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1、Strength of Shear Studs in Steel Deck on Composite Beams and Joists W. SAMUEL EASTERLING, DAVID R. GIBBINGS and THOMAS M. MURRAY INTRODUCTION Composite beam or joist and slab systems typically provide the most efficient design alternative in steel frame construction, and indeed it is one of these sy
2、stems that make steel an economically attractive alternative to concrete framed structures. Composite beam specification requirements and design aids are given in the American Institute of Steel Construction (AISC) Load and Resistance Factor Design (LRFD) Manual.1 The LRFD composite beam design proc
3、edure results in designs that are typically 10-15 percent more economical than those obtained using the AISC allowable stress design (ASD) procedure. The efficiency of composite beam design using LRFD procedures has, in the authors opinions, been the primary motivating factor for the use of the LRFD
4、 specification2 to date. The design strength and stiffness of composite beams depends on the shear connection behavior. The strength of the shear connectors may be reduced because of the influence of the steel deck geometry. An empirical expression for this reduction was developed by evaluating resu
5、lts of composite beam tests in which the deck ribs were oriented perpendicular to the steel beam.3 A reduced stud strength is obtained by multiplying the stud reduction factor, SRF, by the nominal strength of a shear stud, Qn. The expression for the nominal stud strength,4 which has been incorporate
6、d in the AISC LRFD specification and is the basis for the tabular values given in the AISC ASD specification,5 is given by: QAfEA F nscccscu =05 .(1) where Asc= cross-sectional area of a stud shear connector W. Samuel Easterling is assistant professor in the Charles E. Via, Jr. Department of Civil E
7、ngineering, Virginia Polytechnic Institute and State University, Blacksburg, VA. David R. Gibbings is graduate research assistant in the Charles E. Via, Jr. Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA. Thomas M. Murray is Montague-Betts profes
8、sor of structural steel design in the Charles E. Via, Jr. Department of Civil Engineering, Virginia Polytechnic, Blacksburg, VA. fc = specified compressive strength of concrete Ec= modulus of elasticity of concrete Fu= minimum specified tensile stress of the stud shear connector This equation was de
9、veloped based on results from elemental push-out tests.4 The stud reduction factor is given by: SRF N w h H h r r r s r = 085 1010 . (2) where Nr= number of studs in one rib at a beam intersection Wr= average width of concrete rib hr= nominal rib height Hs= length of shear stud after welding This re
10、duction factor applies to cases in which the deck ribs are perpendicular to the steel beam and is used in both the AISC LRFD and ASD specifications. These equations, or similar forms, have been used in several design specifications, both in the United States and abroad. However, in recent years seve
11、ral researchers6-11 have shown that Equation 2 is unconservative for certain configurations. The studies have considered numerous parameters, including depth of steel deck shear stud height, concrete unit weight, position of shear stud in the deck rib relative to the bottom flange stiffener, number
12、of shear studs in a given deck rib, and the amount and position of reinforcement in the slab. The studies reported results from push-out tests alone6,10,11 or a combination of push-out tests and beam tests.7-9 A conclusion common to all of the studies is that a modified, or completely different, stu
13、d reduction factor is needed. Modified calculation procedures have been developed and reported in the recent research studies. However, none of the studies have reported reasons for the discrepancy between the experimental data and Equations 1 and 2. The reason for the discrepancy between recent exp
14、erimental results with those predicted using Equations 1 and 2 is not clear. However, it is clear that a significant base of data exists to substantiate the procedures.3,12,13 A proper resolution of this dilemma will require careful consideration of all the data. A review of the data reported by Gra
15、nt, et al.,3 along with related studies conducted by Henderson12 and Klyce13 44ENGINEERING JOURNAL / AMERICAN INSTITUTE 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 th
16、e written permission of the publisher. reveal two important characteristics that relate directly to the discrepancy. The majority, but not all, of the tests reported by Grant, et al. and all the tests reported by Henderson were detailed such that the studs were placed in pairs within a given rib. Th
17、e single test reported by Klyce had two-thirds of the studs placed in pairs. Also, the deck used in the studies reported by Grant, et al. did not have a stiffener in the bottom flange. Both of these details make the position of the shear stud relative to the stiffener in the bottom flange of the dec
18、k, which is described in greater detail in the following paragraph, of less concern. One of the important parameters identified in some of the recent studies was the position of the shear stud relative to the stiffener in the bottom flange of the deck. Most deck profiles manufactured in the United S
19、tates have a stiffener in the middle of the bottom flange, thus making it necessary to weld shear studs off center. Tests have shown differences in shear stud strengths for the two choices. A stud placed on the side of the stiffener nearest the end of the span is in the “strong“ position and one pla
20、ced on the side of the stiffener nearest the location of maximum moment is in the “weak“ position. A schematic of both strong and weak position stud locations is shown in Figure 1. The difference in strength is partly attributable to the differences in the amount of concrete between the stud and the
21、 web of the deck that is nearest to mid-span for the two positions. This detail will be considered further in subsequent sections of this paper. A characteristic of partial composite beam design must be kept in mind when one evaluates results of beam tests and push-out tests. The relationship betwee
22、n the percentage of shear connection and the moment capacity is shown in Figure 2 for a W1631 A36 section. The curves shown in Figure 2 were developed using the calculation procedure in the Commentary to the LRFD specification.2 The nominal moment capacity, Mn, is shown normalized with respect to th
23、e fully composite moment, Mfc. The percent shear connection is given by Qn/AsFy, where Qn is the sum of the shear connector strength between the points of maximum Fig. 1. Strong and weak position shear stud locations. and zero moment, As is area of steel cross section, and Fy is yield stress of the
24、steel cross section. Curves are shown for three values of Y2, which is the distance from the top of the steel section to the center of the effective concrete flange. Although the curves were generated for a W1631, they are representative of a wide range of cross sections because of the normalization
25、 procedure. A value of Mn/Mfc of about 0.9 is obtained from a partial shear connection value of 0.7. This relation can be extended to evaluating test results, in that if a measured to predicted moment capacity of 0.9 is obtained, then the measured to predicted shear connector capacity is 0.7. Becaus
26、e of this relationship, one can argue that an accurate evaluation of the shear connector strength must be made using carefully controlled elemental push-out tests, as opposed to evaluating stud strengths using only beam tests. The sensitivity of the stud strength to various parameters is difficult t
27、o discern if the strength is back calculated from beam test results. The best approach is to use a combination of the two test configurations, with the push-out tests being used to evaluate a wide range of parameters and formulate strength relationships, and with the beam tests used as confirmatory
28、tests. The remaining sections of this paper describe a research project conducted at Virginia Tech to evaluate the strong vs. weak shear stud position issue.14 Results from a series of four composite beam tests are presented. Additionally, the results from a series of push-out tests are described. T
29、he push-out tests were part of another research project conducted prior to the beam tests.15 An analysis of the results is presented which compares the experimental beam strengths with calculated values based on Equations 1 and 2, as well as values based on the push-out tests. Fig. 2. Normalized mom
30、ent versus percent shear connection. SECOND QUARTER / 199345 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. STRENGTH AND STIFFNESS CALCULATION PROCEDU
31、RES Test results were compared to calculated strength and stiffness values. The calculated shear stud strengths were determined using the LRFD Specification Equations 15-1 and 13-1 (Equations 1 and 2 in this paper). The flexural strength calculations were made using the equations given in the Commen
32、tary to the LRFD Specification. The elastic stiffness values were calculated using the lower bound moment of inertia defined in Part 4 of the LRFD Manual. Measured material properties were used in all calculations. The steel section properties that were measured (depth, flange thickness, flange widt
33、h, and web thickness) were nearly identical to the tabular values given in Part 1 of the LRFD Manual. Therefore, tabulated cross-section properties for the steel shape were used in the calculations. The flexural strength calculation procedure gives three equations for the nominal moment capacity, wi
34、th the governing one determined based on the location of the plastic neutral axis (PNA). Yield stresses were determined separately for the web and flanges, thus the hybrid section idealization was used. All the specimens in this study were designed approximately 40 percent composite and the PNA was
35、located in the web for all tests. The calculated moment capacity, Mc, using Equation C-I3-5,2 is given by: MM C P MCe np yw pw = + 2 (3) where Mp= steel section plastic moment C= compressive force in the concrete slab Pyw= web yield force Mpw= web plastic moment e= distance from center of steel sect
36、ion to the center of the compressive stress block in the slab The force C is given by: C AFA F f swywsfyf c Qn = + min 2 085. Ac(4) where Asw= area of steel web Fyw= yield stress of web steel Asf= area of steel flange Fyf= yield stress of flange steel Ac= area of concrete slab within effective width
37、 The distance e is given by: e = 0.5d + hr + tc 0.5a(5) where d = depth of steel section tc= slab thickness above the steel deck a = depth of compression stress block The lower bound moment of inertia was calculated using the moment of inertia of the steel beam plus an equivalent area of concrete, w
38、hich is a function of the quantity of shear connection provided. The lower bound moment of inertia, ILB, is given by ILB = Ix +A Y d F dYY sENA y ENA Qn + + 2 2 2 2 ()(6) where Ix= moment of inertia about x-axis of structural steel section YENA= the distance from bottom of beam to elastic neutral ax
39、is (ENA) and is given by: Y A dQn F dY A Qn F ENA s y s y = + + + 2 2() (7) TEST PROGRAM Beam Test Specimens The four composite beam tests were similarly constructed. Each specimen consisted of a single W1631 A36 section with a composite slab attached. The span of each specimen was 30 ft and the tot
40、al beam length was 32 ft because of a 1 ft cantilever at each end. The composite slab used for the beam tests was constructed using a 20 gage (0.036 in.), 3 in. deep, composite deck with a total of 6 in. of normal weight (145 pcf) concrete. The steel deck profile is shown in Figure 3. A single layer
41、 of welded wire fabric (WWF 66 W1.4W1.4) was placed directly on the top of the deck. A total of 12 headed shear studs, -in.5 in. after welding, was used in each test. The studs were welded directly through the steel deck. The deck was placed with the ribs perpendicular to the beam span and the slab
42、width was 81 in. A self-drilling screw was placed in each rib that did not have a shear stud in it, thus satisfying the requirement of having one fastener every 12 inches.16 Deck seams were crimped (button- punched) twice on either side of centerline, resulting in an approximately 14-in. spacing. Th
43、e only nominal difference in the specimens was the position of the shear studs. However, the material properties varied for each test. All of the studs were placed in the strong position for Test 1 and the weak position for Test 2. In Tests 3 and 4 the stud positions were alternated, thus there were
44、 3 in the strong position and 3 in the weak position along each half span. The 46ENGINEERING JOURNAL / AMERICAN INSTITUTE 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
45、the written permission of the publisher. stud nearest the support was placed in the strong position and the stud placement was alternated toward midspan. This resulted in a symmetric stud pattern in the two half-spans. (Test 4 was a repeat of the configuration used in Test 3 and was conducted due to
46、 the low concrete strengths obtained in Test 3.) The ribs in which shear studs were placed are shown in Figure 4. Note that all of the studs appear in the center of the deck ribs in Figure 4, however the studs were placed as described above. The concrete slabs were formed using 6-in. cold-formed pou
47、r-stop material, resulting in three inches of cover on the 3-in. steel deck. A detail of the deck and slab is shown in Figure 5. After the concrete was placed, the slab was covered with plastic and cured for seven days. During this curing time the slab was kept moist. After seven days, the plastic a
48、nd the pour-stop on the sides of the specimen were removed and the slab was allowed to cure for at least 21 additional days prior to testing. Concrete cylinders (4 in. 8 in.) were cast at the same time as the concrete slab. The cylinders were kept adjacent to the slab, thus were covered with plastic
49、 and kept moist for the initial seven days. Each specimen was partially supported during construction. Timber supports were used to prop the steel deck along the sides of the slab at the quarter points during concrete placement. This bracing prevented the slab from warping during the placement of the concrete and was not intended to shore the beam. The timber props were cut to allow for the deflection of the beam under the w