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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 in. (mm)
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),
Mn: The nominal flexural strength
Mp: Plastic bending moment
My: Yield moment about the axis of bending, kip-in. (N-mm)
Sx: elastic section modulus, in.3 (mm3)
Sxc: elastic section modulus referred to the compression flange, in.3 (mm3)
Sy: elastic section modulus taken about the y-axis, in.3 (mm3)
tf: the thickness of the flange, in. (mm)
Zy = Plastic section modulus about the y-axis, in.3 (mm3)
λp: Limiting slenderness for a compact flange, defined in Table B4.1b
λr: Limiting slenderness for a noncompact flange, defined 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, flange local buckling, and local buckling of tee stems and double-angle web legs.

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  • The plastic bending moment, Mp, for tee stems and web legs in tension is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize M_p= F_%7By%7DZ_x \le 1.6M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-2) $$

The yield moment about the bending axis, My, is calculated as shown below.

Mathinline
body$$ \normalsize M_y=F_yS_x \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-3) $$

  • The plastic bending moment, Mp, for tee, stems in compression is calculated as shown below.

Mathinline
body$$ \normalsize M_p= M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-4) $$

  • The plastic bending moment, Mp, for double angles with web legs in compression is calculated as shown below.

Mathinline
body$$ \normalsize M_p= 1.5M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-5) $$

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Lateral Torsional Buckling Limit State

For stems and web legs in tension, the The lateral torsional buckling limit state is calculated as followsfor stems and web legs in tension.

  • When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply.

  • When Lp < Lb ≤ Lr

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Limiting laterally unbraced length for the limit state of yielding, Lp 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, is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize L_r =1.95 \bigg( \dfrac%7BE%7D%7BF_y%7D \bigg) \dfrac%7B\sqrt%7BI_yJ%7D%7D%7BS_x%7D \sqrt%7B2.36 \bigg( \dfrac%7BF_y%7D%7BE%7D \bigg) \dfrac%7BdS_x%7D%7BJ%7D+1 %7D \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-9) $$

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For tee stems and web legs in compression, the elastic lateral-torsional buckling moment, Mcr, and The nominal flexural strength, Mn, are calculated below.

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

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

For double-angle web legs, 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

  • The limit state of flange local buckling does not apply for tee flange sections with compact flanges in flexural compression.

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

Mathinline
body--uriencoded--$$ \normalsize M_n = \Bigg[ M_p-(M_p-0.7F_yS_%7Bxc%7D) \bigg( \dfrac%7B\lambda-\lambda_%7Bpf%7D %7D%7B\lambda_%7Brf%7D-\lambda_%7Bpf%7D%7D \bigg) \Bigg] \le 1.6M_y \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-14) $$

Mathinline
body--uriencoded--$$ \normalsize \lambda = \dfrac%7Bb_f%7D%7B2t_f%7D \; \; ; \; \; \lambda_%7Bpf%7D = \lambda_%7Bp%7D \; \; ; \; \; \lambda_%7Brf%7D = \lambda_%7Br%7D $$

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

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

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

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

The nominal flexural strength, Mn, for tee stems is calculated as shown below.

Mathinline
body--uriencoded--$$ \normalsize M_n = F_%7Bcr%7DS_x \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; \; \; \; \; \;\;\;\;\; (F9-16) $$

The critical stress, Fcr, for tee stems is calculated as shown below.

  • Mathinline
    body--uriencoded--$$ \normalsize F_%7Bcr%7D = F_y \; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathrm%7Bwhen%7D \;\; \dfrac%7Bd%7D%7Bt_w%7D \le0.84 \sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$

  • Mathinline
    body--uriencoded--$$ \normalsize F_%7Bcr%7D = \Bigg( 1.43-0.515\dfrac%7Bd%7D%7Bt_w%7D\sqrt%7B\dfrac%7BF_y%7D%7BE%7D%7D \Bigg)F_y \; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathrm%7Bwhen%7D \;\; 0.84 \sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D < \dfrac%7Bd%7D%7Bt_w%7D \le 1.52\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$

  • Mathinline
    body--uriencoded--$$ \normalsize F_%7Bcr%7D = \dfrac %7B1.52E%7D%7B (d/t_w)%5e2 %7D \; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathrm%7Bwhen%7D \;\; \dfrac%7Bd%7D%7Bt_w%7D > 1.52\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$

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

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Single Angles Flexural Design per AISC 360-16 with ideCAD