Seismic design procedure development for cold-formed steel–special bolted moment frames

Journal of Constructional Steel Research 65 (2009) 860–868

Contents lists available at ScienceDirect

Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr

Seismic design procedure development for cold-formed steel–special bolted moment frames Atsushi Sato a,b , Chia-Ming Uang a,∗ a Department of Structural Engineering, University of California, San Diego, La Jolla, CA, United States b Department of Architecture and Design, Nagoya Institute of Technology, Nagoya, Japan

article

info

Article history: Received 7 February 2008 Accepted 14 March 2008 Keywords: Cold-formed steel Bolted moment frame Friction Bearing Seismic design

a b s t r a c t Seismic design provisions of Cold-Formed Steel–Special Bolted Moment Frames in the proposed AISI Seismic Standard were developed on the basis that ductility capacity is provided through bolt slippage and bearing in bolted beam-to-column moment connections, and that beams and columns are to remain elastic at the design story drift to resist the maximum force that can be developed in the connections. Based on the instantaneous centre of rotation analysis procedure, both the slip and bearing components of the connection resistance, expressed in the form of column shear and story drift, are presented and design values tabulated. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction

2. Objective

The American Iron and Steel Institute (AISI) is in the process of developing the Standard for Seismic Design of Cold-Formed Steel Structural Systems–Special Bolted Moment Frames [1]. The first seismic force-resisting system introduced in the AISI Seismic Standard is termed Cold-Formed Steel–Special Bolted Moment Frames (CFS-SBMF). This type of one-story moment frame is usually composed of cold-formed Hollow Structural Section (HSS) columns and double-channel beams connected by snug-tight highstrength bolts (Fig. 1). Cyclic testing of full-scale beam–column subassemblies [2] showed that the bolted moment connection can provide high ductility capacity through bolt slippage and bearing (Fig. 2). The test results also showed that column and beam local buckling should be avoided because it would result in strength degradation. Therefore, the Standard was developed such that energy dissipation in the form of bolt slippage and bearing in the bolted beam-to-column connections would occur during a major seismic event. Following the capacity design principles, beams and columns are then designed to remain elastic at the design story drift level. Extending the concept of instantaneous centre of rotation, cyclic response of a bolted moment connection can be simulated mathematically with a high accuracy [3]. This mathematical model can be used to compute the expected maximum seismic force in the connection region that beams and columns need to be designed for.

The main objective of this paper is to provide background information for the development of capacity design provisions contained in the proposed AISI Seismic Standard for CFS-SBMF. These design provisions are intended to ensure that inelastic action occurs in the bolted moment connections only during a design earthquake event, and that both beams and columns should remain elastic. 3. Structural response of CFS-SBMF Fig. 2(a) exemplifies the cyclic response of a beam–column subassembly that simulates a portion of a CFS-SBMF [2]. The story drift is contributed by the deformations in the bolted moment connection, beam, and column; the individual contributions are shown in Fig. 2(b)–(d). It is observed that inelastic action (i.e., energy dissipation) is mainly contributed by the bolted connection. Fig. 2(b) also shows that the bolted moment connection behaviour is characterized by four regions: rigid loading, slip, significant hardening, and rigid unloading. Both beam and column remain elastic in the story drift range of practical interest, but these members can still be overloaded and experience buckling if the bolted connection strain hardens significantly at high drift levels (say, beyond 5% story drift). 4. Mathematical model of bolted momnet connection

∗ Corresponding author. Tel.: +1 858 534 9880; fax: +1 858 534 6373. E-mail address: [email protected] (C.-M. Uang). 0143-974X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2008.03.016

The freebody of one column in a frame is shown in Fig. 3. With a shear at the base of the column, VC , the bolt group is in eccentric

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

861

(a) CFS-SBMF.

(b) Typical bolted moment connection detail. Fig. 1. A type of CFS-SBMF.

shear with an eccentricity h. The concept of an instantaneous centre (IC) of rotation [4,5] can be used to compute the response of the bolted connection. Following the assumptions made by Kulak et al. [6], the slip and bearing resistances of a single bolt are: (1)

RS = kT RB = Rult 1 − e−µ(δbr /25.4)

h

iλ

,

(2)

where RS = slip resistance, RB = bearing resistance, k = slip coefficient, T = bolt tension force, Rult = ultimate bearing strength, δbr = bearing deformation (mm), e = 2.718, and µ, λ = regression coefficients. Snug-tight A325 or SAE J429 Grade 5 high-strength bolts with standard holes are commonly used for the construction of CFS-SBMF. With the values of k = 0.33, T = 44.5 kN, Rult = 2.1dtF u , µ = 5, and λ = 0.55, where d = bolt diameter, t = bearing thickness, and Fu = tensile strength of the connected component, the predicted monotonic responses of representative specimens (see Table 1) are compared with the cyclic test data in Fig. 4 [3]. The predicted response envelopes very well the cyclic response of the test specimens with varying member sizes and bolt configurations.

5. Proposed seismic design procedure In accordance with the AISI Seismic Standard [1], a designer would first use a value of R (Response Modification Coefficient) of 3.5 for a preliminary design. Fig. 5 shows the expected performance of a CFS-SBMF. The elastic seismic force corresponding to the Design Basis Earthquake (DBE, point “e”) is reduced by the R factor to point “d” for sizing beams, columns, and bolted moment connections in accordance with the AISI Specification [7]. Unlike other steel seismic force-resisting systems [8] where point “d” represents the first significant yielding event (e.g., the formation of the first plastic hinge in a moment frame), CFS-SBMF actually would “yield” at a lower seismic force level (point “a”) due to slippage of the bolts in moment connections. A horizontal plateau (points “a” to “b”) would result due to the oversize of the bolt holes. As the story drift is increased, the lateral resistance of the frame starts to increase from point “b” once the hole oversize is overcome and the bearing action of the bolts starts to occur. Test results showed that such hardening in strength is very significant [see Fig. 2(a)], and it is not appropriate to assume an elasto-perfectly plastic global response for either analysis or design.

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

862

(a) Overall response.

(b) Bolted moment connection component.

(c) Beam component.

(d) Column component. Fig. 2. Typical response of CFS-SBMF beam–column subassembly.

Fig. 3. Freebody of one column.

Table 1 Member sizes and bolted connection configurations [2] Specimen no.

Beam (mm)

Column (mm)

3

2C406 × 89 × 2.7 (2C16 × 3 21 × 0.105)a 2C406 × 89 × 2.7 (2C16 × 3 21 × 0.105) 2C508 × 89 × 3.4 (2C20 × 3 21 × 0.135)

HSS203 × 203 × 6.4 (HSS8 × 8 × 14 ) HSS203 × 203 × 6.4 (HSS8 × 8 × 14 ) HSS254 × 254 × 6.4 (HSS10 × 10 × 14 )

4 9

a Dimensions in inch. b Bolt: 25.4 mm (1 in.) dia. SAE J429 Grade 5, Bearing Type High-Strength Bolt., see Fig. 1(b).

Bolted connectionb

Bolt bearing plate (mm)

a (mm)

b (mm)

c (mm)

76 (3) 76 (3) 76 (3)

152 (6) 152 (6) 254 (10)

108 (4 14 ) 108 (4 14 ) 159 (6 14 )

N/A 3.4 (0.135) N/A

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

(a) Specimen 3.

863

(b) Specimen 4.

(c) Specimen 9. Fig. 4. Correlation of response envelope.

Fig. 6. Yield mechanism and column shear distribution.

Fig. 5. General structural response of CFS-SBMF.

Considering the effect of such significant hardening, a Deflection Amplification Factor, Cd , was also developed for CFS-SBMF in the AISI Seismic Standard. The value of Cd is equal to 0.83R, unless the period of the structure is short [9]. With the Cd value, the designer then can amplify the story drift at point “d” to estimate the maximum inelastic story drift (∆ at point “c”) that is expected to occur in a Design Basis Earthquake event. To ensure that beams and columns will remain elastic, the challenge then is to evaluate the maximum seismic force corresponding to point “c”. This seismic force level, which is equivalent to the seismic load effect with overstrength, Emh , in ASCE 7 [10], represents the required strength for the beams and columns. It is common that same-size beams and same-size columns are connected by snug-tight high-strength bolts with the same configuration. Referring to the sample frame shown in Fig. 6, interior column(s) will resist more shear than exterior columns in the elastic range. Once the frame responds in the inelastic range to point “c” in Fig. 5, however, it is reasonable to assume that column shears will equalize when the yield mechanism is formed. Capacity Design of the beams and columns can be performed if the

maximum shear force developed in the columns can be evaluated. Specifically, the required moment for both beam and column at the connection location is Me = h (VS + Rt VB ) ,

(3)

where h = story height, Rt = ratio of expected tensile strength to specified tensile strength. VS and VB represent the column shear components corresponding to the resistance of the eccentrically loaded bolt group due to bolt slip and bearing, respectively. The details of these parameters are presented below. 6. Slip drift and slip componet of column shear With a shear at the column base, as shown in Fig. 3, the bolt group is in eccentric shear. To show the components of lateral resistance of the yield mechanism in Fig. 6, Fig. 5 is re-plotted for one column only and is shown as Fig. 7. To calculate the maximum force developed at point “c”, it is necessary to first compute both the column shear (VS ) that causes the bolt group to slip and the amount of slip, expressed in the form of story drift (∆S ). The column shear (VS ) can be computed from a mathematical model proposed by Sato et al. [3], in which the resistance of the bolt is friction only (R = RS , as given in Eq. (1)). Given the bolt hole oversize, the slip drift (∆S ) can also be computed from the

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

864

Table 2 results in the following two expressions: VS = CS kNT /h

(4)

∆S = CDS hOS h,

(5)

where CS , CDS = regressed values from Table 3, N = number of C shaped channels in a beam, and hOS = hole oversize [=1.6 mm (1/16 in.) for standard hole]. 7. Bearing drift and bearing componet of column shear

Fig. 7. Lateral resistance of one column.

analysis based on the instantaneous centre of rotation concept. These two quantities for some commonly used bolt configurations are provided in a normalized form in Table 2. Alternatively, to facilitate design a regression analysis (see Fig. 8) of the values in

Referring to point “c” in Fig. 7, the design story drift (∆) is composed of three components: (i) the recoverable elastic component which is related to the lateral stiffness, K , of the frame, (ii) the slip component, ∆S , which can be computed from Eq. (5), and (iii) the bearing component computed from following equation: ∆B = ∆ − ∆S −

nMe hK

,

(6)

Table 2 Values of GS and GDS for eccentrically loaded bolt group

c (mm [in.])

h (m [ft])

Bolt spacing a and b (mm [in.]) a = 64[2 1 ], b = 76[3] 2

a = 76[3], b = 152[6]

a = 76[3], b = 254[10]

GS

GDS

GS

GDS

GS

GDS

108 [4 14 ]

2.44 [8] 2.74 [9] 3.05 [10] 3.35 [11] 3.96 [13] 4.57 [15] 5.18 [17] 5.79 [19] 6.40 [21] 7.01 [23] 7.62 [25] 8.23 [27] 8.84 [29] 9.45 [31] 10.1 [33] 10.7 [35]

0.296 0.264 0.237 0.216 0.183 0.158 0.139 0.125 0.113 0.103 0.0946 0.0879 0.0818 0.0763 0.0714 0.0678

40.5 45.8 51.0 56.3 66.9 77.5 88.1 98.7 109 120 130 141 152 162 173 183

0.416 0.370 0.333 0.303 0.257 0.223 0.197 0.176 0.159 0.145 0.134 0.124 0.115 0.108 0.101 0.0955

26.6 30.3 34.0 37.7 45.1 52.6 60.1 67.6 75.1 82.6 90.2 97.7 105 113 120 128

0.562 0.501 0.452 0.411 0.349 0.303 0.268 0.240 0.217 0.198 0.182 0.169 0.157 0.147 0.138 0.130

17.6 20.1 22.7 25.3 30.6 35.9 41.4 46.9 52.5 58.1 63.7 69.3 75.0 80.7 86.4 92.1

159 [6 14 ]

2.44 [8] 2.74 [9] 3.05 [10] 3.35 [11] 3.96 [13] 4.57 [15] 5.18 [17] 5.79 [19] 6.40 [21] 7.01 [23] 7.62 [25] 8.23 [27] 8.84 [29] 9.45 [31] 10.1 [33] 10.7 [35]

0.355 0.315 0.284 0.259 0.218 0.189 0.167 0.150 0.135 0.124 0.114 0.105 0.0977 0.0915 0.0859 0.0810

36.2 40.9 45.6 50.4 59.8 69.3 78.7 88.2 97.6 107 117 126 135 145 154 164

0.460 0.410 0.369 0.335 0.284 0.246 0.217 0.194 0.176 0.161 0.148 0.137 0.127 0.119 0.112 0.105

25.8 29.3 32.9 36.4 43.5 50.5 57.6 64.7 71.8 78.9 85.9 93.0 100 107 114 121

0.597 0.531 0.479 0.436 0.370 0.321 0.283 0.253 0.229 0.210 0.193 0.179 0.166 0.156 0.146 0.138

18.2 20.9 23.5 26.2 31.6 37.0 42.5 48.0 53.5 59.0 64.6 70.1 75.7 81.2 86.8 92.4

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

(a) Slip component of column shear (c = 108 mm).

865

(b) Slip component of story drift (c = 108 mm).

Fig. 8. Regression analyses of slip components.

(a) Bearing response curves.

(b) Normalized bearing response curves. Fig. 9. Sample result of bearing response.

Table 3 Values of Coefficients CS , CDS , CB , and CB,0 Bolt spacinga (mm) a

b

CS (m [ft])

CDS (1/m

[1/ft])

CB (m

[ft])

CB,0 (mm/m

[in./ft])

c

64 (2 12 )b 76 (3) 76 (3)

76 (3) 152 (6) 254 (10)

108 (4 14 )

0.723 [2.37] 1.02 [3.34] 1.38 [4.53]

17.1 [5.22] 11.8 [3.61] 8.37 [2.55]

1.28 [4.20] 1.79 [5.88] 2.44 [8.00]

73.9 [0.887] 52.0 [0.625] 39.6 [0.475]

64 (2 12 )b 76 (3) 76 (3)

76 (3) 152 (6) 254 (10)

159 (6 14 )

0.866 [2.84] 1.12 [3.69] 1.46 [4.80]

15.3 [4.66] 11.3 [3.44] 8.47 [2.58]

1.56 [5.11] 2.00 [6.56] 2.59 [8.50]

66.0 [0.792] 48.9 [0.587] 37.9 [0.455]

a See Fig. 1(b). b Dimensions in inch.

where n = number of columns in a frame line (i.e., number of bays plus one), Me = expected moment at the bolt group as computed from Eq. (3). Similarly, following the proposed mathematical model for an eccentrically loaded bolt group, the relationship between the bearing component of the story drift, ∆B , and the bearing component of the column shear, VB , can be established from an instantaneous centre of rotation analysis [3]. Fig. 9(a) shows a sample result. For a given story height (h), the last point of each curve represents the ultimate limit state when the bearing deformation of the outermost bolt reaches 8.6 mm (0.34 in.) [11]. The ultimate bearing shear force of the column, VB,max , and the

corresponding bearing drift, ∆B,max , for some commonly used bolt configurations and story heights are computed and are tabulated in a normalized form in Table 4. VB,max = NGB R0

(7)

∆B,max = CDB ∆B,0 .

(8)

The variable R0 refers to the governing value (i.e., minimum value) of dtF u of the connected components, where t and Fu are, respectively, the web thickness and tensile strength of the connected member (i.e., either beam or column), and d is the bolt diameter. The CDB factor will be explained later. To facilitate design, a regression analysis (see Fig. 10) of the GB and ∆B,0 values in Table 4 was also conducted, which results in the following alternative expressions for Eqs. (7) and (8): VB,max = CB NR0 /h

∆B,max = CB,0 CDB h,

(9) (10)

where the regressed values of CB , CB,0 are also listed in Table 3. The ∆B,0 value in Table 4 corresponds to the maximum story drift when the bearing deformation is contributed by the weaker component (either beam or column) only. That is, it is assumed that the stronger component is rigid. But since each bolt in the moment connection bears against not only the beam web but also the column web, the bearing force exerted by the bolt on both components is identical. Therefore, bearing deformation will also develop in the stronger component, although to a lesser extent. The Bearing Deformation Adjustment Factor, CDB , in Eq. (8) or (10) accounts for this additional contribution from the stronger component. Refer to point “p” in Fig. 11, where the ultimate bearing

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

866

Table 4 Values of GB and ∆B,0 for eccentrically loaded bolt group

c (mm [in.])

h (m [ft])

Bolt spacing a and b (mm [in.]) a = 64[2 1 ], b = 76[3] 2

a = 76[3], b = 152[6]

a = 76[3], b = 254[10]

GB

∆B,0 (mm [in.])

GB

∆B,0 (mm [in.])

GB

∆B,0 (mm [in.])

108 [4 14 ]

2.44 [8] 2.74 [9] 3.05 [10] 3.35 [11] 3.96 [13] 4.57 [15] 5.18 [17] 5.79 [19] 6.40 [21] 7.01 [23] 7.62 [25] 8.23 [27] 8.84 [29] 9.45 [31] 10.1 [33] 10.7 [35]

0.524 0.466 0.420 0.381 0.323 0.281 0.247 0.222 0.200 0.183 0.169 0.156 0.145 0.136 0.127 0.120

176 [6.92] 198 [7.81] 221 [8.71] 244 [9.61] 290 [11.4] 335 [13.2] 381 [15.0] 427 [16.8] 472 [18.6] 518 [20.4] 563 [22.2] 609 [24.0] 655 [25.8] 700 [27.6] 746 [29.4] 792 [31.2]

0.728 0.649 0.586 0.533 0.453 0.393 0.347 0.311 0.281 0.257 0.237 0.220 0.204 0.191 0.180 0.169

121 [4.77] 137 [5.40] 153 [6.04] 170 [6.68] 202 [7.95] 234 [9.23] 267 [10.5] 299 [11.8] 332 [13.1] 364 [14.3] 397 [15.6] 429 [16.9] 462 [18.2] 494 [19.5] 527 [20.7] 559 [22.0]

0.983 0.878 0.794 0.724 0.616 0.536 0.474 0.425 0.385 0.352 0.325 0.301 0.281 0.262 0.247 0.233

89.0 [3.50] 101 [4.00] 114 [4.49] 127 [4.98] 152 [5.97] 177 [6.96] 202 [7.95] 227 [8.94] 252 [9.92] 277 [10.9] 302 [11.9] 327 [12.9] 352 [13.9] 377 [14.9] 402 [15.8] 427 [16.8]

159 [6 14 ]

2.44 [8] 2.74 [9] 3.05 [10] 3.35 [11] 3.96 [13] 4.57 [15] 5.18 [17] 5.79 [19] 6.40 [21] 7.01 [23] 7.62 [25] 8.23 [27] 8.84 [29] 9.45 [31] 10.1 [33] 10.7 [35]

0.637 0.566 0.510 0.464 0.393 0.341 0.302 0.269 0.244 0.222 0.205 0.189 0.176 0.165 0.154 0.146

157 [6.17] 177 [6.97] 197 [7.77] 218 [8.57] 258 [10.2] 299 [11.8] 340 [13.4] 381 [15.0] 421 [16.6] 462 [18.2] 503 [19.8] 544 [21.4] 585 [23.0] 625 [24.6] 666 [26.2] 707 [27.8]

0.814 0.725 0.654 0.595 0.504 0.438 0.387 0.347 0.314 0.287 0.264 0.244 0.228 0.213 0.201 0.189

114 [4.48] 129 [5.08] 144 [5.68] 159 [6.28] 190 [7.48] 220 [8.68] 251 [9.88] 282 [11.1] 312 [12.3] 343 [13.5] 373 [14.7] 404 [15.9] 434 [17.1] 465 [18.3] 495 [19.5] 526 [20.7]

1.05 0.935 0.845 0.771 0.655 0.570 0.504 0.452 0.410 0.374 0.345 0.319 0.298 0.279 0.262 0.247

85.2 [3.36] 97.1 [3.82] 109 [4.29] 121 [4.76] 145 [5.70] 169 [6.65] 193 [7.59] 217 [8.54] 241 [9.48] 265 [10.4] 289 [11.4] 313 [12.3] 337 [13.3] 361 [14.2] 385 [15.2] 409 [16.1]

(a) Bearing component of column shear (c = 108 mm).

(b) Bearing component of story drift (c = 108 mm).

Fig. 10. Regression analyses of bearing components.

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

867

Fig. 11. Bolt bearing deformation in weaker and stronger members.

Table 5 Bearing deformation adjustment factor CDB Relative bearing strength, RBS

0.0

CDB

1.00 1.10 1.16 1.23 1.33 1.46 1.66 2.00

0.4

0.5

0.6

0.7

0.8

0.9

1.0

where relative bearing strength, RBS = (tF u )W /(tF u )S , where weaker (W ) component corresponds to that with a smaller tF u value. t = Thickness of beam or column component. Fu = Tensile strength of beam or column.

deformation [=8.6 mm (0.34 in.)] of the weaker component is reached and the corresponding bearing force based on Eq. (2) is h iλ RB(p) = 2.1d(tFu )W 1 − e−µ(8.6/25.4) ,

(11)

where W stands for the weaker component. Since the bearing force acting on the stronger component is identical to that acting on the weaker component, the corresponding bearing deformation in the stronger component (i.e., deformation at point “q” in Fig. 11) can be solved from the following equation: h iλ RB(p) = 2.1d(tFu )S 1 − e−µ(δbr,S /25.4) ,

(12)

where S stands for the stronger component. The solutions follows:  !1/λ  25.4 tFu )W ( , δbr,S = − (13) ln 1 − c

µ

(tFu )S

where c = 1 − e = 0.817. The CDB factor represents the ratio between the total deformation and 8.6 mm (0.34 in.):  !1/λ  8.6 + δbr,S 2.953 tFu )W ( . CDB = = 1.0 − ln 1 − c (14) 8.6 µ (tFu )S Sample values for CDB are provided in Table 5. The bearing response curve is a function of beam size, column size, bolt configuration, and story height; Eqs. (9) and (10) define the ultimate strength point on the curve. To evaluate the strength for any bearing deformation, an expression that describes the entire curve is needed. Recall that Fig. 9(a) shows an example where the bearing response curves for a given beam size, column size, and bolt configuration vary with the story height. When each curve is normalized by its ultimate strength point, however, Fig. 9(b) shows that all normalized curves fall in a very narrow range which can be described by the following expression:

VB,max

!2

+ 1−

∆B ∆B,max

!1.43

Given the value of ∆B from Eq. (6), Eq. (15) can be used to compute the bearing component of the column shear, VB , and, hence, Me in Eq. (3). But since Eq. (6) also contains Me , iteration is required to compute the expected moment, Me . A suggested flowchart is provided in Fig. 12, where ∆y is the story drift at point “a” in Fig. 7. The following value can be used as the initial value for ∆B : 
 ∆ − ∆S + ∆y K . (16) ∆B = nVB,max /∆B,max + K According to the AISC Seismic Provisions [8], the expected yield stress, Ry Fy , is generally used for capacity design calculations, where Ry represents the ratio between the expected yield stress and the minimum specified yield stress. Since for CFS-SBMF the yielding mechanism includes bolt bearing in the connection region, the expected tensile strength, Rt Fu , should be used to compute the bearing component of the column shear, VB , where Rt represents the ratio between the expected tensile strength and the minimum specified tensile strength [1]. This factor is included in Eq. (3). 8. Design procedure for CFS-SBMF

−µ(8.6/25.4)

VB

Fig. 12. Flowchart for computing expected moment.

= 1.

(15)

A parametric study showed that the above normalized expression also fits very well the curves for a wide range of member sizes, bolt configuration, and story height.

The recommended seismic design procedure for CFS-SBMF is summarized below. Step 1: Preliminary design. Perform a preliminary design of the beams, columns, and bolted connections by considering all basic load combinations in the applicable building code. Use a value of R equal to 3.5. In determining the earthquake load, use a rational method to determine the structural period. (The empirical period formula provided in model code [10] is not intended for the frame system under consideration.) Step 2: Compute both the base shear (nV S ) that causes the bolt groups to slip and the slip range (∆S ) in terms of story drift. For a given configuration of the bolt group, Eqs. (4) and (5) can be used to compute VS and ∆S . Step 3: Compute the design story drift, ∆. Follow the applicable building code to compute the design story drift, where the Deflection Amplification Factor, Cd , is given in the applicable building code or the AISI Seismic Standard [1]. Step 4: Perform capacity design of beams and columns. Beams and columns should be designed based on special seismic load combinations of the applicable building code; the seismic load effect with overstrength, Emh , is to be replaced by the required strength in Eq. (3). To compute

868

A. Sato, C.-M. Uang / Journal of Constructional Steel Research 65 (2009) 860–868

the bearing component of the column shear, VB , the flowchart in Fig. 12 can be used. Step 5: Check P-∆ effects following the applicable building code. 9. Summary and conclusions This paper provides background information for the development of capacity design provisions in the AISI’s first Standard for Seismic Design of Cold-Formed Steel Structural Systems–Special Bolted Moment Frames (CFS-SBMF) [1]. Inelastic action in the form of bolt slippage and bearing in the bolted moment connection is the main source of energy dissipation in a seismic event. Beams and columns are designed to remain elastic at the design story drift for the maximum force that can be developed in the connection region. Test results showed that a bolted connection would first slip and produce a pseudo-yield behaviour. The slip force, expressed in the form of column shear, and slip range, expressed in the form of story drift, can be calculated from an analysis procedure based on the instantaneous centre of rotation concept for an eccentrically loaded bolt group. To facilitate design, values for these two quantities are tabulated. Together with the design story drift, the instantaneous centre of rotation analysis procedure can also be used to compute the bearing component of the connection resistance in terms of column shear and story drift; values are tabulated for the determination of these two quantities. An iterative flowchart is given to demonstrate the proposed capacity design procedure for seismic design of CFS-SBMF.

Acknowledgments This research was sponsored by the American Iron and Steel Institute. The authors would like to acknowledge the advice from the AISI Seismic Task Group, chaired by Dr. Reidar Bjorhovde, for the development of the CFS-SBMF design provisions. References [1] AISI. Standard for seismic design of cold-formed steel structural systems–special bolted moment frames. Washington (DC): AISI S110, American Iron and Steel Institute; 2007. [2] Hong J-K, Sato A, Uang C-M, Wood K. Cyclic testing of cold-formed steel special bolted moment frame connections. Journal of Structural Engineering, ASCE; 2008 [submitted for publication]. [3] Sato A, Hong J-K, Uang C-M. Cyclic modeling of cold-formed steel special bolted moment frame connections. Journal of Structural Engineering, ASCE; 2008 [submitted for publication]. [4] Crawford SF, Kulak GL. Eccentrically loaded bolted connections. Journal of the Structural Division, ASCE 1971;97(ST3):765–83. [5] Salmon CG, Johnson JE. Steel structures design and behaviour. New York (NY): HarperCollins College Publishers; 1996. [6] Kulak GL, Fisher JW, Struik JHA. Guide to design criteria for bolted and riveted joints. Chicago (IL): AISC; 2001. [7] AISI. North American specification for the design of cold-formed steel structural members. Washington (DC): AISI S100, American Iron and Steel Institute; 2007. [8] AISC. Seismic provisions for structural steel buildings. Chicago (IL): ANSI/AISC341-05, American Institute of Steel Construction; 2005. [9] Sato A, Uang C-M. Development of a seismic design procedure for coldformed special bolted frames. Report no. SSRP-07/16. San Diego (La Jolla, CA): University of California; 2007. [10] ASCE. Minimum design loads for buildings and other structures. Reston (VA): ASCE/SEI 7-05, American Society of Civil Engineering; 2005. [11] AISC. Steel construction manual. Chicago (IL): American Institute of Steel Construction; 2005.