis when compression is in the long leg for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_wC: elastic section modulous about w-axis for Point C (see aisc-shapes-database-v16.0) (inch^3)
• E: modulous of elasticity (ksi)
• A_g: gross section area of lshape (inch^2)
• r_z: radius of gyration about the minor principal axis (inch)
• t: thickness of leg (inch)
• β_w: section property for single angles about major principal axis (inch)
• b: length of leg in compression (long leg) (inch)
• S_c: elastic section modulous to the toe in compression relative to the axis of bending (inch^3)
• λ_class: slenderness classification of angle leg
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nw: moment capacity of the section about the w-axis. (kip-in)

Reference

• AISC Section F10

module MinorAxis

LShapes bent about their principal minor axis (z-axis).

There are two sections:

• Positive Bending - when tension is in the toe of the legs
• Negative Bending - when compression is in the toe of the legs

module PositiveBending

LShapes bent about their principal minor axis (z-axis) when tension is in the toe of the legs.

calc_positive_Mnz(F_y, S_min)
calc_positive_Mnz(lshape)

Calculates positive moment about the minor principal axis when tension is in the toe of the legs for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_min: minimum elastic section modulous about z-axis (inch^3)

Returns

• M_nz: moment capacity of the section about the z-axis. (kip-in)

Reference

• AISC Section F10

module NegativeBending

LShapes bent about their principal minor axis (z-axis) when compression is in the toe of the legs.

calc_negative_Mnz(F_y, S_min, E, b, t, S_c, λ_class)
calc_negative_Mnz(lshape, λ_class)
calc_negative_Mnz(lshape)

Calculates negative moment about the minor principal axis when compression is in the toe of the legs for an LShape.

Arguments

• F_y: yield strength of steel (ksi)
• S_min: minimum elastic section modulous about z-axis (inch^3)
• E: modulous of elasticity (ksi)
• b: length of leg in compression (long leg) (inch)
• t: thickness of leg (inch)
• S_c: elastic section modulous to the toe in compression relative to the axis of bending (inch^3)
• λ_class: slenderness classification of angle leg

Returns

• M_nz: moment capacity of the section about the z-axis. (kip-in)

Reference

• AISC Section F10