Column bases in shear and normal force

Column bases in shear and normal force Nol Gresnigt Delft University of Technology, Civil Engineering and Geosciences, the Netherlands Arie Romeijn Delft University of Technology, Civil Engineering and Geosciences, the Netherlands František Wald Czech Technical University, Prague, Czech Republic Martin Steenhuis † Eindhoven University of Technology, Faculty of Architecture, Building and Planning, the Netherlands Connections of steel columns to concrete foundations may be loaded by combinations of normal force, bending moment and shear force. Shear force will primarily be transmitted by friction between the base plate and the grout layer to the concrete foundation. If the compression force is small, or if tension force is present, as may occur in slender high rise structures like towers and masts, the friction will be small or absent. Then, the anchor bolts will be loaded by shear force and bending moment. At the Stevin Laboratory of Delft University of Technology, experimental and theoretical research has been carried out on column bases loaded by combinations of shear force and tension force. In the paper, the main results of this research programme are summarised. The test results are presented and the analytical model that was developed to describe the load deformation behaviour. A comparison is made with the design rules as given by the Comité Euro-International du Béton (CEB, 1994 and 1996). Based on the research, design rules for this load case were proposed to the drafting panel for the revision of Eurocode 3 from ENV to EN status (Part 1.8: Design of Joints). Key words: Base plates, shear and tension, Eurocode 3, analytical model, tests HERON Vol. 53 (2008) No. 1/2 1 Introduction Horizontal shear force in column bases may be resisted by (see Figure 1): (a) friction between the base plate, grout and concrete footing, (b) shear and bending of the anchor bolts, (c) a special shear key, for example a block of I-stub or T-section or steel pad welded onto the bottom of the base plate, (d) (a) direct contact, e.g. achieved by recessing the base plate into the concrete footing. (b) (c) (d) Figure 1: Column bases loaded by horizontal shear force In most cases, the shear force can be resisted through friction between the base plate and the grout. The friction depends on the compressive load and on the coefficient of friction. Pre-stressing the anchor bolts will increase the shear force transfer by friction. Sometimes, for instance in slender buildings, it may happen that due to horizontal forces (wind loading) columns are loaded in tension. In such cases, the horizontal shear force usually cannot be transmitted through friction. If no other provisions are installed (e.g. shear studs), the anchor bolts will have to transmit these shear forces. Because the grout does not have sufficient strength to resist bearing stresses between the bolt and the grout, considerable bending of the anchor bolts may occur, as is indicated in Figure 2. The main failure modes are rupture of the anchor bolts (local curvature of the bolt exceeds the ductility of the bolt material), crumbling of the grout, failure (splitting) of the concrete footing and pull-out of the anchor bolt. Due to the horizontal displacement, not only shear and bending in the bolts will occur, but also the tensile force in the bolts will be increased due to second order effects. The horizontal component of the increasing tensile force gives an extra contribution to the shear resistance and stiffness. The increasing vertical component gives an extra contribution to the transfer of load by friction and increases resistance and stiffness as well. These factors explain the shape of the load deformation diagram as given in Figure 2. The increase of the load continues till fracture occurs in one of the components of the connection. If the connection is well designed and executed, such fracture will occur at 88 very large deformation (much larger than acceptable in serviceability and ultimate limit state). Fv Fh Fh δh δh 0 Figure 2: Column base loaded by shear and tension force The thickness of the grout layer has an important influence on the horizontal deformations. In the tests carried out by the Stevin Laboratory (Stevin, 1989), the deformations at rupture of the anchor bolts were between about 15 and 30 mm, whilst grout layers had a thickness of 15, 30 and 60 mm. The deformations have to be taken into account in the check of the serviceability limit state. Because of the rather large deformations that may occur, this check may govern the design. The size of the holes may have a considerable influence on the horizontal deformations, especially when oversized holes are applied. In such cases it may be useful to apply larger washers under the nuts, to be welded onto the base plate after erection, or to fill the hole by a two component resin. For the application of such resin, reference is made to the ECCS recommendations (1994) and EN 1993-1-8 (2006). In the Stevin Laboratory (Stevin, 1989), a model for the load deformation behaviour of base plates loaded by combinations of normal force and shear has been developed, see section 2. Section 4 gives an overview of the tests carried out in Delft. For the design of fasteners, the CEB has published a Design Guide (CEB, 1996). The CEB model (the CEB design rules for "fixtures") has been compared with the Stevin Laboratory model and the tests. It appears that the CEB model gives very conservative results, especially when large tensile forces are present and / or the thickness of the grout layer is large. The main reason is that the CEB model does not take account of the positive influence of the grout layer (COST, 1999). In section 3 a summary of the CEB model is presented. In section 5 the test results are compared with the Stevin Laboratory model and the CEB model. Section 6 gives a summary of the design rules proposed for part 1.8 of EN 1993. 89 It is noted that in steel construction, usually only the steel part of the base plate connection is considered. In the CEB Design Guide much attention is paid to the concrete part. It is recommended to the steel designer to acquire knowledge about the requirements to the reinforced concrete. For detailed design guidance and the various failure modes that may occur in the concrete, reference is made to the CEB Design Guide (CEB, 1996). For an interesting test series on anchor bolts, reference is made to the work of Nakashima (1998). He studied the mechanical properties of steel column base anchor bolts, particularly those parts of such anchor bolts which are exposed, i.e., not embedded in concrete footings. He studied the anchor bolts which are often subjected to combined stresses which are caused by tension, shear and in addition bending moments. Special attention is paid to the influence of the thread and other factors on the deformation capacity. 2 The Stevin Laboratory model In most cases the shear force can be transmitted via friction between the base plate and the grout. The friction capacity depends on the normal force (compression) between the base plate and the grout and the friction coefficient. At increasing horizontal displacement the shear force increases till it reaches the friction capacity. At that point the friction resistance stays constant with increasing displacements, while the load transfer through the anchor bolts increases further. Because the grout does not have sufficient strength to resist the bearing stresses between the bolts and the grout, considerable bending of the anchor bolts may occur, as is indicated in Figures 2 and 3. The test specimen shows the bending deformation of the anchor bolts, the crumbling of the grout and the final cracking of the concrete. Figure 3: Test specimen loaded by shear force and tensile force (Stevin, 1989) 90 2.1 Derivation of the analytical model In Figure 4, the deformations and some important measures are indicated. Figure 5 shows the schematisation of the deformations and the forces, which are taken into account in the analytical model. In the derivations, the following symbols are used: Ab, s = tensile stress area of the anchor bolt Ft = applied tensile force Fh = applied shear force (horizontal force) Fw = friction force between base plate and grout Nb = normal force in the grout Fa = normal force in the anchor bolt db = diameter of the anchor bolt δa = elongation of the anchor bolt δb = compression of the grout layer δh = horizontal displacement of the base plate v = actual thickness of the grout layer vr = thickness of the grout layer in the analytical model: vr = v + 0.5d b ( vr = A as in the CEB model, see section 3) Figure 4: Deformation and some measurements of the anchor bolts Figure 5: Schematisation of the deformations and forces in the analytical model Due to the horizontal displacement of the base plate, bending of the bolts will occur and the tensile force in the bolts (Fa) will increase. This causes an increase of the compression 91 force between the base plate and the grout, resulting in a larger friction force (Fw) between the grout and the base plate, see equations (2) and (3). At rather small horizontal deformations (δh), the tensile force Fa in the bolt reaches the yield force Fyb = As ⋅ f yb . This means that the bending moments in the anchor bolts rapidly decrease and the horizontal component Fah of Fa (Figure 5) rapidly increases. Because of the high tensile force in the bolts, the bending moment capacity in the bolts will be small. Therefore, in the analytical model the bending moments in the bolts are not taken into account. The bearing stresses of the grout-bolt contact are not taken into account either, because they are small compared to other forces. For the horizontal equilibrium it follows: Fh = Fa δh vr + δ a + Fw vr − δ b − Ft ) vr + δ a Fw = f w ( Fa (1) (2) In these equations fw is the coefficient of friction between the grout and the base plate. For the deformation it follows: 2 2 δ 2h = ( v r + δ a ) - ( v r - δ b ) (3) Because δ 2h is small compared with δ h this can be simplified to: 2 δ h = 2 vr ( δ a + δb ) (4) For the "elastic" part of the behaviour, δa and δb can be written as: δa = Fa vr E Ab, s (5) δb = ( F a - F t ) vr E grout A grout (6) Because Egrout Agrout is much greater than EAb,s , δb will be small compared with δa. Therefore δb is not taken into account further. From the geometry it follows: v r + δ a = δ h2 + v r2 (7) For (1), (2) and (4) can be written with (7): Fh = Fa δh δ h2 + v r2 + Fw ⎛ ⎞ vr Fw = f w ⎜ F a - Ft ⎟ ⎜ ⎟ 2 2 δ h + vr ⎝ ⎠ 92 (8) (9) δh = 2 v r δ a (10) For every δh the elongation δa can be calculated via (10), then with (5) the force Fa and with (8) and (9) the horizontal force Fh. The above equations are valid for Fa ≤ Fa,y where Fa , y = As ⋅ f y ,b (11) For Fa = Fa,y it follows with (8), (9) and (11): Fh = f y ,b Ab, s (δh + f wvr ) − f w Ft δ h2 + v r2 (12) with 2 f y ,b δ h = vr (13) E For the design value of the coefficient of friction fw,d the following values are proposed: • sand-cement mortar: fw,d = 0,20 • special grout (e.g. Pagel IV): fw,d = 0,30 2.2 Comparison with one of the tests To demonstrate the analytical model, one of the test results is calculated, namely DT6 in (Stevin, 1989), see Figure 6. In this test, a tensile force Ft = 141 kN was kept constant in the column, while the horizontal force Fh was increased. Figure 7 gives the test result together with the result of the analytical model. With equations (13) and (12) it follows: δ h = vr Fh = 2 f y ,b E f y ,b Ab, s δ h2 + vr2 = 40 2 ⋅ 861 = 3,6 mm 210 000 (δ h + f wvr ) − f w Ft = 861 ⋅ 245 3,62 + 402 (3,6 + 0,20 ⋅ 40) ⋅ 2 − 0,20 ⋅ 141 = 94 kN A linear relationship is assumed until the value of δh equals δh according to equation (13) and Fa equals As fy,b. This part of the load deformation curve is called the elastic stage, see Figure 7. For larger values of δh the load deformation curve is called the plastic stage. E.g. for δh = 15 mm, it follows with equation (12): Fh = 227 - 28 = 199 kN. In the test, failure occurred in the anchor bolts (rupture) at the edge of the base plate, due to local high bending strains. The value Fv.Rd = 105 kN in Figure 7 is explained in the next section. 93 • 2 anchor bolts M20, grade 8.8 • Fu,b = 1076 N/mm2 (measured tensile strength of the bolt material) • fy;b = 861 N/mm2 (assumed as 0,8 fu,b) • εu,b = 12% (measured rupture strain of the bolt material) • As = 245 mm2 • grout = sand-cement mortar • v = 30 mm • vr = 30 + 0,5 ⋅ 20 = 40 mm Figure 6: Set-up of test DT6 Figure 7: Comparison of the analytical model with result of test DT6 2.3 Ultimate design strength The ultimate strength is a function of the strength of the various parts in the column base and the ductility of the anchor bolts. A greater ductility allows a greater horizontal displacement and thus a greater Fah (Figure 5) and consequently a greater Fh . 94 It can also be noted that δh should be limited, both at serviceability and at ultimate limit state. To predict the ultimate strength (if governed by the anchor bolt), a relation is needed between the local strain in the bolt and the horizontal deformation. Furthermore, the strain capacity (ductility) of the various anchor materials must be known. In the tests, it appeared, as could be expected, that 4.6 grade anchor bolts were much more ductile than the 8.8 grade bolts. A difference in ductility can also be found in the requirements in the relevant product standards. It is not easy to establish a reliable model to determine the strains in the anchor bolts and to find reliable data for the bending strain capacity of various anchor bolt materials. Therefore, a simplified method is proposed for the shear resistance of 4.6 and 8.8 grade anchor bolts. This simplified method is adopted in the Dutch Standard (NEN 6770, 1990): 4.6 anchors: Fv.Rd = 8.8 anchors: Fv.Rd = 0,375 f u ,b ⋅ Ab, s γMb 0,25 f u ,b ⋅ Ab, s γMb (14) (15) with γMb = 1,25. Differences in ductility cause differences in ultimate strength, see Fig 7. This is the reason for the different factors in (14) and (15). Note that the resistance functions (14) and (15) are similar to the "normal" Eurocode 3 functions for bolts loaded in shear: 4.6 and 8.8 bolts: Fv. Rd = 0 ,60 fu ,b ⋅ Ab, s γMb (16) After checking the design resistance, the horizontal displacements should be checked for the serviceability limit state and for the ultimate limit state. 3 The CEB Design Guide model In the CEB Design Guide (CEB, 1996), the load transfer from a fixture (e.g. base plate) into the concrete is covered. The CEB Design Guide covers many types of anchors and possible failure modes of the concrete. The design of the fixture (e.g. the base plate) must be performed according to the appropriate code of practice. In case of steel fixtures, a steel construction code is used. 95 Background information can be found in a separate CEB state of the art report: "Fastenings to concrete and masonry structures" (CEB, 1994). It reviews the behaviour of fastenings in concrete and masonry for the entire range of loading types (including monotonic, sustained, fatigue, seismic and impact loading), as well as the influence of environmental effects, based on experimental results. For the transfer of shear forces, two methods are considered, namely: • Friction between the fixture (e.g. base plate) and the grout or concrete, • Shear/bending of the anchors. 3.1 Friction between base plate and grout/concrete In section 4.1 of the CEB Guide it is stated that when a bending moment and/or a compression force is acting on a fixture, a friction force may develop, which for simplicity may conservatively be neglected in the design of the anchorage. If it is to be taken into account, then the design value of this friction force VRd,f may be taken as: VRD , f = VRk , f / γ Mf = µ ⋅ CSd / γ Mf (17) with VRk,f = characteristic shear force VRd,f = design shear force µ = coefficient of friction CSd = compression force under the fixture due to design actions γMf = 1,5 (ultimate limit state) γMf = 1,3 (limit state of fatigue) γMf = 1,0 (serviceability 1imit state) In general, the coefficient of friction between a fixture and concrete may be taken as µ = 0,4. The friction force VRd,f should be neglected if the thickness of grout beneath the fixture is thicker than 3 mm (e.g. in case of levelling nuts) and for anchorages close to an edge. In conclusion, it can be stated that for "normal column bases", according to the CEB Guide, load transfer through friction should be neglected because in normal steel constructions the thickness of the grout is always more than 3 mm. 3.2 Shear/bending of anchor bolts For the resistance of anchor bolts, two cases are considered, namely (b) and (c): (b) 96 Shear loads without lever arm Shear loads acting on anchors may be assumed to act without a lever arm if both of the following conditions are fulfilled. (1) The fixture must be made of metal and in the area of the anchorage be fixed directly to the concrete without an intermediate layer or with a levelling layer of mortar with a thickness ≤ 3 mm. (2) (c) The fixture must be adjacent to the anchor over its entire thickness. Shear loads with lever arm If the conditions (1) and (2) of the preceding section (b) are not fulfilled, the length A of the lever arm is calculated according to equation (18): A = a3 + e1 (18) with el = distance between shear load and concrete surface a3 = 0,5 d for post-installed and cast-in-place anchors (Figure 8) a3 = 0 if a washer and a nut are directly clamped to the concrete surface d = nominal diameter of the anchor bolt or thread diameter (Figure 8) The design moment acting on the anchor is calculated according to equation (19): M Sd = VSd ⋅ A αM (19) The value of αM depends on the degree of restraint at the side of the fixture. No restraint (αM = 1,0) should be assumed if the fixture can rotate freely. Full restraint (αM = 2,0) may be assumed only if the fixture cannot rotate (see Figure 8b) and the hole is smaller than 1,2d. Figure 8: Examples of fastenings (a) without and (b) with full restrain of the anchor at the side of the fixture (Figure 27 in the CEB Design Guide) 97 3.3 Plastic analysis In section 4.2.2 of the CEB Guide it is stated that in a plastic analysis it is assumed that significant redistribution of anchor tension and shear forces will occur in a group of anchor bolts. Therefore, plastic analysis is acceptable only when the failure is governed by ductile steel failure of the anchors. To ensure this failure mode, the CEB Guide gives several conditions that should be met: (1) The arrangement of the anchors. It is assumed that base plates meet these conditions. (2) The ultimate strength of a fastening as governed by concrete failure, should exceed its strength as governed by steel failure (equation (20)): Rd , c ≥ 1.25 Rd , s ⋅ fuk / f yk (20) with Rd,c = design concrete capacity of the fastening (concrete cone, splitting or pull out failure (tension loading) or concrete pry-out or edge failure (shear loading), Rd,s = design steel capacity of the fastening, fuk = the characteristic ultimate tensile strength (nominal value), fyk = the characteristic yield strength or proof strength respectively (nominal value). Equation (20) should be checked for tension, shear and combined tension and shear forces. (3) The nominal steel strength of the anchors should not exceed fuk = 800 MPa. The ratio of nominal steel yield strength to nominal ultimate strength should not exceed fyk / fuk = 0,8, while the rupture elongation (measured over a length equal to 5d) should be at least 12%. (4) Anchors that incorporate a reduced section (e.g. a threaded part) should satisfy the following conditions: (a) For anchors loaded in tension, the tensile strength Nuk of the reduced section should either be greater than 1.1 times the yield strength Nyk of the unreduced section, or the stressed length of the reduced section should be ≥ 5d (d = anchor diameter outside the reduced section). (b) For anchors loaded in shear or which are to redistribute shear forces, the beginning of the reduced section should either be ≥ 5d below the concrete 98 surface or in the case of threaded anchors the threaded part should extend ≥ 2d into the concrete. (c) For anchors loaded in combined tension and shear, the conditions (a) and (b) above should be met. (5) The steel fixture should be embedded in the concrete or fastened to the concrete without an intermediate layer or with a layer of mortar with a thickness ≤ 3 mm. The diameter of the clearance hole in the fixture should be ≤ 1,2d (the bolt is (6) assumed to bear against the fixture). From the above equations, especially equation (20), it follows that according to the CEB Design Guide plastic design is only allowed for base plates without grout layer or with a grout layer not thicker than 3 mm. For usual base plate construction this means that according to the CEB Design Guide, plastic design is not allowed. In equation (20) the relation between the required design concrete capacity of the fastening and the design steel capacity of the fastening is given. It appears that for e.g. 8.8 anchors it gives: Rd ,c ≥ 1,56 Rd , s (21) In the Stevin Laboratory design model it is assumed that measures are taken to ensure that failure of the concrete will not occur before failure of the base plate or anchor. The above requirements seem adequate to ensure this prerequisite. Resistance functions for the shear load 3.4 In section 9.3.1 of the CEB Design Guide (1994), the following required verifications are given in the case of shear loading (elastic design approach): • Steel failure, shear load without lever arm (VRd,s) • Steel failure, shear load with lever arm (VRd,sm) • Concrete pry-out failure (VRd,cp) • Concrete edge failure (VRd,c) For the design values VRd,s and VRd,sm the following equations are given: VRd,s = VRk.s γ Ms VRd,sm = VRk.sm γ Ms with VRk,s = k 2 ⋅ As ⋅ f yk with VRk.sm = α M ⋅ M Rk,s A (22) (23) with k2 = 0,6 (24) 99 As = M Rk , s = 0 M Rk ,s = N Rd , s = N Rk , s / γ Ms (27) N Rk , s = As ⋅ f y , k (28) γ Ms = 1,20 if f uk ≤ 800 MPa and f yk / f uk ≤ 0,8 (29) γ Ms = 1,50 if f uk ≥ 800 MPa or f yk / f uk ≥ 0,8 (30) N Sd = applied normal force αM = factor depending on the support conditions, see Figure 8 A = length of lever arm stressed cross-section of the anchor in the shear plane 0 M Rk , s (1 − N Sd / N Rd , s ) (25) 0 characteristic bending resistance of individual anchor M Rk , s = 1,5 WeA f uk (26) Type of grout: • Special grout Pagel IV • Sand - cement mortar 2:1 • No grout Thickness of grout: • 15 mm • 30 mm • 60 mm Anchor bolt: • M20 - 4.6 • M20 – 8.8 Anchoring length: • 250 mm with a bend at the end of the bar • 600 mm with anchor plate Concrete reinforcement: Figure 9: Test specimens; in the tests with 4.6 grade anchor bolts, four bolts were applied and in the tests with 8.8 grade anchors two bolts 100 • with reinforcement • without reinforcement Table 1: Summary of test results and comparison with design values according to the proposed kN Test / design value kN Design value Fv.Rd **) mm shear force Fh MPa Failure mode *) Tensile force Ft Ultimate stress fub MPa grout v Yield stress fyb Class number Test Thickness of the Anchors Measured ultimate resistance functions (Stevin, 1989) kN D7 4 4.6 290 423 30 0 310 Rupture 124 2,50 D8 4 4.6 290 423 30 0 310 Rupture 124 2,50 D9 4 4.6 290 423 30 0 260 Rupture 124 2,10 D10 2 8.8 - 1196 30 0 300 Rupture 117 2,56 D11 4 4.6 283 423 30 0 234 Rupture 124 1,89 D12 2 8.8 - 1176 60 0 295 Rupture 115 2,57 ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- DT1 4 4.6 290 423 30 182 170 Cracking 124 1,37 DT2 4 4.6 290 423 30 121 250 Cracking 124 2,06 DT3 4 4.6 290 423 30 121 240 Rupture 124 1,94 DT4 4 4.6 290 423 30 121 240 Rupture 124 1,94 DT5 2 8.8 - 1152 30 141 178 Rupture 113 1,57 DT6 2 8.8 - 1076 30 141 200 Rupture 105 1,90 DT7 2 8.8 - 1070 30 141 190 Rupture 105 1,81 DT8 2 8.8 - 1045 60 141 230 Rupture 102 2,25 DT9 4 4.6 290 423 60 121 180 Pull-out 124 1,45 DT10 2 8.8 - 1049 60 141 228 Rupture 102 2,23 DT11 4 4.6 290 423 15 121 270 Cracking 124 2,17 DT12 2 8.8 - 1176 15 141 255 Rupture 115 2,21 DT13 4 4.6 280 414 60 121 320 Rupture 122 2,62 DT14 4 4.6 283 411 60 121 305 Cracking 121 2,52 DT15 2 8.8 - 1089 30 200 200 Cracking 107 1,87 DT16 4 4.6 309 443 30 200 255 Rupture 130 1,96 *) **) Cracking = cracking of the concrete after large deformation of the anchor, e.g. for test DT2 compare Figure 2. Rupture = rupture of the anchor Pull-out = pull-out of the anchor These values were calculated with the measured material properties and dimensions. 101 4 Test Results and Comparison with the Models Test programme 4.1 The main dimensions of the test specimens are given in Figure 9, as well as the parameters in the test programme. See also Figures 3 and 6. More information on the test set-up is given in the Stevin Laboratory report (1989). In the test programme (Stevin, 1989), three test series were carried out: • Test series 1 (6 tests D1 – D6), with only shear force. Due to insufficient strength of the concrete, premature splitting of the concrete occurred. These test results are omitted. • Test series 2 (6 tests D7 – D12), with only shear force. In these specimens, more reinforcement bars were applied in the concrete. • Test series 3 (16 tests DT1 – DT16), with a combination of tensile force and shear force. 4.2 Test results and comparison with the Stevin Laboratory model In Table 1 a summary is given of the main test results and a comparison with the proposed resistance functions. 4.3 Comparison with the CEB model The results of the comparison for all tests are given in Table 2. The application of the CEB model for one of the tests (DT5) is demonstrated below. Bolts M20, grade 8.8 fub, measured = 1152 MPa take f yk = 0,8 · 1152 = 922 MPa take γ Ms = 1,20 (for 8.8 bolts) As = π ⋅ d s2 / 4 = 245 mm2 giving ds = 17,66 mm N Rk , s = As ⋅ f yk = 245 ⋅ 922 ⋅ 10 −3 = 226 kN N Rd , s = N Rk , s / γ Ms = 226 / 1,20 = 188 kN N Sd = 141 / 2 = 70,5 kN WeA = 0 M Rk ,s = 102 π ⋅ d s3 32 = π ⋅ 17,663 32 = 541 mm3 1.5 WeA ⋅ f yk = 1,5 ⋅ 541 ⋅ 922 = 748 ⋅ 103 Nmm M Rk , s = 0 3 3 M Rk , s (1 − N Sd / N Rd , s ) = 748 ⋅ 10 (1 − 70,5 / 188) = 468 ⋅ 10 Nmm VRk , s = k 2 ⋅ As ⋅ f yk = 0.6 ⋅ 245 ⋅ 922 ⋅ 10 −3 = 136 kN VRk , sm = α M ⋅ M Rk , s A = 2 ⋅ 468 ⋅ 103 − 3 10 = 23,4 kN ≤ VRk , s = 136 kN 30 + 20 / 2 For the test with 2 bolts it follows 2· 23,4 = 46,8 kN ~ 47 kN, see Table 2. Test / Stevin**) Length A Test / CEB MRk,s*) VRk,sm group*) M0Rk,s*) Nsd / NRd,s Test Nsd per bolt NRd,s per bolt*) Table 2: Comparison of test results with design values - CEB model and Stevin Laboratory model Nm Nm mm kN 0.77 235 54 40 11 15.6 1.4 0.51 235 115 40 23 10.9 2.0 30.25 0.51 235 115 40 23 10.4 1.9 30.25 0.51 235 115 40 23 10.4 1.9 188 70.50 0.37 748 468 40 47 3.8 1.6 176 70.50 0.40 699 418 40 42 4.8 1.9 DT7 175 70.50 0.40 695 414 40 41 4.6 1.8 DT8 171 70.50 0.41 678 398 70 23 10.1 2.3 DT9 59 30.25 0.51 235 115 70 13 13.7 1.5 DT10 171 70.50 0.41 681 401 70 23 10.0 2.2 DT11 59 30.25 0.51 235 115 25 37 7.3 2.2 DT12 192 70.50 0.37 763 483 25 77 3.3 2.2 DT13 57 30.25 0.53 227 107 70 12 26.2 2.6 DT14 58 30.25 0.52 230 109 70 13 24.4 2.5 DT15 178 100.00 0.56 707 310 40 31 6.5 1.9 DT16 63 50.00 0.79 251 52 40 10 24.5 2.0 kN kN DT1 59 45.50 DT2 59 30.25 DT3 59 DT4 59 DT5 DT6 *) Calculated with the measured material properties and dimensions as given in table 1. **) The Stevin Laboratory values are taken from table 1. 103 5 Proposal for Design Rules On request of the Eurocode 3 Project Team for prEN 1993-1-8 Design of Joints, based on the Stevin Laboratory model, the following design rules were proposed by the authors. Resistance to shear forces 5.1 In a column base the design shear resistance Fv.Rd may be derived as follows: Fv.Rd = F f .Rd + nFvb.Rd (31) where: Ff.Rd is the design friction resistance between base plate and grout layer: F f . Rd = C f .d ⋅ N c.Sd Cf.d (32) is the coefficient of friction between base plate and grout layer. The following values may be used: Nc.Sd • for sand-cement mortar Cf,d = 0,20 (33a) • for special grout Cf,d = 0,30 (33b) is the design value of the normal compressive force in the column. If the normal force in the column is a tensile force Ff.Rd = 0. Drafting note: Also, the preload in the anchor bolts contributes to the friction resistance. However, because of its uncertainty (e.g. relaxation and interaction with the column normal force), it was decided to neglect this action. n is the number of anchor bolts in the base plate Fvb.Rd is the smallest of F1.vb.Rd and F2.vb.Rd F1.vb.Rd is the bearing resistance for the anchor bolt - base plate F2.vb.Rd is the shear resistance of the anchor bolt F 2.vb.Rd = α b f ub As γ Mb As is the tensile stress area of the bolt or of the anchor bolt αb is a coefficient depending on the yield strength fyb the anchor bolt: α b = 0,44 − 0,0003 f yb fyb (34) (35) is the nominal yield strength the anchor bolt, where: 235 N/mm2 ≤ fyb ≤ 640 N/mm2 fub is the nominal ultimate strength the anchor bolt, where: 400 N/mm2 ≤ fub ≤ 800 N/mm2 γ Mb 104 is the partial safety factor: γ Mb = 1,25 (36) Deformations 5.2 In a column base the design shear deformations may be derived as follows: • If N c.Sd ≤ F f .Rd the shear deformation δv = 0. • If N c.Sd > F f .Rd the shear deformation δv is the largest of δv1 and δv2. δ v1 = Fv.Sd δ v* (37) Fv* ⎧⎪ ⎛ N c.Sd Fv.Sd − C fd ⎜1 − ⎜ ⋅ ⋅ ⋅ n f A n f yb ⋅ As ⎪⎩ yb s ⎝ δ v 2 = vr ⎨ ⎞⎫⎪ ⎟⎬ ⎟⎪ ⎠⎭ (38) where δ v* = vr 2 f yb (39) Ea ⎛δ* ⎞ Fv* = n ⋅ f yb ⋅ As ⎜⎜ v + C f .d ⎟⎟ − C f .d N c.Sd ⎝ vr ⎠ (40) with NC.Sd is the design value of the normal force in the column (positive value if the normal force is tensile and negative value if the normal force is compression) Ea is the elastic modulus of steel vr is the design value of the thickness of the grout layer: vr = v + 0,5db v (41) is the actual thickness of the grout layer. Remark: The hole clearance may contribute considerably to the horizontal displacements. The hole clearance is not included in the above equations. Displacements due to the hole clearances may be prevented by measures to prevent the bolts moving in the holes, e.g. by filling the hole clearances with a two component epoxy. 5.3 Prerequisites In the above equations, it is a prerequisite that: • The grout layer is of adequate quality. See the applicable reference standard. 105 • The design strength of the anchor – concrete connection is greater than the design rupture strength of the anchor. • Other failure modes, like splitting of the concrete and pull out of the anchor, are prevented by adequate design and execution of the anchor in the concrete block. Reference is made to - EN 1992, Eurocode 2. - CEB, 1994. Fastenings to concrete and masonry structures, state of the art report. Comité Euro-International du Béton. Thomas Telford Publishing, London, ISBN: 0 7277 1937 8. - CEB, 1996. Design of fastenings in concrete, Design Guide. Comité EuroInternational du Béton. Thomas Telford Publishing, London, ISBN: 0 7277 2558 0. 5.4 Application of the equations for the deformation The equations in section 5.2 are somewhat simplified compared to those given in the section 2, where the Stevin Laboratory model is explained. For the example calculation in section 2.2 (test DT6), it follows: • For Fv.Sd = 94,0 kN: δv1 = 3,60 mm, δv2= 3,59 mm; the displacement δv is the largest of δv1 and δv2; in this case, δv = δv1= δv2= 3,6 mm. • For Fv.Sd = 130,0 kN: δv1 = 4,97 mm, δv2= 7,0 mm; the displacement δv is the largest of δv1 and δv2; in this case, δv = δv2= 7,0 mm. These values are in agreement with those in section 2.2. 6 Conclusions 6.1 • On the behaviour of column bases loaded in shear and tension The shear strength of anchor bolts is considerably lower than the shear strength of bolts in bolted connections between steel plates. • The ductility of the anchor bolts is an important factor for the strength. The lower ductility of 8.8 grade bolts compared to 4.6 grade bolts is reflected in the lower coefficient in the resistance function. • The influence of a tensile force Ft in the column can be neglected for the determination of the shear resistance. • The shear resistance is almost independent of the thickness of the grout layer. • The deformations are greatly dependent on the thickness of the grout layer. • A "better" grout, e.g. "Pagel IV" gives lower deformations. 106 • In the design, not only the shear resistance should be checked, but also the deformations at serviceability and ultimate limit state. • 6.2 • Also other failure modes, like splitting of the concrete block, etc., should be checked. On the models The Stevin Laboratory model gives results that are consistent with test results. It also gives rules to determine the deformation. • The CEB model gives very conservative results, especially when a large tensile force is present and / or the thickness of the grout layer is large. The main reason is that the CEB model does not take account of the positive influence of the grout layer. The CEB model does not give rules to determine the deformation. Acknowledgement Within the framework of the European Project COST C1 (Semi-rigid behaviour of civil engineering structural connections) and the Technical Committee 10 of ECCS (European Convention for Constructional Steelwork) an ad-hoc working group prepared a background document on design of column bases for Eurocode 3. Members of this group are: D. Brown, SCI London; A.M. Gresnigt, TU Delft; J.P. Jaspart, University of Liège; Z. Sokol, CTU in Prague; J.W.B. Stark, TU Delft; C.M. Steenhuis, TU Eindhoven; J.C. Taylor, SCI London; F. Wald, CTU in Prague (convener of the group), K. Weynand, RTWH Aachen. 107 References CEB, 1994. Fastenings to concrete and masonry structures, state of the art report. Comité Euro-International du Béton. Thomas Telford Publishing, London, ISBN: 0 7277 1937 8. CEB, 1996. Design of fastenings in concrete, Design Guide. Comité Euro-International du Béton. Thomas Telford Publishing, London, ISBN: 0 7277 2558 0. COST, 1999. Column Bases in Steel Building Frames, COST C1- EU, Brussels, Luxembourg. ECCS, 1994. European recommendations for bolted connections with injection bolts. ECCS publication No. 79, Brussels. EN 1993-1-8, 2006. Eurocode 3: Design of Steel Structures, Part 1.8: Design of joints, CEN, Brussels. NEN 6770, 1990. Staalconstructies TGB 1990, Basiseisen en basisrekenregels voor overwegend statisch belaste constructies (TGB 1990 Steel Structures, Basic requirements and basic rules for calculation of predominantly statically loaded structures), NEN, Delft. Stevin, 1989. Bouwman, L.P., Gresnigt A.M., Romeijn, A. Onderzoek naar de bevestiging van stalen voetplaten aan funderingen van beton. (Research into the connection of steel base plates to concrete foundations), TU-Delft Stevin Laboratory report 25.6.89.05/c6, Delft. Nakashima, Shigetoshi, (1998). Mechanical Characteristics of Exposed Portions of Anchor Bolts in Steel Column Bases under Combined Tension and Shear. Journal of Constructional Steel Research, 1998, 46:1-3, Paper No. 277. 108