## Example

Using LRFD, determine the size of a pair of cover plates to be bolted, using fully tightened bolts, to the flanges of a W24 x 229 section as shown in Figure 4.8 so that its design strength, f cPn, will be increased by 20%. Also determine the spacing of the bolts along the longitudinal axis of the built-up column. The effective lengths of the section about the major (KL)x and minor (KL)y axes are both equal to 20 ft. A992 steel is to be used.

Determine the design strength for the W24 x 229 section: Since (KL)x = (KL)y and rx > ry, (KL/r)y will exceed (KL/r)x and the design strength will be controlled by flexural buckling about the minor axis. Using section properties, ry = 3.11 in. and A = 67.2 in.2, obtained from the AISC-LRFD Manual (AISC 2001), the slenderness parameter 1c about the minor axis can be calculated as follows:

y hV rJ\E 3 .142 y 3.11 / V 29,000 Substituting 1c = 1.02 into Equation 4.17, the design strength of the section is fcPn = 0 . 85 [67.2(0 . 6581'022)50j = 1848 kip

Determine the design strength for the built-up section: The built-up section is expected to possess a design strength that is 20% in excess of the design strength of the W24 x 229 section, so

Determine the size of the cover plates: After the cover plates are added, the resulting section is still doubly symmetric. Therefore, the overall failure mode is still flexural buckling. For flexural buckling about the minor axis (y-y), no modification to (KL/r) is required since the buckling axis is perpendicular to the plane of contact of the component shapes and so no relative movement between the adjoining parts is expected. However, for flexural buckling about the major (x-x) axis, modification to (KL/r) is required since the buckling axis is parallel to the plane of contact of the adjoining structural shapes and slippage between the component pieces will occur. We shall design the cover plates assuming flexural buckling about the minor axis will control and check for flexural buckling about the major axis later.

A W24 x 229 section has a flange width of 13.11 in.; so, as a trial, use cover plates with widths of 14 in. as shown in Figure 4.8. Denoting t as the thickness of the plates, we have

plates

AW-shape "" Aplates

c)y,built-up

0 0