1、16Steel Design Guide SeriesFlush and Extended Multiple-RowMoment End-Plate Connectionscover DG16.qxd 3/21/2002 2:06 PM Page 116Steel Design Guide SeriesThomas M. Murray, P.E., Ph.D.Montague Betts Professor of Structural Steel DesignCharles E. Via Department of Civil EngineeringVirginia Polytechnic I
2、nstitute and State UniversityBlacksburg, VirginiaW. Lee Shoemaker, P.E., Ph.D.Director of Research however, the design procedures also apply to hot-rolled shapes of comparable dimensions to the tested parameter ranges (i.e. Tables 3-6 and 4-7). Rigid frame or continuous frame construction, desig-nat
3、ed Type FR in the American Institute of Steel Con-struction (AISC) Load and Resistance Factor Design (LRFD) Specification or Type 1 in the AISC Allowable Stress Design (ASD) Specification, is usually assumed for the design of the frames. The moment end-plate connec-tion is one of three fully restrai
4、ned moment connections, as defined in the AISC Manual of Steel Construction, Load a strength cri-terion. 2. Determination of bolt forces including prying forces given end-plate geometry, bolt diameter, and bolt type; a bolt force criterion. 3. An assessment of construction type for which the connect
5、ion is suitable; a stiffness criterion. The procedures were verified using a series of full-scale tests of each of the nine connections shown in Fig-ures 1-3 and 1-4 (Srouji, et al. 1983a, 1983b; Hendrick, et al. 1984, 1985; Morrison, et al. 1985, 1986; Abel and Murray 1992a, 1992b; and SEI 1984). T
6、he geometric parameters for each series were varied within limits de-termined from current practice of the low rise building industry. The basis for each part of the design procedure is briefly described in the following sections. More thor-ough descriptions are found in the references cited. 2.2 Yi
7、eld-Line Theory and Mechanics Yield-lines are the continuous formation of plastic hinges along a straight or curved line. It is assumed that yield-lines divide a plate into rigid plane regions since elastic deformations are negligible when compared with plastic deformations. Although the failure mec
8、hanism of a plate using yield-line theory was initially developed for rein-forced concrete, the principles and findings are also ap-plicable to steel plates. The analysis of a yield-line mechanism can be per-formed by two different methods, (1) the equilibrium method, or (2) the virtual work energy
9、method. The latter method is more suitable for the end-plate application. In this method, the external work done by the applied load, in moving through a small arbitrary virtual deflection field, is equated to the internal work done as the plate rotates at the yield lines to facilitate this virtual
10、deflection field. For a selected yield-line pattern and loading, spe-cific plastic moment strength is required along these hinge lines. For the same loading, other patterns may re-sult in larger required plastic moment strength. Hence, the appropriate pattern is the one, which requires the largest r
11、equired plastic moment strength along the yield-lines. Conversely, for a given plastic moment strength along the yield-lines, the appropriate mechanism is that which pro-duces the smallest ultimate load. This implies that the yield-line theory is an upper bound procedure; therefore, one must find th
12、e least upper bound. The procedure to determine an end-plate plastic mo-ment strength, or ultimate load, is to first arbitrarily select possible yield-line mechanisms. Next, the external work and internal work are equated, thereby establishing the relationship between the applied load and the ultima
13、te resisting moment. This equation is then solved for either the unknown load or the unknown resisting moment. By comparing the values obtained from the arbitrarily se-lected mechanisms, the appropriate yield-line mechanism is the one with the largest required plastic moment strength or the smallest
14、 ultimate load. The controlling yield-line mechanisms for each of the nine end-plate connections considered in this Guide are shown in Chapters 3 and 4. 2.3 Bolt Force Predictions Yield-line theory does not provide bolt force predictions that include prying action forces. Since experimental test res
15、ults indicate that prying action behavior is present in end-plate connections, a variation of the method sug-gested by Kennedy, et al. (1981) was adopted to predict bolt forces as a function of applied flange force. MMMM MM2Fb b21 1 2pfpfa aB BQQFigure 2-1 Split-tee model.8 B B2F(a) First Stage / Th
16、ick Plate Behavior QaBaB Q2F(b) Second Stage / Intermediate Plate Behavior 2FaQ BBamaxQmax(c) Third Stage / Thin Plate Behavior Figure 2-2 Flange behavior models. The Kennedy method is based on the split-tee analogy and three stages of plate behavior. Consider a split-tee model, Figure 2-1, consisti
17、ng of a flange bolted to a rigid support and attached to a web through which a tension load is applied. At the lower levels of applied load, the flange behav-ior is termed “thick plate behavior”, as plastic hinges have not formed in the split-tee flange, Figure 2-2a. As the applied load is increased
18、, two plastic hinges form at the centerline of the flange and each web face intersection, Figure 2-2b. This yielding marks the “thick plate limit” and the transition to the second stage of plate behavior termed “intermediate plate behavior.” At a greater applied load level, two additional plastic hi
19、nges form at the cen-terline of the flange and each bolt, Figure 2-2c. The for-mation of this second set of plastic hinges marks the “thin plate limit” and the transition to the third stage of plate behavior termed “thin plate behavior.” For all stages of plate behavior, the Kennedy method predicts
20、a bolt force as the sum of a portion of the applied force and a prying force. The portion of the applied force depends on the applied load, while the magnitude of the prying force depends on the stage of plate behavior. For the first stage of behavior, or thick plate behavior, the prying force is ze
21、ro. For the second stage of behavior, or intermediate plate behavior, the prying force increases from zero at the thick plate limit to a maximum at the thin plate limit. For the third stage of behavior, or thin plate behavior, the prying force is maximum and constant. 2.4 Moment-Rotation Relationshi
22、ps Connection stiffness is the rotational resistance of a con-nection to applied moment. This connection characteristic is often described with a moment versus rotation or M- diagram. The initial slope of the M- curve, typically ob-tained from experimental test data, is an indication of the rotation
23、al stiffness of the connection, i.e. the greater the slope of the curve, the greater the stiffness of the connec-tion. This stiffness is reflected in the three types of con-struction defined in the AISC Specification for Structural Steel Buildings - Allowable Stress Design and Plastic Design (1989):
24、 Type 1, Type 2, and Type 3. Type 1 con-struction, or rigid framing, assumes that the connections have sufficient rigidity to fully resist rotation at joints. Type 2 construction, or simple framing, assumes that the connections are free to rotate under gravity load and that beams are connected for s
25、hear only. Type 3 construction, or semi-rigid framing, assumes that connections have a dependable and known moment capacity as a function of rotation between that of Type 1 and Type 2 construction. The AISC Load and Resistance Factor Design Specifica-tion for Structural Steel Buildings (1999) define
26、s two types of construction: FR and PR. Fully restrained or FR construction is the same as ASD Type 1 construction. Partially restrained or PR construction encompasses ASD Types 2 and 3 construction. Idealized M- curves for three typical connections representing the three AISC types of construction
27、are shown in Figure 2-3. Note that the M- curve for an ideally fixed connection is one which traces the ordinate of the M- diagram, whereas the 9 M- curve for an ideally simple connection is one which traces the abscissa of the M- diagram. For beams, guidelines have been suggested by Salmon and John
28、son (1980), and Bjorhovde, et al. (1987,1990), to correlate M- connection behavior and AISC construction type. Traditionally, Type 1 or FR connections are re-quired to carry an end moment greater than or equal to 90% of the full fixity end moment of the beam and not rotate more than 10% of the simpl
29、e span rotation (Salmon and Johnson 1980). A Type 2 connection is allowed to resist an end moment not greater than 20% of the full fixity end moment and rotate at least 80% of the simple span beam end rotation. A Type 3 connection lies be-tween the limits of the Type 1 and Type 2 connections. A PR c
30、onnection is any connection that does not satisfy the FR requirements. The simple span beam end rotation for any symmetri-cal loading is given by: EILMFs2= (2-1) where MF= fixed end moment for the loading. Setting MFequal to the yield moment of the beam, SFy, and with I/S = h/2: EhLFys= (2-2) Taking
31、 as a limit L/h equal to 24, and E equal to 29,000 ksi: 0.1(ysF5103.8)= radians (2-3) This value was used to determine the suitability of the moment end-plate connections considered in this Guide. It was found that 80% of the full moment capacity of the four flush connections and 100% of the full mo
32、ment ca-pacity of the five extended connections could be used in Type 1 or FR construction. It is noted that these classifi-cations do not apply to seismic loading. More recently, Bjorhovde, et al. (1987,1990) has sug-gested rotation criteria as a function of the connected beam span. Also, Hasan, et
33、 al. (1997) compared an ex-perimental database of M- curves for 80 extended end-plate connection tests to the results of analyses of three frame configurations and concluded that almost all of the extended end-plate connections possessing initial stiffness 106kip-in/rad behave as rigid connections.
34、2.5 Design Procedures Borgsmiller and Murray (1995) proposed a simplified method for the design of moment end-plate connections. The method uses yield-line analysis for determining end-plate thickness as discussed in Section 2.2. A simplified version of the modified Kennedy method was used to determ
35、ine tension bolt forces including prying action ef-fects. The bolt force calculations are reduced because only the maximum prying force is needed, eliminating the need to evaluate intermediate plate behavior prying forces. The primary assumption in this approach is that the end-plate must substantia
36、lly yield to produce prying forces in the bolts. Conversely, if the plate is strong enough, no prying action occurs and the bolts are loaded in direct tension. This simplified approach also allows the designer to directly optimize either the bolt diameter or end-plate thickness as desired. Rotation,
37、Moment,MM = 0.9M Typical Beam LineType I, FR Moment ConnectionType III, PR Moment ConnectionType II, Simple Shear ConnectionFM = 0.5M FM = 0.2M FMF = M /(2EI/L)S FBeam Line Equation, M = MF 2EI/L where: M = beam line end-moment MF= fixed end-moment, (wL2/12) = beam line end-rotation s= simple span b
38、eam end-rotation Figure 2-3 Moment-rotation curves. 10 Specifically, Borgsmiller and Murray (1995) exam-ined 52 tests and concluded that the threshold when pry-ing action begins to take place in the bolts is at 90% of the full strength of the plate, or 0.90Mpl. If the applied load is less than this
39、value, the end-plate behaves as a thick plate and prying action can be neglected in the bolts. Once the applied moment crosses the threshold of 0.90Mpl, the plate can be approximated as a thin plate and maximum prying action is incorporated in the bolt analy-sis. The design procedures used in Chapte
40、r 3 for flush end-plates and in Chapter 4 for extended end-plates are based on the Borgsmiller and Murray (1995) approach. For a specific design, if it is desired to minimize bolt di-ameter, Design Procedure 1 is used. If it is desired to minimize the thickness of the end-plate, Design Proce-dure 2
41、is used. A flow chart is provided in Figure 2-4 that provides a summary of the design procedures outlined in Sections 2.5.1 and 2.5.2. For LRFD designs, Muis the required flexural strength (factored moment). For ASD designs the working mo-ment or service load moment, Mw, is multiplied by 1.5 to obta
42、in Mu. After determining Mu, the design procedures are exactly the same for ASD and LRFD. 2.5.1 Design Procedure 1: Thick End-Plate and Smaller Diameter Bolts: The following procedure results in a design with a rela-tively thick end-plate and smaller diameter bolts. The design is governed by bolt ru
43、pture with no prying action included, requiring “thick” plate behavior. The “summary tables” refer to Tables 3-2 through 3-5 for the flush end-plate connections and Tables 4-2 through 4-6 for the ex-tended end-plate connections. The design steps are: 1.) Determine the required bolt diameter assuming
44、 no prying action, ()=ntureqdbdFMd2,(2-4) where, = 0.75 Ft= bolt material tensile strength, specified in Ta-ble J3.2, AISC (1999), i.e. Ft= 90 ksi for A325 and Ft= 113 ksi for A490 bolts. Mu= required flexural strength dn= distance from the centerline of the nthtension bolt row to the center of the
45、compression flange. Note: This equation is derived from equating Muto Mnpas shown in the “summary tables“ in Chapter 3 for flush end-plates and Chapter 4 for extended end-plates as follows: ( )=ntnpudPMM 2 (2-5) Solving Equation 2-5 for Ptyields: ()=nutdMP2(2-6) Setting Equation 2-6 equal to the bol
46、t proof load equation, tbFdP42t= and solving for dbyields Equation 2-4. 2.) Solve for the required end-plate thickness, tp,reqd, YFMtpynpp,reqdbr)11.1(= (2-7) where, b= 0.90 r= a factor, greater than or equal to 1.0, used to modify the required factored moment to limit the connection rotation at ult
47、imate moment to 10% of the simple span rota-tion. (See Section 3.1.1 for further explana-tion) = 1.25 for flush end-plates and 1.0 for ex-tended end-plates Fpy= end-plate material yield strength Y = yield-line mechanism parameter defined for each connection in the “summary ta-bles“ in Chapter 3 for
48、flush end-plates and Chapter 4 for extended end-plates. Mnp= connection strength with bolt rupture limit state and no prying action (Equation 2-5 based on selected bolt size). Note: This equation is derived from equating Mnpto 90% of the design strength for end-plate yielding, bMpl, given in the “su
49、mmary tables“ as follows: YtFMMppybplbnp290.090.0 = (2-8) Solving for tp,along with the inclusion of the load factor r,yields Equation 2-7. Note that the reciprocal of the 0.90 factor (1.11) is placed in the numerator to avoid confusion with the bending resistance factor bof the same value. 11 2.5.2 Design Procedure 2: Thin End-Plate and Larger Diameter Bolts: The following procedure results in a design with a rela-tively thin end-plate and larger diameter bolts. The design is governed by either the yielding of the end-plate or bol
