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For design members for flexure, sections are automatically classified as compact, non-compact, or slender-element sections, according to AISC 360-16.
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Symbols
Fy = Specified minimum yield stress
E = Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
Mn = The nominal flexural strength
λr = Limiting width-to-thickness parameter for noncompact element
λp = Limiting width-to-thickness parameter for compact element
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The design flexural strength =
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| body | $$ \normalsize \phi_bM_n $$ |
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The allowable flexural strength =
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| body | $$ \normalsize M_n/\Omega_b $$ |
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| body | $$ \normalsize \phi_b=0.90 \;\; (LRFD) \;\;\;\;\;\;\;\;\;\; \Omega_b=1.67 \;\; (ASD) $$ |
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Bending Member Definition
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If λ ≤ λp, the element is compact,
If λp < λ ≤ λpr, the element is noncompact,
If λ > λr, the element is slender.
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TABLE B4.1b
Width-to-Thickness Ratios: Compression Elements Members Subject to Flexure |
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Case | Element Description | Width-to Thickness Ratio | Limiting Width-to-Thickness Ratio | Examples |
λp
(compact/
noncompact) | λr
(noncompact/
slender) |
10 | Flanges of rolled I-shaped sections, channels, and tees | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.38\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 1.0\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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11 | Flanges of doubly and singly symmetric I-shaped built-up sections | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.38\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 0.95\sqrt%7B\dfrac%7Bk_cE%7D%7BF_L%7D%7D $$ |
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12 | Legs of single angles | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.54\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 0.91\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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13 | Flanges of all I-shaped sections and channels in flexure about the minor axis | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.38\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 1.0\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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14 | Stems of tees | d/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.84\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 1.52\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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15 | Webs of doubly symmetric I- shaped sections and channels | h/tw | | Mathinline |
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| body | --uriencoded--$$ \normalsize 3.76\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 5.70\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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16 | Webs of singly symmetric I-shaped sections | hc/tw | | Mathinline |
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| body | --uriencoded--$$ \normalsize \frac %7B\frac%7Bh_c%7D%7Bh_p%7D \sqrt%7B\frac%7BE%7D%7BF_y%7D%7D%7D %7B \Big ( 0.54 \frac%7BM_p%7D%7BM_y%7D -0.09 \Big)%5e2 %7D $$ |
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| body | --uriencoded--$$ \normalsize 5.70\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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17 | Flanges of rectangular HSS | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 1.12\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 1.4\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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19 | Webs of rectangular HSS and box sections | h/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 2.42\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 5.70\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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20 | Round HSS | D/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 0.07 \dfrac%7BE%7D%7BF_y%7D $$ |
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| body | --uriencoded--$$ \normalsize 0.31 \dfrac%7BE%7D%7BF_y%7D $$ |
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21 | Flanges of box sections | b/t | | Mathinline |
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| body | --uriencoded--$$ \normalsize 1.12\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize 1.49\sqrt%7B\dfrac%7BE%7D%7BF_y%7D%7D $$ |
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