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Tip

  • For design members for flexure, sections are automatically classified as compact, noncompact, or slender-element sections, according to AISC 360-16.

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Symbols

d: depth of tee or width of web leg A: cross-sectional area of angle, in.2 (mm2)
b: width of leg, in. (mm)
Cb: The lateral-torsional buckling modification factor
E: Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
Fy: Specified minimum yield stress of the type of steel being used, ksi
h: Distance as defined in AISC 360-16 Table 4.1b
Lb: Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross-section, in. (mm)
Lp: The limiting laterally unbraced length for the limit state of yielding, in. (mm)
Lr: The limiting unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm),
Mcr: The elastic lateral-torsional buckling moment
Mn: The nominal flexural strength
Mp: Plastic bending moment
My: Yield moment about the axis of bending, kip-in. (N-mm)
Sxc: elastic section modulus , in.3 (mm3)
Sxc: elastic section modulus referred to the compression flangeto the toe in compression relative to the bending axis, in.3 (mm3)
Sy: elastic section modulus taken about the y-axis, in.3 (mm3)
tf: the thickness of the flangeangle leg, in. (mm)
Zy = Plastic section modulus about the y-βw: section property for single angles about major principal axis, in. 3 (mm3)
λp: Limiting slenderness for a compact flange, defined in Table B4.1bλr: Limiting slenderness for a noncompact flange, described in Table B4.1b

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The nominal flexural strength, Mn, should be the lower value obtained according to the limit states of yielding (plastic moment), lateral torsional buckling, and leg local buckling.

The nominal flexural strength of single-angle members is calculated by considering both the geometric axis and principal axis -es cross-sectional properties. For bending about the minor principal axis, only the Only the limit states of yielding and leg local buckling apply for bending about the minor principal axis.

Yielding Limit State

Mathinline
body$$ \normalsize M_n = 1.5M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F10-1) $$

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The nominal flexural strength, Mn, For for single angles without continuous lateral-torsional restraint along the length is calculated as shown below.

  • Mathinline
    body--uriencoded--$$ \normalsize \mathrm%7BWhen%7D \;\; \dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D \le 1.0 \; \;\;\;\;\;\;\;\;\;\; M_%7Bn%7D = \Bigg( 1.92-1.17 \sqrt%7B\dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D%7D \Bigg)M_y \le 1.5 M_y \; \;\;\;\;\;\;\;\;\;\;\;\;\; (F10-2) $$

  • Mathinline
    body--uriencoded--$$ \normalsize \mathrm%7BWhen%7D \;\; \dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D > 1.0 \; \;\;\;\;\;\;\;\;\;\; M_%7Bn%7D = \Bigg( 0.92-\dfrac%7B0.17M_%7Bcr%7D%7D%7BM_%7By%7D%7D \Bigg)M_y \; \;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\; (F10-3) $$
    When Lb ≤ Lp, the limit state of

The elastic lateral-torsional buckling

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When Lp < Lb ≤ Lr

moment, Mcr, for bending about the major principal axis of single angles is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize M_n %7Bcr%7D = M_p-(M_p-M_y) \dfrac%7B9EAr_ztC_b%7D%7B8L_b%7D \Bigg[ \sqrt%7B1+ \bigg( \dfrac%7BL_b-L_p%7D%7BL_r-L_p%7D \bigg) \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-6) $$

  • When Lb > Lr

Mathinline
body--uriencoded--$$ \normalsize M_n = M_%7Bcr%7D4.4\dfrac%7B \beta_wr_z %7D%7BL_bt%7D \bigg)%5e2 %7D +4.4\dfrac%7B \beta_wr_z %7D%7BL_bt%7D \Bigg] \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9F10-74) $$

Limiting laterally unbraced length for the limit state of yielding, Lp The elastic lateral-torsional buckling moment, Mcr, for bending about one of the geometric axes of an equal leg angle with no axial compression of single angles is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize L_p =1.76r_y \sqrt%7B \dfrac%7BE%7D%7BF_y%7D %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-8) $$

Limiting unbraced length for the limit state of inelastic lateral-torsional buckling, Lr With no lateral-torsional restraint:

  • With maximum compression at the toe, Mcr is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize

...

M_

...

%7Bcr%7D =

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\dfrac%7B0.58Eb%5e4tC_b%7D%7BL_b%5e2%7D \Bigg[ \sqrt%7B1+ 0.88\bigg(\

...

dfrac%7B L_

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bt%7D%7Bb%5e2%7D \bigg)

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%5e2 %7D -1 \Bigg] \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (

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F10-

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5a) $$

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  • With maximum tension at the toe, Mcr is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize M_%7Bcr%7D = \dfrac %7B1.95E%7D%7B L_b %7D \sqrt%7BI_yJ%7D (B+\sqrt%7B1+B%5e2%7D ) \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-10) $$
Mathinline
body--uriencoded--$$ \normalsize B =2.3 \bigg( \dfrac%7Bd%7D%7BL_b%7D \bigg) \sqrt%7B \dfrac%7BI_y%7D%7BJ%7D %7D dfrac%7B0.58Eb%5e4tC_b%7D%7BL_b%5e2%7D \Bigg[ \sqrt%7B1+ 0.88\bigg(\dfrac%7B L_bt%7D%7Bb%5e2%7D \bigg)%5e2 %7D +1 \Bigg] \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9F10-115b) $$

where

d: depth of tee or width of web leg in tension, in. (mm)

For tee stems and web legs in compression, the My should be taken as 0.80 times the yield moment calculated using the geometric section modulus.

With lateral-torsional restraint at the point of maximum moment only:

The elastic lateral-torsional buckling moment, Mcr, and The nominal flexural strength, Mn, are calculated below.

Mathinline
body--uriencoded--$$ \normalsize M_n = M_%7Bcr%7D \le M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-13) $$

Mathinline
body--uriencoded--$$ \normalsize M_%7Bcr%7D = \dfrac %7B1.95E%7D%7B L_b %7D \sqrt%7BI_yJ%7D (B+\sqrt%7B1+B%5e2%7D ) \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-10) $$

Mathinline
body--uriencoded--$$ \normalsize B =-2.3 \bigg( \dfrac%7Bd%7D%7BL_b%7D \bigg) \sqrt%7B \dfrac%7BI_y%7D%7BJ%7D %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-12) $$

where

d: depth of tee or width of web leg in compression, in. (mm)

The nominal flexural strength, Mn, is calculated for double-angle web legs given the title.

Flange Local Buckling Limit State of Tees and Double-Angle Legs

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is calculated as 1.25 times Mcr computed using Equations F10-5a or F10-5b. My should be calculated using the geometric section modulus as the yield moment.

Leg Local Buckling Limit State

  • The limit state of leg local buckling does not apply when the toe of the leg is in compression with compact section in compression.

  • The nominal flexural strength, Mn Mn, is calculated as shown below for tee flange sections with noncompact flanges in flexural compression. legs

mathinline
Mathinline
body--uriencoded--$$ \normalsize M_n =F_yS_c \Bigg[ M_p-(M_p-0.7F_yS_%7Bxc%7D) 2.43-1.72 \bigg(\dfrac%7Bdfrac%7Bb%7D%7Bt%7D \lambda-\lambda_%7Bpf%7D %7D%7B\lambda_%7Brf%7D-\lambda_%7Bpf%7D%7D \bigg) \Bigg] \le 1.6M_y bigg) \sqrt%7B \dfrac%7BF_y%7D%7BE%7D %7D \Bigg] \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9F10-146) $$
body--uriencoded--$$ \normalsize \lambda = \dfrac%7Bb_f%7D%7B2t_f%7D \; \; ; \; \; \lambda_%7Bpf%7D = \lambda_%7Bp%7D \; \; ; \; \; \lambda_%7Brf%7D = \lambda_%7Br%7D $$

  • The nominal flexural strength, Mn Mn, is calculated as shown below for tee flange sections with slender flanges in flexural compression.

Mathinline
body--uriencoded--$$ \normalsize M_%7Bn%7D = \dfrac %7B0.7ES_%7Bxc%7D%7D%7B\Big( \dfrac%7Bb%7D%7B2t_f%7D \Big)%5e2%7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-15) $$

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  • legs

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Local Buckling Limit State of Tee Stems and Double-Angle Web Legs in Flexural Compression

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  • .

Mathinline
body--uriencoded--$$ \normalsize M_n = F_%7Bcr%7DS_x c \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9F10-167) $$

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Mathinline
body--uriencoded--$$ \normalsize F_%7Bcr%7D =

...

\dfrac %7B0.71E%7D%7B (d/t)%5e2 %7D \; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;

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\;\;

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\

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; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;

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(F10-8)$$

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Single Angles Flexural Design Design of Steel Members for Shear per AISC 360-16 with ideCAD§G