Chapter F - Design of Members for Flexure
This chapter applies to members subject to simple bending about one principal axis. For simple bending, the member is loaded in a plane parallel to a principal axis that passes through the shear center or is restrained against twisting at load points and supports.
- F1. General Provisions
- F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent about Their Major Axis
- F3. Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact or Slender Flanges Bent about Their Major Axis
- F4. Other I-Shaped Members with Compact or Noncompact Webs Bent about Their Major Axis
- F5. Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent about Their Major Axis
- F6. I-Shaped Members and Channels Bent about Their Minor Axis
- F7. Square and Rectangular HSS and Box Sections
- F8. Round HSS
- F9. Tees and Double Angles Loaded in the Plane of Symmetry
- F10. Single Angles
- F11. Rectangular Bars and Rounds
- F12. Unsymmetrical Shapes
- F13. Proportions of Beams and Girders
F1. General Provisions
F2. Doubly Symmetric Compact I-Shaped Members and Channels Bent about Their Major Axis
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.
AISCSteel.ChapterFFlexure.F2
— Modulemodule 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.
AISCSteel.ChapterFFlexure.F2.calc_Fcr
— Methodcalc_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 factorE
: 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)
AISCSteel.ChapterFFlexure.F2.calc_Lp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F2.calc_Lr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F2.calc_Mn
— Functioncalc_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
AISCSteel.ChapterFFlexure.F2.calc_MnFY
— Methodcalc_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
AISCSteel.ChapterFFlexure.F2.calc_MnLTB
— Functioncalc_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
AISCSteel.ChapterFFlexure.F2.calc_Mp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F2.calc_variables
— Functioncalc_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
F3. Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact or Slender Flanges Bent about Their Major Axis
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.
AISCSteel.ChapterFFlexure.F3
— Modulemodule 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.
AISCSteel.ChapterFFlexure.F3.calc_Mn
— Functioncalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeC_b
: lateral torsional buckling modification factor (default = 1)
Returns
M_n
: moment capacity of the section. (kip-in)
Reference
- AISC Section F3
AISCSteel.ChapterFFlexure.F3.calc_MnCFLB
— Methodcalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flange
Returns
M_nCFLB
: moment capacity of the section for compression flange local buckling. (kip-in)
Reference
- AISC Section F3.2
AISCSteel.ChapterFFlexure.F3.calc_MnLTB
— Functioncalc_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
AISCSteel.ChapterFFlexure.F3.calc_variables
— Functioncalc_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
F4. Other I-Shaped Members with Compact or Noncompact Webs Bent about Their Major Axis
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.
AISCSteel.ChapterFFlexure.F4
— Modulemodule 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.
AISCSteel.ChapterFFlexure.F4.calc_FL
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_Fcr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_Lp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_Lr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_Mn
— Methodcalc_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 flangeλ_pw
: compact slenderness ratio limit of the webλ_rw
: noncompact slenderness ratio limit of the webλ_f
: slenderness ratio of the flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeL_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
AISCSteel.ChapterFFlexure.F4.calc_MnCFLB
— Methodcalc_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 factorM_yc
: yield moment in the compression flangeF_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flange
Returns
M_nCFLB
: moment capacity of the section for compression flange local buckling. (kip-in)
Reference
- AISC Section F4.3
AISCSteel.ChapterFFlexure.F4.calc_MnCFY
— Methodcalc_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 factorM_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
AISCSteel.ChapterFFlexure.F4.calc_MnLTB
— Functioncalc_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 factorM_yc
: yield moment in the compression flangeF_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
AISCSteel.ChapterFFlexure.F4.calc_MnTFY
— Methodcalc_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 stateM_yt
: yield moment in the tension flangeS_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
AISCSteel.ChapterFFlexure.F4.calc_Myc
— Methodcalc_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
AISCSteel.ChapterFFlexure.F4.calc_Myt
— Methodcalc_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
AISCSteel.ChapterFFlexure.F4.calc_Rpc
— Methodcalc_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 flangeλ_pw
: compact slenderness ratio limit of the webλ_rw
: noncompact slenderness ratio limit of the webM_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)
AISCSteel.ChapterFFlexure.F4.calc_Rpt
— Methodcalc_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 flangeλ_pw
: compact slenderness ratio limit of the webλ_rw
: noncompact slenderness ratio limit of the webM_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)
AISCSteel.ChapterFFlexure.F4.calc_aw
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_rt
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F4.calc_variables
— Methodcalc_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 flangeλ_pw
: compact slenderness ratio limit of the webλ_rw
: noncompact slenderness ratio limit of the webL_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 factorR_pt
: web plastification factor corresponding to the tension flange yielding limit state
Reference
- AISC Section F4
F5. Doubly Symmetric and Singly Symmetric I-Shaped Members with Slender Webs Bent about Their Major Axis
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.
AISCSteel.ChapterFFlexure.F5
— Modulemodule 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.
AISCSteel.ChapterFFlexure.F5.calc_FcrCFLB
— Methodcalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
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)
AISCSteel.ChapterFFlexure.F5.calc_FcrLTB
— Methodcalc_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 factorF_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)
AISCSteel.ChapterFFlexure.F5.calc_Lr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F5.calc_Mn
— Functioncalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeL_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
AISCSteel.ChapterFFlexure.F5.calc_MnCFLB
— Methodcalc_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 factorF_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
AISCSteel.ChapterFFlexure.F5.calc_MnCFY
— Methodcalc_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
AISCSteel.ChapterFFlexure.F5.calc_MnLTB
— Methodcalc_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 factorF_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
AISCSteel.ChapterFFlexure.F5.calc_MnTFY
— Methodcalc_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
AISCSteel.ChapterFFlexure.F5.calc_Mp
— Methodcalc_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 factorF_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)
AISCSteel.ChapterFFlexure.F5.calc_Rpg
— Methodcalc_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 F4-12h_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)
AISCSteel.ChapterFFlexure.F5.calc_variables
— Functioncalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeL_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 factorF_crLTB
: critical stress relating to lateral torsional buckling (ksi)F_crCFLB
: critical stress relating to compression flange lateral buckling (ksi)
Reference
- AISC Section F5
F6. I-Shaped Members and Channels Bent about Their Minor Axis
This section applies to I-shaped members and channels bent about ther minor axis.
AISCSteel.ChapterFFlexure.F6
— Modulemodule F6
This section applies to I-shaped members and channels bent about ther minor axis.
AISCSteel.ChapterFFlexure.F6.calc_Fcr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F6.calc_Mn
— Methodcalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flange
Returns
M_n
: moment capacity of the section. (kip-in)
Reference
- AISC Section F6
AISCSteel.ChapterFFlexure.F6.calc_MnFLB
— Methodcalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeF_cr
: critical stress (ksi)
Returns
M_nFLB
: moment capacity of the section for flange lateral buckling. (kip-in)
Reference
- AISC Section F6.2
AISCSteel.ChapterFFlexure.F6.calc_MnFY
— Methodcalc_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
AISCSteel.ChapterFFlexure.F6.calc_Mp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F6.calc_variables
— Methodcalc_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
F7. Square and Rectangular HSS and Box Sections
This section is not implemented.
F8. Round HSS
This section is not implemented.
F9. Tees and Double Angles Loaded in the Plane of Symmetry
This section applies to tees and double angles loaded in the plane of symmetry.
AISCSteel.ChapterFFlexure.F9
— Modulemodule 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
AISCSteel.ChapterFFlexure.F9.calc_Lp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.calc_Lr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.calc_Mcr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.calc_MnY
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.calc_My
— Methodcalc_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)
WT Shapes
AISCSteel.ChapterFFlexure.F9.WT
— Modulemodule 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
Positive Bending
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_B
— Methodcalc_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 compressionL_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)
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_Mn
— Methodcalc_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 compressionL_b
: unbraced length (inch)S_xc
: elastic section modulous referred to compression flange (inch^3)λ_f
: slenderness ratio of the flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeb_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
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_MnFLB
— Methodcalc_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 flangeλ_pf
: compact slenderness ratio limit of the flangeλ_rf
: noncompact slenderness ratio limit of the flangeλ_fclass
:compact
noncompact
orslender
classification for the flangeM_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)
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_MnLTB
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_Mp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.WT.PositiveBending.calc_variables
— Methodcalc_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 compressionL_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
Negative Bending
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_B
— Methodcalc_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 compressionL_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)
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_Fcr
— Methodcalc_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 compressiont_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)
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_Mn
— Methodcalc_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 compressionL_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
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_MnLB
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_MnLTB
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_Mp
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F9.WT.NegativeBending.calc_variables
— Methodcalc_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 compressionL_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
F10. Single Angles
This section applies to single angles with and without continuous lateral restraint along their length.
Geometric Axis Bending
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending
— Modulemodule 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
Positive Bending
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.PositiveBending
— Modulemodule PositiveBending
LShapes bent about their geometric axis (x-axis, y-axis) when compression is in the toe of the leg.
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.PositiveBending.calc_Mcr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.PositiveBending.calc_positive_Mn
— Methodcalc_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 legL_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
Negative Bending
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.NegativeBending
— Modulemodule NegativeBending
LShapes bent about their geometric axis (x-axis, y-axis) when tension is in the toe of the leg.
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.NegativeBending.calc_Mcr
— Methodcalc_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)
AISCSteel.ChapterFFlexure.F10.GeometricAxisBending.NegativeBending.calc_negative_Mn
— Methodcalc_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
Principal Axis Bending
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending
— Modulemodule 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
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.calc_Mcr
— Methodcalc_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)
Major Axis
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis
— Modulemodule 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
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis.calc_variables
— Methodcalc_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
Positive Bending
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis.PositiveBending
— Modulemodule PositiveBending
LShapes bent about their principal major axis (w-axis) when compression is in the short leg.
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis.PositiveBending.calc_positive_Mnw
— Methodcalc_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 legL_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
Negative Bending
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis.NegativeBending
— Modulemodule NegativeBending
LShapes bent about their principal major axis (w-axis) when compression is in the long leg.
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MajorAxis.NegativeBending.calc_negative_Mnw
— Methodcalc_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 legL_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
Minor Axis
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MinorAxis
— Modulemodule 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
Positive Bending
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MinorAxis.PositiveBending
— Modulemodule PositiveBending
LShapes bent about their principal minor axis (z-axis) when tension is in the toe of the legs.
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MinorAxis.PositiveBending.calc_positive_Mnz
— Methodcalc_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
Negative Bending
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MinorAxis.NegativeBending
— Modulemodule NegativeBending
LShapes bent about their principal minor axis (z-axis) when compression is in the toe of the legs.
AISCSteel.ChapterFFlexure.F10.PrincipalAxisBending.MinorAxis.NegativeBending.calc_negative_Mnz
— Methodcalc_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
F11. Rectangular Bars and Rounds
This section is not implemented.
F12. Unsymmetrical Shapes
This section is not implemented.
F13. Proportions of Beams and Girders
This section is not implemented.