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Chapter E - Design of Members for Compression

This chapter applies to members subject to axial compression.

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.calc_Fe — Method
calc_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)
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AISCSteel.ChapterECompression.E3.calc_Fn — Method
calc_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
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AISCSteel.ChapterECompression.E3.calc_Pn — Method
calc_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)
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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 — Module
module 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 $b/t > 0.71*sqrt{E/F_y}$

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AISCSteel.ChapterECompression.E4.calc_Fex — Method
calc_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)
source
AISCSteel.ChapterECompression.E4.calc_Fey — Method
calc_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)
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AISCSteel.ChapterECompression.E4.calc_Fez — Method
calc_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)
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AISCSteel.ChapterECompression.E4.calc_H — Method
calc_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)
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AISCSteel.ChapterECompression.E4.calc_Pn — Method
calc_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)
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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.calc_Ae — Method
calc_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 is d; for webs this is h)
  • 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
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AISCSteel.ChapterECompression.E7.calc_Fel — Method
calc_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 factor
  • λ_r: onslender slenderness ratio limit
  • λ: slenderness ratio
  • F_y: yield strength of steel (ksi)

Returns

  • F_el: elastic local buckling stress (ksi)

Reference

  • AISC Section E7 (F7-5)
source
AISCSteel.ChapterECompression.E7.calc_Pn — Method
calc_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)
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AISCSteel.ChapterECompression.E7.calc_be — Method
calc_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 ratio
  • λ_r: onslender slenderness ratio limit
  • F_y: yield strength of steel (ksi)
  • F_n: nominal stress (ksi)
  • c_1: effective width imprtfection adjustment factor
  • F_el: elastic local buckling stress (ksi)

Returns

  • b_e: effective width for slender elements (inch)

Reference

  • AISC Section E7 (F7-2 and E7-3)
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