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a Ry is the ratio of expected yield strength to minimum specified yield strength Fy.

(From AISC-Seismic Table I-6-1.)

where l = length of the bracing member r = governing radius of gyration K = effective length factor

Es = modulus of elasticity of steel = 29,000 ksi (200,000 Mpa) Fy = specified minimum yield stress of the type of steel to be used, ksi. Yield stress in LRFD denotes either the minimum specified yield point for those steels that have a yield point, or the specified yield strength for those steels that do not have a yield point.

Thus, the limiting slenderness ratio is expressed as

Fy ry

Design Example

Given. A two-story OCBF shown in Fig. 3.40c that forms part of the building frame system in SDC E. The axial loads on the ground floor brace B1 are as follows:

Dead load D = 30 kips

Live load L = 15 kips

Seismic force QE = ±80 kips

Snow load S = 0 kips

Hydrostatic load H = 0

The redundancy coefficient p = 1.1.

Mapped two-second sapectral acceleration, SDS = 0.826 g.

Required. Determine a pipe section for brace B1, ASTM A53 Grade B steel; Fy = 35 ksi, Fu = 60 ksi

Solution. When gravity loads are additive, the basic load combination including earthquake effects E, is given by

Figure 3.40c. Ordinary concentric brace frame (OCBF) example.

where

U = 1.2 D + 0.5L + 0.2S + pQe + 0.2SDSD = 1.2 x 30 + 0.5 x 15 + 0.2 x 0 + 1.1 x 80 + 0.2 x 0.826 x 30 = 136.5 kips, compression governs

When gravity loads counteract seismic loads, the basic load combination is given by U = 0.9D + 1.6H + 1.0E

where

E = -pQE - 0.2SdsD U = 0.9D + 1.6H - pQE - 0.2SDSD = 0.9 x 30 + 1.6 x 0 - 1.1 x 80 - 0.2 x 0.826 x 30 = -66 kips, tension

The given frame in SDC E has a height of 32 ft, which is less than the maximum permitted height of 35 ft. Therefore OK.

The unbraced length of the brace B1, using centerline dimensions, is l = a/162 + 152 = 21.93 ft, use 22 ft for the design.

The effective length factor k for the brace, assuming hinged ends, is equal to 1.0. The effective length of the brace is

The design strength in axial compression is given by fcPn = f cAgFcr (LRFD E 2-1)

resistance factor for compression 0.85

gross area of member critical stress nominal axial strength

From LRFD Table 4.8, select an 8-in.-diameter standard steel pipe that has a design strength in axial compression of 165 kips for an effective length of 22 feet.

The section properties of an 8-in.-diameter standard pipe are given in LRFD Table 4.8 as

8.6 in.2 2.94 in. 0.332 in. 8.625 in. 35 ksi 60 ksi where fc =

The diameter-to-thickness ratio of a circular hollow section is limited by AISC-Seismic to a maximum value of

The actual diameter-to-thickness ratio is 8.63

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