Chapter 1: Introduction

Transcription

1 Chapter 1: Introdution 1.1 Pratial olumn base details in steel strutures Pratial olumn base details Every struture must transfer vertial and lateral loads to the supports. In some ases, beams or other members may be supported diretly, though the most ommon system is for olumns to be supported by a onrete foundation. The olumn will be onneted to a baseplate, whih will be attahed to the onrete by some form of so-alled holding down assembly. Typial details are shown in Figure 1.1. The system of olumn, baseplate and holding down assembly is known as a olumn base. This publiation proposes rules to determine the strength and stiffness of suh details. I or H Setion olumn Grout Base plate Foundation Paks Tubular sleeve Conial sleeve Anhor plates Holding down bolts Anhor plates Hook bolts Cast in setion Stub on underside of base to transfer shear Cover plate Oversize hole 'T' bolt Underut anhors Cast in hannel Figure 1.1 Typial olumn base details 1.1

2 Other olumn base details may be adopted, inluding embedding the lower portion of olumn into a poket in the foundation, or the use of baseplates strengthened by additional horizontal steel members. These types of base are not overed in this publiation, whih is limited to unstiffened baseplates for I or H setions. Although no detailed guidane is given, the priniples in this publiation may be applied to the design of bases for RHS or CHS setion olumns. Foundations themselves are supported by the sub-struture. The foundation may be supported diretly on the existing ground, or may be supported by piles, or the foundation may be part of a slab. The influene of the support to the foundation, whih may be onsiderable in ertain ground onditions, is not overed in this doument. Conrete foundations are usually reinfored. The reinforement may be nominal in the ase of pinned bases, but will be signifiant in bases where bending moment is to be transferred. The holding down assembly omprises two, but more ommonly four (or more) holding down bolts. These may be ast in situ, or post-fixed to the ompleted foundation. Cast in situ bolts usually have some form of tubular or onial sleeve, so that the top of the bolts are free to move laterally, to allow the baseplate to be aurately loated. Other forms of anhor are ommonly used, as shown in Figure 1.. Baseplates for ast-in assemblies are usually provided with oversize holes and thik washer plates to permit translation of the olumn base. Post-fixed anhors may be used, being positioned aurately in the ured onrete. Other assemblies involve loose arrangements of bolts and anhor plates, subsequently fixed with ementiious grout or fine onrete. Whilst loose arrangements allow onsiderable translation of the baseplate, the lak of initial fixity an mean that the olumn must be propped or guyed whilst the holding down arrangements are ompleted. Anhor plates or similar embedded arrangements are attahed to the embedded end of the anhor assembly to resist pull-out. The holding down assemblies protrude from the onrete a onsiderable distane, to allow for the grout, the baseplate, the washer, the nut and a further threaded length to allow some vertial tolerane. The projetion from the onrete is typially around 1 mm, with a onsiderable threaded length. Post-fixed assemblies inlude expanding mehanial anhors, hemial anhors, underut anhors and grouted anhors. Various types of anhor are illustrated in Figure

3 a b d e f a, b d e f ast in plae post fixed, underut post fixed hemial or ementiius grout post fixed expanding anhor fixed to grillage and ast in-situ Figure 1. Alternative holding-down anhors The spae between the foundation and the baseplate is used to ensure the baseplate is loated at the orret absolute level. On smaller bases, this may be ahieved by an additional set of nuts on the holding down assemblies, as shown in Figure 1.3. Commonly, the baseplate is loated on a series of thin steel paks as shown in Figure 1.4, whih are usually permanent. Wedges are ommonly used to assist the plumbing of the olumn. Figure 1.3 Baseplate with levelling nuts The remaining void is filled with fine onrete, mortar, or more ommonly, non-shrink ementiious grout, whih is poured under and around the baseplate. Large baseplates 1.3

4 generally have holes to allow any trapped air to esape when the baseplate is grouted. Permanent k Temporar wedge Grout h l Figure 1.4 Baseplate loated on steel paks The plate attahed to the olumn is generally retangular. The dimensions of the plate are as required by design, though pratial requirements may mean the base is larger than neessitated by design. Steel eretors favour at least four bolts, sine this is a more stable detail when the olumn is initially ereted. Four bolts also allow the baseplate to be adjusted to ensure vertiality of the olumn. Bolts may be loated within the profile of the I or H setion, or outside the profile, or both, as shown in Figure 1.1. Closely grouped bolts with tubular or onial sleeves are to be avoided, as the remaining onrete may not be able to support the olumn and superstruture in the temporary ondition. Bases may have stubs or other projetions on the underside whih are designed to transfer horizontal loads to the foundations. However, suh stubs are not appreiated by steelwork eretors and should be avoided if possible. Other solutions may involve loating the base in a shallow reess or anhoring the olumn diretly to, for example, the floor slab of the struture. Columns are generally onneted to the baseplate by welding around part or all of the setion profile. Where orrosion is possible a full profile weld is reommended. 1.4

5 1.1. Pinned base details Pinned bases are assumed in analysis to be free to rotate. In pratie pinned bases are often detailed with four holding down bolts for the reasons given above, and with a baseplate whih is signifiantly larger than the overall dimensions of the olumn setion. A base detailed in this way will have signifiant stiffness and may transfer moment, whih assists eretion. In theory, suh a base should be detailed to provide onsiderable rotational apaity, though in pratie, this is rarely onsidered Fixed base details Fixed (or moment-resisting) bases are assumed in analysis to be entirely rigid. Compared to pinned bases, fixed bases are likely to have a thiker baseplate, and may have a larger number of higher strength holding down assemblies. Oasionally, fixed bases have stiffened baseplates, as those shown in Figure 1.5. The stiffeners may be fabriated from plate, or from steel members suh as hannels. Stiffener Figure 1.5 Typial stiffened olumn base detail 1.5

6 1.1.4 Resistane of olumn bases Euroode 3, Setion 6 and Annex L ontain guidane on the strength of olumn bases. Setion 6 ontains priniples, and Annex L ontains detailed appliation rules, though these are limited bases subjet to axial loads only. The priniples in Setion 6 over the moment resistane of bases, though there are no appliation rules for moment resistane and no priniples or rules overing the stiffness of suh bases. Traditional approahes to the design of moment-resisting bases involve an elasti analysis, based on the assumption that plane setions remain plane. By solving equilibrium equations, the maximum stress in the onrete (based on a triangular distribution of stress), the extent of the stress blok and the tension in the holding down assemblies may be determined. Whilst this proedure has proved satisfatory in servie over many years, the approah ignores the flexibility of the baseplate in bending, the holding down assemblies and the onrete Modelling of olumn bases in analysis Traditionally, olumn bases are modelled as either pinned or as fixed, whilst aknowledging that the reality lies somewhere within the two extremes. The opportunity to either alulate or to model the base stiffness in analysis was not available. Some national appliation standards reommend that the base fixity be allowed for in design. The base fixity has an important effet on the alulated frame behaviour, partiularly on frame defletions. 1. Calulation of olumn base strength and stiffness 1..1 Sope of the publiation In reent years, Wald, Jaspart and others have direted signifiant researh effort to the determination of resistane and stiffness. Based on the results of this researh, reommendations for the design and verifiation of moment-resisting olumn bases ould be drafted. This permits the modelling in analysis of semi-ontinuous bases in addition to the traditional pratie of pinned and fixed bases. Both resistane and stiffness an be determined. This publiation ontains proposals for the alulation of the apaity and of the stiffness of moment-resisting bases, with the intention that these be inluded in Euroode 3. This publiation is foused on I or H olumns with unstiffened baseplates, though the priniples in this publiation may be applied to baseplates for RHS or CHS olumns. Embedded olumn base details are exluded from the reommendations in this publiation 1.6

7 The effet of the onrete-substruture interation on the resistane and stiffness of the olumn base is exluded. 1.. Component method The philosophy adopted in this publiation is known as the omponent method. This approah aords with the approah already followed in EC3 and, in partiular, Annex J, where rules for the determination of beam to olumn strength and stiffness are presented. The omponent approah involves identifying eah of the important features in the base onnetion and determining the strength and stiffness of eah of these omponents. The omponents are then assembled to produe a model of the omplete arrangement. Eah individual omponent and the assembly model are validated against test results. 1.3 Doument struture Setion of this doument ontains details of the omponents in a olumn base onnetion, namely: The ompression side - the onrete in ompression and the flexure of the baseplate. The olumn member. The tension side - the holding-down assemblies in tension and the flexure of the baseplate. The transfer of horizontal shear. Eah sub-setion overs a omponent and follows the following format: A desription of the omponent. A review of existing relevant researh. Details of the proposed model. Results of validation against test data. Setion 3 desribes the proposed assembly model and demonstrates the validity of the proposals ompared to test data. Setion 4 makes reommendations for the pratial use of this doument in analysis of steel frames. Setion 5 makes reommendations for the lassifiation of bases as sway or non-sway, in braed and unbraed frames. 1.7

8 1.8

9 Chapter : Component harateristis.1 Conrete in ompression and base plate in bending.1.1 Desription of the omponent The omponents onrete in ompression and base plate in bending inluding the grout represent the behaviour of the ompressed part of a olumn base with a base plate. The strength of these omponents depend primarily on the bearing resistane of the onrete blok. The grout is influening the olumn base bearing resistane by improving the resistane due to appliation of high quality grout, or by dereasing the resistane due to poor quality of the grout material or due to poor detailing. The deformation of this omponent is relatively small. The desription of the behaviour of this omponent is required for the predition of olumn bases stiffness loaded by normal fore primarily..1. Overview of existing material The tehnial literature onerned with the bearing strength of the onrete blok loaded through a plate may be treated in two broad ategories. Firstly, investigations foused on the bearing stress of rigid plates, most were onerned the prestressed tendons. Seondly, studies were onentrated on flexible plates loaded by the olumn ross setion due to an only portion of the plate. The experimental and analytial models for the omponents onrete in ompression and plate in bending inluded the ratio of onrete strength to plate area, relative onrete depth, the loation of the plate on the onrete foundation and the effets of reinforement. The result of these studies on foundations with punh loading and fully loaded plates offer qualitative information on the behaviour of base plate foundations where the plate is only partially loaded by the olumn. Failure ours when an inverted pyramid forms under the plate. The appliation of limit state analysis on onrete an inlude the three-dimensional behaviour of materials, plastifiation and raking. Experimental studies (Shelson, 1957; Hawkins, 1968, DeWolf, 1978) led to the development of an appropriate model for olumn base bearing stress estimation that was adopted into the urrent odes. The separate hek of the onrete blok itself is neessary to provide to hek the shear resistane of the onrete blok as well as the bending or punhing shear resistane aording to the onrete blok geometry detailing. The influene of a flexible plate was solved by replaing the equivalent rigid plate (Stokwell, 1975). This reasoning is based on reognition that uniform bearing pressure is unrealisti and.1

10 that maximum pressure would logially follow the profile shape. This simple pratial method was modified and heked against the experimental results, (Bijlaard, 198; Murray, 1983). Euroode 3 ( Annex L, 199) adopted this method in onservative form suitable for standardisation using an estimate inluding the dimensions of the onrete blok ross-setion and its height. It was also found (DeWolf and Sarisley, 198; Wald, 1993) that the bearing stress inreases with larger eentriity of normal fore. In this ase is the base plate in larger ontat with the onrete blok due to its bending. In ase, when the distane between the plate edge and the blok edge is fixed and the eentriity is inreased, the ontat area is redued and the value of bearing stress inreases. In ase of the rushing of the onrete surfae under the rigid edge is neessary to apply the theory of damage. These ases are unaeptable from design point of view and are determining the boundaries of above desribed analysis..1.3 Proposed model Strength The proposed design model resistane of the omponents onrete in ompression and base plate in bending is given in Euroode 3 Annex L, 199. The resistane of these omponents is determined with help of an effetive rigid plate onept. The onrete blok size has an effet on the bearing resistane of the onrete under the plate. This effet an be onservatively introdued for the strength design by the onentration fator k = j a b 1 1 a b (.1.1) where the geometry onditions, see Figure.1.1, are introdued by a 1 = a + a 5 a min, a a a h + 5 b 1 r 1 (.1.) b 1 = b + b 5 b min, b b b h + 5 a 1 r 1 (.1.3) This onentration fator is used for evaluation of the design value of the bearing strength as.

11 follows f = j β j k γ j f k (.1.4) where joint oeffiient is taken under typial onditions with grout as β j = / 3. This fator βj represents the fat that the resistane under the plate might be lower due to the quality of the grout layer after filling. F Rd a a 1 a r t h b b 1 b r Figure.1.1 Evaluation of the onrete blok bearing resistane The flexible base plate, of the area Ap an be replaed by an equivalent rigid plate with area A eq, see Fig.1.. The formula for alulation of the effetive bearing area under the flexible base plate around the olumn ross setion an be based on estimation of the effetive width. The predition of this width an be based on the T-stub model. The alulation seures that the yield strength of base plate is not exeeded. Elasti bending moment resistane of the base plate per unit length should be taken as M = 1 t f y 6 (.1.4) and the bending moment per unit length on the base plate ating as a antilever of span is, see Figure.1.3. M = 1 f j (.1.4).3

12 A p A A eq Figure.1. Flexible base plate modelled as a rigid plate of effetive area with effetive width When these moments are equal, the bending moment resistane is reahed and the formula evaluating an be obtained 1 1 f t f j 6 = (.1.4) y as = t 3 f f y j γ M (.1.5) The omponent is loaded by normal fore FSd. The strength, expeting the onstant distribution of the bearing stresses under the effetive area, see Figure.1.3 is possible to evaluate for a omponent by = = + (.1.6) F F A f ( t ) L f sd Rd eq j w j olumn F Sd F Rd L t base plate t w f j Figure.1.3 The T stub in ompression, the effetive width alulation The improvement of effetive area due to the plate behaviour for plates fixed on three or four edges an be based on elasti resistane of plates (Wald, 1995) or more onservatively an be limited by the deformations of plate as is reahed for antilever predition. This improvement is not signifiant for open ross setions, till about 3%. For tubular olumns the plate.4

13 behaviour inrease the strength up to 1% aording to the geometry. The pratial onservative estimation of the onentration fator, see Eq. (.1.1), an be preised by introdution of the effetive area into the alulation; into the proedure Eq. (.1.1) - (.1.3). This leads however to an iterative proedure and is not reommended for pratial purposes. The grout quality and thikness is introdued by the joint oeffiient βj, see SBR (1973). For β j = / 3, it is expeted the grout harateristi strength is not less than, times the harateristi strength of the onrete foundation f.g, f and than the thikness of the grout is not greater than, times the smaller dimension of the base plate t g, min (a ; b). In ases of different quality or high thikness of the grout tg, min (a ; b), it is neessary to hek the grout separately. The bearing distribution under 45 an be expeted in these ases, see Figure.1.4., (Bijlaard, 198). The influene of paking under the steel plate an be negleted for the design (Wald at al, 1993). The influene of the washer under plate used for eretion an be also negleted for design in ase of good grout quality f.g, f. In ase of poor grout quality f.g, f it is neessary to take into aount the anhor bolts and base plate resistane in ompression separately. tg t t g tg washer under base plate h o 45 t g 45 o paking Figure.1.4 The stress distribution in the grout.1.3. Stiffness The elasti stiffness behaviour of the T-stub omponents onrete in ompression and plate in bending exhibit the interation between the onrete and the base plate as demonstrated for the strength behaviour. The initial stiffness an be alulated from the vertial elasti deformation of the omponent. The omplex problem of deformation is influened by the flexibility of the base plate, and by the onrete blok quality and size..5

14 The simplified predition of deformations of a rigid plate supported by an elasti half spae is onsidered first inluding the shape of the retangular plate. In a seond step, an indiation is given how to replae a flexible plate by an equivalent rigid plate. In the last step, assumptions are made about the effet of the size of the blok to the deformations under the plate for pratial base plates. The deformation of a retangular rigid plate in equivalent half spae solved by different authors is given in simplified form by Lambe & Whitman, 1967 as δ r = F α ar, (.1.6) E A r where δr is the deformation under a rigid plate, F the applied ompressed fore, ar the width of the rigid plate, E the Young's modulus of onrete, A r the area of the plate, A r = a r L, L the length of the plate, α a fator dependent on ratio between L and a r. The value of fator α depends on the Poison's ratio of the ompressed material, see in Table.1.1, for onrete (ν,15). The approximation of this values as α,85 L an be read from the following Table.1.1. L / a r Table.1.1 Fator α and its approximation α aording to (Lambe and Whitman, 1967) Approximation as α 85, L / a r 1,9,85 1,5 1,1 1,4 1,5 1, 3 1,47 1,47 5 1,76 1,9 1,17,69 / a r With the approximation for α, the formula for the displaement under the plate an be rewritten.6

15 = 85, F δ r E L a r (.1.7) A flexible plate an be expressed in terms of equivalent rigid plate based on the same deformations. For this purpose, half of a T-stub flange in ompression is modelled as shown in Figure.1.5. δ fl E Ip x Figure.1.5 A flange of a flexible T-stub The flange of a unit width is elastially supported by independent springs. The deformation of the plate is a sine funtion, whih an be expressed as δ (x) = δ sin ( ½π x / fl ) (.1.8) The uniform stress on the plate an then be replaed by the fourth differentiate of the deformation multiplied by E Ip, where E is the Young's modulus of steel and Ip is the moment of inertia per unit length of the steel plate with thikness t (I p = t 3 / 1). σ (x) = E s I p ( ½π / fl ) 4 δ sin (½π x / fl ) = E s t 3 The onrete part should be ompatible with this stress 1 (½π / fl ) 4 δ sin ( ½π x / fl ) (.1.9) δ(x) = σ(x) hef / E (.1.1) where h ef is the equivalent onrete height of the portion under the steel plate. Assume that h ef = ξ fl hene δ(x) = σ(x) ξ fl / E (.1.11) Substitution gives δ sin (½π x / fl ) = E t 3 / 1 (½π / fl ) 4 δ sin ( ½π x / fl ) ξ fl / E (.1.1) This may be expressed as.7

16 = t fl 3 π ( ) 1 4 ξ E E (.1.13) The flexible length fl may be replaed by an equivalent rigid length r suh that uniform deformations under an equivalent rigid plate give the same fore as the non uniform deformation under the flexible plate: r = fl / π (.1.14) The fator ξ represents the ratio between hef and fl. The value of hef an be expressed as α ar. From Tab..1 an be read that fator α for pratial T-stubs is about equal to 1,4. The width ar is equal to tw + r, where tw is equal to the web thikness of the T-stub. As a pratial assumption it is now assumed that t w equals to,5 r whih leads to h ef = 1,4 (,5 + ) r = 1,4,5 fl / π =, fl (.1.15) hene ξ =, For pratial joints an be estimated by E 3 N / mm leads to and E 1 N / mm, whih = t fl π ( ) E ( ) ξ t π 1, 198,. (.1.16) E or r = 1,6 t 1,5 t, (.1.17) whih gives for the effetive width alulated based on elasti deformation a = t +,5 t eq.el w (.1.18) The influene of the finite blok size ompared to the infinite half spae an be negleted in pratial ases. For example the equivalent width ar of the equivalent rigid plate is about tw + r. In ase t w is,5 r and r = 1,5 t the width is a r = 3,1 t. That means, peak stresses are even in the elasti stage spread over a very small area. In general, a onrete blok has dimensions at least equal to the olumn with and olumn depth. Furthermore it is not unusual that the blok height is at least half of the olumn depth. It means, that stresses under the flange of a T-stub, whih represents for instane a plate under a olumn flange, are spread over a relative big area ompared to a r = 3,1 t. If stresses are spread, the strains will be low where stresses are low and therefore these strains will not ontribute signifiantly to the deformations of the onrete just under the plate. Therefore, for.8

17 simpliity it is proposed to make no ompensation for the fat that the onrete blok is not infinite. From the strength proedure the effetive with of a T-stub is alulated as a = t + = t + t eq.str w w 3 f f y j γ M (.1.19) Based on test, see Figure , and FE simulation, see Figure.1.9, it may our that the value of aeq.str is also a suffiient good approximation for the width of the equivalent rigid plate as the expression based on elasti deformation only. If this is the ase, it has a pratial advantage for the appliation by designers. However, in the model a eq.str will beome dependent on strength properties of steel in onrete, whih is not the ase in the elasti stage, On Figure.1.6 is shown the influene of the base plate steel quality for partiular example on the onrete quality - deformation diagram for flexible plate t = tw = mm, L eff = 3 mm, F = 1 kn. From the diagram it an be seen that the differene between a eq.el = t w +,5 t and a eq.str = t w + is limited. Deformation, mm,5, a eq.str for strength, S 35 for strength, S 75 for strength, S 355,15,1 t w = mm t = mm F = 1 kn L = 3 mm a eq.el elasti model, S 35, S 75, S 355 δ,5, Conrete, f, MPa k Figure.1.6 Comparison of the predition of the effetive width on onrete - deformation diagram for partiular example for unlimited onrete blok k j = 5, base plate and web thikness mm, L = 3 mm, fore F = 1 kn The onrete surfae quality is affeting the stiffness of this omponent. Based on the tests Alma and Bijlaard, (198), Sokol and Wald, (1997). The redution of modulus of elastiity.9

18 of the upper layer of onrete of thikness of 3 mm was proposed (Sokol and Wald, 1997) aording to the observation of experiments with onrete surfae only, with poor grout quality and with high grout quality. For analytial predition the redution fator of the surfae quality was observed from 1, till 1,55. For the proposed model the value 1,5 had been proposed, see Figure.1.1 and.1.13, see Eq. (.1.). The simplified proedure to alulate the stiffness of the omponent onrete in ompression and base plate in bending an be summarised in Euroode 3 Annex J form as where k F E aeq.el L E aeq.el L = =, (.1.) δ E 1,5*,85E 1,75 E = a eq.el the equivalent width of the T-stub, a e.el = t w +,5 t, L the length of the T-stub, t the flange thikness of the T-stub, the base plate thikness, the web thikness of the T-stub, the olumn web or flange thikness. t w.1.4 Validation The proposed model is validated against the tests for strength and for stiffness separately. 5 tests in total were examined in this part of study to hek the onrete bearing resistane (DEWOLF, 1978, HAWKINS, 1968). The test speimens onsist of a onrete ube of size from 15 to 33 mm with entri load ating through a steel plate. The size of the onrete blok, the size and thikness of the steel plate and the onrete strength are the main variables..1

19 f j / f d Anal. Exp. e t / e Figure.1.7 Relative bearing resistane-base plate slenderness relationship (experiments DeWolf, 1978, and Hawkins, 1968) Figure.1.7 shows the relationship between the slenderness of the base plate, expressed as a ratio of the base plate thikness to the edge distane and the relative bearing resistane. The design approah given in Euroode 3 is in agreement with the test results, but onservative. The bearing apaity of test speimens at onrete failure is in the range from 1,4 to,5 times the apaity alulated aording to Euroode 3 with an average value of 1,75. N, kn <> <> <> f e d b a t =,76 mm 1,5 mm 3,5 mm 6,35 mm 8,89 mm 5,4 mm Anal. a b d ef Exp. <> f, MPa d a x b = 6 x 6 mm Figure.1.8 Conrete strength - ultimate load apaity relationship (Hawkins, 1968).11

20 The influene of the onrete strength is shown on Figure.1.8, where is shown the validation of the proposal based on proposal t w +. A set of 16 tests with similar geometry and material properties was used in this diagram from the set of tests (Hawkins, 1968). The only variable was the onrete strength of 19, 31 and 4 MPa Fore, kn Calulated strength, Eq. (.1.6) Experiment Conrete and grout Conrete Predition based on loal and global deformation, Eq. (.1.) and elasti deformation of the onrete blok Predition based on loal deformation only, Eq. (.1.),1,,3,4,5,6,7,8,9 Deformation, mm t t w δ F L Figure.1.9 Comparison of the stiffness predition to Test.1, (Alma and Bijlaard, 198), onrete blok 8x4x3 mm, plate thikness t = 3, mm, T stub length L = 3 mm The stiffness predition is ompared to tests Alma and Bijlaard, (198) in Figure.1.9. and.1.1. The tests of flexible plates on onrete foundation are very sensitive to boundary onditions (rigid tests frame) and measurements auray (very high fores and very small deformations). The predited value based on eq. (.1.7) is the loal deformation only. The elasti global and loal deformation of the whole onrete blok is shown separately. Considering the spread in test results and the auray ahievable in pratie, the omparison shows a suffiiently good auray of predition..1

21 16 Fore, kn F Calulated strength, Eq. (.1.6) Experiment Conrete and grout Conrete t t w δ L 6 4 Predition based on loal and global deformation, Eq. (.1.) and elasti deformation of the onrete blok Predition based on loal deformation only, Eq. (.1.),1,,3,4,5,6,7,8,9 Deformation, mm Figure.1.1 Comparison of the stiffness predition to Test., (Alma and Bijlaard, 198), onrete blok 8x4x3 mm, plate thikness t = 19 mm, T stub length L = 3 mm Fore, kn Predition, Eq. (.1.) 6 Exluding onrete surfae quality fator 5 4 Experiment W97-15 t F t w L 3 1,1,,3,4,5,6 Parallel line to predition Deformation, mm δ Figure.1.11 Comparison of the stiffness predition to Test W97-15, repeated loading, leaned onrete surfae without grout only (Sokol and Wald, 1997), onrete blok 55 x 55 x 5 mm, plate thikness t = 1 mm, T stub length L = 335 mm.13

22 Fore, kn 6 Exluding onrete surfae quality fator Predition, Eq. (.1.) Experiment W97-1 Parallel lines t to predition d Deformation, mm F t w L,5 1 1,5,5 Figure.1.1 Comparison of the stiffness predition to Test W97-15 repeated and inreasing loading, leaned onrete surfae low quality grout (Sokol and Wald, 1997), onrete blok 55 x 55 x 5 mm, plate thikness t = 1 mm, T stub length L = 335 mm The omparison of loal and global deformations an be shown on Finite Element (FE) simulation. In Figure.1.11 the predition of elasti deformation of rigid plate 1 x 1 mm on onrete blok 5 x 5 x 5 mm is ompared to alulation using the FE model. Vertial deformation at the surfae, mm Vertial deformation along the blok height,,1 F top of the onrete blok elasti deformation of the whole blok }loal deformation under plate predited value eq. (.1.) elasti deformation δ glob deformation at the edge δ edge deformation at the axis δ axis edge axis foot of the onrete blok Vertial deformation, mm,1 Figure.1.13 Calulated vertial deformations of a onrete blok,5 x,5 x,5 m loaded to a defletion of,1 mm under a rigid plate,1 x,1 m; in the figure on the right, the deformations along the vertial axis of symmetry δ axis are given and the alulated deformations at the edge δedge, inluded are the global elasti deformations aording to δglob = F h /(E A ), where A is full the area of the onrete blok Based on these omparisons, the reommendation is given that for pratial design, besides the loal effet of deformation under a flexible plate, the global deformation of the supporting onrete struture must be taken into onsideration..14

23 . Column flange and web in ompression..1 Desription of the omponent In this setion, the mehanial harateristis of the olumn flange and web in ompression omponent are presented and disussed. This omponent, as its name learly indiates, is subjeted to tension fores resulting from the applies bending moment and axial fore in the olumn (Figure..1). The proposed rules for resistane and stiffness evaluation given hereunder are similar to those inluded in revised Annex J of Euroode 3 for the beam flange and web in ompression omponent in beam-to-olumn joints and beam splies. Risk of yielding or instability Figure..1 Component olumn flange and web in ompression.. Resistane When a bending moment M and a axial fore N are arried over from the olumn to the onrete blok, a ompression zone develops in the olumn, lose to the olumn base; it inludes the olumn flange and a part of the olumn web in ompression. The ompressive fore F arried over by the joint may, as indiated in Figure.., is quite higher than the ompressive fore F in the olumn flange resulting from the resolution, at some distane of the joint, of the same bending moment M and axial fore N. In Figure.., the fores F and F are applied to the entroï d of the olumn flange in ompression..15

24 This assumption is usually made for sake of simpliity but does not orrespond to the reality as the ompression zone is not only limited to the olumn flange. The fore F, quite loalized, may lead to the instability of the ompressive zone of the olumn ross-setion and has therefore to be limited to a design value whih is here defined in a similar way than in Annex J for beam flange and web in ompression : where : F = M /( h t ) (..1). fb. Rd. Rd f M.Rd h b t fb is the design moment resistane of the olumn ross-setion redued, when neessary, by the shear fores; M.Rd takes into onsideration by itself the potential risk of instability in the olumn flange or web in ompression; is the whole depth of the olumn ross-setion; is the thikness of the olumn flange. h - tf F M and N applied as in Figure..1 F = N/ + M/(h b -t fb ) F = N/ + M/z F < F It has to be pointed out that Formula (..1) limits the maximum fore whih an be arried over in the ompressive zone of the joint beause of the risk of loss of resistane or instability in the possibly overloaded ompressive zone of the olumn loated lose to the joint. It therefore does not replae at all the lassial verifiation of the resistane of the olumn rossz F Figure.. Loalized ompressive fore in the olumn ross-setion loated lose to the olumn base.16

25 setion. It has also to be noted that formula (..1) applies whatever is the type of onnetion and the type of loading ating on the olumn base. It is also referred to in the preliminary draft of Euroode 4 Annex J in the ase of omposite onstrution and applies also to beam-to-olumn joints and beam splies where the beams are subjeted to ombined moments and shear and axial ompressive or tensile fores. It is therefore naturally extended here to olumn bases. The design resistane given by Formula (..1) has to be ompared to the ompressive fore F (see Figure..) whih results from the distribution of internal fores in the joint and whih is also assumed to be applied at the entroï d of the olumn flange in ompression. It integrates the resistane of the olumn flange and of a part of the olumn web; it also overs the potential risk of loal plate instability in both flange and web...3 Stiffness The deformation of the olumn flange and web in ompression is assumed not to ontribute to the joint flexibility. No stiffness oeffiient is therefore needed..3 Base plate in bending and anhor bolt in tension When the anhor bolts are ativated in tension, the base plate is subjeted to tensile fores and deforms in bending while the anhor bolts elongate. The failure of the tensile zone may result from the yielding of the plate, from the failure of the anhor bolts, or from a ombination of both phenomena. Two main approahes respetively termed "plate model" and "T-stub model" are referred to in the literature for the evaluation of the resistane of suh plated omponents subjeted to transverse bolt fores. The first one, the "plate model", onsiders the omponent as it is - i.e. as a plate - and formulae for resistane evaluation are derived aordingly. The atual geometry of the omponent, whih varies from one omponent to another, has to be taken into onsideration in an appropriate way; this leads to the following onlusions : the formulae for resistane varies from one plate omponent to another; the omplexity of the plate theories are suh that the formulae are rather ompliated and therefore not suitable for pratial appliations..17

26 The T-stub idealisation, on the other hand, onsists of substituting to the tensile part of the joint T-stub setions of appropriate effetive length l eff, onneted by their flange onto a presumably infinitely rigid foundation and subjet to a uniformly distributed fore ating in the web plate, see Figure.3.1. web e m F l eff t flange Figure.3.1 T-stub on rigid foundation In omparison with the plate approah, the T-stub one is easy to use and allows to over all the plated omponents with the same set of formulae. Furthermore, the T-stub onept may also be referred to for stiffness alulations as shown in (Jaspart, 1991) and Yee, Melhers, 1986). This explains why the T-stub onept appears now as the standard approah for plated omponents and is followed in all the modern haraterisation proedures for omponents, and in partiular in Euroode 3 revised Annex J (1998) for beam-to-olumn joints and olumn bases. In the next pages, the evaluation of the resistane and stiffness properties of the T-stub are disussed in the partiular ontext of olumn bases and proposals for inlusion in forthoming European regulations are made..3.1 Design resistane of plated omponents Basi formulae of Euroode 3 The T-stub approah for resistane, as it is desribed in Euroode 3, has been first introdued by Zoetemeijer (1974) for unstiffened olumn flanges. It has been then improved (Zoetemeijer, 1985) so as to over other plate onfigurations suh as stiffened olumn flanges and end-plates. In Jaspart (1991), it is also shown how to apply the onept to flange leats in bending..18

27 In plated omponents, three different failure modes may be identified : a) Bolt frature without prying fores, as a result of a very large stiffness of the plate (Mode 3) b) Onset of a yield lines mehanism in the plate before the strength of the bolts is exhausted (Mode 1) ) Mixed failure involving yield lines - but not a full plasti mehanism - in the plate and exhaustion of the bolt strength (Mode ). Similar failure modes may be observed in the atual plated omponents (olumn flange, end plates, ) and in the flange of the orresponding idealised T-stub. As soon as the effetive length l eff of the idealised T-stubs is hosen suh that the failure modes and loads of the atual plate and the T-stub flange are similar, the T-stub alulation an therefore be substituted to that of the atual plate. In Euroode 3, the design resistane of a T-stub flange of effetive length l eff is derived as follows for eah failure mode : Mode 3: bolt frature (Figure.3..a) F =Σ B (.3.1) Rd, 3 t. Rd Mode 1: plasti mehanism (Figure.3..b) F Rd, 1 4 = l eff m m pl, Rd (.3.) Mode : mixed failure (Figure.3..) F Rd, l = m + ΣB n eff pl, Rd t. Rd m+ n (.3.3).19

28 e n m Mode 3 Mode 1 Mode FRd.3 F B t.rd B t.rd Rd.1 B B B t.rd F Rd. B t.rd Q Q Q Q Figure.3. Failure modes in a T-stub In these expressions : m pl,rd is the plasti moment of the T-stub flange per unit length ( t f y / γ M ) with t = flange thikness, f y = yield stress of the flange, γ M = partial safety fator) m and e are geometrial harateristis defined in Figure.3.. Σ Bt.Rd n l eff is the sum of the design resistanes Bt.Rd of the bolts onneting the T-stub to the foundation (B t.rd =,9 A s f ub / γ Mb where A s is the tensile stress area of the bolts, fub the ultimate stress of the bolts and γmb a partial safety fator) designates the plae where the prying fore Q is assumed to be applied, as shown in Figure.3. (n = e, but its value is limited to 1,5 m). is derived at the smallest value of the effetive lengths orresponding to all the possible yield lines mehanisms in the speifi T-stub flange being onsidered. The design strength F Rd of the T-stub is derived as the smallest value got from expressions (.3.1) to (.3.3) : FRd = min( FRd, 1, FRd,, FRd, 3 ) (.3.4) In Jaspart (1991), the non-signifiative influene of the possible shear-axial-bending stress interations in the yield lines on the design apaity of T-stub flanges has been shown. In Annex J, the influene on Mode 1 failure of baking plates aimed at strengthening the olumn flanges in beam-to-olumn bolted joints is also onsidered. A similar influene may result, in 1 4.

29 olumn bases, from the use of washer plates. The effet of the latter on the base plate resistane will be taken into onsideration in a similar way than it is done in Annex J for baking plates. This alulation proedure reommended first by Zoetemeijer has been refined when revising the Annex J of Euroode 3. Euroode 3 distinguishes now between so-alled irular and non-irular yield lines mehanisms in T-stub flanges (see Figure.3.3.a). These differ by their shape and lead to speifi values of T-stub effetive lengths noted respetively l eff,p and l eff,np. But the main differene between irular and non-irular patterns is linked to the development or not of prying fores between the T-stub flange and the rigid foundation : irular patterns form without any development of prying fores Q, and the reverse happens for non-irular ones. The diret impat on the different possible failure modes is as follows : Mode 1 : Mode : Mode 3 : the presene or not of prying fores do not alter the failure mode whih is linked in both ases to the development of a omplete yield mehanism in the plate. Formula (.3.) applies therefore to irular and non-irular yield patterns. the bolt frature learly results here from the over-loading of the bolts in tension beause of prying effets; therefore Mode only ours in the ase of non-irular yield lines patterns. this mode does not involve any yielding in the flange and applies therefore to any T-stub. As a onlusion, the alulation proedure differs aording to the yield line mehanisms developing in the T-stub flange (Figure.3.3.b) : F = min( F ; F ) Rd Rd, 1 Rd, 3 F = min( F ; F ; F ) Rd Rd, 1 Rd, Rd, 3 for irular patterns (.3.5.a) for non-irular patterns (.3.5.b) In Annex J, the proedure is expressed in a more general way. All the possible yield line patterns are onsidered through reommended values of effetive lengths grouped into two ategories : irular and non-irular ones. The minimum values of the effetive lengths - respetively termed l eff,p and l eff,np - are therefore seleted for ategory. The failure load is then derived, by means of Formula (.3.4), by onsidering suessively all the three possible failure modes, but with speifi values of the effetive length :.1

30 Mode 1 : l eff, 1 = min( l eff, p ; l eff, n ) (.3.6.a) Mode : leff, = leff, n (.3.6.b) Mode 3 : - (.3.6.) Cirular pattern (l eff,p ) Non-irular patterns (l eff,n ) (a) Different yield line patterns 1,8 F/ Σ Bt.Rd Mode Mode 3,6 Mode 1 Mode 1*,4, 4 leff M pl.rd / Σ B t.rd,5 1 1,5,5 (b) Design resistane Figure.3.3 T-stub resistane aording revised Annex J.3.1. Alternative approah for Mode 1 failure The auray of the T-stub approah is quite good when the resistane is governed by failure modes and 3. The formulae for failure mode 1, on the other hand, has been seen quite onservative, and sometimes too onservative, when a plasti mehanism forms in the T-stub flange (Jaspart, 1991)..

31 Therefore the question raised whether refinements ould be brought to the T-stub model of Euroode 3 with the result that the amended model would provide a higher resistane for failure mode 1 without altering signifiantly the auray regarding both failure modes and 3. In (Jaspart, 1991), an attempt has been made in this respet. In the Zoetemeijer s approah, the fores in the bolts are idealised as point loads. Thus, it is never expliitly aounted for the atual sizes of the bolts and washers. If this is done, the following resistane may be expressed for Mode 1 (Jaspart, 1991): F Rd, 1 ( 8n e ) l 1m = w eff, pl, Rd [ mn e ( m+ n) ] w (.3.7) with ew =.5 dw (dw designates the diameter of the bolt/srew or of the washer if any. Of ourse, Equation (.3.7) onfines itself to Zoetemeijer's formulae (.3.) when distane e w is vanishing. During the reent revision of Annex J of Euroode 3, formula (.3.7) whih desribes the Mode 1 failure as dependent on the atual bolt dimensions has been agreed for inlusion as an alternative to formula (.3.)..3

32 .3. Initial stiffness of plated omponents.3..1 Appliation of the T-stub approah For plated omponents, it is also referred to the T-stub onept, see Figure.3.4. F p * a B Q,75n m 4/5 a B F B Q,75n m Q l Figure.3.4 T-stub elasti deformability In a T-stub, the tensile stiffness results from the elasti deformation of the T-stub flange in bending and of the bolts in tension (the role of the latter is plaid by the anhor bolts in setion.3.3 dealing expliitly with olumn bases). When evaluating the stiffness of the T-stub, the ompatibility between the respetive deformabilities of the T-stub flange and of the bolts has to be ensured : * p = b (.3.8) where p* b is the deformation of the end-plate at the level of the bolts; is the elongation of the bolts. In Jaspart (1991), expressions providing the elasti initial stiffness of the T-stub are proposed; they allow the oupling effet between the T-stubs to be taken into onsideration. These expressions slightly differ from those given in the original publiation of Yee and Melhers (1986). The elongation b of the bolts simply results from the elongation of the bolt shank subjeted to tension:.4

33 B b = Lb (.3.9) E A S where Lb is approximately defined as the length of the bolt shank in Euroode 3. From these onsiderations, the elasti deformation of the two T-stub may be derived : F p = (.3.1) E k i,p where the stiffness oeffiient k i,p is expressed as : k i,p Z ( q ) = α 8 4 (.3.11) Z q = Z α p a 1 l b + A S (.3.1) In these formulae : Z 3 = l / b t 3 l = ( m +,75 n ) α 3 1 = 1,5 α α b is the T-stub length α 3 = 6 α 8 α α =,75 n / l All the geometrial properties are defined in Figure The validity of these formulae has been demonstrated in Jaspart (1991) on the basis of a quite large number of omparisons with test results on joints with end-plate and flange leated onnetions got from the international literature..3.. Simplified stiffness oeffiients for inlusion in Euroode 3 The appliation of the T-stub onept to a simplified stiffness alulation - as that to be inluded in a ode suh Euroode 3 - requires to express the equivalene between the atual omponent and the equivalent T-stub in the elasti range of behaviour and that, in a different way than at ollapse; this is ahieved through the definition of a new effetive length alled l eff, ini whih differs from the l eff value to whih it has been referred to in setion.3.1. In.5

34 view of the determination of the stiffness oeffiient k ip, two problems have to be investigated: the response of a T-stub in the elasti range of behaviour; the determination of l eff, ini. These two points are suessively addressed hereunder. T-stub response The T-stub response in the elasti range of behaviour is overed in setion The orresponding expressions are rather long to apply, but some simplifiations may be introdued: to simplify the formulae: n is onsidered as equal to 1,5 m; to dissoiate the bolt deformability (Figure.3.5.) from that of the T-sub (Figure.3.5.b). The value of q given by expressions (.3.1) may then be simplified to : q 1,5 α α 3 α1 = = (.3.13) 3 α 6 α 8 α as soon as it is assumed, as in Figure.3.5.b, that the bolts are no more deforming in tension ( A s = ). q further simplifies to: q = 1,8 (.3.14) by substituting 1,5 m to,75 n as assumed previously. The stiffness oeffiient given by formula (.3.11) therefore beomes : k i,p 3 193,64 193,64 t l eff, ini = = (.3.15) 3 Z ( 4,5m ) The effetive length l eff,ini has been substituted to b..6

35 Figure.3.5 Elasti deformation of the T-stub Finally : k i,p 3 3 l eff,init l eff, init = 1,63 (.3.16) 3 3 m m In the frame of the assumptions made, it may be shown that the prying effet inreases the bolt fore from,5 F to,63 F (Figure.3.5.). In Euroode 3, the deformation of a bolt in tension is taken as equal to : B L b b = (.3.17) E As By substituting B by,63 F in (.3.17), the stiffness oeffiient of a bolt row with two bolts may be derived : A s k i b, = 1,6 (.3.18) Lb Definition of effetive length l eff,ini In Figure.3.5., the maximum bending moment in the T-stub flange (points A) is expressed as M max =,3 F m. Based on this expression, the maximum elasti load (first plasti hinges in the T-stub at points A) to be applied to the T-stub may be derived : F 4l t f l t f eff,ini y eff, ini y el = = (.3.19) 1,88 m 4γ M 1,88 m γ M.7

36 In Annex J, the ratio between the design resistane and the maximum elasti resistane of eah of the omponents is taken as equal to 3/ so : F l t f = 3 eff, ini y Rd Fe = l,859 m γ (.3.) MO As, in Figure.3.5.b, the T-stub flange is supported at the bolt level, the only possible failure mode of the T-stub is the development of a plasti mehanism in the flange. The assoiated failure load is given by Annex J as: F Rd l t f eff y = FRd = (.3.1) m γ Mo where l eff is the effetive length of the T-stub for strength alulation. By identifiation of expressions (.3.) and (.3.1), l eff, ini may be derived : l = = l l (.3.) eff,ini,859 eff, 85 eff Finally, by introduing equation (.3.) in the expression (.3.18) giving the value of k i,p for any plated omponent : k i, p 3,85 l eff,1 t = (.3.3) m Extension to base plates To evaluate the resistane and stiffness properties of a base plate in bending and anhor bolts in tension, referene is also made to the T-stub idealisation Resistane properties Three failure modes are identified in Setion for equivalent T-stubs of beam endplates and olumn flanges: Mode 1, Mode and Mode 3. Related formulae may be applied to olumn base plates as well. But in the partiular ase of base plates, it may happen that the elongation of the anhor bolts.8

37 in tension is suh, in omparison to the flexural deformability of the base plate, that no prying fores develop at the extremities of the T-stub flange. In this ase, the failure results either from that of the anhor bolts in tension (Mode 3) or from the yielding of the plate in bending (see Figure.3.6) where a two hinges mehanism develops in the T-stub flange. This failure is not likely to appear in beam-to-olumn joints and splies beause of the limited elongation of the bolts in tension. This partiular failure mode is named Mode 1*. F* Rd.1 B B Figure.3.6 Mode 1** failure The orresponding resistane writes : F ** Rd.1 l eff m pl. Rd = (.3.4) m When the Mode 1* mehanism forms, large base plate deformations develop; they may result in ontats between the onrete blok and the extremities of the T-stub flange, i.e. in prying fores. Further loads may therefore be applied to the T-stub until failure is obtained through Mode 1 or Mode. But to reah this level of resistane, large deformations of the T-stub are neessary, what is not aeptable in design onditions. The extra-strength whih separates Mode 1* from Mode 1 or Mode in this ase is therefore disregarded and Formula (.3.4) is applied despite the disrepany whih ould result from omparisons with some experimental tests. As a result, in ases where no prying fores develop, the design resistane of the T-stub is taken as equal to : Rd ** ( FRd,1, FRd,3 ) F = min (.3.5) when FRd,3 is given by formula (.3.1). In other ases, the ommon proedure explained in setion.3.1 is followed. The riterion to distinguish between situations with and without prying fores is disussed in setion As explained in Setion.3.1.1, irular and non-irular yield line patterns have to be.9