Recent developments in the design of anchor bolts

Transcription

1 Recent developments in te design of ancor bolts N. Subramanian Many structures suc as microwave and transmission line towers, industrial buildings, etc require tat te superstructure be secured safely into te foundations using ancor bolts. However, rational metods are not available in te Indian code for calculating te tensile and sear load capacity of ancor bolts. Till recently, te metods suggested by te ACI code were used by designers. Based on extensive experimental results, empirical formulae ave been suggested by researcers from Germany. An innovative metod, called te concrete capacity design (CCD), as been found to give reasonable estimates of tensile and sear load capacity of ancor bolts. Moreover, te calculations made using te CCD metod are simple and less complex tan te ACI code metod. For foundations involving ig strengt concrete, wic tend to be brittle, linear fracture mecanics metods sould be applied. In tis metod, instead of te tensile strengt of concrete, te total crack formation energy as to be used to find te tensile capacity of te ancor bolts. Te article deals wit te recent developments in te design of ancor bolts and presents a comparative study of ACI and CCD metods. Microwave towers, transmission line towers, towers used for oil well derricks and mine saft equipment, beacon supports, observation platform towers, etc are examples of self- supporting towers. Normally, in te case of transmission line towers, te stub angle is taken inside te pad portion of te foundation, and cleat angle and keying rods ancor tis stub angle, Fig. But, in te case of microwave towers, te stub angle is connected to te pad portion troug base plate Dr N. Subramanian, Ci Executive, Computer Design Consultants, 9, Nort Usman Road, T. Nagar, Cennai wit te elp of ancor bolts. Also, in all te industrial buildings, te columns are connected to te foundation concrete by means of ancor bolts. However, metods to design suc ancorages are not given in te Indian code. Till recently, te only available source for teir design was te American codes for nuclear safety related structures,2. However, a number of researcers all over te world ave conducted numerous experiments and based on tem, ave suggested formulae for te design of different kinds of fasteners 3,4,5. In India, cast in-situ ancors are used often in practice, and ence, te design metods of ACI 349 are applicable to tem. It is well known tat te concrete cone failure model, as suggested by ACI 349, results in complex calculations, especially wen multiple ancorages are used 6. Hence, after an exaustive number of experiments, Eligeausen and is associates ave suggested a truncated pyramid failure model 7,8,9. Tis model as several advantages over te ACI code metod. Tey ave also suggested modifications to te formula for taking into account cracked concrete 0. Tese formulae ave recently been incorporated in te Euro code. A description of tese metods is given in tis paper along wit a comparison wit te ACI code metod. Te worked out examples clearly illustrate te ease of applying tis metod for te design of ancorages. Te design pilosopy developed so far is based on te tensile strengt of concrete. It as been observed tat in many kinds of failures were tensile capacity governs, tere was a disturbing size-fect tat could not be explained 2. According to fracture mecanics principles, it as been sown tat te failure load of eaded studs ancored in concrete depends on te material parameters, E C and G F and not, as usually July 2 * Te Indian Concrete Journal

2 w b Stub angle (a) Studs 3w8w Cleat angle Diagonal member Pier Mat typical spacing 3w8w assumed, on te tensile strengt. Tis is of great interest, especially in ig strengt concrete, wic tends to be brittle. Tensile capacity of ancor bolts w (c) Stub angle Fig Typical foundation for transmission line towers (a) foundation wit stub angle (b) foundation wit base plate (c) typical stub angle details Based on te results of numerous pullout tests wit eadedancors, an empirical formula for te calculation of te maximum load N u of fastenings as been derived,2,3,4,5,6. Generally, tis equation is of te form: N u = a(f ck ) b ( ) c () were, f ck = concrete compressive strengt, N/mm 2 = embedment lengt, mm and a,b,c = constants. Te influence of embedment lengt is given by c, found to be in te range of.5 to.54, wic means tat te failure load does not increase in proportion to te surface of te failure cone, Fig 2. However, in te ACI code, te value of c as been cosen as 2, wic anticipates a direct proportionality between te failure load and te size of te failure cone surface. Te factor a is used to calibrate te measured failure load wit te predicted values and to assure te dimensional correctness of eqn. (). Te expression (f ck ) b represents te (b) Base plate Ancor bolts Top of concrete tensile strengt of concrete, derived from te compressive strengt, and a value of 0.5 is assumed for b. Tensile capacity as per ACI code Fig 2 sows concrete breakout cones for single ancors under tension and sear load, respectively, idealised according to ACI From te figure, it is evident tat te concrete cone failure load depends on te tensile capacity of te concrete. ACI committee 349 is concerned wit nuclear power-related structures. Because of tis, te pilosopy as been to design ductile fastenings. Te cone model as sown in Fig 2 was developed to obtain a limit to guard against brittle concrete failure. Under tension loading, te concrete capacity of an arbitrary fastening is calculated assuming a constant tensile stress acting on te projected area of te failure cone, taking te inclination between te failure surface and concrete surface as 45 o, Fig 2(a): N u = f ct (2) were, f ct = tensile strengt of concrete and = actual projected area of stress cones radiating toward attacment from bearing edge of ancors. Effective area sall be limited by overlapping stress cones, intersection of cones wit concrete surfaces, bearing area of ancor eads, and overall tickness of te concrete member. Substituting for and f ct, we get for a single ancor unlimited by edge influences or overlapping cones: 2 d N uo = 0.96 f ck ( + ) (3) were, f ck = compressive strengt measured on 200-mm cubes and and d are dined in Fig 2. For fastenings wit edge fects (c< ) and/or affected by oter concrete breakout cones (s < 2 ), te average failure load follows from eqn. (3) as under: were, o N u = d No uo = projected area of stress cone of a single ancor 2 + d N (a) d 45 o O Fig 2 Concrete breakout bodies according to ACI 349 (a) tensile loading (b) sear loading (b) 45 o A vo 2 Te Indian Concrete Journal * July 2

3 N 35 o N o As per te above assumption, te concrete cone failure load N uo of a single ancor in uncracked concrete, unaffected by edge influences or overlapping cones of neigbouring ancors loaded in tension, is given by.5 N uo = k k 2 k 3 f ( ) 5. (8) ck Fig 3 Idealised concrete cone for individual fastening under tensile loading as per CCD metod were, c s ( a ) 2 = π ( ) ( + ( d / ) = distance from centre of ancor bolt to edge of concrete = distance between ancor bolts (spacing). Sear load capacity of bolt as per ACI code Te capacity of an individual ancor failing in sear (Fig 2(b)) (provided tat te concrete alf-cone is fully developed) is given by: uo = 0.48 f ck ( ) 2 (6) If te dept of te concrete member is small ( < ) and/ or te spacing is close (s < 2 ) and/or te edge distance perpendicular to te load direction is small (c 2 < ), te load as to be reduced wit te aid of te projected area on te side of te concrete member as below: ( b ) were, k, k 2 and k 3 are calibration factors. Note tat, by basing te tensile failure load on te fective embedment dept, te computed load will always be conservative, even for an ancor tat migt experience pullout 8. Assuming k 4 = k k 2 k 3 N uo = k 4 f ck ( ).5 (9) were, k 4 = 3.5 for post-installed fasteners = 5.5 for cast in-situ eaded studs and eaded ancor bolts = embedment lengt, Fig 3. Eligeausen and Balog 0 ave furter suggested tat te above values of k 4 may be multiplied by a factor equal to 0.75 to take into account cracked concrete. If eaded studs are located in te intersection of cracks running in two directions (example in slabs spanning in two directions), te concrete cone failure load is about 20 percent lower tan te value according to eqn. (9). u = A A uo (7) vo A = actual projected area, and A vo = projected area of one fastener unlimited by edge influences, cone overlapping or member tickness = ( p/2) ( ) 2 Te determination of te projected areas and A for tensile and sear loading respectively based on te ACI code involves complex calculations 6. Hence, Eligeausen and is associates ave developed a metod called te concrete capacity design (CCD) metod based on te results of numerous pullout tests conducted by tem on various types of ancors 7. Tensile capacity as per CCD metod In tis metod, under tension loading, te concrete capacity of a single fastening is calculated assuming an inclination between te failure surface and surface of te concrete member of about 35 o, Fig 3. Tis corresponds to te widespread observation tat te orizontal extent of te failure surface is about tree times te fective embedment AN = ( single fastening ) o = ( 2 x.5 ) ( 2 x.5 ) = 9 2 ( a ).5 s.5.5 AN = ( +.5 ) ( 2 x.5 ) if : < _.5 Fig 4 Projected areas for different fastenings under tensile loading according to CCD metod s.5 ( b ) s.5 AN = ( 2 x.5 + s ) ( 2 x.5 ) = ( + s +.5 ) ( c 2 + s ) if : s < _ 3.0 if : c, c 2 < _.5 s, s 2 < _ 3.0 ( c ) ( d ) July 2 * Te Indian Concrete Journal 3

4 (a) o Fig 5 Concrete failure cone for individual fastener in tick concrete member under sear loading towards edge: (a) from test results (b) simplified design model according to CCD metod Higer coficients for eaded studs and eaded ancor bolts in eqn. (9) are valid only if te bearing area of eaded studs and ancors is so large tat concrete pressure under te ead is 9 f ck (3 f ck for uncracked concrete) 8. Because te concrete pressure under te ead of most postinstalled undercut ancors exceeds 3 f ck at failure, k 4 = 3.5 is recommended for all post-installed ancors 3. Fracture mecanics teory indicates tat, in te case of concrete tensile failure wit increasing member size, te failure load increases less tan te available failure surface; tat means te nominal stress at failure (peak load divided by failure area) decreases 2. Tis size fect is not unique to fastenings but as been observed for all concrete members wit a strain gradient. For instance, it is well known tat te bending strengt of unreinforced concrete beams and sear strengt of beams and slabs witout sear reinforcement decrease wit increasing member dept. Size fect as been verified for fastenings by experimental and teoretical investigations 3,5,3. Since strain gradient in concrete for fastenings is very large, size fect is minimum and very close to te linear elastic fracture mecanics solutions. Terore, te nominal stress at failure decreases in proportion to / and te failure load increases wit ( ).5. (b).5.5 c were, o y = projected area of one ancor at te concrete surface unlimited by edge influences or neigbouring ancors, idealising te failure cone as a pyramid wit a base lengt s cr = 3, Fig 4(a), = actual projected area at te concrete surface, assuming te failure surface of te individual ancors as a pyramid wit a base lengt s cr = 3. For examples, see Fig 4(b), 4(c), 4(d), = factor taking into account te eccentricity of te resultant tensile force on tensioned ancor bolts; in te case were eccentric loading exists about two axes, y sall be computed for eac axis individually and te product of te factors used as y y = /( + 2e N /(3 )) (0a) e N = distance between te resultant tensile force of tensioned ancor bolts of a group and te centroid of tensioned ancor bolts, y 2 = tuning factor to consider disturbance of te radial symmetric stress distribution caused by an edge, valid for ancors located away from edges, y 2 = if ³.5 (0b) A c y 2 = , c c A v c (0c) If fastenings are located so close to an edge tat tere is not enoug space for a complete concrete cone to develop, te load-bearing capacity of te ancorage is also reduced. (Note tat wit an edge distance in all directions c ³ 60d, it may be assumed tat no concrete edge failure will occur). Tis is also true for fasteners spaced so closely tat te breakout cones overlap. One of te principal advantages of te CCD metod is tat calculation of te canges in capacity due to factors suc as edge distance, spacing, geometric arrangement of groupings and similar variations can be readily determined troug use of relatively simple geometrical relationsips based on rectangular prisms. Te concrete capacity can be easily calculated based on te following equation: N u = A A N No ΨΨ 2 Nuo (0).5 c.5 c 3 c c2.5 A v = A vo ( single fastening ) A v =.5 (.5 + c 2 ) =.5 ( 2 x.5 ) if : c 2 _ <.5 2 = 4.5 ( a ) ( b ) A v.5 c.5 c A v = 2 x.5 x if : <.5 ( c ) Fig 6 Projected areas for different fastenings under sear loading according to CCD metod A v.5 c s.5 c Av = ( 2 x.5 + s ) x if : < _.5 s < _.5 ( d ) 4 Te Indian Concrete Journal * July 2

5 Load e v = e' v f A t f A t Load B Micro cracking starts E L t Dormation A G F arc tan C Eo Aggregate interlock and oter frictional fects D crack zone dormation, w Dormation ( a ) ( b ) s 3 s s s Fig 9 Tensile testing of concrete (a) test wit load control wic gives a brittle failure. (b) test wit load - dormation control Fig 7 Example of multiple fastening wit cast-in-situ eaded studs close to edge under eccentric sear loading were, = edge distance to te closest edge, = fective ancorage dept, Fig 3. For fastenings wit tree or four edges and c max.5 (c max = largest edge distance), te embedment dept to be inserted in eqn. (0) is limited to = c max /.5. Tis gives a constant failure load for deep embedments 8. Examples for calculation of projected areas are given in Fig 4. Note te relatively simple calculation for te CCD metod compared to tat of te ACI 349 metod 6. Sear load capacity as per CCD metod Te concrete capacity of an individual ancor in a tick uncracked structural member under sear loading toward te free edge, Fig 5, is uo = (l/d) 0.2 d f ck ( ).5 () were, l = activated load bearing lengt of fastener in mm 8d = for fasteners wit a constant overall stiffness, suc as eaded studs, undercut ancors and torque-controlled expansion ancors, were tere is no distance sleeve = 2d for torque-controlled expansion ancors wit distance sleeve separated from te expansion sleeve d = diameter of ancor bolt in mm and c l = edge distance in loading direction in mm. According to eqn. () te sear failure load does not increase wit te failure surface area, wic is proportional to ( ) 2. Rater, it is proportional to ( ).5. Tis is again due to size fect. Furtermore, te failure load is influenced by te ancor stiffness and diameter. Te size fect on te sear failure load as been verified teoretically and experimentally 8. T u/ Nu.0 Equation 3 Te sear load capacity of single ancors and ancor groups loaded toward te edge can be evaluated from eqn. (2) in te same general manner as for tension loading by 0.8 Equation Nu = 2. EG F.5 Test a =.5 a = 2.0 Max load, kn 400 N u 0.2 a L B / u embedment dept, mm Fig 8 Interaction diagram for combined tension and sear loads Fig 0 Concrete cone failure load of eaded studs as a function of embedment dept 3 July 2 * Te Indian Concrete Journal 5

6 taking into consideration te fact tat te size of te failure cone is dependent on te edge distance in te loading direction, wile in tension loading, it is dependent on te ancorage dept 7,8 were, u = A A A A o y 4 v vo ΨΨ 4 5 uo (2) = actual projected area at side of concrete member, idealising te sape of te fracture area of individual ancors as a alf-pyramid wit side lengts.5 and 3, Fig 6 = projected area of one fastener unlimited by corner influences, spacing, or member tickness, idealising te sape of te fracture area as a alf-pyramid wit side lengt.5 and 3, Figs 5(b) and 6(a) = fect of eccentricity of sear load y 4 = (2a) + 2e' v /( 3c ) e = distance between resultant sear force of te group of fasteners resisting sear and centroid of seared fasteners, Fig 7. y 5 = tuning factor considering disturbance of symmetric stress distribution caused by corner = if c 2 ³.5 c2 = c if c 2.5 (2b) = edge distance in loading direction, in Fig 6; for fastenings in a narrow, tin member wit c 2,max <.5 (c 2,max = maximum value of edge distances perpendicular to te loading direction) and <.5, te edge distance to be inserted in eqn. (2a) and (2b) is limited to = max (c 2,max /.5; /.5); tis gives a constant failure load independent of te edge distance ( ) 8 c 2 = edge distance perpendicular to load direction, Fig 6 Examples for calculation of projected areas are sown in Fig 6. Te relatively simple calculation compared to te more complex geometry of te ACI 349 procedures can be easily identified. Resistance to combined tension and sear loads For combined tension and sear loads, te following conditions Fig 8 sould be satisfied. Tu N u (3a) u (3b) (T u /N u ) + (/ u ).2 (3c) were, T u = tensile load acting on te fixture = sear force acting on te fixture. It as been found tat te eqn. (3) yields conservative results for steel failure. More accurate results are obtained by eqn. (4). (T u /N u ) a + (/ u ) a (4) Te value of a is taken as 2 if N u and u are governed by steel failure and as.5 for all oter failure modes. Comparison of ACI 349 and CCD metods Te main differences between tese two design approaces are summarised in Table. Hig strengt concrete During te past 0 to 5 years, ig strengt concrete (aving strengt greater tan 40 N/mm 2 ) as been used increasingly te world over. In spite of all its enanced properties, ig strengt concrete tends to be brittle tan normal concrete. In normal concrete, te tensile strengt of concrete is assumed to give a brittle fracture at a low tensile stress as sown in Fig 9(a). However, in failures were te tensile capacity governs (as in te case of cone failure of ancorages) tere is a size-fect. To explain tese failure types, te complete load-dormation curve as sown in Fig 9(b) in tension as to be taken into account 2. Eligeausen and Sawade found tat te bearing beaviour of ancor bolts wit long embedment depts can be reasonably predicted by linear fracture mecanics 3. Using linear fracture mecanics approac, tey derived te maximum load in tension (for a/ B = 0.45) N u = 2.(E C G F ) 0.5 ( ).5 (5) were, G F = total crack formation energy (corresponding to te area below te load-dormation curve as sown in Table : Comparison of te influence of main parameters on maximum load predicted by ACI 349 and CCD metods Factor ACI CCD metod Ancorage dept, tension ( ) 2 ( ).5 Edge distance, sear ( ) 2 ( ).5 Slope of failure cone a = 45 o a = 35 o Required spacing to develop ancorage capacity 2, tension 3, tension 2, sear 3, sear Required edge distance to develop full ancor, tension.5, tension capacity, sear.5, sear Small spacing direction nonlinear linear or close to reduction reduction edge 2 direction nonlinear reduction Eccentricity of load ¾ taken into account 6 Te Indian Concrete Journal * July 2

7 Fig 9(b). A value of 0.07 N/mm was used. E C = modulus of elasticity of concrete (a value of N/mm 2 was used). A comparison of te above equation wit te test results is sown in Fig 0. It is found tat te agreement between teory and test result is sufficiently close for practical purposes. Conclusion Metods for te design of ancorages are not available in te Indian code. Te metods suggested in te ACI involve complex calculations. Based on te extensive experimental study, equations for te ultimate tensile capacity and ultimate sear capacity of eaded ancor bolts ave been derived by Eligeausen and is associates. Tese equations are easy to apply for multiple ancorages, since tey involve squarebased, truncated pyramids. Te differences between tis approac and te ACI approac ave been brougt out. For foundations using ig strengt concrete, instead of te tensile strengt of concrete, te total crack formation energy as to be taken to compute te ultimate tensile load. Acknowledgements Te autor is igly indebted to Prof. Eligeausen, professor and ead for fastening tecniques at te Institute for Building Materials, University of Stuttgurt, Germany for making available numerous publications, based on wic tis article is written. Rerences. Code requirements for nuclear safety related concrete structures (ACI ). ACI Committee 349, American Concrete Institute, Detroit, Micigan 4829, USA, Design Guide to ACI , ACI Committee 349, American Concrete Institute, Detroit, Micigan 4829, USA, ELIGEHAUSEN, R., MALLEE, R., and REHM, G., Besttigungstecknik, Beton- Kalender 997, Ernst & Son, Berlin, 45 pp. 4. HAWKINS, N. Strengt in sear and tension of cast-in place ancor bolts in Ancorage to Concrete, SP-03, American Concrete Institute, Detroit, 985, pp BODE, H., and ROIK, K. Headed studs embedded in concrete and loaded in tension in Ancorage to Concrete, SP-03, American Concrete Institute, Detroit, 993, pp SUBRAMANIAN, N., and ASANTHI,., Design of ancor bolts in concrete. Te Bridge and Structural Engineer. September 99, ol. XXI, No.3, pp FUCHS, W., ELIGEHAUSEN, R., and BREEN, J.E., Concrete capacity design (CCD) approac for fastenings to concrete, ACI Structural Journal. January-February 995, ol 92, No, pp Engineering Mecanics Division. ASCE, April 984, ol 0, No 4, pp ELIGEHAUSEN, R., and SAWADE, G., Fracture mecanics based description of te pull-out beaviour of eaded studs embedded in concrete in RILEM report on Fracture Mecanics of Concrete Structures From teory to Applications, Elfgren, L, Ed, Capman & Hall, London, 989, pp Illustrative examples Example Calculate te tensile and sear capacities of a single eaded ancor bolt as per ACI and CCD metod. Assuming tat concrete alf cone is fully developed in case of sear failure and tere is no edge influences or overlapping cones. d = 45.2 mm (for d = 27mm) = 300 mm (for eaded ancors = ) = 300 mm f ck = 20 N/mm 2 Tensile capacity as per ACI code 2 N u = ( + 2 ) = 444,609 N 300 Tensile capacity as per CCD metod N uo = (300).5 = 360,87 N Sear capacity as per ACI metod u = (300) 2 = 93,96 N Sear capacity as per CCD metod u = (300/27) (300).5 = 95,445 N It is clearly seen tat te values predicted by te CCD metod are quite reasonable as compared to te ACI code metod. Example 2 Calculate te tensile and sear capacities of a eaded ancor bolt arrangement as sown in Fig. d d = 27 mm = 45.2 mm = 500 mm = 300 mm f ck = 25 N/mm 2 Tensile load capacity 8. FUCHS, W., and ELIGEHAUSEN, R., Das CC-erfaren fur die Berecnung der Betonausbruclast von erankerungen, Beton und Stalbetonbau, H. /995, pp. 6-9, H. 2/995, pp , H. 3/995, pp ELIGEHAUSEN, R. et al., Tragveralten von Kopfbolzenverankerungen bei zentriscer Zugbeansprucung, Bauingenieur, 992, pp ELIGEHAUSEN, R. and BALOGH, T., Beaviour of fasteners loaded in tension in cracked reinforced concrete, ACI Structural Journal. May-June 995, ol 92, No 3, pp Comite Euro-International du Beton, Design of Fastenings in Concrete, Design Guide, Tomas Telford, UK, BEZANT, Z.P., Size fect in blunt fracture: concrete, rock, metal, Journal of te Fig A typical eaded ancor bolt arrangment July 2 * Te Indian Concrete Journal 7

8 = 500 >.5 s = terore, Rerring Fig 4a and 4c =( ) ( ) =,350, mm 2 o =9 2 = = 80, mm 2 N uo = (300).5 = 402,70 N N u = Sear load capacity (see Fig 6) Example 3 350, 402, 70= 67,68 N 80, uo = (300/27) (300).5 = 28,56 N A v = ( ) 300 = 450, mm 2 A vo = = 405, mm 2 c 2 > = 450 terore, y 5 = 450, u = 405, 2856, = 242,795 N Design te post-installed ancor system as sown in Fig 2 for te given data. Assume tat tere is no eccentricity. Tensile force = 300, N Sear force= 60, N f y = 240 N/mm 2 f ut = 420 N/mm 2 f ck = 20 N/mm 2 Assuming = 250-mm and 20-mm diameter bolts (core area = 244 mm 2 ) Fig 2 A typical post-installed ancor system = 409,920 N > 300, N uo = (250/20) (300).5 = 72,224 N y 4 = y 5 = (300/(.5 300)) = 0.9 A vo = = 405, mm 2 <.5 s >.5 terore, A v = = 450, mm 2 u = 450, , 224 = 72,224 N 405, Assuming tat tere is no reinforcement and te concrete will ave cracks u = ,224 = 20,556 N Sear capacity of bolts = = 35,36 N > 20, N Ceck for combined tension and sear 8 d = mm = 300 mm <.5 Tu Nu = 300, 453, 88 = 0.66 < c 2 = 300 mm <.5 s, s 2 = 600 mm < 3 u = 60, = < 20, 556 N uo = (250).5 = 238,648 N = ( ) ( ) =,625,625 mm 2 o = = 562,500 mm 2 y 2 = (300/(.5 250)) = 0.94 N u, 625, 625 = , = N 562, 500 Assuming te concrete as cracked N u = = 453, 88 N > 300, N Tensile capacity of bolts = (T u /N u ) + (/ u ) = =.59 <.2 (T u /N u ).5 + (/ u ).5 = (0.66).5 + (0.498).5 = = < Hence, 4 nos. 20-mm diameter ancor bolts wit te arrangement as sown in Fig 2 is safe. Tese examples clearly sow te ease of calculation by using te CCD metod. 8 Te Indian Concrete Journal * July 2