Horizontal Shear Strength Of Composite Concrete Beams With .
Horizontal Shear Strength ofComposite Concrete BeamsWith a Rough InterfaceRobert E. LoovD. Phil., P. Eng.Professor of Civil EngineeringThe University of CalgaryCalgary, AlbertaCanadaThe latest version of the ACI Building Code requires fiveequations to prescribe the limiting horizontal shear stress fordiffering amounts of reinforcing steel. The test results from the16 beams tested in this study indicate that a more consistentlimit can be obtained by replacing four of the present equations with a parabolic equation modified from the one used inthe PC/ Design Handbook. The proposed equation combinesthe effect of concrete strength and clamping stress. It isequally applicable for lightweight and semi-lightweight concrete. The test results indicate that an as-cast surface with thecoarse aggregate left protruding from the surface, but withoutspecial efforts to produce a rough surface, can develop adequate shear resistance and simplify production of the precastconcrete beams. Also, the tests show that stirrups are typically unstressed and ineffective until horizontal shear stressesexceed 1.5 to 2 MPa (220 to 290 psi).omp osite construc tio n is aneconomical way of combiningprecast and cast-in-place concrete while retaining the continuityand efficiency of monolithic construction. A composite beam is small er,shallower and lighter, thus leading tooverall cost sav ings . A compositebeam requires the flange or cast-inplace slab and the girder to act as asingle unit.This monolithic behavior is possibleonly if the horizontal shear resultingfro m bending of the beam is effectively transferred between the fla ngeCAnil K. Patnaik, Ph. D.Structural EngineerWholohan Grill and PartnersPerth, Western AustraliaAustralia48and the girder at their interface. Thero ughness of the top of the precastconcrete beam, the amount of steelcrossi ng the joi nt and the concretestrength are the major factors affectingthe shear strength of the interface.Provisions for the design of the steelcrossing the interface between cast-inplace slabs and precast beams first appeared in the ACI Code' in 1963. Theseprov isio ns were based on the ACIASCE 333 report2 which summarizedthe research of Hanson3 and Kaar et al.4Based on pu sh-off tests by Birkelandand Birkeland, 5 Mast,6 Kriz and Raths7PCI JOURNAL
and Hotbeck et al., 8a new concept called "shear-friction" wasintroduced into the ACI Code in 1970. Saemann and Washa9and Nosseir and Murtha10 studied the interface shear strengthof composite beams to some extent. However, no other significant or systematic evaluation of horizontal shear strengthappears to have been made thereafter.We believe that the study presented here will provide newinsight into the behavior of "rough" joints in composite concrete beams and their capacity to develop interface shear fora wide range of steel ratios.PREVIOUS RESEARCHIn earlier studies, the shear strength of a joint was assumed to vary directly with the amount of reinforcing steelcrossing it. However, parabolic equations for shear transferstrength were suggested as early as 1968 by Birkeland 11 andlater by Raths 12 and Loov. 13 Based on a report by Shaikh, 14peps adopted a procedure which indirectly uses a parabolicequation. Walraven et al. 16 did an extensive statistical analysis on most of the data available from push-off tests andsuggested an equation which provides a good fit but is notconvenient for use in a design office. In their discussion ofthis paper, Mau and Hsu suggested a simpler design equation.16 A detailed literature review of the subject can befound in Patnaik's Ph.D. thesis. 17Some equations applicable for reinforcement crossingperpendicular to the interface are given here. More than 30shear-friction equations have been proposed by various researchers; therefore, symbols have been modified for consistency. The term Pv fy is referred to as the clamping stress.Linear Shear-Friction EquationThis equation was first introduced in 1958 by Mast6 andwas later developed further by Birkeland, Anderson 18 andtheir co-workers:(1)where f.1 is the coefficient of friction.The equation is simple but is very conservative for lowclamping stresses and unsafe for high clamping stresses.Birkeland's Equation.Birkeland 11 was the first to introduce a parabolic functionfor the shear strength along a joint:vn 2. 78 pJY (MPa)vn 33.5 pJY(2)(psi)Shaikh's EquationShaikh, 14 in his proposed revisions to shear-friction provisions, suggested an equation which can be rearranged as:(3a)in whichJanuary-February 1994f.1 6 · 9 ,1 2 (MPa)ef.leVu 1000/l}(psi)Vuwhere LOA has been substituted for f.1 and A is a constantused to account for the effect of concrete density.A 1.0 for normal weight concreteA 0.85 for sand-lightweight concreteA 0.75 for all-lightweight concreteThe design requirements of the peps are based on thisequation. If these two equations are combined, a parabolicequation for vu with respect to the clamping force is obtained:vu A 6. 9 /Jpvfy 0.25f;A 2 and 6. 9A 2 (MPa)(3b)vu A{fOOO (JpJY 0.25f;A 2 and 1000A2 (psi)where the capacity reduction factor, P 0.85 for shear.This equation is similar to Rath's equation 12 and Eq. (2).Eq. (3) represents the test data more closely than Eq. (1), butit does not include the effect of concrete strength variations.Loov's EquationLoov 13 was apparently the first to incorporate the influence of concrete strength:Vn k pvfYJ;(4)where k is a constant.A k of 0.5 was suggested for initially uncracked shear interfaces. For fJ 30.9 MPa (4480 psi), this equation is thesame as Eq. (2). One advantage of this equation is that anyconsistent system of units can be used without changes.Walraven's EquationA statistical analysis was conducted by Walraven et al. 16on the results of 88 push-off tests. The following equationwas suggested for a precracked shear interface:Vn Ct(Pvfy)cz (MPa)(5)vn C3(0.007 Pvfy)c4 (psi)if J; is assumed to be equal to 0.85 of the compressivestrength of 150 mm (6 in.) cubes:c 1 o.878 J;c3 16.8 J;04060406 0.167 ;o3o3andC2andc 4 o.o371J;0303Based on this equation, for J; 30 MPa or 4350 psi, theshear is roughly proportional to J; to the power 0.4 and theclamping stress to the power 0.47.Mattock's EquationIn his discussion of the paper by Walraven et al., Mattockadded the effect of concrete strength into his previous equation19 and reintroduced it as:49
Limiting Slips(6)Hanson 3 considered the maximum horizontal shearstrength to have been reached when a slip of 0.13 mm(0.005 in.) occurred, and this limit was later adopted by Saemann and Washa9 in their study . However, the fixing of alimiting value was not without controversy (Grossfield andBirnstiel) .2 ' Larger shear strengths would be recorded iflarger slips were permitted. In their discussion of Ref. 9,Hall and Mast suggested that, as for composite steel beams,there should be no limit for slip.and vn 0.3J;Equations for the shear strength of lightweight concretecan be found in Mattock et al.2 Mau and Hsu 's EquationIn their discussion of Eq. (5), Mau and Hsu' 6 suggested anequation similar to Eq. (4) with k 0.66. They assumed thatthe factor 0.66 would be the same for both initially crackedand uncracked shear interfaces.ACI Code 1The test data corresponding to horizontal shear failure ,found in previous studies, are shown in Fig. 1 along with thenominal shear specified by the ACI Code for a rough interface. The code provisions are a combination of special provisions for horizontal shear from Clause 17.5 ( 1 to 3 in thefollowing list) along with shear-friction provisions fromClause 11.7 (listed as 4 and 5 here). The lines shown inFig. 1 are based on a coefficient of friction J1 of 1.0 and aconcrete strength of at least 27.5 MPa (4000 psi).Push-Off TestsAttempts were made by Hanson 3 to correlate push-off testsand beam tests. By comparing shear-slip relations for the twotypes of specimens, he concluded that push-off tests are representative of beam tests for "rough bonded" connections.Clamping Stress, P}y, psi04002006001000BOOB10000000 6f'c 27.5 MPo (4000 psi)0BOO00c-;:;0.*:2VlVl !)'-ll4oro(/)0'-("()u"'0. 0600 0.c (/)0*20Evans & ChungHansonv)t/) !) (/)'C'O !)H u.cKaar. Kriz & RathsMattock & KaarNosseir & MurthaSaemann & Washa400(/)2000002468Clamping Stress, PJy, MPaFig. 1. Shear stresses- ACI 318-M92 compared with previous test results.50PCI JOURNAL
Clamping Stress RangeShear Stress Lirrllt1. 0 to 0.33 MPa(0 to 50 psi)2. 0.33 to 2.83 MPa(50 to 400 psi)tal shear stresses at 0.13 mm (0.005 in.) slip fall somewhatlower.The maximum clamping stress which has been used in theprevious beam tests is only 3 MPa (430 psi); therefore, forhigher clamping stresses there appear to be no publishedbeam data to support the code equations.0.6 MPa (80 psi)1.8 0.6pvf y MPa(260 0.6pvfY psi)3. 2.83 to 3.5 MPa(400 to 500 psi)4. 3.5 to 5.5 MPa(500 to 800 psi)5. Over 5.5 MPa(over 800 psi)3.5 MPa (500 psi)ANALYSIS METHODSWhen a beam is uncracked and linearly elastic, horizontalshear stresses can be evaluated by the equation:5.5 MPa (800 psi)VQv - h-The concrete strength does not affect the stress limits inany of these ranges except for Range 5. In this range, theshear stress is limited to 0.2J; when concrete strengths lessthan 27.5 MPa (4000 psi) are used. In Ranges 2 and 3 listedabove, these code provisions are a considerable improvement over those used in previous editions of the ACI Code.Although all of the plotted values have been described ashorizontal shear failures , a certain amount of caution is advised so that failures due to other causes are not ascribed tohorizontal shear. In particular, the result plotted for BeamIII-0.6-1.66, tested by Kaar et al. ,' indicates that the beamreached a load equivalent to 98 percent of the theoreticalflexural capacity before apparently failing in horizontalshear.On the other hand, the photograph of this beam shows acomplete web failure . Thus, failure may have been due to acombination of all three failure modes. Complete information on the tests by Hsu 24 is not available. The plotted valuesfrom Hanson correspond to those near failure. The horizon-V transverse shear fo;-ce at location under considerationQ first moment of area of portion above interface withrespect to neutral axis of sectionI moment of inertia of entire cross sectionbv width of interfaceThis equation can be used to evaluate the horizontal shearstress for cracked beams if Q and I are based on the crackedsection. Because it provides a common basis for comparison, this equation was adopted in previous studies eventhough Hanson 3 and Saemann and Washa9 recognized that itdoes not give an exact representation of the horizontal shearstress at failure. This expression was included in the ACICode untill970.Clause 17.5.3 of the ACI Code 1 allows design based onequilibrium conditions by: "computing the actual change incompressive or tensile force in any segment, and provisionsIBeamWidth ofinterface, b,,Length offlangeNo.mmmmArea oflongitudinalsteel, A,mm 2(7)vwhereTable 1. Properties of test beams.IIbEffectivedepth,dSpacing of#3 stirrupscrossinginterface, smmmmYieldstrength, f yMPaLongitudinal- -IlIStirrupsClampingstress, oo4S44281.6278I7S3200240028 4312885004314200.80288soo4314200.80IIIII0.82Note: 1 mm 0.0394 in.; 1 MPa 145 psi ; area of #3 bars 71 mm' .January-February 199451
made to transfer that force as horizontal shear to the supporting element." This relationship can be expressed as:(8)where Cis the total compression in the flange and v is thelength over which horizontal shear is to be transferred.The ultimate condition for horizontal shear cannot beachieved unless slip occurs between the precast and cast-inplace parts of a beam. The validity of the analysis of a composite concrete section using the procedures for a normalconcrete section is somewhat questionable after slip has occurred. In the closure of their paper, Saemann and Washa9justify the use of Eq. (7) even after slip has occurred. Theyassert that the designs will be safe if shear stresses, evaluated by using the elastic formula with cracked section properties, are less than the corresponding test strengths determined using the same procedure.In contrast to the common use of the entire length of theshear span for transferring the horizontal shear force, CTN'recommends that all the compressive force in the flange betransferred in a length equal to one quarter of the span of thebeam.By requiring that the horizontal shear strength be greaterthan the factored shear force at the section under consideration [see Eq. (17-1) and Section 17.5 where the horizontalshear is related to bvd], the code implies the following equation for horizontal shear stresses:(9)Eqs. (7), (8) and (9) appear to be quite different from oneanother and a designer could, understandably, be confusedas to which should be used.In f ct, the three equations are closely related. The termsVQ/1 in Eq. (7) give the rate of change of force in the flange.In Eq. (8), C 1 Cv is the average rate of change of force inthe flange between a section with a force C and a section adistance v away with zero force in the flange. This is thesame as Eq. (7) for point loads because the shear is constant.It is unsafe for uniform loading because the shear varies.Eq. (9) is similar to the others because V oM/ox is therate of change of moment. If the compression zone is entirely within the flange, and the small variation in depth ofthe stress block is ignored, then the compression force Cwill be equal to Ml(d - a/2) and the rate of change of forcein the flange will be V/(d- a/2). Therefore, Vuld in Eq. (9)is simply a non-conservative simplification of Eq. (7).TEST PROGRAMSixteen composite concrete beams were tested in thisstudy.2. The concrete strength was varied for a fixed clampingstress of about 0.8 MPa (120 psi).For the first variable, beams were tested with clampingstresses of 0.40, 0.77, 1.64, 2.73, 4.36, 6.06 and 7.72 MPa (58,112, 238, 396, 632, 879 and 1120 psi). The test values coverthe practical range of clamping stresses. To study the effect ofvariations in concrete strength, two beams were tested with acylinder strength of about 19.4 MPa (2800 psi) and with concrete strengths of 44 and 48.3 MPa (6400 and 7000 psi).MaterialsThree different concrete mixes were used. Fine aggregatewas washed local river sand and coarse aggregate was wellgraded with a maximum size of 14 mm (0.55 in.). The concrete control cylinders and the corresponding test beamwere cured under similar conditions. The concrete strengthfd of the web and the flange concrete was evaluated usingstandard cylinders. The modulus of elasticity of concretewas assumed to be (CAN3-A23.3-M84): 26orEc 5000{1; (MPa)Er 60200-JJ: (psi)The average observed modulus obtained from the concrete cylinders was 4100-J]: MPa, or 494001/77 psi, whichis considerably less. 17The average yield strength of longitudinal bars and stirrupsteel in different beams is given in Table 1. Steel crossingthe interface in all the beams consisted of #3 (9.5 mm diameter) bars. The modulus of elasticity for the reinforcing steel. was taken as 200 GPa (29000 ksi).Sizes of Test BeamsElevation views of the test beams are shown in Fig. 2.Beams 1 to 8 had flanges for their full length, while Beams9 to 16 had their flanges discontinued at 1.2 m (3 ft 11 in.)from the center of the beam. The two different shapes ofcross sections used for the test beams are shown in Fig. 3.The amount of steel crossing the interface and the width ofthe precast concrete girder at the interface (bv) were adjustedto achieve the desired level of clamping stress. The dimensions for different beams are summarized in Table 1.Two types of web reinforcement were used for beamswith a 75 mm (3 in.) web width. Stirrups crossing the interface were L-shaped and were provided in pairs. Stirrupsbelow the interface were U-shaped (see Fig. 3). Closed rectartgular stirrups were used for the precast concrete girder ofuniform width. Longer stirrups crossed the interface whileshorter stirrups were within the precast concrete girder. Stirrups were well anchored on both sides of the joint so theywere able to reach yield at the interface (Mattock). 27Typical details of beam reinforcement are shown in Fig.4. Complete details of all test beams are given by Patnaik. 17VariablesTwo major variables were investigated:1. The clamping stress was varied while maintaining theconcrete strength at about 35 MPa (5000 psi).52Joint PreparationThe test specimens were constructed to simulate beamswith a precast concrete girder and a cast-in-place flange.PCI JOURNAL
FlangeWebT(a) Test Beam with Full Length Flanges400FlangeWeb(b) Test Beam with Short Flanges-rs -----------------------------3-o so 4--All Dimensions ore in mm(1mm 0. ()394")Fig. 2. Elevation of test beams.400I··I Illf0.,1/)I·150400I··Ic: -1J1-- by 150(3 00 for Beom11)I· 150·IAll Dimensions ore in mm(300 for Beom11)(a) Beam Section with Thin Web( 1mm 0.0394")(b) Beam Section with Uniform Web WidthFig. 3. Typical sections of test beams.January-February 199453
The web portion was first fabricatedwith stirrups projecting from it. Flangeconcrete was placed three days later.To simplify construction, the interfacewas left as-cast with some of thecoarse aggregate protruding, instead ofmade as a "rough" surface with an amplitude of 5 mm (0.25 in.) required bythe ACI Code. 1The typical surface achieved in thistest program is shown in Fig. 5. Alarge percentage of the 14 mm (0.55in.) coarse aggregate can be seen protruding from the surface. This surfacecan be described as: well compactedhaving a rough surface, clean and freeof laitance, with coarse aggregate protruding but firmly fixed in the matrix.An unintenti onal variation in surface roughness occurred in this testingprogram. Very little coarse aggregateprotruded from the top surface ofBeam 14. The roughness of this surface, therefore, did not match the otherbeams of this test series.S}'n:!metric'XC 95Imm SupportBrs0 4 125 0 2000 mm 2Stirrups: Crossing Interface 9.5 mm 0 300 cjcBelow Interface 9.5 mm 0 300 c/cLong;tud;nol Steel:Details of Beam 3(a) Typical for a Beam with Full Length Flanges I!1supportLongaud;nol Steel: 4 125 0 2000 mm2Stkrups: Cross;nQ Interface 9.5 mm 0 500 c/c8 mm8 a rsul Below Interface -Instrumentation8 mmSpacer BorWelded toLongitudinalSteel0 125 c/c (Central 2.0 m)9.5 mm 0 75 c/c (End Portion)Slip gauges were provided in pairsDetails of Beams 13 to 16(1mm 0.0,394" )on either side of the web. This newtype of gauge was devised to record(b) Typical far a Beam with Short Flangesslips to an accuracy of 0.01 mm(0.0004 in.). The principles of theFig. 4. Typical reinforcement details of test beams.method are illustrated schematically inFig. 6. When the flange slides relativeto the web, the metal strip moves with the flange. The end ofthe strip is restrained by the pointed end of the screw, whichdeflects the strip as a short cantilever. These slip gauges aredescribed in detail by Patnaik.17Shear-friction equations assume yielding of the reinforcement crossing the interface. To investigate this assumption,strain gauges were glued on selected stirrups at the level of theinterface and strains were recorded at regular load intervals.Fig. 5. Typical roughness achieved for the test beams.TestingBeams were simply supported and loaded with a pointload at centerspan. These beams were intended to be verystrong in diagonal shear and flexure so that they would failin horizontal shear prior to failing in any other mode
Composite Concrete Beams With a Rough Interface Robert E. Loov D. Phil., P. Eng. Professor of Civil Engineering The University of Calgary Calgary, Alberta Canada Anil K. Patnaik, Ph. D. Structural Engineer Wholohan Grill and Partners Perth, Western Australia Australia 48 The latest version of the ACI Building Code requires five
Residual shear strength of a soil represents the lowest possible shear strength that a soil exhibits at large shear strains and this mobilized strength plays a significant role in the stability analyses. A slope does not fail if the applied shear stress is less than the residual shear strength (Gilbert et al. 2005).
If shear reinforcement is provided, the concrete contribution to shear strength in a reinforced concrete member is a function of both the aggregate interlock and the dowel action between the concrete and reinforcement. Once a shear crack forms, the shear reinforcement engages, providing the remaining shear capacity of the section V s. For
Chapter 3 3.1 The Importance of Strength 3.2 Strength Level Required KINDS OF STRENGTH 3.3 Compressive Strength 3.4 Flexural Strength 3.5 Tensile Strength 3.6 Shear, Torsion and Combined Stresses 3.7 Relationship of Test Strength to the Structure MEASUREMENT OF STRENGTH 3.8 Job-Molded Specimens 3.9 Testing of Hardened Concrete FACTORS AFFECTING STRENGTH 3.10 General Comments
Shear Stress vs Shear Displacement 0 20 40 60 80 100 0 2040 6080 100 Shear Displacement (mm) Shear Stress (kPa) Normal Stress - 20.93 kPa Field id: MID-AAF-0002-1 Measured Cohesion 14.99 Water Content 5.62 Shear box size 5.08 Peak Shear Stress 31.34 Intrinsic Cohesion 14.45 Wet Density 2240 Matri
Concrete contribution to the shear force capacity of a beam [N] V d Design shear force [N] V s Steel stirrups contribution to the shear force capacity of a beam [N] V p Axial load contribution to the shear force capacity of a beam [N] V i Other contributions to the shear capacity of a beam [N] V frp FRP contribution to the shear capacity [N]
The peak strength line has a slope of Φ and an intercept of c on the shear strength axis. The residual strength line has a slope of Φ r. The relationship between the peak shear strength . p. and the normal stress σ n can be represented by the Mohr-Coulomb equation: (1) where . c. is the cohesive strength of the cemented surface and . Φ
A-3 Short Beam Shear (ASTM D 2344) A-4 Two-Rail Shear (ASTM D 4255) A-5 Three-Rail Shear (ASTM D 4255) A-6 Shear Strength by Punch Tool (ASTM D 732) A-7 Sandwich Panel Flatwise Shear (ASTM C 273) A-8 Special Sandwich Panel Shear Fixture (ASTM C 273) SEZIONE B: PROVE DI COMPRESSIONE B-1 Wyoming Combined Loading Compression (ASTM D 6641) B-2 Modified ASTM D 695 (Boeing BSS 7260) B-3 IITRI .
Shear Tab fits in beam T dimension. Shear Tab moment capacity is less than the bolt group moment capacity. Shear Tab weld size is adequate. Shear Tab weld is double sided. Weld develops the strength of the Shear Tab. Bolt spacing is adequate. Bolt edge distances are adequate. Design Loads
