C-L2L2 Deflections

Excessive vertical deflections and misalignment arise primarily from three sources: (a) gravity loads, such as dead, live, and snow loads; (b) effects of temperature, creep, and differential settlement; and (c) construction tolerances and errors. Such deformations may be visually objectionable; cause separation, cracking, or leakage of exterior cladding, doors, windows, and seals; and cause damage to interior components and finishes. Appropriate limiting values of deformations depend on the type of structure, detailing, and intended use (Galambos and Ellingwood, 1986). Historically, common deflection limits for horizontal members have been 1/360 of the span for floors subjected to reduced live load and 1/240 of the span for roof members. Deflections of about 1/300 of the span (for cantilevers, 1/150 of the length) are visible and may lead to general architectural damage or cladding leakage. Deflections greater than 1/200 of the span may impair operation of moveable components such as doors, windows, and sliding partitions.

Deflection limits depend very much on the function of the structure and the nature of the supported construction. Traditional limits expressed as a fraction of the span length should not be extrapolated beyond experience. For example, the traditional limit of 1/360 of the span worked well for controlling cracks in plaster ceilings with spans common in the first half of the twentieth century. Many structures with more flexibility have performed satisfactorily with the now common, and more forgiving, ceiling systems. On the other hand, with the advent of longer structural spans, serviceability problems have been observed with flexible grid ceilings where actual deflections were far less than 1/360 of the span, because the distance between partitions or other elements that may interfere with ceiling deflection are far less than the span of the structural member. Proper control of deflections is a complex subject requiring careful application of professional judgment. AISC Design Guide 3, Serviceability Design Considerations for Steel Buildings, 2nd Edition (West et al., 2003), provides an extensive discussion of the issues.

Deflection computations for composite beams should include an allowance for slip, creep, and shrinkage as discussed in Commentary Section I3.

In certain long-span floor systems, it may be necessary to place a limit, independent of span, on the maximum deflection to minimize the possibility of damage of adjacent nonstructural elements (ISO, 1977). For example, damage to non-load-bearing partitions may occur if vertical deflections exceed more than about $\frac{3}{8}$ in. (10 mm) unless special provision is made for differential movement (Cooney and King, 1988); however, many components can and do accept larger deformations.

Load combinations for checking static deflections can be developed using a first-order reliability analysis (Galambos and Ellingwood, 1986). Current static deflection guidelines for floor and roof systems are adequate for limiting superficial damage in most buildings. A combined load with an annual probability of being exceeded of $5 \%$ is appropriate in most instances. For serviceability limit states involving visually objectionable deformations, repairable cracking, or other damage to interior finishes, and other short-term effects, the suggested load combinations are as follows:

$D+L$ $D+0.5 S$

For serviceability limit states involving creep, settlement, or similar long-term or permanent effects, the suggested load combination is

$D+0.5 L$

The dead load effect, $D$, may be that portion of dead load that occurs following attachment of nonstructural elements. For example, in composite construction, the dead load effects frequently are taken as those imposed after the concrete has cured. For ceiling related calculations, the dead load effects may include only those loads placed after the ceiling structure is in place.