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through bolt slippage and bearing Figure 2 The test results also showed that. column and beam local buckling should be avoided because it would result in a. strength degradation, This paper provides the background information for the development of. capacity design provisions contained in the proposed AISI Seismic Standard for. CFS SBMF The objective of these design provisions is 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. For double channel, HSS Column, Channel Beam, A A B Bolt Bearing Plate. c Optional, Bolt Bearing Plate a, Channel Beam, Channel Beam. HSS Column, HSS Column, ELEVATION VIEW B B, FIGURE 1 BOLTED MOMENT CONNECTION. Story Drift Ratio, 10 5 0 5 10, 60 Specimen 3 Beam.

40 Slip Bearing, Components mm, 200 100 0 100 200 1 2 3 4 5 6 7 8 9 10. Story Drift mm Story Drift Ratio, a Hysteresis Response b Story Drift Components. FIGURE 2 BOLTED MOMENT CONNECTION, EXPECTED SEISMIC RESPONSE. In accordance with the AISI Seismic Standard AISI S110 a designer. would first use a value of R Response Modification Coefficient of 3 5 for. preliminary design Figure 3 shows that 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 Unlike other. seismic force resisting systems where point d represents the first significant. yielding event e g formation of the 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 point a to. b would result due to the oversize of the bolts As the story drift is increased. the lateral resistance starts to increase from point b Test results showed that. such hardening in strength is very significant see Figure 2 and it is not. appropriate to assume an elastic perfectly plastic EPP global response for either. analysis or design, Considering the effect of such significant hardening a Deflection. Amplification Factor Cd was also developed for CFS SBMF in the AISI Seismic. Standard AISI S110 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 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 represents the. required seismic strength for the beams and columns. Base Shear, 1 R c Actual Response, Story Drift, FIGURE 3 GENERAL STRUCTURAL RESPONSE OF CFS SBMF.

VS RtVB VS RtVB VS RtVB, FIGURE 4 YIELD MECHANISM AND COLUMN SHEAR DISTRIBUTION. h IC Instantaneous Center of Rotation, Channel Beam CG Center of Bolt Group. h Story Height Eccentricity, HHS Column P Applied Load. VC r0 Distance from CG, dmax Arm length to outermost bolt. FIGURE 5 FREEBODY OF ONE COLUMN, Column Shear, elastic slip bearing.

Story Drift, FIGURE 6 LATERAL RESISTANCE OF ONE COLUMN. It is common that same size beams and same size columns are connected by. high strength bolts with the same configuration Referring to a sample frame. shown in Figure 4 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. Figure 3 however it is reasonable to assume that column shears will equalize as. shown in Figure 4 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, M e h VS RtVB 1, where h story height and Rt the ratio of expected tensile strength to specified. tensile strength VS and VB represent resistance due to bolt slippage and bearing. SLIP COMPONENT OF COLUMN SHEAR AND SLIP DRIFT, The freebody of one column is shown in Figure 5 With the shear at the base of. the column the bolt group is in eccentric shear To show the components of lateral. resistance of the yield mechanism in Figure 4 Figure 3 is replotted for one column. only and shown as Figure 6 To calculate the maximum force developed at point c. it is necessary to first compute the column shear VS that causes the bolts to slip and. the amount of slip expressed in the form of story drift S. Since the bolt group is in eccentric shear the instantaneous center of rotation. concept Crawford and Fisher 1971 Salmon and Johnson 1996 can be used to. compute VS Given the bolt oversize the slip drift S can also be computed in. the analysis These two quantities for some commonly used bolt configuration are. provided in Table 1 To facilitate design a regression analysis of the values. contained in Table 1 was also conducted which resulted in the following two. expressions, VS CS kNT h 2, S C DS hOS h 3, where CS CDS regressed values from Table 2 k slip coefficient N number of. channels in a beam T snug tight bolt tension hOS hole oversize 1 16 in for. standard holes and h story height A value of k equal to 0 33 and value of T. equal to 10 kips were used Uang et al 2008, BEARING COMPONENT OF COLUMN SHEAR AND BEARING DRIFT.

Referring to point c in Figure 6 the design story drift is composed of. three components i the recoverable elastic component which is related to the. TABLE 1 VALUES OF GS AND GDS FOR ECCENTRICALLY LOADED. BOLT GROUP, TABLE 2 VALUES OF COEFFICIENTS CS CDS CB AND CB 0. Bolt spacing in, CS ft CDS 1 ft CB ft CB 0 in ft, 2 3 2 37 5 22 4 20 0 887. 3 6 4 3 34 3 61 5 88 0 625, 3 10 4 53 2 55 7 80 0 475. 2 3 2 84 4 66 5 10 0 792, 3 6 6 3 69 3 44 6 56 0 587. 3 10 4 80 2 58 8 50 0 455, See Figure 1, Beam 2C12 3 0 105.

h 5 ft Column HSS8 8 0 8, 30 VB max Bolt Bearing Plate 0 135 in. 10 0 2 16 curves, B max h 20 ft shown, 0 0 0 0 2 0 4 0 6 0 8 1 0. 0 10 20 30 40, a Typical Bearing Response Curves b Normalized Response Curves. FIGURE 7 SAMPLE RESULT OF BEAING RESPONSE, lateral stiffness K of the frame ii the slip component S which can be. computed from Eq 3 and iii the bearing component computed from following. where n number of column in a frame line i e number of bays plus 1 Me. expected moment at a bolt group computed from Eq 1. Applying the instantaneous center of rotation concept to an eccentrically. loaded bolt group Uang et al 2008 the relationship between the bearing. component of the story drift B and the bearing component of the column shear. VB can be established Figure 7 a shows a sample result For a given frame. height the last point of each curve represents the ultimate limit state when the. bearing deformation of the outermost bolt reaches 0 34 in 8 6 mm AISC 2005. Ultimate bearing shear of the column VB max and corresponding bearing drift. deformation B max for some commonly used bolt configuration and story heights. TABLE 3 VALUES OF GS AND GDS FOR ECCENTRICALLY LOADED. BOLT GROUP, Bearing Resistance RB, Stronger Weaker.

Component Component, FIGURE 8 BOLT BEARING DEFROMATION IN STRONGER AND. WEAKER COMPONENTS, are computed and are tabulated in Table 3 The variable R0 refers to the governing. value or minimum value of dtFu of the connected components beam and column. Each bolt in the moment connection bears against not only the column web. but also the beam web The bearing force exerted by the bolt to both components. is identical But the bearing deformation can be different between these two. components depending on the relative bearing strength tFu where t thickness. of the component Fu tensile strength The B 0 values in Table 3 correspond to. the maximum 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 The Bearing Deformation Adjustment Factor CDB in Table 3. accounts for the additional contribution to bearing deformation from the stronger. component Refer to point p in Figure 8 where the ultimate bearing deformation. 0 34 in 8 6 mm of the weaker component is reached Since the bearing force. of the bolt on both weaker and stronger components is identical it can be shown. that the corresponding bearing deformation unit in inch of the stronger. component i e point q is, S ln 1 0 817 5, The CDB factor represents the ratio between the total bearing deformation and 0 34. TABLE 4 BEARING DEFORMATION ADJUSTMENT FACTOR CDB, Bearing 0 0 0 4 0 5 0 6 0 7 0 8 0 9 1 0. CDB 1 00 1 10 1 16 1 23 1 33 1 46 1 66 2 00, relative bearing strength RBS tFu weaker tFu stronger.

t Thickness of beam or column component, Fu Tensile strength of beam or column. 0 34 S tFu W, CDB 1 0 0 588 ln 1 0 817 6, 0 34 tFu S. A regression analysis of Table 3 was conducted to derive the following design. formulae and Table 4 is provided for the bearing deformation adjustment factor. CDB to facilitate design, VB max CB NR0 h 7, B max CB 0CDBh 8. where CB CB 0 regressed values from Table 2, For a given beam size column size and a bolt configuration Figure 7 a. shows that the response curve is dependent on the story height Eqs 7 and 8. define the ultimate bearing strength point of each curve in the bearing response. curve see Figure 7 a Normalizing each curve by its ultimate bearing strength. point however Figure 7 b shows that the normalized curves can be approximated. very well by the following expression, B max B max.

Given a value of B from Eq 4 Eq 9 can be used to compute the bearing. component of the column shear VB and hence Me in Eq 1 But since Eq 4. also contains Me iteration is required to compute the expected moment Me A. flowchart is provided in Figure 9 The following value is suggested as the initial. value for B, nVB max B max K, where y is the story drift at point a in Figure 6. Compute B per Eq 10 Me VSh, Compute VB per Eq 9, Compute Me per Eq 1. Compute B per Eq 4, No Is computed B close Yes, to assumed value. FIGURE 9 FLOWCHART FOR COMPUTING EXPECTED MOMNET, DESIGN PROCEDURE FOR CFS SBMF. The recommended seismic design procedure follows, 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, Step 2 Compute both the base shear nVS 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 2 and 3 can be used to. compute both VS and S n represents the number of columns in a frame line. Step 3 Compute the design story drift, Follow the applicable building code to compute the design story drift where. the Deflection Amplification Factor is given in the AISI Seismic Standard AISI. 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 Em is to be replaced by the required strength in Eq 1 The. flowchart in Figure 9 can be used for this purpose. Step 5 Check P effects following the applicable building code. ACKNOWLEDGMENT, 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 Professor Reidar Bjorhovde for the development of CFS SBMF. design provisions, REFERENCES, American Institute of Steel Construction AISC Steel Construction Manual 13th.

Edition 2005, American Iron and Steel Institute AISI S110 07 Standard for Seismic Design of. Cold Formed Steel Structural Systems Special Bolted Moment Frames. Crawford S F and Fisher J W Eccentrically Loaded Bolted Connections. Journal of the Structural Division 97 ST3 1971 765 783. Salmon C G and Johnson J E Steel Structures Design and Behavior 4th. Edition HarperCollins College Publishers 1996, Uang C M Hong J K Sato A and Wood K Cyclic Testing and Modeling of. Cold Formed Steel Special Bolted Moment Frame Connections. The American Iron and Steel Institute AISI is in the process of developing a seismic design Standard for cold formed steel Standard for Seismic Design of Cold Formed Steel Structural Systems Special Bolted Moment Frames AISI S110 AISI 2007 The first seismic force resisting system introduced in the AISI