IShapes

struct HPShape <: AbstractRolledIShapes

HPShape in the AISC steel database.

Fields

• shape: name of the HPShape
• weight: weight of section (plf)
• area: area of wshape (inch2)
• d: depth of wshape (inch)
• b_f: width of flange (inch)
• t_w: thickness of web (inch)
• t_f: thickness of flange (inch)
• k: Distance from outer face of flange to web toe of fillet used for design (inch)
• k_1: Distance from web center line to flange toe of fillet used for detailing (inch)
• h: clear distance between flanges less the fillets (inch)
• I_x: Moment of inertia about the x-axis (inch4)
• Z_x: Plastic section modulus about the x-axis (inch3)
• S_x: Elastic section modulus about the x-axis (inch3)
• r_x: Radius of gyration about the x-axis (inch)
• I_y: Moment of inertia about the y-axis (inch4)
• Z_y: Plastic section modulus about the y-axis (inch3)
• S_y: Elastic section modulus about the y-axis (inch3)
• r_y: Radius of gyration about the y-axis (inch)
• J: Torsional constant (inch4)
• C_w: Warping constant (inch6)
• W_no: Normalized warping function, as used in Design Guide 9 (inch2)
• S_w1: Warping statical moment at point 1 on cross section, as used in AISC Design Guide 9 (inch4)
• Q_f: Statical moment for a point in the flange directly above the vertical edge of the web, as used in AISC Design Guide 9 (inch3)
• Q_w: Statical moment for a point at mid-depth of the cross section, as used in AISC Design Guide 9 (inch3)
• r_ts: Effective radius of gyration (inch)
• h_0: Distance between the flange centroids (inch)
• PA: Shape perimeter minus one flange surface (or short leg surface for a single angle), as used in Design Guide 19 (inch)
• PB: Shape perimeter, as used in AISC Design Guide 19 (inch)
• PC: Box perimeter minus one flange surface, as used in Design Guide 19 (inch)
• PD: Box perimeter, as used in AISC Design Guide 19 (inch)
• T: Distance between web toes od fillets at the top and bottom of web (inch)
• WG_i: The workable gage for the inner fastener holes in the flange that provides for entering and tightening clearances and edge distance and spacing requirements. The actual size, combination, and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. See AISC Manual Part 1 for additional information (inch)
• WG_0: The bolt spacing between inner and outer fastener holes when the workable gage is compatible with four holes across the flange. See AISC Manual Part 1 for additional information (inch)
• E: Elastic section modulus (ksi) = 29000ksi
• F_y: Yield strength(ksi) = 50ksi

HPShape(shape; E=29000ksi, F_y=50ksi, C_b=1)

Constructor for HPShape.

struct MShape <: AbstractRolledIShapes

MShape in the AISC steel database.

Fields

• shape: name of the MShape
• weight: weight of section (plf)
• area: area of wshape (inch2)
• d: depth of wshape (inch)
• b_f: width of flange (inch)
• t_w: thickness of web (inch)
• t_f: thickness of flange (inch)
• k: Distance from outer face of flange to web toe of fillet used for design (inch)
• k_1: Distance from web center line to flange toe of fillet used for detailing (inch)
• h: clear distance between flanges less the fillets (inch)
• I_x: Moment of inertia about the x-axis (inch4)
• Z_x: Plastic section modulus about the x-axis (inch3)
• S_x: Elastic section modulus about the x-axis (inch3)
• r_x: Radius of gyration about the x-axis (inch)
• I_y: Moment of inertia about the y-axis (inch4)
• Z_y: Plastic section modulus about the y-axis (inch3)
• S_y: Elastic section modulus about the y-axis (inch3)
• r_y: Radius of gyration about the y-axis (inch)
• J: Torsional constant (inch4)
• C_w: Warping constant (inch6)
• W_no: Normalized warping function, as used in Design Guide 9 (inch2)
• S_w1: Warping statical moment at point 1 on cross section, as used in AISC Design Guide 9 (inch4)
• Q_f: Statical moment for a point in the flange directly above the vertical edge of the web, as used in AISC Design Guide 9 (inch3)
• Q_w: Statical moment for a point at mid-depth of the cross section, as used in AISC Design Guide 9 (inch3)
• r_ts: Effective radius of gyration (inch)
• h_0: Distance between the flange centroids (inch)
• PA: Shape perimeter minus one flange surface (or short leg surface for a single angle), as used in Design Guide 19 (inch)
• PB: Shape perimeter, as used in AISC Design Guide 19 (inch)
• PC: Box perimeter minus one flange surface, as used in Design Guide 19 (inch)
• PD: Box perimeter, as used in AISC Design Guide 19 (inch)
• T: Distance between web toes od fillets at the top and bottom of web (inch)
• WG_i: The workable gage for the inner fastener holes in the flange that provides for entering and tightening clearances and edge distance and spacing requirements. The actual size, combination, and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. See AISC Manual Part 1 for additional information (inch)
• WG_0: The bolt spacing between inner and outer fastener holes when the workable gage is compatible with four holes across the flange. See AISC Manual Part 1 for additional information (inch)
• E: Elastic section modulus (ksi) = 29000ksi
• F_y: Yield strength(ksi) = 50ksi

MShape(shape; E=29000ksi, F_y=50ksi, C_b=1)

Constructor for MShape.

struct SShape <: AbstractRolledIShapes

SShape in the AISC steel database.

Fields

• shape: name of the SShape
• weight: weight of section (plf)
• area: area of wshape (inch2)
• d: depth of wshape (inch)
• b_f: width of flange (inch)
• t_w: thickness of web (inch)
• t_f: thickness of flange (inch)
• k: Distance from outer face of flange to web toe of fillet used for design (inch)
• k_1: Distance from web center line to flange toe of fillet used for detailing (inch)
• h: clear distance between flanges less the fillets (inch)
• I_x: Moment of inertia about the x-axis (inch4)
• Z_x: Plastic section modulus about the x-axis (inch3)
• S_x: Elastic section modulus about the x-axis (inch3)
• r_x: Radius of gyration about the x-axis (inch)
• I_y: Moment of inertia about the y-axis (inch4)
• Z_y: Plastic section modulus about the y-axis (inch3)
• S_y: Elastic section modulus about the y-axis (inch3)
• r_y: Radius of gyration about the y-axis (inch)
• J: Torsional constant (inch4)
• C_w: Warping constant (inch6)
• W_no: Normalized warping function, as used in Design Guide 9 (inch2)
• S_w1: Warping statical moment at point 1 on cross section, as used in AISC Design Guide 9 (inch4)
• Q_f: Statical moment for a point in the flange directly above the vertical edge of the web, as used in AISC Design Guide 9 (inch3)
• Q_w: Statical moment for a point at mid-depth of the cross section, as used in AISC Design Guide 9 (inch3)
• r_ts: Effective radius of gyration (inch)
• h_0: Distance between the flange centroids (inch)
• PA: Shape perimeter minus one flange surface (or short leg surface for a single angle), as used in Design Guide 19 (inch)
• PB: Shape perimeter, as used in AISC Design Guide 19 (inch)
• PC: Box perimeter minus one flange surface, as used in Design Guide 19 (inch)
• PD: Box perimeter, as used in AISC Design Guide 19 (inch)
• T: Distance between web toes od fillets at the top and bottom of web (inch)
• WG_i: The workable gage for the inner fastener holes in the flange that provides for entering and tightening clearances and edge distance and spacing requirements. The actual size, combination, and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. See AISC Manual Part 1 for additional information (inch)
• WG_0: The bolt spacing between inner and outer fastener holes when the workable gage is compatible with four holes across the flange. See AISC Manual Part 1 for additional information (inch)
• E: Elastic section modulus (ksi) = 29000ksi
• F_y: Yield strength(ksi) = 50ksi

SShape(shape; E=29000ksi, F_y=50ksi, C_b=1)

Constructor for SShape.

struct WShape <: AbstractRolledIShapes

WShape in the AISC steel database.

Fields

• shape: name of the WShape
• weight: weight of section (plf)
• area: area of wshape (inch2)
• d: depth of wshape (inch)
• b_f: width of flange (inch)
• t_w: thickness of web (inch)
• t_f: thickness of flange (inch)
• k: Distance from outer face of flange to web toe of fillet used for design (inch)
• k_1: Distance from web center line to flange toe of fillet used for detailing (inch)
• h: clear distance between flanges less the fillets (inch)
• I_x: Moment of inertia about the x-axis (inch4)
• Z_x: Plastic section modulus about the x-axis (inch3)
• S_x: Elastic section modulus about the x-axis (inch3)
• r_x: Radius of gyration about the x-axis (inch)
• I_y: Moment of inertia about the y-axis (inch4)
• Z_y: Plastic section modulus about the y-axis (inch3)
• S_y: Elastic section modulus about the y-axis (inch3)
• r_y: Radius of gyration about the y-axis (inch)
• J: Torsional constant (inch4)
• C_w: Warping constant (inch6)
• W_no: Normalized warping function, as used in Design Guide 9 (inch2)
• S_w1: Warping statical moment at point 1 on cross section, as used in AISC Design Guide 9 (inch4)
• Q_f: Statical moment for a point in the flange directly above the vertical edge of the web, as used in AISC Design Guide 9 (inch3)
• Q_w: Statical moment for a point at mid-depth of the cross section, as used in AISC Design Guide 9 (inch3)
• r_ts: Effective radius of gyration (inch)
• h_0: Distance between the flange centroids (inch)
• PA: Shape perimeter minus one flange surface (or short leg surface for a single angle), as used in Design Guide 19 (inch)
• PB: Shape perimeter, as used in AISC Design Guide 19 (inch)
• PC: Box perimeter minus one flange surface, as used in Design Guide 19 (inch)
• PD: Box perimeter, as used in AISC Design Guide 19 (inch)
• T: Distance between web toes od fillets at the top and bottom of web (inch)
• WG_i: The workable gage for the inner fastener holes in the flange that provides for entering and tightening clearances and edge distance and spacing requirements. The actual size, combination, and orientation of fastener components should be compared with the geometry of the cross section to ensure compatibility. See AISC Manual Part 1 for additional information (inch)
• WG_0: The bolt spacing between inner and outer fastener holes when the workable gage is compatible with four holes across the flange. See AISC Manual Part 1 for additional information (inch)
• E: Elastic section modulus (ksi) = 29000ksi
• F_y: Yield strength(ksi) = 50ksi

WShape(shape; E=29000ksi, F_y=50ksi, C_b=1)

Constructor for WShape.

module Compression

This module includes useful functions to calculate compression capacity of rolled i-shape sections (WShape, MShape, SShape, HPShape).

Functions

• classify_flange - classify flange for slenderness
• classify_web - classify web for slenderness
• calc_Pn - Compressive capacity of the shape

calc_Pn(shape::T, L_cx, L_cy) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes
calc_Pn(shape::T, L_cx, L_cy, λ_f, λ_rf, λ_fclass, λ_w, λ_rw, λ_wclass) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Pn of the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_cx: effective length of member for buckling about the x-axis (inch)
• L_cy: effective length of member for buckling about the y-axis (inch)
• λ_f: slenderness ratio of the flange
• λ_rf: nonslender slenderness ratio limit of the flange
• λ_fclass: nonslender or slender classification for the flange
• λ_w: slenderness ratio of the web
• λ_rw: nonslender slenderness ratio limit of the web
• λ_wclass: nonslender or slender classification for the web

Returns

• P_n: nominal compressive strength of the section (kip)

Reference

• AISC Section E3, E7

classify_flange(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies flange for compression for the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(λ_f, λ_rf, λ_fclass)

• λ_f: slenderness ratio of the flange
• λ_rf: nonslender slenderness ratio limit of the flange
• λ_fclass: nonslender or slender classification for the flange

classify_web(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies web for compression for the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(λ_w, λ_rw, λ_wclass)

• λ_w: slenderness ratio of the web
• λ_rw: nonslender slenderness ratio limit of the web
• λ_wclass: nonslender or slender classification for the web

module Flexure

This module includes useful functions to calculate bending capacity of rolled i-shape sections (WShape, MShape, SShape, HPShape).

Functions

• classify_flange_major_axis - classify flange for slenderness when bent about the x-axis
• classify_flange_minor_axis - classify flange for slenderness when bent about the y-axis
• classify_web - classify web for slnderness
• calc_Mnx - moment capacity about the x-axis
• calc_Mny - moment capacity about the y-axis

Modules

• F2 - includes functions specific for F2 sections
• F3 - includes functions specific for F3 sections
• F4 - includes functions specific for F4 sections
• F5 - includes functions specific for F5 sections
• F6 - includes functions specific for F6 sections

calc_Mnx(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mnx of the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_nx: nominal moment of the section (kip-ft)

Reference

• AISC Section F2-F5

calc_Mny(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mny of the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

• M_ny: nominal moment of the section (kip-ft)

Reference

• AISC Section F6

classify_flange_major_axis(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies flange for flexure for the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(λ_f, λ_pf, λ_rf, λ_fclass)

• 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

classify_flange_minor_axis(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies flange for flexure for the shape in minor axis bending.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(λ_f, λ_pf, λ_rf, λ_fclass)

• 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

classify_section(w::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies section for flexure for the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

• section_class: F2, F3, F4, or F5

classify_web(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function classifies web for flexure for the shape.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(λ_w, λ_pw, λ_rw, λ_wclass)

• λ_w: slenderness ratio of the web
• λ_pw: compact slenderness ratio limit of the web
• λ_rw: noncompact slenderness ratio limit of the web
• λ_wclass: compact noncompact or slender classification for the web

calc_Mn(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mn of the shape for AISC Section F2.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: nominal moment of the section (kip-ft)

Reference

• AISC Section F2

calc_variables(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates the following miscellaneous variables that are used to calculate Mn of the shape for AISC Section F2.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• 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-ft)
• 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

calc_Mn(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mn of the shape for AISC Section F3.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: nominal moment of the section (kip-ft)

Reference

• AISC Section F3

calc_variables(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates the following miscellaneous variables that are used to calculate Mn of the shape for AISC Section F3.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (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-ft)
• 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

calc_Mn(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mn of the shape for AISC Section F4.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: nominal moment of the section (kip-ft)

Reference

• AISC Section F4

calc_variables(shape::T, L_b, λ_w, λ_pw, λ_rw, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates the following miscellaneous variables that are used to calculate Mn of the shape for AISC Section F4.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

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-ft)
• M_yc: yield moment in the compression flange
• M_yt: yield moment in the tension flange
• 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

calc_Mn(shape::T, L_b, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mn of the shape for AISC Section F5.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

• M_n: nominal moment of the section (kip-ft)

Reference

• AISC Section F5

calc_variables(shape::T, L_b, λ_f, λ_pf, λ_rf, λ_fclass, C_b=1) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates the following miscellaneous variables that are used to calculate Mn of the shape for AISC Section F5.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• L_b: unbraced length (inch)
• C_b: lateral torsional buckling modification factor (default = 1)

Returns

(;M_p, R_pg, F_crLTB, F_crCFLB)

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

Reference

• AISC Section F5

calc_Mn(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates Mn of the shape for AISC Section F6.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)
• 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: nominal moment of the section (kip-ft)

Reference

• AISC Section F6

calc_variables(shape::T) where T <: AISCSteel.Shapes.IShapes.AbstractRolledIShapes

This function calculates the following miscellaneous variables that are used to calculate Mn of the shape for AISC Section F6.

Arguments

• shape: rolled i-shape section (WShape, MShape, SShape, HPShape)

Returns

(;M_p, F_cr)

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

Reference

• AISC Section F6