Design of Anchor Plates Based on the Component Method; Rybinski & Kulhmann

7/29/2019 Design of Anchor Plates Based on the Component Method; Rybinski & Kulhmann

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Design of anchor plates based on the component method

Prof. Dr.-Ing. Ulrike KuhlmannInstitute of Structural Design

Universität StuttgartStuttgart, Germany

[email protected]

Markus Rybinski

Institute of Structural DesignUniversität StuttgartStuttgart, Germany

[email protected]

ABSTRACT

Steel or composite joints can be designed and optimised by the component method accordingto Eurocodes [EN 1993-1-8:2005] and [EN 1994-1-1:2004]. The structural behaviour (strength,stiffness, ductility) of these joints is defined by assembled components. Their individual behav-iour is described by a mechanical spring model. For the extension of the component method to

anchor plates, which are used to transfer loads between steel and concrete structures, a me-chanical model has been developed. The model is based on several test series with anchorplates carried out by the Institute of Structural Design (Universität Stuttgart) and describes theload-carrying capacity of anchor plates. In some tests supplementary reinforcement has beentaken into account influencing the load capacity and ductility of these steel-to-concrete joints.Additional tests have been performed to study the influence of a flexible anchor plate on thestructural behaviour of the joint. Altogether, the component model shows transparency of loaddistribution and may easily be transferred to alternative situations.

APPLICATION OF ANCHOR PLATESIn mixed buildings various steel or composite elements like girders, columns or bracing tieshave to be connected to concrete members like staircases and fire protection walls, columns,strip foundations or foundation slabs. An effective solution for the load transfer between thesestructural steel and concrete elements is the application of anchor plates allowing for a quickand easy connection.

In Figure 1a-c different solutions for a pinned joint with anchor plates and welded headed studsare shown. The steel or composite elements are connected by a butt strap or a connection withwelded bolts developed by the steelwork and engineering companies. These fastening solutionsmeet basic demands like an economical and easy fabrication and a quick and easy erectionalso allowing for the adjustment of tolerances. By using post-installed anchors these joints can



also be used to connect steel members to existing concrete structures. Also rigid or semi-rigid joint solutions for steel members may be realized by taking into account the moment resistance,

stiffness and ductility of the joint. The joints of composite joints may be enhanced by assigningshear and compression loads to the anchor plate and using the slab reinforcement for tensionload transfer. So there is a variety of possibilities for the use of anchor plates as joints betweensteel / composite and concrete elements.

But typically problems occur where steel and concrete meet, due to a gap between the rules offastening design in concrete and steel design. There are different design methods for anchorplates as shown in the following section with different limitations in applicability and calculatedload capacity. Therefore new experimental and numerical investigations have been conductedto aim for an integrative solution of steel and concrete design rules based on the componentmethod which is already used for steel and composite joints.

EXISTING DESIGN METHODS FOR ANCHOR PLATES

At present, in European countries anchor plates are designed according to technical approvals[EOTA 2006]. The load distribution on anchors is calculated by elastic theory as shown in Fig-ure 2. For example, the anchor forces of an anchor plate loaded by a moment can be deter-mined by taking into account the stiffness of the anchors with positive elongation and the stiff-ness of the concrete under compression. The stiffness is proportional to the stressed cross-section and the modulus of elasticity. The stiffness of anchors under compression is neglected.The calculation is based on the assumption of a stiff anchor plate with full contact to the base,where the anchor plate remains plane and stays in the elastic range. The yielding of the anchorplate has to be avoided and the anchor displacements are normally insignificant.

(a) (b) (c)

Figure 1 – Application of anchor plates for connecting steel to concrete members

Figure 2 – Load distribution of anchors by elastic theory



The ultimate resistance of the anchors is calculated by the Concrete Capacity-Method [EOTA2006], [Eligehausen and Mallée and Silva 2006] which describes very well the load capacity ofanchors in plain concrete. If necessary, the influence of edge distances of the anchors has to

be taken into account. The possibilities to consider supplementary reinforcement are limitedand if both shear and tension forces occur, a conservative interaction relation has to be verified.Also in some cases, supplementary reinforcement may even not be considered for anchors withsmall edge distances.

The final draft of the Technical Specification [prCEN/TS 1992-4-2:2007] considers hanger rein-forcement for anchors loaded by tension forces by a strut and tie model, see Figure 3a. Thetension forces of the studs are anchored by stirrups. The resistance of the stirrups is calculatedwith the effective anchor length l1 and the concrete bond strength in the concrete breakout conefollows [EN 1992-1-1:2004]. In addition by surface reinforcement acting rectangular to theedges another strut and tie model is applied to take up shear forces, see Figure 3b. So the ac-tual situation to consider reinforcement for the transfer of shear/tension forces has much im-

proved.

The design of anchor plates with elastic theory often leads to thick, uneconomic steel plates.Therefore an optimization of the joint may be achieved by a plastic design approach.

In [prCEN/TS 1992-4-2:2007] rules for a flexible, thin anchor plates are given. Focus is given toa maximum utilization of the fasteners, so no yielding of the base plate on the tension side isallowed whereas yielding of the base plate on the compression side is possible. However, independence of the stiffness of the anchor plate, a reduced inner lever arm of the resultant con-crete compression force and the tension stud force has to be taken into account. Thus, a cer-tain optimization of the construction of the joint may be realized but this plastic design approachdoes not include any regulations for the design of the joint stiffness and ductility what is neces-sary for a complete plastic design approach.

So the application of the component method offers the possibility to determine the structural

joint behaviour like strength, stiffness and ductility. But the implementation of this method forthe design of column bases in [EN 1993-1-8:2005] shows up to now some limitations andweaknesses [Stark 2007]. For example, the types of fasteners are restricted to anchor boltswith sufficient anchorage length of the anchor bolts to avoid a concrete failure mode, othertypes are not sufficiently described or included. Also a very conservative position of the con-crete compression force directly under the compression flange of the column has to be consid-ered.

A combination of the introduced design methods with consideration of the needs of steel andfastenings designer on basis of the component method will help to realize an economic andsafe design of the mentioned steel-to-concrete joints. Therefore different experimental und nu-merical investigations have been started to improve the component method for anchor plates.

(a) (b)

Figure 3 – Strut and tie models for load transmission between studs and reinforcement[prCEN/TS 1992-4-2:2007]



(a) (b)

Figure 5 – Load capacity of anchor plates in dependence of (a) the effective stud lengthhef and (b) the number of stirrups within the concrete breakout cone

INVESTIGATIONS ON ANCHOR PLATES WITHOUT INFLUENCE OF EDGE DISTANCES

Within the first experimental investigations [Kuhlmann and Imminger 2004] main focus was

given to the load capacity of stiff anchor plates with headed studs without influence of edge dis-tances in dependence of different joint parameters like the effective stud length hef, the distances between the stud axis, the number n of stirrups in the concrete breakout cone, the surface

reinforcement as⊥ and asII, the concrete grade and the load eccentricity e (related to the con-crete surface), see Figure 4a. The anchor plate was installed flush with the concrete surface.Due to an installed soft strip at the edges of the anchor plate shear loads were only transmittedby mechanical shear elements and friction. The tests were performed deformation-controlled toexamine the joint ductility, the load capacity and the structural behaviour after failure. The test

setup for pure shear loading (α=0°) is shown in Figure 4b.

Due to the variation of only one parameter within a test row, the influence of each parametercould be identified. The most effective way to increase the joint load capacity was to extend theeffective stud length hef, as shown in Figure 5a. Beside the increasing load-carrying capacity ofthe concrete breakout cone, an increased transmission length between headed studs and stir-rups enhances the load capacity of the whole joint.

The influence of the number n of stirrups within the concrete breakout cone is shown in Figure5b. The load capacity increases by 30 percent when using an additional stirrup within the con-crete breakout cone and can be increased up to 45 percent by using several stirrups.

Also the ductility of these steel-to-concrete joints is increased clearly due to the ductile behav-iour of the supplementary reinforcement instead of a brittle failure of the concrete cone.

(a) (b)

Figure 4 – Tests without edge distances: (a) varied parameters and(b) test setup for shear loading



(a) (b)

Figure 6 – Deformed anchor plate at maximum load with indication of resultant forces and

normal stress distribution: (a) normal stresses σz and (b) normal stresses σy

(a) (b)

Figure 7 – Column base and strip foundation: (a) possible loading and (b) test specimen

The experimental investigations were accompanied by numerical investigations with the pro-

gram MASA © developed for non-linear calculations of fastenings in concrete at the Institute ofConstruction Materials, Universität Stuttgart. The numerical model showed satisfying correlationbetween test and calculated load capacity of the anchor plates with supplementary reinforce-ment. So the numerical model was used for further parameter studies to identify the decisiveparameters for the mechanical model.

As an example, for an anchor plate loaded by a shear force V the inner load distribution may bedescribed as follows: due to the eccentricity of the shear force a tension stud force N on thenon-loaded side of this configuration appears, see Figure 6a. The integrated normal stress ofthe other studs sums up to nearly 0, so that these studs have no tension forces which have tobe considered for the design of the inner moment resistance. In Figure 6a and 6b sketches of

the normal stresses σz and σy calculated for the anchor plate at maximum load are shown. The

shear force V is transmitted into the concrete specimen mostly by the shear studs V 2 on theloaded side as well as by the shear studs V1 and friction Vf between anchor pate and concretesurface.

INVESTIGATIONS ON ANCHOR PLATES CLOSE TO THE EDGE

Anchor plates with studs in short edge distances like strip foundations, see Figure 7a, or con-crete columns are often designed by technical approvals [EOTA 2006]. Here consideration ofsupplementary reinforcement like stirrups is not included sufficiently. Therefore some experi-mental and numerical studies have started [Kuhlmann and Rybinski 2007] to take into accountthe influence of stirrups on the load-capacity for longitudinal shear loading, see Figure 7b.



(a) (b)

Figure 8 –Anchor plate with edge distances loaded by an eccentric shear force:

(a) load-displacement curve and (b) load-strain curve of stirrups

Figure 9 – Test loads under shear loading

The test specimens were loaded by shear forces with an eccentricity e=45 mm, combined ten-sion / shear forces or tension forces. Beside variation of the concrete grade, the main focuswas given to the variation of the hanger reinforcement. The tests were performed with a mini-

mal configuration (stirrups ∅6/150mm), a basic configuration (stirrups ∅8/150mm) and an ad-

vanced configuration (stirrups ∅10/150mm and additional stirrups beside stud rows).

In Figure 8a the load-displacement curve for the basic configuration is shown. When first cracksappeared, the tension load of the stud row 1 was transferred to the nearby stirrups with increas-ing loading, see Figure 8b. Due to the application of stirrups in the concrete breakout cone, aductile joint failure could be observed. However, for this configuration the measured strains in

the stirrups remained in the elastic range.In Figure 9 the influence of the different stirrup configurations on the load capacity is shown.For the minimal configuration a pure concrete failure mode is decisive whereas the configura-

tion with stirrups ∅8/150mm is about the borderline between stirrup and concrete failure. Anincreased load-capacity can be achieved by the configuration with more stirrups. For the studsin short edge distances the most effective way to increase the load-capacity however is ahigher concrete grade.

For anchor plates close to the edges more failure modes like concrete edge failure have to beconsidered than for fastenings in continuous slabs. The calculative consideration in the compo-nent model is possible by existing design rules for the fastenings [prCEN/TS 1992-4-2:2007],[EN 1994-2:2005].



Figure 10 – Calculation scheme for anchor plates with shear loading

MECHANICAL MODEL FOR DESIGN OF ANCHOR PLATES

Based on the component method, a first mechanical model for stiff anchor plates was devel-

oped and verified by the accomplished tests [Kuhlmann and Imminger 2004], [Kuhlmann andRybinski 2007] where the calculated load capacity slightly underestimates the test results. Thedesign model may be used for anchor plates under shear, tension or combined forces inde-pendent of the kind of fastener and with consideration of supplementary reinforcement.

Within the scope of this first model only the maximum strength was considered. The stiffnessand the ductility of the components as also of the joint were not been taken into account, due toa clear inner load distribution, e.g. as there is only one type of fastener for tension load transfer.If shear forces are transmitted by several rows of fastener or different fasteners, the stiffness ofthe fastener has to be considered in order to calculate the inner distribution of the shear force.If, in addition, the connection device is designed according plastic resistance, the ductility of thefastener has to be considered as well. However, for the examined anchor plates the stiffnessand ductility of the components may be neglected.

For each configuration of anchor plate three different component groups in dependence on thecomponent loading are identified: tension, shear and compression. The component group "ten-sion" may be modeled as several springs in a row. Each failure mode of the component groupcan be understood as a single spring and the load capacity of the component group is definedby the weakest spring. The component group "shear" may be understood as spring model withsprings in parallel. Each shear component is defined as a single spring. Thus, a failure of onecomponent does not cause a complete failure of the whole joint. The load capacity of the com-ponent group "shear" can be determined as the sum of the shear components.

The maximum resistance of anchor plates loaded by shear forces may be calculated followingthe calculation scheme in Figure 10. The scheme may be adopted for other types of loading.



(a) (b)

Figure 11 – Two states of equilibrium (a) tension and compression forces acting rectan-gular to the concrete surface and (b) shear forces acting parallel to the concrete surface

So in the first step the maximum strength of the component group "tension" Nb1,R has to be cal-culated taking into account the different failure modes like steel failure NR,s, pull-out failure NR,p,

blow-out failure NR,cb and concrete cone failure with or without reinforcement NR,c or NR,re ac-cording to [prCEN/TS 1992-4-2:2007], see Equation (1). Figure 3a shows the strut and tiemodel [prCEN/TS 1992-4-2:2007] for determining the transferable load of the reinforcement.The load of the reinforcement is limited by steel and anchorage failure [EN 1992-1-1:2004].

(1) ( )re ,R c ,R cb ,R p ,R s ,R R ,b N ; N max ; N ; N ; N min N =1

Then the assumption is made that the component group "tension" is decisive for joint failureN j=Nb1,R. Figure 11a shows the equilibrium of forces acting rectangular to the concrete surface,where the concrete compression force Nc has to be equal to the tension force of stud row Nb1,R.The height of the compression zone x can be determined by the allowable stress f j according[EN 1993-1-8:2005] and [EN 1992-1-1:2004]. Thus the inner lever arm and the inner moment

resistance of the anchor plate can be determined, see Equation (2).

(2) ( ) i c c R ,i z N x .d N M ⋅=⋅−⋅= 50

In Figure 11b the shear forces acting parallel to the concrete surface are identified. The friction

force Vf may be calculated with the coefficient of friction µ between steel and concrete and thecompression force Nc. The maximum shear strength VR(Mi,R) in dependence on the calculatedinner moment resistance Mi,R of the anchor plate may be calculated by the equilibrium of mo-ment in the point of application of the resultant shear force Vb2 of the studs whereas it is as-sumed that inner lever arm eb1 is approximately equal to eb2. The inner lever arm can be esti-mated in dependence of the stud diameter dstud, the concrete grade and the degree of utilisationof the stud. In the component model the inner lever arm was set equal to 0.5-1.0 dstud.

The maximum shear strength of the component group "shear" consists of the friction force V f,the shear resistance of stud row Vb2,R and the residual shear resistance Vb1,R(N j) considering theinteraction relation between shear and tension forces of the studs. The maximum shear resis-tance of the studs has to be calculated taking into account the different failure modes like localconcrete failure VR,cl=PRd,2 [EN 1994-2-1:2004], steel failure VR,s, concrete pry-out failure VR,cp orconcrete edge failure VR,c. If the concrete edge failure becomes decisive, the stirrups can betaken into account to strengthen the component load capacity as shown in Figure 12. They takeup the rectangular acting splitting forces comparable to the design model for horizontally lying

shear studs in concrete slabs of composite girders [EN 1994-2:2005]. The factor ψ a,c takes intoaccount the orientation of the shear loading Vbi and position of the stirrups [Kuhlmann and Ry-binski 2007].



Figure 12 – Strut and tie model for concrete edge failure

In the last step the assumption of a tension failure mode has to be checked. If the calculatedstrength VR(Mi,R) exceeds the calculated shear resistance of the stud rows V b1,R and Vb2,R and

the friction force Vf, the assumption of a tension failure mode is not fulfilled and the load capac-ity of the anchor plate has to be recalculated iteratively with a reduced tension stud forceN j+1 < N j unless the assumption is fulfilled and the maximum shear resistance is determined asVR(Mi,R).

The introduced model is valid for stiff anchor plates in pure or reinforced concrete members farwith or without influence of edges and if the loading of the anchor plate is in longitudinal orienta-tion of the concrete member. The load transfer inside of the concrete member is assumed onboth sides of the anchor plate as shown in the simplified strut and tie model for tension andshear loading in Figure 13. First studies of anchor plates in a cantilever have started, but needmore general investigations for validation.

SEMI-RIGID COLUMN BASES FOR PLASTIC DESIGN

Steel and composite structures like mixed buildings or steel frames shown in Figure 14a areoften designed using plastic design methods. Beside the load capacity also the stiffness andductility of the joints have to be taken into account because they determine the inner forces, theframe displacements and the joint loading.

Especially the design of steel structures like sway frames as shown in Figure 14b is very sensi-tive to the joint stiffness. The usual assumption of a rigid or pinned connection for column basesoften does not comply with the real behaviour of the steel-to-concrete joints. Therefore an ap-propriate design model for steel-to-concrete joints is needed, determining the realistic structuralbehaviour of column bases under normal and shear forces and bending moments.

(a) (b)

Figure 13 – Simplified strut and tie model for an anchor plate in a reinforced concretemember (a) loaded by a tension force and (b) loaded by an eccentric shear force



(a) (b)

Figure 15 – (a) Test-setup for large load eccentricity and (b) adapted component modelfor column bases with stiff or flexible anchor plates

An interdisciplinary research collaboration [Kuhlmann et al 2008] of the Institute of StructuralDesign and the Institute of Construction Materials has been started where several tests on col-umn bases have been conducted examining the structural behaviour of semi-rigid steel-to-

concrete joints. The project aims at a design model determining a realistic structural behaviourof column bases under combined loading (shear and normal forces, bending moment) consid-ering the different methods for steel and fastenings design.

INVESTIGATIONS FOR FLEXIBLE ANCHOR PLATES

Within the experimental investigations in the frame of the interdisciplinary research project[Kuhlmann et al 2008] different parameters were varied like the thickness and stiffness of theanchor plate, the eccentricity of the applied shear force (e=50/1000mm, see Figure 15a), thetype of fastener (headed studs and undercut anchors with mortal layer), the diameter and effec-tive length hef of the studs as also the normal force in the column. The measurements also con-sidered the influence of friction coefficient between the anchor plate and concrete ele-

ment/mortal layer. So different failure modes like concrete cone failure, concrete pry-out failure,steel failure of the studs in tension or shear and yielding of the anchor plate could be observedand used for verification of the adapted component model. Altogether the test program included12 tests with headed studs and 8 tests with undercut anchors and mortal layer without edge dis-tances and without supplementary reinforcement. By application of strain gauges and conduc-tors the tension forces in the studs as also the deformations of the anchor plate in the com-

(a) (b)

Figure 14 – Steel frames: (a) typical structural system and (b) frame with semi-rigid joints



Figure 16 – Measured and calculated M-φ-curves for ductile steel failure

pression and tension zone were monitored during loading and are basis for followed numericalexaminations.

The component model was adapted by considering the stiffness of the anchor plate on the ten-sion and compression zone. The non-linear behaviour of the anchor plate was defined in com-parison to the equivalent T-stub model [EN 1993-1-8:2005]. The basic calculation principle oftwo equilibriums of forces was retained unchanged, see Figure 15b. In the first step the anchorplate was calculated for a M-N-interaction, where the stiffness of the flexible anchor plate (Ka,T and Ka,C), the stiffness of the studs, considering the elongation of the studs Kb1,1 and the dis-placement at the head of the studs Kb1,2, and the concrete compression zone Kc, simulated byseveral non-linear concrete springs, were considered. In the second step the shear resistanceof the anchor plate is checked considering the stiffness of the different stud rows Kb1,V and Kb2,V and the friction forces in the concrete compression zone. The interaction effects of the twostates were considered by interaction of the structural behaviour of the studs.

Altogether the component model slightly underestimates the load-capacity of the anchor platesfor flexible anchor plates in particular. The moment-rotation-curves for a ductile steel failure ofthe fastener are shown in Figure 16, whereas Figure 17 shows a non-ductile concrete breakoutfailure each for a stiff and a flexible anchor plate. The calculated failure modes and the load-displacement curves were sufficiently described compared to the test results, so that the com-ponent model shows good correlation to the performed tests.

CONCLUSION

The developed component model for the design of anchor plates considers the different possi-ble failure modes of the studs, of the concrete member, of the supplementary reinforcementand of the anchor plate. The structural behaviour of the components is described on basis of

Figure 17 –Measured and calculated M-φ-curves for non-ductile concrete failure



existing European Codes [EN 1993-1-8:2005], [EN 1992-1-1:2004] and Technical Specifica-tions [prCEN/TS 1992-4-2:2007]. The structural behaviour of the whole joint like load-capacity,stiffness and ductility is determined quite well, but still needs more investigations and verifica-

tion to achieve a better acceptance of the component model for steel-to-concrete joints.

ACKNOWLEDGEMENT

Acknowledgement is given to the research funding associations "Deutsche Forschungsgemein-schaft (DFG)", "Forschungsvereinigung Stahlanwendung e.V." as also to the companies Gold-beck West GmbH and Köster &Co. GmbH for their financial support of the carried out researchprojects. The authors also want to thank the staff members of the testing laboratories of the In-stitute of Construction Materials and the Otto-Graf-Institute (FMPA) at Universität Stuttgart.

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rules for buildings, European Committee for Standardization, 2004.

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EN 1993-1-8:2005: Eurocode 3: Design of steel structures – Part 1-8: Design of joints, Euro-pean Committee for Standardization, 2005.

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Kuhlmann and Eligehausen and Rybinski and Fichtner 2008: Modellierung biegeweicher Stüt-zenfüße im Stahl- und Verbundbau als integriertes System von Tragwerk und Fundament,Report, Deutsche Forschungsgemeinschaft (DFG), 2008.

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Design of Anchor Plates Based on the Component Method; Rybinski & Kulhmann