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1、Column Web Compression Strength at End-Plate Connections ALAN HENDRICK and THOMAS M. MURRAY INTRODUCTION Current North American specifications provide design criteria to prevent local failure of H-shaped columns when flanges or moment connection plates are welded to the column flange, as in Fig. 1.
2、This design criterion was developed strictly for these types of connections. Application of these criteria when bolted end-plate connections are used, (a) All Welded Connection (b) Welded and Eolted Connection Fig. 1. Continuous beam-to-column connections Alan Hendrick is formerly Research Assistant
3、, Fears Structural Engineering Laboratory, University of Oklahoma, Norman, Oklahoma. Thomas M. Murray is Professor-in-Charge, Fears Structural Engineering Laboratory, University of Oklahoma, Norman, Oklahoma. Fig. 2, may result in the unnecessary use of column stiffeners opposite beam flanges. Insta
4、llation of column stiffeners is expensive and stiffeners can interfere with weak axis framing into the column, as in Fig. 3. If stiffeners between the flanges of H-shaped columns can be eliminated, the fabrication process is greatly simplified. Fig. 2. Typical end-plate moment connection A critical
5、location in the column web of beam-to-column moment connections is at the toe of the column web fillet. For design of welded connections, the present (1978) AISC Specification1 criterion is based on a load path assumed to vary linearly on a 2:1 slope from the beam flange through the column flange an
6、d fillet, as in Fig. 4. If the stress at this critical section exceeds the yield stress of the column material, a column web stiffener is required opposite the beam compression flange. In the case of end-plate moment connections, the width of the stress pattern at the critical section may be conside
7、rably wider due to insertion of the end-plate into the load path. The fillet weld connecting beam and end-plate may also influence the width, as well as end-plate stiffeners of the type in Fig. 2. To verify or discredit these assertions, an extensive literature THIRD QUARTER / 1984161 (a) Shallow Be
8、am (b) Deep Beam Fig. 3. Weak axis framing details Fig. 4. Distribution of stresses at beam compression flange survey was conducted,2 followed by experimental and analytical studies. The result is a proposed design criterion for column web yield compression strength at end-plate connections. LITERAT
9、URE REVIEW Graham, Sherbourne, and Khabbaz3 conducted a series of tests in which a bar was welded to the column flange to simulate the beam compression flange in a welded connection (Fig. 1a). This simulated beam-flange connection neglected possible effects of column axial load and the effect of the
10、 compression from the beam web on the column-web strength. Based on test results using the simulated beam flange, the authors conservatively suggest that compressive stress distributes through the column web on a 3:1 slope. Using this relationship, results in the following equation for the maximum f
11、orce which can be resisted by the column web, Pmax = Fyctwc(tfb + 7k)(1) where Pmax = maximum force the column web is capable of resisting (kips), Fyc = yield stress of column material (ksi), twc = column web thickness (in.), tfb = beam flange thickness (in.), k = column “k“ distance (in.). Because
12、of additional compression supplied by the beam web, subsequent full connection tests gave lower results than obtained in the simulated beam flange test. According to the authors, if the stress is distributed on 2 :1 slope through the column, a conservative estimate for the full connection test is ob
13、tained. Hence, they recommend for design Pmax = Fyctwc(tfb + 5k)(2) Newlin and Chen4 attempted to develop a method of determining ultimate loads for the compression region of column sections having slender webs. Further, they attempted to develop a single formula for predicting the maximum web capac
14、ity of a column section regardless of the dc/twc ratio rather than separate equations for strength and stability. Fifteen tests in several series were performed to investigate the effect of varying flange and loading conditions. In addition, results from tests conducted by Chen and Oppenheim5 were a
15、lso included in the study. One series of tests investigated the effect of opposing beams of unequal depth at an interior beam-to-column moment connection. This geometry results in a situation where the loads applied to the compression region are eccentric. A second series investigated the contributi
16、on of the column flange to the load carrying capacity of the column web. In this series, cover plates 1-in. thick, 20-in. long and slightly wider than the specimen flanges to permit fillet welding all around were used. All tests were performed with simulation of the beam flange by welding a bar to e
17、ither the cover plate or directly to the column. Test results show the ultimate load of a column web is 162ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION “essentially unaffected by the eccentric load condition.“ It appears eccentric loading has the effect of adding a small amount of
18、stiffening to the stiffness of the web. The conclusion was that Eq. 2 is conservative for eccentric loading conditions. To investigate the contribution of the column flange on column web buckling, W1029 and W1227 A36 column sections were first tested as control specimens. Plates, 1 in. by 20 in., we
19、re then welded to both flanges of each section and the tests repeated. The resulting load vs. deflection curves for the W1029 tests are shown in Fig. 5. The increase in ultimate load with the cover plates added was approximately 31% for the W1029 section and 33% for the W1227 section. However, a res
20、erve strength of only 4.8% existed for both sections at ultimate load with very limited ductility. As a result, the authors state the “presence of a cover plate on a column flange should not be considered as part of the k dimension,“ and “these results further support the relative insignificance of
21、the column flange thickness as compared with web dimensions.“ It is noted the Pmax values shown in Fig. 5 are based on measured dimensions and measured yield stress. The W1029 control test k value was reported as 0.73 in. compared to a value of 1 1/16 in. from the 7th Edition AISC Manual of Steel Co
22、nstruction.6 No explanation was found for this rather large difference. The k value used to compute Fig. 5. Effect of cover plate on web capacity (from Ref. 3). Pmax for the cover plate test was taken as 1.73 in., the sum of the beam k and the 1 in. cover plate thickness. Newlin and Chen4 recommend
23、that Eq. 2 not be used for design and that an interaction equation of the form P Fd t F d ycc wc yc cmax = 3/2 180 125 4 (4) be used to check both web strength and stability. Or, in lieu of Eq. 4, a strength check be made using Eq. 2 and a stability check using P tF d wcyc c max = 4100 3 (5) Mann an
24、d Morris7 reviewed the results of several research programs pertaining to column webs at end-plate connections and proposed design criteria. They stated the 1977 European Convention of Constructional Steelwork Recommendations for Steel Construction gives the following expression for the maximum load
25、 carrying capacity of the column web in the presence of an end-plate. Pmax = Fyctwc (tfb + 5k + tp + d)(6) where tp = end-plate thickness (in.), and d = projection of the end-plate beyond the compression flange of the beam but not greater than tp (in.). The expression is based on the assumption that
26、 the stress is distributed on a 1:1 slope through the end-plate and on a 2:1 slope through the column. Witteveen, Start, Bijlaard and Zoetemeijer8 conducted tests in the Netherlands in an attempt to develop design rules to compute the moment capacity of unstiffened welded (no end plate) and bolted (
27、end plate) connections. For beams welded directly to the column flange, it is recommended that the column web strength be calculated from: Pmax = Fyctwc tfb + 5(tfc + rc)(7) where tfc = column flange thickness (in.), and rc = fillet between the flange and the web of the column (in.). For bolted end-
28、plate connections, it is recommended that the end- plate and weld be considered in determining the ultimate load carrying capacity of the web according to: Pmax = Fyctwctfb + 2 2 a + 2tp + 5(tfc + rc)(8) where a = weld dimension (in.). In this expression the stress distribution is assumed to be 1:1
29、through both the weld and end-plate. Aribert, Lachal and Nawawy9 tested European column sections with end-plate connections.* The compression beam *This paper is in French. A translation of a pertinent section is found in Ref. 2. THIRD QUARTER / 1984163 flange was simulated by welding a bar to the e
30、nd-plate. In addition to the testing, a numerical model was developed and maximum elastic, plastic and ultimate load expressions were obtained. After comparison with test results the following expressions were proposed. Maximum elastic load: Pemax= Fyctwc (tp + 2.3k)(9) Maximum plastic load: Ppmax=
31、Fyctwc(2tp + 5k)(10) Ultimate load: Pumax= Fyctwc(6tp + 7k)(11) Section 1.15.5.2 of the 1978 AISC Specification1 specifies the required stiffener area to prevent column web crippling when flanges or moment connection plates for end connections of beams and girders are welded to the flange of H-shape
32、d columns as A PF ttk F st bfyc wcfb yst = +()5 (12) where Ast = stiffener area (in.2), Pbf = the computed force delivered by the flange or moment connection plate multiplied by 5/3, when the computed force is due to live and dead load only, or by 4/3, when the computed force is due to live and dead
33、 load in conjunction with wind or earthquake forces (kips), and Fyst = stiffener yield stress (ksi). Stiffeners are not required if Ast is negative. In the commentary on Sect. 1.15.5, it is stated that the actual force times the load factor, i.e. Pbf, need not exceed the area of the flange or connec
34、tion plate delivering the force times the yield strength of the material. In addition to Eq. 12, a column web stability check is required. Compression flange stiffeners are required if the column web depth clear of fillets, dc, is greater than 4100 3 ,tF P wcyc bf (13) which is the same expression a
35、s recommended by Newlin and Chen4 (Eq. 5 of this paper). No mention of end-plate connections is made in the 1978 AISC Specification. In an end-plate design example in the 8th Edition AISC Manual of Steel Construction,10 page 4- 115, it is suggested that end-plate effects can be “conservatively“ acco
36、unted for by assuming a stress distribution on a 1:1 slope through the end-plate. This would result in the following equation for stiffener area () A PF ttkt F st bfyc wcfbp yst = +52 (14) No mention is made of possible weld effects and it is not known if the assumed distribution is based on test re
37、sults. In the literature survey,2 only two tests were found where end-plate effects were considered with American sections.4 From these tests it was concluded that cover plates (end- plates) were not effective because of minimal reserve strength above first yield (5%) and lack of ductility in the co
38、nnection. Literature concerning European testing and design practices are consistent in recommending an assumed stress distribution through the end plate of 1:1. In addition, one paper recommends use of the beam-flange to end-plate weld dimension when calculating the length of the critical section f
39、or determining the column-web compressive strength. To verify the European practices with American sections, a limited analytical and experimental research program was conducted. ANALYTICAL STUDY To determine analytically stress distributions and yield patterns in the compression region of the colum
40、n web at end- plate connections, an inelastic, two-dimensional, finite element program developed by Iranmanesh11 was used. To reduce computational costs and to more closely model the test set up used in the experimental phase of the study, only a portion of the beam consisting of the flange and web
41、was used. Load was applied directly to the beam flange. Figure 6a shows a typical mesh, support conditions and loading. Smaller elements were used in the region on the web at approximately the k distance from the edge of the column flange. Since the computer program used was limited to two- dimensio
42、nal elements, variation in thickness through the depth of the model, i.e. web, flange, weld and fillet thicknesses, was modeled by increasing the element stiffness based on the ratio of the element thickness to the thickness of the column web elements. A modulus of elasticity of 29,000 ksi in the el
43、astic range and an assumed yield stress of 36 ksi were used. For purposes of defining load levels, first yield was defined as the load at which the first element reached the yield strain, y. Second yield was defined as when any element reached 3y, third yield at 5y, fourth yield at 7y, fifth yield a
44、t 9y with an upper limit of 12y when the analysis was terminated. Typical progression of yielding through the web is demonstrated in Fig. 6. EXPERIMENTAL STUDY Test Setup In the literature review, it was found a number of research projects have been conducted to determine the column-web strength at
45、beam-to-column moment connections. However, except for one test, all of the research conducted in the U.S. 164ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION (a) 1st Yield, 145.1 Kips (b) 2nd Yield, 227.8 Kips (c) 3rd Yield, 246.8 Kips Fig. 6. Typical yield pattern progression from fi
46、nite element analysis has been limited to welded moment connections, and results of that test are considered inconclusive. European studies reviewed involved only their own sections. Thus, a limited number of tests were conducted to substantiate that load in the compression region of beam-to-column
47、moment end-plate connections is distributed over a greater length of the column web than for welded connections. (d) 4th Yield, 283.1 kips (e) 5th Yield, 298.7 kips Six tests were conducted with combinations of beam and column sections, shown in Table 1. The test set up is shown schematically in Fig
48、. 7. Figure 8 is a photograph of the set up. Each column section was placed in a horizontal position with the load applied through the flange of the WT section using a hydraulic ram. Load was monitored with a load cell located between the ram and specimen. Lateral movement of the upper column flange
49、 was restricted by a lateral brace mechanism attached to the test frame. Instrumentation consisted of strain gages and displacement transducers. For all six tests, strain was measured on each side of the column web at the toe of the fillet. Strain gages were located along the web to cover the expected load distribution length. In addition to the gages on the column web, strain gages were placed on the flange and stem of the WT beam section. Figure 7 shows typical locations. Two displacement transducers were used to measure vertical displacement of the co
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