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1、Shear Lag Effects in Steel Tension Members W. SAMUEL EASTERLING and LISA GONZALEZ GIROUX INTRODUCTION The non-uniform stress distribution that occurs in a tension member adjacent to a connection, in which all elements of the cross section are not directly connected, is commonly referred to as the sh
2、ear lag effect. This effect reduces the design strength of the member because the entire cross section is not fully effective at the critical section location. Shear lag effects in bolted tension members have been accounted for in the American Institute of Steel Construction (AISC) allowable stress
3、design specification1 (ASD) since 1978. The 1986 load and resistance factor design specification2 (LRFD) and the 1989 ASD specification3 stipulate that the shear lag effects are applicable to welded, as well as bolted, tension members. Past research on the subject of shear lag has focused primarily
4、on bolted tension members. Recently, more attention has been given to welded members, evident by their inclusion in the AISC specifications. Shear lag provisions for welded members were introduced into the specifications primarily because of a large welded hanger plate failure.8 To maintain a unifor
5、m approach to both welded and bolted members, the same provisions for shear lag in bolted members were applied to welded members. Additional requirements for welded plates were added. However, the application of the shear lag requirements to welded members has raised several questions. This paper ex
6、amines shear lag in steel tension members in the following context. First, the background for the current AISC specification provisions is reviewed. Second, the results of an experimental research program in which 27 welded tension members were loaded to failure is presented. Third, based on the fir
7、st two parts of the paper, recommended changes to the AISC specifications are presented. BACKGROUND FOR CURRENT DESIGN PROVISIONS Bolted Connections The shear lag provisions in the current AISC specifications2,3 are based on work reported by Chesson and Munse.6,11 This W. Samuel Easterling is associ
8、ate professor in the Charles E. Via, Jr. Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA. Lisa Gonzalez Giroux is staff engineer, Hazen and Sawyer, P.C., Raleigh, NC. work included experimental tests of riveted and bolted tension members conducted
9、 by Chesson and Munse and a review of experimental tests by other researchers. Chesson and Munse6 defined test efficiency as the ratio, in percentage, of the ultimate test load to the product of the material tensile stress and the gross area of the specimen, and used this ratio to evaluate the test
10、results. Several factors influence the test efficiency of connections failing through a net section: the net section area, a geometrical efficiency factor, a bearing factor, a shear lag factor, and a ductility factor. The data base Chesson and Munse gathered included tests that failed in a variety o
11、f ways, including rupture of the net section, rivet or bolt shear, and gusset plate shear or tear- out. However, only tests exhibiting a net section rupture, approximately 200, were included in the validation of the tension member reduction coefficients. Munse and Chesson seldom observed efficiencie
12、s greater than 90 percent and therefore recommended, for design use, an upper limit efficiency of 85 percent.11 Chesson5 reported on two additional studies that recommended maximum efficiencies of 0.75 and 0.85. Fourteen of the 30 tests conducted by Chesson and Munse6 failed by net section rupture.
13、Nine of the 14 tests failed at load levels exceeding the gross cross section yield load. Tests reported by Davis and Boomslitter7 were used in the overall data base and also exhibited net section failures at load levels exceeding gross section yield. References to other tests are given by Chesson an
14、d Munse. Research reported prior to 1963 indicated that shear lag was a function of the connection length5 and the eccentricity of the connected parts.7 Combining previous research results with their own investigation of structural joints, Munse and Chesson11 developed empirical expressions to accou
15、nt for various factors influencing the section efficiency. The two most dominant parts of their formulation were the net section calculation, which accounts for stagger of the fasteners, and the shear lag effect. The shear lag expression is given by U x l =1 _ (1) where U = shear lag coefficient x _
16、 = connection eccentricity l = connection length An AISC Task Committee concluded from a review of Munse and Chessons results that the recommended design THIRD QUARTER / 199377 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not b
17、e reproduced in any form without the written permission of the publisher. procedure could be simplified.10 The simplification is in the form of coefficients given in the AISC Specifications.2,3 Although the work of Chesson and Munse included the effects of several factors on the net section efficien
18、cy, the AISC specifications only account for the two dominant factors, net area and shear lag. The commentaries of both specifications include Equation 1 as an alternate approach for determining the shear lag coefficients. The calculation of the effective net area, Ae, incorporates the shear lag coe
19、fficient and is given by AUA en =(2) where An = net area Welded Connections In 1931 the American Bureau of Welding published the results of an extensive study in which safe working stresses for welds were determined. The American Bureau of Welding was an advisory board for welding research and stand
20、ardization of the American Welding Society (AWS) and the National Research Council Division of Engineering.4 The study was a collaborative effort between three steel mills, 39 fabricators, 61 welders, 18 inspectors, and 24 testing laboratories. Several specimen configurations were used in the test p
21、rogram and were assigned a series designation, e.g. 2400, 2500, etc., based on the configuration. Those directly applicable to this discussion consist of flat plate specimens, welded either longitudinally or both longitudinally and transversely. Both single and double plate tension specimens, as sho
22、wn in Figure 1, were tested in the research program. Most of the tests in the AWS program failed through the throat of the weld; but several of the specimens ruptured through the plate. The tests that ruptured are the ones applicable to the study described here. Key results from these tests have bee
23、n taken from the report and are presented in Table 1. Figure 2 is a plot of the results in terms of plate thickness vs. experimental shear lag coefficient (efficiency), Ue. Several trends are apparent in Figure 2. First, as the plate thickness increases, the scatter in the data tends to increase, wi
24、th the average experimental shear lag coefficient increasing slightly. This trend appears to hold except for the -in. group, which shows the least scatter, although this is the group with the smallest number of tests. Second, the amount of scatter in the -in. group is unexpectedly high. There are gr
25、oups of tests in which specimens have virtually identical details, yet the results vary by as much as 30 percent. For instance, consider the two - in. specimens in series 2200. The specimen details are nearly the same, yet the experimental efficiency varies from 0.69 to 1.03. Likewise, the -in. spec
26、imens of series 2400 had very similar details, but the experimental efficiencies varied from 0.65 to 0.94. A number of factors may have caused the scatter, including variation in the quality of the welds. An interesting observation pertaining to the issue of weld quality was made reviewing the AWS r
27、eport. The last column of Table 1 is a code used in the report to indicate the welding process (arc or gas), fabricating shop, welder, and mill that supplied the steel. Nine specimens, all of which were arc-welded, failed at an efficiency less that 0.80. Most of these specimens had companion specime
28、ns, which had similar fabrication details, yet they exhibited test efficiencies well above 0.80. A hypothesis that welding techniques, which may have created gouges or notches in the base material, caused the scatter in the data was formed by the authors of this paper. This seems plausible because t
29、he nine tests with efficiencies below 0.80 were fabricated in two shops, by three welders, using steel from two mills (3 heats), and seven of those were welded in the same shop by two welders. Unfortunately, this hypothesis cannot be confirmed for tests conducted more than 60 years ago. The results
30、of the AWS research were considered in the development of the AISC specification provisions accounting for shear lag in welded members. However, as will be presented later in this paper, questions have arisen regarding Fig. 1. AWS test specimen configuration. 78ENGINEERING JOURNAL / AMERICAN INSTITU
31、TE OF STEEL CONSTRUCTION 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. Table 1. AWS Test Results a AWS Series tp (in.) w (in.) l (in.) Fy (ksi) Fu (k
32、si) AgF (kips) AgFu kips) Test Load (kips) Us Proc-Fab- Weld-Mill b 22000.757.512.036.3572043212210.69A-Q-A-C 22000.757.512.033.256.91873203291.03G-AZ-B-I 24000.3757.56.035.7582013262480.76A-Q-B-C 24000.57.58.037.260.22794524060.9A-P-A-C 24000.57.58.03759.22784453030.68A-Q-B-C 24000.57.58.039.262.22
33、944673820.82G-AZ-B-I 24000.757.512.036.559.24116674320.65A-C-A-B 24000.757.512.036.459.64106714840.72A-Q-B-C 24000.757.512.033.5573776416000.94G-AZ-B-I 25000.754.04.035.660.4106.8181.2170.60.94G-AZ-A-I 26000.57.54.03759.31392221490.67A-Q-A-C 26000.757.58.036.559.22053331860.56A-C-A-B 26000.757.58.03
34、6.459.62053352000.6A-Q-B-C 27000.54.02.036.862.1147.2248.4237.60.96G-AZ-A-I 27000.754.04.035.660.4213.6362.43500.97G-AZ-B-I 27000.754.04.035.660.4213.6362.43450.95G-AZ-B-I 28000.3757.52.035.7582013262820.87A-N-A-C 28000.3757.52.035.7582013262390.73A-Q-A-C 28000.3757.52.037.558.22113272780.85G-AZ-B-I
35、 28000.3757.52.037.558.22113272750.84A-CZ-A-I 28000.57.54.039.262.22944674170.89G-AZ-A-I 28000.6257.56.036.661.63435785000.87A-C-A-B 28000.6257.56.037.3573505344750.89A-Q-A-C 28000.6257.56.033.4573135344990.93G-AZ-B-I 28000.6257.56.033.4573135345200.97A-CZ-A-I 28000.757.58.036.459.64116716060.90A-N-
36、A-C 28000.757.58.036.459.64116715900.88A-P-A-C a. All welds nominally -in.; measured variation between and -in. b. Procwelding process; A = arc welding G = gas welding Fabfabricator designation Weldwelder designation (within particular fabricating shop) Millmill designation for steel supply the appl
37、ication of the provisions to welded members. A research program was initiated to address the questions. The remainder of this paper presents the results of the research program. RESEARCH PROGRAM FOR WELDED TENSION MEMBERS This section of the paper summarizes a research project conducted at Virginia
38、Tech focusing on the application of shear lag specification provisions to welded tension members, presenting both experimental and analytical results. The experimental program included tests of 27 welded tension members, along with the associated tensile coupon tests. Analytical studies included ela
39、stic finite element analyses of the experimental specimens, as well as a review of the AISC specification provisions pertaining to shear lag. Description of Experimental Specimens Each test specimen consisted of two members welded back- to-back to gusset plates, as shown in Figure 3. The gusset plat
40、es were then gripped in a universal testing machine and pulled until failure. Use of double members minimized the distortion due to the out-of-plane eccentricity, however, eccentric effects were ignored in the design of the test specimens. Three types of member were tested: plates, angles, and chann
41、els. Fillet weld configurations used for each member type, except the plates, were longitudinal, transverse, and a THIRD QUARTER / 199379 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the wr
42、itten permission of the publisher. combination of both longitudinal and transverse. For the plates, two different lengths of longitudinal weld and a combination of longitudinal and transverse welds were used. For a given specimen configuration, three nominally identical tests were conducted; specime
43、ns with only transverse welds were the exception. Calculations indicate that tension members connected with only transverse fillet welds will always fail through the welds. For the purpose of confirming the calculations three specimens were fabricated with only transverse welds. Details of the speci
44、mens are given in Table 2. Test designations in Table 2 indicate the type of member (P = plate, L = angle, C = channel), weld configuration (L = longitudinal, T = transverse, B = longitudinal and transverse) and specimen number for a given Fig. 2. Plate thickness vs. experimental shear lag coefficie
45、nt for AWS tests. Fig. 3. Test specimen configuration. member type and weld configuration. For instance, test designation P-B-2 is a plate specimen with both longitudinal and transverse welds and is the second test in that particular group. An additional number appears in the weld designation for so
46、me of the plate specimens (e.g. P-L2-3). This is because the longitudinal weld lengths were varied in some of the plate specimens that were fabricated with only longitudinal welds. In an attempt to ensure net section failures in the members, all welds, except the transverse welds, were designed to h
47、ave 10-15 percent greater strength than the gross section tensile strength of the member. The width and thickness of the connected member elements prevented oversizing of the transverse welds. Welds were balanced by size for all angle specimens, except L-B-1a, with the longitudinal weld lengths bein
48、g equal on each specimen. Specimen L-B-1a was unbalanced with the two longitudinal welds being the same size and length. Strain gages were used in one of the tests for each member type to study the stress distribution near the critical section of the member and the distribution of stress in the memb
49、er along the length of the connected region. A displacement transducer was used to monitor the overall cross head movement. This measurement is only of qualitative value since it includes any slip between the specimen and the testing machine grips. Each specimen was whitewashed before testing to permit the observance of qualitative yield pattern formation. Complete specimen details are reported by Gonzalez and Easterling.9 Two aspects of the authors research program should be kept in mind while reviewing the following results. The first is that the number of tests was limited,
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