Chapter E - Design of Members for Compression
This chapter applies to members subject to axial compression.
- E1. General Provisions
- E2. Effective Length
- E3. Flexural Buckling of Members without Slender Elements
- E4. Torsional and Flexural-Torsional Buckling of Single Angles and Members without Slender Elements
- E5. Single Angle Compression Members
- E6. Built-Up Members
- E7. Members with Slender Elements
E1. General Provisions
The design compressive strength, ${\phi}_c P_{n}$, and the allowable compressive strength, $P_n/{\Omega}_c$, are determined as follows.
The nominal compressive strength, $P_n$ shall be the lowest value obtained based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling.
$ {\phi}_c = 0.90 \text{(LRFD)} $
E2. Effective Length
The effective length, $L_c$, for calculatios of member slenderness, $L_c/r$, shall be determined in accordance with Chapter C or Appendix 7.
E3. Flexural Buckling of Members without Slender Elements
This section applies to nonslender-element compression members, as defined in Section B4.1, for elements in axial compression.
AISCSteel.ChapterECompression.E3
— Modulemodule E3
This section applies to nonslender element compression members, as defined in Section B4.1, for elements in axial compression.
AISCSteel.ChapterECompression.E3.calc_Fe
— Methodcalc_Fe(E, L_c, r)
Calculates the elastic buckling stress of the applicable section.
Description of applicable member: member without slender elements.
Arguments
E
: modulous of elasticity (ksi)L_c
: effective length of member (inch)r
: radius of gyration (inch)
Returns
F_e
: elastic buckling stress (ksi)
Reference
- AISC Section E3 (E3-4)
AISCSteel.ChapterECompression.E3.calc_Fn
— Methodcalc_Fn(L_c, r, F_y, F_e)
calc_Fn(F_y, F_e)
Calculates the nominal stress of the applicable section.
Description of applicable member: member without slender elements.
Arguments
L_c
: effective length of member (inch)r
: radius of gyration (inch)F_y
: yield strength of steel (ksi)F_e
: elastic buckling stress (ksi)
Returns
F_n
: nominal stress (ksi)
Reference
- AISC Section E3
AISCSteel.ChapterECompression.E3.calc_Pn
— Methodcalc_Pn(F_n, A_g)
calc_Pn(E, L_c, r, F_y, A_g)
Calculates the nominal compressive strength for flexural buckling of the applicable section.
Description of applicable member: member without slender elements.
Arguments
F_n
: nominal stress (ksi)A_g
: gross area of member (inch^2)
Returns
P_n
: nominal compressive strength for flexural buckling (kip)
Reference
- AISC Section E3 (E3-1)
E4. Torsional and Flexural-Torsional Buckling of Single Angles and Members without Slender Elements
This section applies to singly symmetric and unsymmetric members, certain doubly symmetric members, such as cruciform or built-up members, and doubly symmetric members when the torsional unbraced length exceeds the lateral unbraced length, all without slender elements. These provisions also apply to single angles with $b/t > 0.71\sqrt{E/F_y}$ , where $b$ is the width of the longest leg and $t$ is the thickness.
AISCSteel.ChapterECompression.E4
— Modulemodule E4
This section applies to singly symmetric and unsymmetric members, certain doubly symmetric members, such as cruciform or built-up members, and doubly symmetric members when the torsional unbraced length exceeds the lateral unbraced length, all without slender elements. These provisions also apply to single angles with $b/t > 0.71*sqrt{E/F_y}$
AISCSteel.ChapterECompression.E4.calc_Fex
— Methodcalc_Fex(E, L_cx, r_x)
Calculates the elastic buckling stress of the applicable section about the x-axis.
Description of applicable member: member without slender elements.
Arguments
E
: modulous of elasticity (ksi)L_cx
: effective length of member for buckling about the x-axis (inch)r_x
: radius of gyration about the x-axis (inch)
Returns
F_ex
: elastic buckling stress about the x-axis (ksi)
Reference
- AISC Section E4 (E4-5)
AISCSteel.ChapterECompression.E4.calc_Fey
— Methodcalc_Fey(E, L_cy, r_y)
Calculates the elastic buckling stress of the applicable section about the y-axis.
Description of applicable member: member without slender elements.
Arguments
E
: modulous of elasticity (ksi)L_cy
: effective length of member for buckling about the y-axis (inch)r_y
: radius of gyration about the y-axis (inch)
Returns
F_ey
: elastic buckling stress about the y-axis (ksi)
Reference
- AISC Section E4 (E4-6)
AISCSteel.ChapterECompression.E4.calc_Fez
— Methodcalc_Fez(E, C_w, L_cz, G, J, A_g, r̄_0)
Calculates the elastic buckling stress of the applicable section about the z-axis.
Description of applicable member: member without slender elements.
Arguments
E
: modulous of elasticity (ksi)C_w
: warping constant (inch^6)G
: shear modulus elasticity of steel (ksi)J
: torsional constant (inch^4)A_g
: gross area of member (inch^2)r̄_0
: polar radius of gyration about the shear center (inch)
Returns
F_ez
: elastic buckling stress about the z-axis (ksi)
Reference
- AISC Section E4 (E4-7)
AISCSteel.ChapterECompression.E4.calc_H
— Methodcalc_H(x_0, y_0, r̄_0)
Calculates the flexural constant.
Description of applicable member: member without slender elements.
Arguments
x_0
: x-coordinate of the shear center with respect to the centroid (inch)y_0
: y-coordinate of the shear center with respect to the centroid (inch)r̄_0
: polar radius of gyration about the shear center (inch)
Returns
H
: flexural constant
Reference
- AISC Section E4 (E4-8)
AISCSteel.ChapterECompression.E4.calc_Pn
— Methodcalc_Pn(F_n, A_g)
Calculates the nominal compressive strength for flexural buckling of the applicable section.
Description of applicable member: member without slender elements.
Arguments
F_n
: nominal stress (ksi)A_g
: gross area of member (inch^2)
Returns
P_n
: nominal compressive strength for flexural buckling (kip)
Reference
- AISC Section E4 (E4-1)
E5. Single Angle Compression Members
This section is not implemented.
E6. Built-Up Members
This section is not implemented.
E7. Members with Slender Elements
This section applies to slender-element compression members, as defined in Section B4.1 for elements in axial compression.
AISCSteel.ChapterECompression.E7
— Modulemodule E7
This section applies to slender element compression members, as defined in Section B4.1 for elements in axial compression.
AISCSteel.ChapterECompression.E7.calc_Ae
— Methodcalc_Ae(A_g, b, b_e, t)
Calculates the effective area for slender elements of the applicable section.
Description of applicable member: member with slender elements.
Arguments
A_g
: gross area of member (inch^2)b
width of element (for tees this isd
; for webs this ish
)b_e
: effective width for slender elements (inch)t
: thickness of element
Returns
A_e
: effective area of member (inch^2)
Reference
- AISC Section E7
AISCSteel.ChapterECompression.E7.calc_Fel
— Methodcalc_Fel(c_2, λ_r, λ, F_y)
Calculates the elastic local buckling stress of the applicable section.
Description of applicable member: member with slender elements.
Arguments
c_2
: second effective width imprtfection adjustment factorλ_r
: onslender slenderness ratio limitλ
: slenderness ratioF_y
: yield strength of steel (ksi)
Returns
F_el
: elastic local buckling stress (ksi)
Reference
- AISC Section E7 (F7-5)
AISCSteel.ChapterECompression.E7.calc_Pn
— Methodcalc_Pn(F_n, A_e)
Calculates the nominal compressive strength for local buckling of the applicable section.
Description of applicable member: member with slender elements.
Arguments
F_n
: nominal stress (ksi)A_e
: effective area of member (inch^2)
Returns
P_n
: nominal compressive strength for local buckling (kip)
Reference
- AISC Section E7 (E7-1)
AISCSteel.ChapterECompression.E7.calc_be
— Methodcalc_be(λ, λ_r, F_y, F_n, c_1, F_el)
Calculates the effective width for slender elements of the applicable section.
Description of applicable member: member with slender elements.
Arguments
λ
: slenderness ratioλ_r
: onslender slenderness ratio limitF_y
: yield strength of steel (ksi)F_n
: nominal stress (ksi)c_1
: effective width imprtfection adjustment factorF_el
: elastic local buckling stress (ksi)
Returns
b_e
: effective width for slender elements (inch)
Reference
- AISC Section E7 (F7-2 and E7-3)