B4Member properties

B4.1a Unstiffened Elements

For unstiffened elements supported along only one edge parallel to the direction of the compression force, the width shall be taken as follows:

• (a) For flanges of I-shaped members and tees, the width, $b$, is one-half the full-flange width, $b_{f}$.
• (b) For legs of angles and flanges of channels and zees, the width, $b$, is the full leg or flange width.
• (c) For plates, the width, $b$, is the distance from the free edge to the first row of fasteners or line of welds.
• (d) For stems of tees, $d$ is the full depth of the section.

User Note: Refer to Table B4.1 for the graphic representation of unstiffened element dimensions.

B4.1b Stiffened Elements

For stiffened elements supported along two edges parallel to the direction of the compression force, the width shall be taken as follows:

• (a) For webs of rolled sections, $h$ is the clear distance between flanges less the fillet at each flange; $h_{c}$ is twice the distance from the centroid to the inside face of the compression flange less the fillet or corner radius.
• (b) For webs of built-up sections, $h$ is the distance between adjacent lines of fasteners or the clear distance between flanges when welds are used, and $h_{c}$ is twice the distance from the centroid to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used; $h_{p}$ is twice the distance from the plastic neutral axis to the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used.
• (c) For flange plates in built-up sections, the width, $b$, is the distance between adjacent lines of fasteners or lines of welds.

TABLE B4.1a Width-to-Thickness Ratios: Compression Elements Members Subjected to Axial Compression

Case: Unstiffened Elements Description of Element: (1) Flanges of rolled I-shaped sections (2) Plates projecting from rolled I-shaped sections (3) Outstanding legs of pairs of angles connected with continuous contact (4) Flanges of channels (5) Flanges of tees Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $0.56\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 2 Description of Element: (1) Flanges of built-up l-shaped sections (2) Plates or angle legs projecting from built-up l-shaped sections Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $0.64\sqrt{\frac{k_{c}E}{F_{y}}}$[a] Examples: <empty>

Case: 3 Description of Element: (1) Legs of single angles (2) Legs of double angles with separators (3) All other unstiffened elements Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $0.45\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 4 Description of Element: Stems of tees Width-to- Thickness Ratio: $d/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $0.75\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: Stiffened Elements Description of Element: Webs of doubly symmetric rolled and built-up I-shaped sections and channels Width-to- Thickness Ratio: $h/t_{w}$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $1.49\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 6 Description of Element: Walls of rectangular HSS Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $1.40\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 7 Description of Element: Flange cover plates between lines of fasteners or welds Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $1.40\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 8 Description of Element: All other stiffened elements Width-to- Thickness Ratio: $b/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $1.49\sqrt{\frac{E}{F_{y}}}$ Examples: <empty>

Case: 9 Description of Element: Round HSS Width-to- Thickness Ratio: $D/t$ Limiting Width-to- Thickness Ratio $\lambda_{r}$ (nonslender/ slender): $0.11\frac{E}{F_{y}}$ Examples: <empty>

$E=\operatorname{modulus}$ of elasticity of steel $=29,000 \mathrm{ksi}(200000 \mathrm{MPa})$

$F_{y}=$ specified minimum yield stress, ksi (MPa)

[a] k_c = 4/√(h/t_w), but shall not be taken as less than 0.35 nor greater than 0.76 for calculation purposes.

• (d) For flanges of rectangular hollow structural sections (HSS), the width, $b$, is the clear distance between webs less the inside corner radius on each side. For webs of rectangular HSS, $h$ is the clear distance between the flanges less the inside corner radius on each side. If the corner radius is not known, $b$ and $h$ shall be taken as the corresponding outside dimension minus three times the thickness. The thickness, $t$, shall be taken as the design wall thickness, per Section B4.2.
• (e) For flanges or webs of box sections and other stiffened elements, the width, $b$, is the clear distance between the elements providing stiffening.
• (f) For perforated cover plates, $b$ is the transverse distance between the nearest line of fasteners, and the net area of the plate is taken at the widest hole.
• (g) For round hollow structural sections (HSS), the width shall be taken as the outside diameter, D, and the thickness, t, shall be taken as the design wall thickness, as defined in Section B4.2.

$\left[\mathrm{c}^{l}\right] M_{y}$ is the moment at yielding of the extreme fiber, kip-in. (N-mm); $M_{p}=F_{y} Z_{x}$, plastic moment, kip-in.

(N-mm), where $Z_{x}=$ plastic section modulus taken about the x-axis, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

ENA = elastic neutral axis

PNA = plastic neutral axis

User Note: Refer to Table B4.1 for the graphic representation of stiffened element dimensions.

For tapered flanges of rolled sections, the thickness is the nominal value halfway between the free edge and the corresponding face of the web.

B4.3a Gross Area

The gross area, $A_{g}$, of a member is the total cross-sectional area.

B4.3b Net Area

The net area, $A_{n}$, of a member is the sum of the products of the thickness and the net width of each element computed as follows:

In computing net area for tension and shear, the width of a bolt hole shall be taken as 1/16 in. (2 mm) greater than the nominal dimension of the hole.

For a chain of bolt holes extending across a part in any diagonal or zigzag line, the net width of the part shall be obtained by deducting from the gross width the sum of the diameters or slot dimensions as provided in this section, of all holes in the chain, and adding, for each gage space in the chain, the quantity s²/4g,

where

• g = transverse center-to-center spacing (gage) between fastener gage lines, in. (mm)
• s = longitudinal center-to-center spacing (pitch) of any two consecutive bolt holes, in. (mm)

For angles, the gage for bolt holes in opposite adjacent legs shall be the sum of the gages from the back of the angles less the thickness.

For slotted HSS welded to a gusset plate, the net area, $A_{n}$, is the gross area minus the product of the thickness and the total width of material that is removed to form the slot.

In determining the net area across plug or slot welds, the weld metal shall not be considered as adding to the net area.

For members without holes, the net area, $A_{n}$, is equal to the gross area, $A_{g}$.