where b is the actual width of the stiffened element, t is the wall thickness, E is the modulus of elasticity, f is the computed elastic compressive stress in the stiffened elements, and D is the outside diameter of circular sections.

shapes are to act as one unit rather than as individual units), the following conditions must be satisfied:

1. Slippage of component elements near the ends of the built-up member must be prevented.

2. Adequate fasteners must be provided along the length of the member.

3. The fasteners must be able to provide sufficient gripping force on all component elements.

Condition 1 is satisfied if all component elements in contact near the ends of the built-up member are connected by a weld having a length not less than the maximum width of the member or by bolts spaced longitudinally not more than four diameters apart for a distance equal to one and a half times the maximum width of the member. Condition 2 is satisfied if continuous welds are used throughout the length of the built-up compression member. Condition 3 is satisfied if either welds or fully tightened bolts are used as the fasteners. While condition 1 is mandatory, conditions 2 and 3 can be violated in design. If condition 2 or 3 is violated, the built-up member is not fully effective and slight slippage among component elements may occur. To account for the decrease in capacity due to slippage, a modified slenderness ratio is used to compute the design compressive strength when buckling of the built-up member is about an axis coinciding or parallel to at least one plane of contact for the component shapes. The modified slenderness ratio (KL/r)m is given as follows:

If condition 2 is violated

KL r

0.82 a2

If condition 3 is violated

In the above equations, (KL/r)o = (KLlr)x if the buckling axis is the x-axis and at least one plane of contact between component elements is parallel to that axis; (KL/r)o = (KL/r)y if the buckling axis is the a be — b otherwise.

FIGURE 4.8 Design of cover plates for a compression member.

y-axis and at least one plane of contact is parallel to that axis. a is the longitudinal spacing of the fasteners, ri is the minimum radius of gyration of any component element of the built-up cross-section, rib is the radius of gyration of individual component relative to its centroidal axis parallel to the axis of buckling of the member, and h is the distance between centroids of components elements measured perpendicularly to the buckling axis of the built-up member.

No modification to (KL/r) is necessary if the buckling axis is perpendicular to the planes of contact of the component shapes. Modifications to both (KL/r)x and (KL/r)y are required if the built-up member is so constructed that planes of contact exist in both the x and y directions of the cross-section.

Once the modified slenderness ratio is computed, it is to be used in the appropriate equation to calculate Fa in allowable stress design, or f cPn in load and resistance factor design.

An additional requirement for the design of built-up members is that the effective slenderness ratio, Ka/ri, of each component element, where K is the effective length factor of the component element between adjacent fasteners, does not exceed | of the governing slenderness ratio of the built-up member. This provision is provided to prevent component element buckling between adjacent fasteners from occurring prior to overall buckling of the built-up member.

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