7.1Design Strength

7.1.2.1

The design compressive stress, $f_{\mathrm{cd}}$, of axially loaded compression members shall be calculated using the following equation:

where

• $\phi=0.5\left[1+\alpha(\lambda-0.2)+\lambda^{2}\right]$
• $\lambda \quad=$ non-dimensional effective slenderness ratio

$=\sqrt{f_{y} / f_{c c}}=\sqrt{f_{y}}\left(\frac{\mathrm{KL}}{r}\right)^{2} / \pi^{2} E$

$f_{c c}=\text { Euler buckling stress }=\frac{\pi^{2} E}{\left(K L / r\right)^{2}}$

where

• $K L / r=$ effective slenderness ratio or ratio of effective length, $K L$ to appropriate radius of gyration, $r$;
• $\alpha \quad=$ imperfection factor given in Table 7;
• $\begin{aligned} \chi & =\text { stress reduction factor (see Table 8) } \\ & \text { for different buckling class, } \\ & \text { slenderness ratio and yield stress }\end{aligned}$

$=\frac{1}{\left[\phi+\left(\phi^{2}-\lambda^{2}\right)^{0.5}\right]}$

$\begin{aligned} \lambda_{\mathrm{m} 0} & =\text { partial safety factor for material } \\ & \text { strength. }\end{aligned}$

Figure description:

FIG. 7 BLOCK SHEAR FAILURE

• 7A Plate: Illustrates block shear failure in a flat steel plate.

  • Entities: Four bolts (labeled 1-4 in a rectangular pattern.
  • Mechanism: Tensile force pulls a block of material out. Dashed lines indicate failure paths: longitudinal shear planes through bolt holes and a transverse tension plane between bolts 2 and 3.
  • Force Diagram: Small inset shows shear forces acting along the sides and tension acting at the rear of the failing block.

• 7B Angle: Illustrates block shear failure in an L-shaped angle section.

  • Entities: Four bolts (labeled 1-4 positioned on one leg of the angle.
  • Mechanism: Tension causes failure along a path through the bolts to the edge of the section.
  • Force Diagram: Inset shows the combination of shear along the longitudinal bolt line and tension across the path leading to the member's edge.

FIG. 7 BLOCK SHEAR FAILURE

NOTE — Calculated values of design compressive stress, $f_{\mathrm{cd}}$ for different buckling classes are given in Table 9.

7.1.2.2

The classification of different sections under different buckling class a, b, c or d, is given in Table 10. The stress reduction factor $\chi$, and the design compressive stress $f_{\mathrm{cd}}$, for different buckling class, yield stress, and effective slenderness ratio is given in Table 8 for convenience. The curves corresponding to different buckling class are presented in non-dimensional form, in Fig. 8.

Table 7 Imperfection Factor, $\alpha$

(Clauses 7.1.1 and 7.1.2.1)