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10 2.1 Physical Testing A comprehensive test program was conducted to evaluate the performance of elastomeric bearings under static and dy- namic rotation. Seventy-eight bearings were tested in seven major test series. Table 2.1 summarizes the major test series, and the complete test matrix is presented in Table 2.2. Table 2.1 provides a brief overview of the seven test series included in the study. Most test bearings were 9 in. à 22 in. steel- reinforced elastomeric bearings, approximately 2 in. thick over- all, with a shape factor of approximately 6. The bearings were made of Neoprene with a Shore A durometer hardness of ap- proximately 50. The use of a standard bearing permitted: ⢠Consistent evaluation of theories and design models, ⢠Comparisons of bearings produced by different manufac- turers and manufacturing methods, and ⢠comparisons of the effects of different loads and deformations. Discussion with elastomeric manufacturers showed that this 22 in. à 9 in. bearing is the most commonly manufactured size in the United States. It is the standard bearing for the state of Texas, which uses many thousand of these bearings each year, and is commonly produced by all major manufacturers. The size is suitable for medium-span bridges with moderate movements and rotations, so it provided a good basis for the research study. However, additional bearings of different shapes, sizes, shape factors, and material properties were tested to provide a broad basis for the experimental investigation. Each bearing was carefully inspected before testing. An in- dividual test required a minimum of several hours and a max- imum of several weeks to complete. Electronic instruments were used to monitor the bearing throughout each test, but each bearing also was inspected visually and manually at in- tervals throughout each test. PMI series tests were usually completed in one day, but all other tests included cyclic rota- tion and lasted longer. The longest test (CYC15) lasted more than 2 weeks. The bearings in this test program were subjected to rotations much larger than currently permitted in design or expected under normal bridge service conditions in order to accelerate the onset of damage. This procedure was adopted to shorten each individual test and to permit a larger number of differ- ent tests to be conducted. Had the researchers applied realis- tic rotation levels to the bearings, each test would have required many millions of cycles, and the test program would have lasted many, many years. The cyclic rotation rate was selected to be as fast as possible without introducing spurious effects on the bearing response. A pilot test program was first carried out to investigate the rate of heat build-up. The data gathered was used to construct a thermal analytical model that related temperature rise to bear- ing geometry, rotation amplitude, and frequency. The model was used to determine suitable rotation frequencies that would permit the main testing to be conducted as rapidly as possible while limiting the temperature rise of the bearing. A complete, detailed description of each test cannot be pro- vided here because of the large volume of test data. However, Appendix A and Appendix D provide significant detail on each test and more detailed interpretation of the test results. Appen- dix A provides summary information on the properties and characteristics of each individual test. Plots of force-deflection, moment-rotation, bearing deformation, progression of dam- age, and deterioration of resistance and stiffness are provided for each specimen. Specific data values at key points of the tests are tabulated. Appendix D contains more detailed compar- isons, analyses, and evaluations of the test data and identifies trends in behavior. It contains initial conclusions regarding test results, and these conclusions are combined with the analytical studies to develop final design recommendations. Appendix C provides details of the test apparatus and procedures. A full battery of material property and quality control tests was required of the manufacturer for each bearing purchase. C H A P T E R 2 Findings
11 Series Type of test No. of specs. Primary goals of tests PMI Monotonic or cyclic compression. Some with static rotation. 24 To develop an interaction diagram for failure under monotonic axial force and moment. (âP-M Interactionâ). CYC Tests with constant axial load and cyclic rotation. 29 Establish relationship among static axial load, cyclic rotation, number of cycles and damage level. MAT As CYC tests, but different materials. 3 Determine effect of material properties on resistance to combined axial load plus cyclic rotation. SHR As CYC tests, but with constant shear deformation added. 6 Determine effect of shear displacements on resistance to combined axial load plus cyclic rotation. SHF As CYC tests, but with different S. 6 Determine effect of shape factor on resistance to combined axial load plus cyclic rotation. ASR As CYC tests, but different aspect ratio. 4 Determine effect of bearing geometry on resistance to combined axial load plus cyclic rotation. PLT As CYC tests, but shims have various edge profiles. 6 Determine effect of shim plate edge treatment on resistance to combined axial load plus cyclic rotation. Table 2.1. Summary of the test series. Additional tests were performed at the University of Wash- ington on some bearings to evaluate material properties and estimate the deterioration in performance at various times during the tests. They are summarized in Appendix D. The progression of tensile debonding, followed by shear delamination failure, is illustrated in Figure 2.1 through Figure 2.4. (The initial debonding is quite difficult to see in Figure 2.2, but occurs in the foreground, where two discrete bulges have coalesced into one.) Those figures illustrate the difficulty in distinguishing from outside the bearing between tensile debonding and shear delamination. The tests showed that limited debonding does not have a significant or immediate impact on bearing performance, but delamination develops in the presence of large or repeated shear strains. If delamination becomes severe, as illustrated in Figure 2.3, it adversely affects the service performance of the bearing to the extent that the bearing may be considered to have failed. Thus, while limited debonding is tolerable, exten- sive delamination requires replacement of the bridge bearing. The extent of both debonding and delamination increases with increasing numbers of rotation cycles, and their rates of propagation are higher, with larger cyclic rotations or larger compressive loads. The growth is illustrated in Figure 2.4. The tests showed that large shear strains associated with ro- tation, compressive load, and shear deformation combine to cause delamination of the bearing. Repeated cycles of shear strain also were found to be significantly more damaging than constant shear strains of the same magnitude. The number of cycles required to achieve a given damage level decreases with an increase in the cyclic strain level. However, considerable scatter was evident in the results, especially among the differ- ent manufacturers. For example, Figures F-24 and F-25 in Ap- pendix F show that the bearing from Manufacturer B per- formed the best in test CYC09 but not in test CYC11. However, despite this scatter, the effects of the amplitude and number of the cyclic strain cycles remain the dominant influence on the accumulation of debonding damage. These parameters characterize the loading aspect of the equation. The resistance side is characterized by the material properties, shape factor, and plan geometry of the bearing. A higher shape factor is predicted to improve axial load capac- ity by reducing the shear strain for a given load. This predic- tion was borne out in the tests. The improvement in per- formance with shape factor was even better than predicted, but the number of high shape factor tests was too small to permit development of a better theory to explain this result. The manufacturing process, and particularly the treat- ment of the edges of the shims, also is important. This was first observed when testing in rotation bearings that had been specially ordered for testing in the torsion box rig de- scribed in Section C.4 of Appendix C. That rig was intended for diagnostic tests, to determine the level of debonding damage at various intervals throughout the main rotation tests. The bearings required nonrectangular shims, which were produced by machining, and that process left their edges sharp and square. Under cyclic rotation, the sharp edges caused debonding to occur faster than in the other bearings.
12 Table 2.2. Bearing test matrix. Figure 2.1. Undamaged bearing under load. Figure 2.2. Initial debonding of bearing.
13 In order to isolate the effect of the shim edge shape from the effect of the nonstandard plan geometry of the shim, more bearings were ordered with standard rectangular shims, and edges prepared in three different ways: sharp and square- cut (as-sheared), deburred (using a belt-sander) or perfectly rounded (with the edge machined to a radius equal to half the shim thickness). These test results are in Figure 2.5. Deburring of the as-sheared, sharp edges leads to a significant increase in the bearing life expectancy up to about 75% debonding, but machine-rounding of the edges does not provide much addi- tional benefit. In the figure, the relative ranking of the curves representing the different processes is important, but the ab- solute number of cycles is not, because the amplitude of the rotation was 0.0375 radians. That value is 10 to 30 times larger than the cyclic rotation expected in practice. Bridge bearings experience shear strains due to rotation, compression, and shear displacements. The strains caused by shear deformations differ from those caused by rotation and compression in two respects. First, in most cases, the shear displacements are caused by expansion and contraction of the bridge deck, so the number of cycles is small compared with those induced by traffic. (In some bridges, the super- structure may be configured in such a way that truck passage causes shear as well as rotation and compression in the bear- ing. In that case the shear strains due to shear displacement are clearly more numerous and should be treated as cyclic loading. Theoretically, this is true in all bridges, since bend- ing of the girders implies elongation of the bottom flange. However, in most cases the corresponding horizontal move- Figure 2.3. Internal damage caused by severe cyclic loading. Figure 2.4. Progression of debonding with increased load cycles. D vs N. Test CYC07 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 Cycles (thousands) Pe rc en t D eb on de d A2 B1 C1 D1 D vs N. Tests PLT 2,4,6. 0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 2500 3000 Cycles Pe rc en t D eb on de d PLT2, Sharp Edges PLT4, Deburred Edges PLT6, Rounded Edges Figure 2.5. Debonding for PLT test series.
ment causes shear deformations in the elastomer that are too small to be of much consequence.) Second, if the shear displacements of the bearing are large, they may involve some roll-over at the end of the layer, which leads to a complex state of stress there, consisting of combined shear and vertical tension. That combination appears to pro- mote cracking at the end of the shim, as shown in Figure 2.6, taken from NCHRP Report 298 (Roeder, Stanton, and Taylor 1987). Thus, one feature of shear displacements leads to their being less important than traffic effects, and one suggests that they are more important. However, tests conducted in this re- search suggest that shear displacements play only a small role and that the cyclic rotations under traffic loads are expected to be a more critical aspect of bearing design. 2.2 Finite Element Analysis 2.2.1 Objectives The project focused mainly on the experimental investiga- tion of the rotational behavior of elastomeric bearings and the development of suitable design procedures. This requires the identification of characteristic engineering design param- eters which (1) can be measured in the experiment (directly or indirectly), and (2) lead to a simple design methodology. FEA provides a tool to simulate structural behavior and evaluate states of deformation and stress. It is particularly valuable when internal quantities, such as stress or strain, can- not be measured. Then external quantities such as load and displacement can be measured experimentally, and FEA can be used to correlate them with local, internal quantities that are sought. However, this is possible only for a well-defined structure made of materials whose properties are homoge- neous and known. The level of accuracy of the end result de- pends on the type of material and the quality of the available material properties. For rubber, the constitutive laws are non- linear and complicated, and depend on many characteristic constants, some of which are not readily available. Despite this limitation, FEA was used to identify the relationship be- tween external loads or applied displacements and rotations, and the engineering design parameters, such as shear strain, used in a design procedure. These relationships were then used to evaluate and justify simplified design equations. The structural testing and evaluation of the experimental data identified the local shear strain γzx in the elastomer at (or near) the ends of the reinforcing steel shims as a suitable engi- neering design parameter. (The coordinate system is that x is parallel to the bridge axis, y is transverse, and z is vertical.) Gent and Lindley (1959a) presented a simplified linear analysis for incompressible elastomeric bearings. Stanton and Lund (2006) extended this theory for slightly compressible elastomers and rectangular shapes of all aspect ratios. Both formulations pro- vide simple relations between axial force and average axial strain, as well as between moment and rotation. The shape of the bear- ings enters these relations solely through the shape factor S of its layers. The formulations also provide a convenient correla- tion between those global deformation measures and the local shear strain γzx,max inside the bearing. Their linearity provides a convenient basis for a design procedure. That approach, how- ever, utilizes superposition of responses to different loadings, and the validity of doing so has to be proven. Appendix E presents a series of numerical simulations by which the following hypotheses will be proven to hold for common bearings: ⢠Superposition of axial and rotational effects provides a rea- sonably accurate representation of the response predicted by nonlinear FEA at small strain levels. ⢠The stiffness coefficients predicted by the linear theory of bearings by Stanton and Lund are in good agreement with a nonlinear FEA at small strain levels. ⢠The local shear strain predicted by the linear theory of bearings by Stanton and Lund are in good agreement with a nonlinear FEA at small strain levels. ⢠Internal rupture due to excessive tensile hydrostatic stress can only occur in bearings with bonded external plates and very low axial loads. Proving these four hypotheses is necessary if use of the simple linear analysis approach of Stanton and Lund (2006) is to be justified in design. A further problem arises in the effort to validate the linear model. The simplicity of that model is achieved partly by treating the bearing as uniform across the cross-section. This implies the absence of edge cover, which is present in field bearings and in the FE model. In the linear model, the critical strains occur at the outer edge. In the FE model, that location 14 Figure 2.6. Damage due to cyclic shear displacements (from NCHRP Report No. 298).
15 is occupied by the cover, in which the displacement field is drastically different from that in the body of the bearing layer. It is necessary in the FE model to extrapolate the strain field from a point just inside the edge of the shim to the outer edge of the bearing, if strains in corresponding locations are to be compared. When the strain field is linear, such extrapolation is simple. When it is nonlinear, as is the case under combined compression and rotation, the exact procedure to be used for extrapolation becomes less clearly defined, and correlation of the linear and nonlinear FE models becomes more difficult. 2.2.2 Modeling Techniques The model may be discussed in terms of three main char- acteristics: geometry of the model and the boundary condi- tions, constitutive models for the materials, and loading. All nonlinear analyses presented in this chapter were per- formed using the multipurpose FEA program MSC.Marc 2003r2 by MSC software (MSC.Marc, 2003). All analyses were performed in 2-D, using a large deformation plane strain analysis in a Lagrange setting. The 2-D analysis implies an infinite strip bearing, with an aspect ratio of zero. Three- dimensional analyses could not be performed at the neces- sary level of refinement due to numerical instabilities of the nearly incompressible element formulation at high hydro- static stress. The computational demands of 3-D analyses, in terms of run time and file size, are also much heavier than those of comparable 2-D analyses, and acted as a further dis- incentive for 3-D analysis. Simulations of physical tests revealed that the commonly known problems of large deformation simulations of elas- tomers, that is, extensive mesh distortion and the potential loss of element stability, impose a serious limitation on the numerical analysis. (Element instability is illustrated by the hourglass modes visible in the right hand side of the mesh in Figure E-14 in Appendix E.) This problem is intrinsic to the element formulation for nearly incompressible materials and varies little between different software packages. Local mesh distortions always were observed near the end of the reinforcing steel shims. When they reached a critical value, an element inverted and the analysis stopped. This limited the analysis to average stresses of Ï = 2 to 3 GS and rotations of 0.008 to 0.020 rad./layer. However, these values include essentially the full range relevant to practice. When the loading caused hydrostatic tension stresses, hour- glass modes occurred (for example, Figure E-14 in Appendix E) and eventually caused the analysis to become unstable. How- ever, reliable results were available for hydrostatic tensile stresses (that is, positive values of mean normal stress) up to Ï = E â 3G, where G is the shear modulus and E is Youngâs modulus. This is approximately the magnitude described by Gent and Lindley (1959b) for the onset of internal rupture. Hence, the FEA model can be used to evaluate hydrostatic tension stress up to the level corresponding to rupture in real bearings. 2.2.2.1 Geometry and Boundary Conditions Figure 2.7 shows the geometry and the typical FEA mesh for a 3-layer bearing with S = 9. (Symmetry allows only the top half of the bearing to be modeled. The figure is also not to scale.) Reference Point A is the point at which shear strains are evaluated for comparison with those predicted by the lin- ear theory. Due to the applied rotation, the model possesses only one symmetry plane. More detail on the meshes used is available in Section E.2 of Appendix E. Bearings with rigid top and bottom plates were modeled using the same mesh and loading, but the interface properties were changed from frictional contact to glue. This perma- nently attached the bearing surface to the rigid loading surface and allowed identical load histories to be applied to bearings with and without rigid end-plates. 2.2.2.2 Materials The elastomer was modeled as a nonlinear, elastic, nearly incompressible material. Bearing manufacturers typically report Shore A hardness, elongation at break, and nominal stress at failure, but these properties alone do not uniquely define the material. This presents a challenge because it allows some variability on the manufacturerâs side, and leads to a problem for the analyst of nonuniqueness of material 0.25 in. 8.5 in. Reference Point A 0.25 in. 0.50 in. 0.12 in. 0.25 in. in. in. Figure 2.7. Geometry and FEA mesh for a strip bearing with S 9.
16 parameters. Following a suggestion by the project Advisory Group, the simplifying assumptions by Yeoh (1993) were adopted. The shear modulus G was estimated from the hard- ness. It was later confirmed by shear tests performed on elas- tomer samples extracted from the bearings tested in the lab- oratory. The bulk modulus K was estimated from Holownia (1980) and was later verified through a similar process. Parameters for Yeohâs model were calibrated to match these values and an appropriately scaled representative stress-strain curve for rubber taken from Yeoh (1993). Yeohâs model can be represented as a subset of the generalized Mooney model (Ogden 1984) which is available in MSC.Marc2003r2. 2.2.2.3 Loading One major consideration of creating the model was how to portray the loading conditions realistically. In all the physical tests the bearing was placed between two metal plates to en- sure uniform loading. To simulate the experimental condi- tions the loading plates were represented using rigid surfaces and frictional contact between these surfaces and the bear- ings. The coefficient of friction used was 1.0. The motion of the rigid loading surface can be controlled in the simulation by defining the position (or velocity) of a reference point on the surface and an angle (or angular velocity) to identify its orientation. This requires the loading to be displacement-controlled rather than load-controlled. The loading of the bearing was composed of slow axial compres- sion to various levels of average axial strain, εa, followed by rigid body rotation of the loading surface. Forces and mo- ments on the loading surface, as well as local strain and stress measures, were recorded for each load history. 2.2.3 Analyses Conducted Bearings of various shape factors were considered in the nu- merical analysis. The most representative bearings were those with a cross section similar to the 9 in. à 22 in. bearings with S = 6 that were tested in the experimental program. Analyses were conducted on plane strain, 2-D models, which corre- spond to infinite strips, so either the shape factor or the layer dimensions could be kept the same, but not both. Most of the analyses were made with t = 0.75 in. which gives S = 6, but some also were conducted using layer thicknesses of 0.50 in. and 0.375 in., which correspond to S = 9 and S = 12. The load histories were characterized by the normalized load intensity Ï / GS and the imposed rotation per, θL. All combinations of shape factors (6, 9, and 12) and load histories were carried out until excessive mesh distortion near the ends of the shims or the presence of hourglass mode patterns caused the analysis to fail. For most bearings, reliable analyses were possible within the range of 0 < Ï / GS < 2 and 0 < θy < 0.006 rad./layer. Depending on axial load intensity and applied rotations, some analyses could be performed beyond that do- main. These were used to verify conclusions drawn based on the reduced data set. However, these extended analyses did not support an extended parameter domain but rather repre- sent subdomains with tighter restrictions on achievable rota- tions outside the confidence domain. Several analyses were performed to help understand effects of imperfect seating or non-parallel bearing surfaces on the observed test data. These simulations are not documented in Appendix E since they do not contribute independent knowl- edge. However, they were very helpful for the identification and interpretation of initial loading effects. All bearings were analyzed separately as (1) bearings with the potential for lift-off and (2) bearings with bonded external plates. From the analysis perspective, the first set of analyses allowed the rigid loading surface to separate from the bearing, using the friction interface property. Postprocessing was per- formed to identify the amount of lift-off, its effect on the local strain distribution, and maxima of local shear strain. The sec- ond set of analyses treated the bearings as permanently at- tached to the loading surface. These analyses were used to in- vestigate the hydrostatic tensile stresses identified by Gent and Lindley (1959b) as responsible for internal rupture. 2.2.4 Results 2.2.4.1 Evaluation and Validation of Stiffness Coefficients Gent and Meinecke (1970) demonstrated that axial stiff- ness and rotational stiffness of bearings can be expressed in terms of shear modulus G and shape factor S. Introducing four coefficients Aa, Ba, Ar, and Br yields the following relations for the equivalent Youngâs modulus for axial stiffness (in the z-direction) and the effective Youngâs modulus for bending stiffness about the y-axis Stanton and Lund extended the formulation for slightly compressible material and proved that by properly adjust- ing the stiffness coefficients, the general form of Equations (2-1) and (2-2) remains valid. They also adopted Gent and Meineckeâs assumption that for all strip bearings. In their analyses, they included the effects of the slight com- pressibility of the elastomer by defining the Compressibility Index, λ, λ = S G K 3 (2-3) A Aaz ry= = 4 3 E I G A B S Ir r r= +( )3 2 (2-2) E A G A B S Aa a a= +( )3 2 (2-1)
and making the coefficients such as Ba functions of λ. In Equation (2-3), G is the shear modulus, K is the bulk modu- lus of the elastomer, and S is the shape factor. Figure 2.8 shows the coefficients that relate the characteris- tic mechanical quantities. The left side of the figure shows the variables used for axial analysis, and the right side addresses rotation, or bending. The first circle contains the global force loading (Ï/GS or M), the second shows the corresponding global displacement, and the third defines the peak internal local strain (γzx,max, with superscript ε or θ to indicate the load- ing that causes it). These local shear strains from the two load- ings are superimposed in the linear theory, and it is the valid- ity of that process that is evaluated here using FEA. The symbols next to the arrows indicate the dimensionless coeffi- cients defined in the linear theory that relates the quantities in the circles. The typical design input is the average load inten- sity, Ï / GS, and the total rotation θy (or rotation per layer θL). The average axial strain εa or the applied moment M also may be used as input values, but their use is uncommon in practice. The aim of this section is to back-calculate these coeffi- cients based on numerical results from nonlinear FEA. This provides insight into both the potential model error of the linear theory by Stanton and Lund (2004) and the signifi- cance of nonlinearity over the common load range for elas- tomeric bearings. Details of the analysis are provided in Sec- tion E.3 of Appendix E. 2.2.4.1.1 Summary for the axial stiffness coefficient Ba. The stiffness coefficient Ba was evaluated for bearings with S = 6, 9, and 12. These shape factors are nominal values com- puted using the total length of the bearing (9.0 in.). The ana- lytical equations by Stanton and Lund (2006), however, are based on bearings without edge cover. To evaluate the signif- icance of the cover layer for the computation of the axial stiff- ness of a bearing, Ba was back-calculated from the FEA results using Equation (2-1) and three different ways of defining the shape factor: ⢠Using the total length of the bearing, that is, including the cover layer (L = 9.0 in), ⢠Using the length of the shim (L = 8.5 in), and ⢠Using the average of shim length and total length of the bearing (L = 8.75 in). These three different definitions of S lead to three different back-calculated values for Ba. Figure 2.9 compares the three Ba values obtained from the FEA (see Figures E-11 through E-13 in Appendix E) with one taken from linear theory (see Fig- ure F-3 in Appendix F) for λ. The value of Ba computed from the FEA changes with the mesh size used in the FEA, the way that L is defined, and the compressive stress. The mesh size effect is essentially an error in FEA, so the mesh used was the finest practical, and was the same for all three definitions, so it is expected to make little difference in the comparison. The load level has an effect on the comparison because the load- deflection curve is nonlinear, so the value of the secant stiff- ness depends on the stress applied. Thus, in Figure 2.9 the rel- ative error is presented both at zero load and at Ï = 1.0 GS, and six curves are shown (three nominal shape factors and two different load levels). If the objective of the comparison is to determine whether the linear theory is correct, the comparison should be made at zero load, which represents as closely as possible the as- sumption of infinitesimally small displacements that under- lies the theory. If the objective is to find a value of Ba that pro- vides the best match for design purposes, the comparison should be made at the design load level. And that varies from bearing to bearing. The approach adopted here was to ad- dress separately the errors due to geometric modeling (that is, can the linear model without cover model the real bearing with cover, under linear conditions?) from the errors associ- ated with constitutive laws (linear versus nonlinear stressâ strain relationships). Thus the best match was selected using zero load, and was found to occur when the length of the 17 GS Ar, BrAa, Ba zx, max M n CrCa Superposition Ï Îµa θy γε γzx, max zx, max γθ Figure 2.8. Relation between engineering quantities and coefficients for the linear analysis by Stanton and Lund (2006). Ba. Comparison of FEA and linear models 0.90 0.95 1.00 1.05 1.10 1.15 1.20 8.50 8.75 9.00Bearing length (in) B a (F E/ lin ea r) S=6, 0.0GS S=9, 0.0GS S=12, 0.0GS S=6, 1.0GS S=9, 1.0GS S=12, 1.0GS Figure 2.9. Stiffness coefficient Ba for various S, based on various definitions of L.
bearing was taken as the average of the gross length and the shim length. Nonlinear effects also were found to become less important as the shape factor increased. No significant nonlinear effect was observed for SF 12. This behavior is attributed to the fact that the displacement field is different in the core of the bearing, where it is nearly parabolic, and near the edge where it is highly nonuniform. The nonuniform, outer displacement field pene- trates about one half a layer thickness back from the edge of the shim. This distance can be expressed as (0.5/S) of the half-width of the bearing, which implies that the influence of that region decreases for larger S, as was observed in the FEA. 2.2.4.1.2 Summary for rotational stiffness coefficient Br. The rotational stiffness coefficient Br was analyzed for four different combinations of axial compression and simultane- ous rotation. Back-calculation was performed for the same three definitions of the shape factor that were used for axial loading. The question of the conditions under which the com- parison should be made is similar to that faced with the axial loading, except that an additional complication is present. The analyses were conducted by applying an axial displace- ment first, which then was held constant while the rotation was applied. Different axial loads were used in the four analy- ses, thereby presenting a larger variety of conditions under which the comparison could be made. For the same reasons used in the Ba comparison, the analyses were compared at zero axial load and low rotation (Figures E-15 through E-17 in Ap- pendix E). Again, the best match was found when L was de- fined as the average of the gross and shim dimensions, and S was computed from it. Furthermore that match was essen- tially perfect. This finding is convenient for development of a design method, because it allows a single definition of L to be used for all loadings. That definition was used in the subse- quent development of design procedures (Appendix F), and in the proposed specifications (Appendix G). 2.2.4.1.3 Shear strain coefficient Ca for axial loading. In linear theory, the shear strain due to axial force is obtained using the coefficient Ca defined in Equation (F-21) of Appen- dix F. Stanton and Lund (2006) used linear theory to compute values of Ca for different bearing geometries and compress- ibility indices, and their values are presented in Figure F-4. Comparable FEA values were obtained by taking the local shear strain predicted by the FEA and solving Equation (F-21) for Ca, knowing the average axial strain, εa, and the shape factor, S. The difference between the values obtained by FEA and linear theory was found to be less than 7.5% in all cases. The difference is attributed to the error introduced by the simpli- fying assumption of an isotropic stress state in the linear analy- ses versus a general stress state under plane strain conditions in the FEA. The relatively small model error justifies the use of theo- retical relations for the definition of design strains. 2.2.4.1.4 Shear strain coefficient Cr for rotation loading. Due to extreme but local mesh distortion, the numerical analysis could not provide the local shear strain at the very end of the shim. (See Appendix E for a detailed discussion of the issue.) Instead, the shear strain at a distance of 1â4 in. in from the end of the shim was recorded from the FEA and extra- polated to the end of the shim. This location corresponds to a distance of a half layer thickness in from the shim end for the bearing with S = 9. The distribution of shear strain along the shim is parabolic rather than linear, which makes the extra- polation difficult and subject to error. The extrapolation can be based on the location of zero shear strain along the shim, but for load combinations other than pure rotation, that point moves as the imposed rotation changes, introducing signifi- cant uncertainty and hence error to the procedure. Due to the unreliable nature of the extrapolation procedure outlined in Section E.4.4 of Appendix E, analyses for bearings with different shape factors were not conducted. Instead, an alternative procedure was developed to verify the basic hypo- thesis that use of superposition results in an acceptably small error. This procedure and the results obtained are discussed in detail in Section E.5 of Appendix E. 2.2.4.1.5 Effect of lift-off on local shear strain. If lift-off occurs, it affects the relationship between local shear strain and applied rotation. The behavior was studied by analyzing load combinations for which an axial load is applied first, and then is held constant while the rotation is applied. Force, moment, local strain, and length of lift-off were recorded. In the unloaded region of the bearing, that is, the region where the lift-off occurs, the shear strain remains small and approximately constant after the start of lift-off. By contrast, the loaded region experiences a significant increase in shear strain. Because the dimensions of the loaded area change with the applied rotation, by definition the behavior is geometri- cally nonlinear. In the FEA, both the axial and rotation components of the loading were displacement-controlled. This approach reduces the amount of iteration that would otherwise be necessary in the analyses and reduces the run times. However, the use of applied displacements in a geometrically nonlinear problem leads to nonconstant axial loads. This caused the FEA to un- derestimate the amount of lift-off compared with what would be seen under conditions of constant load, which are the ones likely in practice. Despite this difference between test and analysis, the FEA provided an understanding of the mecha- nism of lift-off and aided the development of the simplified semilinear formulation for design of bearings with lift-off, as described in Appendix F. 18
2.2.4.1.6 Local effects at the ends of the steel shims. Var- ious levels of mesh refinement were applied to study local ef- fects near the end of the steel shims. The shim itself remained elastic and almost rigid throughout the analysis. Very large strains were observed in the elastomer locally near the edge of the shim. If linear analysis were to be conducted, the sharp edge of the shim would introduce a singularity. The numerical sim- ulation would predict a finite rather than infinite value of stress there, but its magnitude would increase as the mesh size was re- duced. The shape of real edges of shims varies between manu- facturers from sharp cuts (as-sheared) to slightly rounded (with a deburring tool or belt-sander). Both numerical limitations and variability of the real product require some special con- sideration when analyzing and comparing numerical data and results from a linear analysis. This subsection contains a brief discussion of special phenomena observed at the ends of the steel shims. At high axial strains or applied rotations, the effect of out- ward expansion of the elastomer becomes the dominant mech- anism in the vicinity of the end of a shim. This mechanism forces the elastomer of the cover layer to expand outward and, due to the nearly incompressible nature of the material, to ex- perience vertical contraction (that is, perpendicular to the di- rection of maximum principal strain) of approximately 50%. Figure 2.10 illustrates the situation. At zero load, the top and bottom boundaries of all the elements were straight and hori- zontal. The extreme local deformations visible in the figure cause tension in both the horizontal and vertical directions. They create locally high hydrostatic tension stress, despite the factthattheaverage vertical stress on the bearing is compressive. The figure shows that over most of the domain the hydro- static stress is compressive. It is shown grey, corresponding to the very bottom block of the scale. (The stress in the figure is given in Pa.) However, at the edge of the shim and at the outer surface of the cover, it is tensile and locally quite large. The re- sults are shown for an average maximum stress on the bearing of Ïa = 1.02GS. The high hydrostatic tension at the edge of the shim leads to local debonding there. The tension at the surface occurs at the mid-height of the layer and can cause a split under extreme loading. Such splits have been seen in practice, especially in bearings with thick layers. At the shim edge, the volume of material subjected to hydrostatic tension is larger at low load levels and shrinks as loading progresses. However, the intensity of the hydrostatic tension stress, Ïhyd, increases as the applied load increases. At Ïa â 1.02 GS, the localized hydrostatic tension at the end of the shim reaches the magnitude of Ïhyd â E â 3G. This has to be viewed in relation to observations by Gent and Lindley (1959b), that showed internal rupture of rubber starts at Ïhyd â 0.9E (with E = 300 psi â 2.0 MPa). This observation has far-reaching consequences since it indicates that separation of the cover layer can be initiated by internal rupture of the elastomer rather than failure of the adhesive bond between the elastomer and steel. During visual inspection, the failure mechanism could be incorrectly attrib- uted to debonding since the highest hydrostatic tension occurs close to the interface. The intensity of the local hydrostatic tension and the local extreme shear strains cannot be predicted by the linear theory, which ignores the cover. However, they are directly related to 19 Figure 2.10. Computed hydrostatic stress, hyd , (in Pa) at average stress on bearing of a = 1.02GS.
the shear strain at the elastomerâsteel interface close to the edge of the shim and are predicted by the linear theory. This permits the shear strain obtained from the linear theory to be used as a proxy for the local hydrostatic tension. 2.2.4.2 Bearings with Rigid External PlatesâUplift Bearings with rigid end-plates are used where lift-off can- not be permitted, or where low axial forces provide insuffi- cient friction to hold the bearing in place against applied shear forces. These bearings do not experience the nonlinear geometric effects observed in bearings with lift-off. A prob- lem that can arise in bearings with rigid end-plates is the presence of hydrostatic tension in the interior of the layer. (This is distinct from the hydrostatic tension at the end faces of steel shims discussed in Section 2.2.4.1.6.) Internal hydro- static tension becomes most significant under combinations of light axial load and large rotation, at which conventional elastomeric bearings experience lift-off. FEAs were conducted on such bearings to investigate the phenomenon. In most of the FE analyses conducted for this research, the load or rotation was limited by inversion of the elements near the end of the shims when the local compression strain becomes too large. However, for these analyses of uplift, the local compression strain there was modest, and the analyses were limited by âhour-glassingâ of the elements in the hydro- static tension region. The elements should remain approxi- mately rectangular, but when hydrostatic tension becomes too large they become unstable and assume the waisted shape of an hour glass. Results obtained after the onset of this phenome- non are unreliable. However, in all cases the analyses were able to progress until the hydrostatic stress reached approximately E, the value at which Gent and Lindley (1959b) found internal rupture in their experiments. That physical and analytical in- stabilities occur at the same load is purely coincidental, but they allowed the analyses to cover the critical range. Hydrostatic tension is addressed in Section F.1.1.5 of Ap- pendix F. Peak hydrostatic stress can be predicted using the linear theory using only the variables α, a function of the load combination, and λ, a function of the bearing properties. Furthermore, the influence of λ is small. FEAs were conducted on strip bearings with S = 6 and S = 9. The results were converted to the form of Figure F-14, which shows the dependence of the peak hydrostatic stress on α and λ. The comparison of FEA and linear model analysis is shown in Figure 2.11. Results were obtained using linear theory for both incom- pressible and compressible cases. (G and K were taken as 100 psi and 450,000 psi, so the Compressibility Index was only 0.18 and 0.27 for S = 6 and 9 respectively. The effect of compress- ibility was therefore small.) FEAs were conducted by applying an axial load, holding constant the compressive displacement at the middle of the bearing, and then rotating the top surface. Results are shown for a bearing with S = 6 and various axial loads, expressed in terms of the average axial stress, normalized with respect to GS. As can be seen, the agreement is very good and substantiates use of the linear theory for design. The slight flattening out at the top of the FEA curves is due to the onset of hour-glass instability in the elements, which caused the analy- sis to become invalid before reaching the higher rotations that would lead to higher hydrostatic tension stresses. The linear theory assumes that the hydrostatic tension is uniform through the thickness of the layer, and equal to the vertical direct stress. The FEA showed that neither statement is 20 Normalized hydrostatic stress 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -0.4 -0.3 -0.2 -0.1 0 0.1 alpha f(a lph a) Ax 1 - sigma / GS = 0.0928 Ax 2 - sigma / GS = 0.248 Ax 3 - simga / GS = 0.481 Ax 4 - sigma / GS = 0.684 Ax 1.5 - sigma / GS = 0.187 Linear, incompressible Linear, compressible Figure 2.11. Hydrostatic stress: comparison between linear theory and FEA results.
precisely true, but especially at low loads, they both prove to be excellent approximations. They are particularly true for thin rubber layers, which correspond to high shape factors, which in turn are the conditions under which hydrostatic tension is likely to be critical. The hydrostatic tension is largest at the in- terface between the shim and the rubber. There the lateral con- straint provided by the bond to the steel increases the mean tension stress for a given vertical stress. The behavior is analo- gous to the hydrostatic compression found when a short con- crete cylinder is tested between platens with high friction. 2.2.4.3 Significance of Nonlinear Effectsâ Superposition Error One key research question behind the numerical analysis concerns the validity of the superposition principle based on the design relations by Stanton and Lund (2006). Strictly speaking, after considering the nonlinear elastic nature of elas- tomers and the locally large strains as observed near the ends of the steel shims, superposition is not valid for the given problem. However, nonlinear analysis provides the means to quantify the error introduced by the use of a linear theory and by application of the superposition principle. The following analysis proves that the error introduced by these assumptions remains within acceptable bounds for all reasonable combina- tions of axial loads and imposed rotations. This proof is performed as follows: 1. Verify that the obtained results from nonlinear FEA and those obtained from the linear theory by Stanton and Lund are closely related. This was performed in Section 2.2.4.1. 2. Represent a characteristic numerical result, for example, the local shear strain at the end of a shim, as a smooth function of average axial stress and the applied rotation. 3. Extract the linear portion of the function. This represents all possible combinations as characterized by superposi- tion of linear models for axial and rotational behavior. 4. Analyze the difference between both functions, that is, the error introduced by linearization and superposition. This provides an error map over the entire range of average axial stress and applied rotation. 5. Verify that the model error does not exceed an acceptable value. Evaluating the significance of nonlinear behavior requires analysis of numerical data over the given load history for a large number of different load combinations. For elastomeric bearings, the numerical information of primary interest is the maximum local shear strain at the end of each steel shim. Each loading consists of a different sequence of axial loads and rotations. Thus each nonlinear simulation represents a single curve on a force-rotation plot. Processing data curves for information such as load combi- nations that cause equivalent γzx,max, or the significance of non- linear effects, is difficult. The simulation data were analyzed by fitting an approximating surface to the data points in axial- force-rotation space. That surface then could be used to repre- sent the data for comparing it with other models such as the lin- ear one. In the present case, the simulation data was fitted, using a least squares criterion, by a function of the following type: where i and j were restricted to i + j ⤠m. Using the full series given in Equation (2-4) did not improve the fit obtained. This fitting analysis was performed for four series of simulations: ⢠Strip bearings with S = 6 and bonded external plates. This series creates uplift at larger rotations. ⢠Strip bearings with S = 9 and bonded external plates. This series creates uplift at larger rotations. ⢠Strip bearings with S = 6 without bonded external plates. This series allows for lift-off with increasing rotation at low axial forces. ⢠Strip bearings with S = 9 without bonded external plates. This series allows for lift-off with increasing rotation at low axial forces. For both S = 6 and S = 9 an almost linear relation between Ï / GS, θL, and the local shear strain γzx was observed over most of the range of practical loads and rotations. However, the re- lation became nonlinear at small axial loads. This reflects the effect of lift-off. The smooth fitted function defined by Equation (2-4) pro- vided further insight into the overall behavior and allowed further interpretation of the analysis. Use of the linear terms in (2-4) that is, provides the ideal approximation of the nonlinear behavior by means of a linear theory of bearing deformation. It is used to identify the difference between using a geometrically and phys- ically nonlinear theory and a much simpler (and thus more usable) linear theory. This difference is measured in terms of a relative error of a linear solution defined as Equation (2-6) defines the error caused by analyzing a non- linear mechanism with a linear model. Figure 2.12 shows an iso-error plot for bearings with bonded external plates for SF 9 up to normalized load levels of Ï / GS â 2.5 and rotations per Errormodel nonlinear line = ( ) â ( )γ γzx zx,max ,max ar linear (2-6) γ zx ,max( ) γ Ï Î¸zx ij i L j i j a a GS a,max , = + âââ ââ â ( ) = = = â00 1 1 1 00 + âââ ââ â + ( )a GS a L10 01 Ï Î¸ (2-5) γ Ï Î¸zx ij j m i m i L j a GS ,max = âââ ââ â ( ) == ââ 00 (2-4) 21
layer of θL = 0.006 rad./layer. An iso-error plot shows con- tours of constant error, or difference, between linear and nonlinear results. Figure 2.13 shows the equivalent results for similar bearings without bonded external plates. Bearings that have bonded external plates and are sub- jected to rotations typically show a model error less than 5%, reaching maxima around 10%. (Higher error values on the left side of Figure 2.12 lie outside the domain in which the elements remained stable.) The largest model error is observed along the rotation axis (Ï / GS = 0). Bearings without bonded external plates experience lift-off at low load levels. This is reflected in the iso-error plots shown 22 0 0.5 1 1.5 2 2.5 0 0.002 0.004 0.006 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 5 5 5 5 7.5 7.5 7.5 10 10 10 12.5 12.5 1 15 17.5 2022 P / GSA n (rad) θyθL = Figure 2.12. Iso-error plot (in %) for shear strain, zx. Bearing with S 9 and bonded external plates, based on a fourth-order fit. (Constructed for Shear Strain at 1â4 in. Distance from the Critical Edge of the Shim). 0 0.5 1 1.5 2 2.5 0 0.002 0.004 0.006 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 5 5 5 5 5 5 5 5 5 7.5 7.5 7.5 7.5 7.5 10 10 12.5 1 15 17.5 2022.5 25 P / GSA n (rad) θyθL = Figure 2.13. Iso-error plot (in %) for shear strain, zx. Bear- ing with S 9 and no external plates, based on a fourth- order fit. (Constructed for Shear Strain at 1â4 in. Distance from the Critical Edge of the Shim).
in Figure 2.13. The typical model error lies below 5%. The ex- ception is the region at the left of the plot, where lift-off occurs, behavior becomes nonlinear and the error increases. At high axial loads, higher error values are observed outside the sup- ported domain and represent extrapolation errors introduced by the fit functions. At low axial force, the higher error value may be affected by extrapolation errors, but also due to the geometric nonlinearity due to lift-off. This latter contribution has to be addressed in a semi-linear analysis by introducing the amount of lift-off into the analysis. This issue of imple- menting the effect of lift-off into a semi-linear analysis model is addressed in Appendix F. 2.2.5 Discussion Section 2.2 has presented key results from the numerical simulations. The extracted information provided proof of the key hypotheses needed for an effective, simple design proce- dure. These findings support the following statements. ⢠Superposition of axial and rotational effects provides a rea- sonably accurate representation of nonlinear FEA. The error analyses proved that model errors combined with er- rors due to superposition are typically below 7.5%. Only load combinations that cause significant lift-off were found to reach model errors in shear strain of up to 20%. ⢠The stiffness coefficients predicted by the linear theory of bear- ings by Stanton and Lund are in good agreement with a non- linear FEA and thus provide a simple way to predict axial and rotational stiffness of elastomeric bearings. Typical model er- rorsarebelow5%forloadcombinations expected in practice. ⢠The local shear strain predicted by the linear theory of bear- ings by Stanton and Lund is in good agreement with a non- linear FEA. Typical model errors are in the range of 5%. ⢠The predicted tensile hydrostatic stress agreed closely with the predictions of the linear theory. The relatively small overall error identified in this section justifies the general use in design of the linear analysis by Stanton and Lund (2006). The worst model error of approximately 20% occurs in bearings where lift-off is permitted. Most standard bearings can be designed safely within this error range. For special bearings in which extensive lift-off is expected to occur, the additional accuracy obtainable by using a custom nonlinear FE analysis may be warranted. 2.3 Development of Design Procedures Design of structural components for service loads usually includes calculation of stresses caused by different load cases. The stresses then can be added and compared with an allow- able value. Because elastomeric bearings are composite struc- tures, and one of the materials is very nearly incompressible, it is not the peak direct stresses that should be added, but rather the peak shear strains. Compression, rotation and shear loadings all cause shear strains in the elastomer, as shown in Figure 2.14, and the values within the layer are all maximal at the same location, namely at the edge of the steel shim. The shear strains eventually lead to delamination of the elastomer from the steel. This process may occur under a monotonic load of sufficient intensity, but is more commonly caused by cyclic loading. That process is one of fatigue. De- riving a precise limit that the total strain must satisfy then is more difficult than it would be if failure were controlled by a single application of monotonic load. Regardless of whether the loading is cyclic or monotonic, a method for computing the shear strains is needed. This, too, is complicated by the fact that elastomers can and do un- dergo strains that are very large compared with those that occur in conventional structural materials. The elastomer also is materially nonlinear. For these reasons accurate analy- sis for loads other than very small ones can only be achieved using FEA, as discussed in Section 2.2 and Appendix E. How- ever, such analyses are not appropriate for the design office, so a simpler alternative is needed. An approximate, linearized theory is discussed in Section 2.3.1. 2.3.1 Computation of Shear Strains using the Linearized Theory Gent and his coworkers (for example, Gent and Lindley, 1959a, Gent and Meinecke, 1970, and Lindley and Teo, 1978) pioneered the analysis of laminated bearings and developed a linearized analysis procedure. Conversy (1967) extended it to allow for finite values of bulk modulus, and Stanton and Lund (2006) provided numerical values of all necessary coefficients for different bulk modulus values. That approach forms the 23 (a) Compression (b) Rotation (c) Shear Steel plates steel plate bulging elastomer Shear strain Shear strain Shear strain x z x y Figure 2.14. Shear strains in the elastomer due to different loadings.
basis of the procedure used for the design method used in this research, and is summarized here. It is approximate because it assumes a parabolic distribution of displacement through the thickness of the elastomer within a layer, but, as the FEA shows, that approximation proves to be remarkably good, and, for the geometries and stresses used in practical bearings, the errors are small compared with those arising from other sources, such as characterization of material properties. Its simplicity compared with any other alternative makes it an attractive choice. In a bearing that does not lift off, either because the rota- tion is too small or external bonded plates prevent it, the girder always remains in contact with the bearing. The boundary conditions then remain constant during the loading. The lin- earized theory can then be used to relate three fundamental quantities shown in Figure 2.8. For compression they are: ex- ternal load (average stress or force), external displacement (average strain or deflection), and maximum local internal de- formation (defined here by shear strain γa). Similar parameters exist for rotation (bending). The parameters that relate these quantities define functional relationships that are analogous to those used in conventional beam theory (for example, M = EI curvature, stress = My/I). As shown in Appendix E and Section 2.2, the full nonlinear model of a bearing reduces to Gentâs linear theory if the strains are small enough. This finding satisfies a basic require- ment for using the linear theory for design. The strain levels expected in practice are not infinitesimally small, so the prob- lem strictly is no longer linear, superposition no longer strictly holds, and strains from different load cases strictly cannot be added directly. However it was shown in Appendix E that in practice errors involved in doing so are acceptably small com- pared with other uncertainties in the problem. Details of the linear theory are given in Appendix F. How- ever, for the no lift-off case, two results are important. First, for a bearing subjected to combined compression and rotation, the peak shear strain on the compressive side must be com- puted. That can be done by computing the shear strain caused by each loading separately and adding the results. Second, if the load is light and the rotation is large, and the bearing has external plates, the interior of the elastomer may experience hydrostatic tension stress on the tension side. Gent and Lind- ley (1959b) showed that such stress can lead to brittle rupture of the elastomer at a relatively low stress (in the range 0.9E to 1.0E, or 2.7G to 3.0G). Equations for computing the hydro- static stress also were developed using the linearized theory, and values were verified against the FEA. The validation process is complicated slightly because the location of the peak hydro- static stress varies with the ratio of axial deformation to rota- tion. This causes a need to search for the element with the highest stress in the FEA, rather than simply monitoring a sin- gle element. For the case where lift-off is possible, a closed-form analy- sis is more difficult, because even under small strains and using the linear theory the dimensions of the contact region between the sole plate and bearing change throughout the loading. The problem then becomes inherently geometrically nonlinear. Hydrostatic tension is essentially eliminated, so the important issue concerns computation of the peak shear strain on the compressive side. A geometrically nonlinear, approximate variant of the linear theory was developed in closed form by assuming that the bearing can be divided into two parts, one that lies under the loaded region and the other remains unstressed, as shown in Figure 2.15. It is described in detail in Appendix F. This semi-linear model ignores any horizontal stresses ap- plied by the elastomer on one side of the interface to material on the other. The response that it predicts was compared with the nonlinear FEA, and reasonable agreement was found. (Shear strains differed by 20% in the worst case.) As explained in Section 2.2, precise comparisons were difficult because they required extrapolation in the FE model. However, the semi- linear model showed that total shear strain (due to rotation plus compression) always was smaller than that computed using the truly linear no-lift-off model, with a peak error of approximately 20%. This result provides support for the use of the semilinear model. Appendix F described not only the mathematical development, but also offers a physical expla- nation of why the strains in the semilinear model should be an upper bound to the true peak strain on the compressive side. This result is valuable because it allows the linear no-lift-off model to be used safely for prediction of the critical shear strains. Doing so simplifies the calculations because it allows one model to be used for all load cases. 2.3.2 Shear Strain Capacity The procedures outlined in Section 2.3.1 are sufficiently simple for use in design and can be used to compute the crit- ical shear strains. However design involves the computation 24 L/2 ηL L/2 Figure 2.15. Lift-off: bearing behavior assumed in âsemi- linearâ model.
of both shear strain demand and capacity. This section ad- dresses capacity. The shear strain capacity of the elastomer was indirectly established by test, using test procedures detailed in Appen- dix C and results given in Appendices A and D. The test results were modeled for monotonic and cyclic loads. The cyclic modeling in particular was done in some de- tail, so as to provide the best possible basis for a design proce- dure. Several difficulties were encountered. The primary ones were: ⢠The shear strains in the elastomer cannot be measured dur- ing the test because the deformations are too large for con- ventional instrumentation and because the presence of sen- sors would alter the strain field where the measurements are needed. Indirect methods for establishing the strains were necessary. One approach was to measure the heights of bulges of the rubber layers with a micrometer gage. However, the rubber cover smoothed out the serious shear distortions in the underlying material so the bulge height measurements, though accurate, ultimately proved unusable. ⢠The shear strains were computed from the axial strains using the constants Ca and so forth, developed using linear theory. Even the average axial strains could not be mea- sured during the rotation tests, because the instrumenta- tion could be installed only after the bearing was secured in place by the clamping action of the plates of the test rig, and by that time the axial strain had been imposed. Thus the average axial stress versus average axial strain relation- ship for each bearing was obtained from the axial test se- ries (PMI 1b) on that bearing batch. Separate calibrations were needed for each batch because of the slight differ- ences in material properties. For example, for batch A2 bearings, the axial stress-strain curve was obtained from Test PMI 1b-A2 and was used in obtaining the axial strain from the measured axial stress in tests CYC05-A2 through CYC012-A2. Use of the linear theory to link axial and shear strains, through constants Ca and so forth, was justified be- cause the same constants would be used in both the design procedure and the analysis of the test data. ⢠The axial response of the bearing was not linear, even at low loads. At higher loads, the nonlinearity became significant. This behavior has been observed by many researchers. ⢠The material was not elastic, so cyclic loading caused a re- sponse that was both hysteretic (because of slight visco- elasticity) and, at least during the first few cycles, nonrepeat- able because of the gradual breakdown of crystallization. Despite these difficulties, the shear strain capacity of the bearings was characterized at various levels of damage. Both debonding and delamination damage were observed. Both caused bulge patterns that appeared similar from outside the bearing, and they could be distinguished only by cutting open the bearing, which precluded further testing. That pro- cedure was used sparingly. As discussed in Sections 1.3 and 2.2.4.1.6, debonding always started by separation of the rub- ber cover from the vertical edge of the shim. As loading pro- gressed, and only if it was severe, the internal cracks caused by the tension debonding then propagated as shear delami- nation into the interior of the rubber layers. An example is shown in Figure 2.16. The crack typically propagated through the rubber and not along the steel-rubber interface. That indicates good bond. The tension debonding has essentially no adverse effect on the performance of the bearing, but the shear delamination renders it less stiff and less able to resist load. The monotonic tests consisted of different combinations of axial and rotation loading. All monotonic specimens that debonded started doing so at approximately the same com- puted shear strain of approximately 6.7. Details are given in Table F-1. This provided a value for the static shear strain ca- pacity. All of the pure axial tests were taken up to the test ma- chine capacity of 2400 kips (a stress of 12 ksi, or approxi- mately 10 times the present AASHTO limit for that bearing). In some cases the shims fractured, but only at the very end of the loading, some bearings suffered some debonding, while in others there was no damage at all. The cyclic loading test produced a large amount of data, and developing a model to represent the results was difficult. Two approaches were used. In the first, the Nonlinear Model, the axial strains were obtained from the axial stresses using an empirical, nonlinear model, because the measured axial load- deflection curves in the PMI series were clearly nonlinear. The shear strains then were derived from the axial strains using Gentâs linear theory. The shear strains due to rotation were derived directly from the rotations using Gentâs linear 25 Extent of cracking Figure 2.16. Shear crack propagation into elastomer layer.
theory. In the second approach, the Linear Model, all strains were obtained from stresses using Gentâs linear model. The next step required that the shear strains applied in the tests be related to a capacity. Because capacity is not a fixed number but depends on the extent of debonding that is tolera- ble, an attempt was made to reflect that fact in the equations. In addition, the shear strain demand depends on the number of cycles applied, evident from the fact that the damage increases as more cycles are applied. Therefore the cyclic component of the shear strain demand, which in the tests consisted only of the rotation component, was multiplied by an amplification factor that was a function of the number of cycles. The final form of the Nonlinear Model is described by Equation (2-7). Details of the capacity equation were developed first for the Nonlinear Model. The load amplification factor cN was treated as a function of the number of cycles of loading, and the ca- pacity γcap was treated as function of the level of debonding, D. The model fitted the data well, and reflected appropriate as- ymptotic behavior as the relevant variables approached their limits (for example, as N, the number of cycles, reached 1 or infinity). However, when the model was applied to a typi- cal bearing for a freeway overpass, it predicted extensive dam- age after only a million cycles. Such damage has not been re- ported from the field, so the constants were recalibrated. However, no set of constants could be found that matched the test data well and gave plausible results for common field bearings. The calibration and evaluation of the Nonlinear Model is described in detail in Appendix F. These difficulties appeared to raise insurmountable obsta- cles to the generation of workable design provisions. There- fore the Nonlinear Model was not developed to the stage of design provisions. However, it is described in detail in Ap- pendix F so that it could be developed to form design provi- sions if the necessary cyclic axial load data were to become available in the future. A second model, the Linear Model, was created. Its general form again is given by Equation (2-7). It is similar to the Nonlinear Model, but differs in three major respects: ⢠The shear strains are all derived from stresses using Gentâs linear theory, ⢠The cyclic amplification factor is a constant and not a function of the number of cycles, and ⢠The shear strain capacity, represented here by the term γcap, is a constant and not an explicit function of the level of debonding deemed acceptable. These simplifications make the model easier to use. How- ever, because the amplification factor is not a function of the number of cycles, it is not possible to relate the pro- γ γ γ γ γ γ γa st r st s st N a cy r cy s cyc, , , , , ,+ +( ) + + +( ) ⤠cap (2-7) gressive damage continuously to the cycle count. Instead, the total shear strain was correlated with the cycle count for two discrete levels of debonding. The plot for 25% debond- ing is shown in Figure 2.17. It includes all the test data that reached 25% debonding, that is, all the tests except SHF-05. That was a high shape factor bearing that hardly debonded at all and had not reached 25% debonding when the test was abandoned to allow other specimens to be tested. Spec- imen SHF-06, with S = 12, also performed much better than the average. In Figure 2.17, it is the point highest and furthest to the right on the graph, with a total strain of 10.5 at log(N) = 4.2. The cycle count is plotted on a log scale, to reflect the dis- tribution of the data. The best fit line through the data then can be used to predict the number of cycles needed to reach 25% debonding for a given effective strain demand. The ef- fective strain is the quantity on the left hand side of Equation (2-7), and consists of the total static strain plus the amplified cyclic strain. A similar plot, but for 50% debonding, is shown in Figure F-20 in Appendix F. Rather than the initiation of debonding, 25% debonding was used because of the scatter in the latter. In the Linear Model, the only two parameters to calibrate are cN and γcap. To establish cN, different values were tried and the scatter of the data, as represented by the correlation coef- ficient R2, was plotted against cN, as shown in Figure 2.18. The best correlation was found with cN = 2.0, so that value was accepted for design. To establish γcap, the best fit line was ex- tended to a cycle count of 50 million, on the basis that that represents the number of passages of fully laden trucks over the lifetime of a heavily used freeway lane. The correspond- ing effective strain was 4.7 at 25% debonding. It is argued (see Appendix F) that the number would be higher if the plot had included the bearings that did not debond at all. (That is by definition impossible in a plot to 25% debonding.) For that 26 25% Debonding y = -0.6634x + 9.8959 R2 = 0.3211 0 2 4 6 8 10 0 2 4 6 log (N cycles) Ef fe ct ive s tra in 12 8 Figure 2.17. Effective strain vs. number of cycles: 25% debonding.
reason, the strain capacity was rounded up to 5.0. This value is still significantly less than the 6.7 corresponding with the start of debonding in the PMI series of monotonic tests. That static data was not included in the calibration of the Linear Model because of minor questions over its accuracy; observ- ing the start of debonding was in some cases not easy, because the lateral shift of the steel plates under large rotations pulled the critical region of the elastomer inwards so that seeing it was difficult. Checks of the Linear Model against the performance of typical field bearings suggested that its predictions were sat- isfactory, in that it predicted very low levels of damage in a typical freeway overpass bearing after 50 million cycles. (A typical 22 in. à 9 in. freeway overpass bearing is shown as an open circle at 50 million cycles in Figure 2.17, and lies well below the design line.) The Linear Model was accepted as the basis for the proposed design procedure. Its advantages over the Nonlinear Model are that it is simpler to use, it fits the test data in an average sense at discrete levels of debonding, and it gave plausible values for typical bearings in practice. The disadvantages are it does not reflect the nonlinearity in the observed axial forceâdisplacement curves from the PMI test series, and it does not provide a way of tracking the progres- sion of damage with increasing cycles. 2.3.3 Analysis of Rotation and Axial Force Demand The primary demands on the bearing consist of axial com- pression and rotation. Sample bridges were analyzed to deter- mine the combinations of load and rotation that are imposed by truck traffic crossing the bridge. Details are in Appendix F. The analyses demonstrated two important findings. The first was the truck imposes a cyclic axial force, which causes shear strains due to compression γa that are much larger than the shear strains due to the corresponding rotation γr. Both are cyclic. If cyclic shear strains are the appropriate measure for determining the propagation of debonding damage, the shear strains caused by axial loading will dominate the cal- culation. This finding came to light after the bearing testing was complete, so the time and resources were not available to conduct cyclic axial compression tests. Cyclic axial fatigue tests have been conducted in the past (Roeder et al., 1987), but the specimens had no cover and the debonding was measured in a different way than was done here. Those tests were considered in Appendix F in an attempt to account for the axial fatigue experienced by a bearing. The findings from them were consistent with the expected trends, but the dif- ferences in test conditions prevented use of numerical values from them. The second finding is the cyclic rotation due to truck load- ing almost always will be less than ±0.003 radians and may be as low as ±0.001 radians if the bridge satisfies the AASHTO re- quirement that the midspan deflection under live load be less than l/800. A simple check of typical prestressed concrete girders showed that their stiffnesses were significantly greater than the minimum needed to meet this criterion. Steel bridges are typically more flexible than their prestressed concrete counterparts, especially if high-strength steel is used, so their midspan deflections are likely to be closer to the limit. The value of the cyclic rotation that is relevant may be further re- duced by the fact that the peak shear strain of interest is the one caused by the combination of axial and rotation effects. For bridges less than 200 ft. long (which constitute the great majority), the peak combined shear strain in the bearing oc- curs as the truck is just entering the bridge. Then, the axial load component is at its individual maximum, but the rota- tion typically is not. Therefore, the use of the sum of the shear strains due to the individual peak compression and peak rota- tion is inherently conservative. Last, an evaluation was conducted to determine the contri- bution of thermal camber to girder end rotation. The AASHTO temperature gradients were used, and bridges from 80 to 180 ft. span were considered. Only concrete girder bridges were eval- uated, because the specified thermal gradient is higher for them. Details of the analyses are given in Appendix F. Figure 2.19 shows the results for a high and a low tempera- ture zone (AASHTO Zones 1 and 3 respectively). As can be seen, the rotations vary from about 0.0010 to 0.0016 radians. This value is the same order of magnitude as the rotation caused by truck loading. However, because it occurs much less fre- quently, its damaging effects are likely to be much less and may reasonably be regarded as a static rotation. It can be concluded that thermal rotations play only a minor role. Furthermore, thermal effects typically cause upward camber, whereas the live load causes downward deflection, so the two are usually not additive. 27 vs. Cyclic Factor 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 1 2 Cyclic Amplification Factor R 2 43 25% 50% Correlation Coefficient Figure 2.18. Correlation coefficient vs. cyclic factor.
2.3.4 Evaluation of the Design Model The Linear Model for design was evaluated in the light of the findings described in Sections 2.3.1 to 2.3.3. It brought to light several issues summarized here and discussed in detail in Appendix F. First, the analysis of demand showed that the cyclic axial load caused shear strains that were 5 to 10 times larger than those caused by cyclic rotations. (See Appendix F, Section F.3.3.2, and the illustration in Figure F-36). If damage attributable to debonding is to be the basis for failure, it is appropriate that the shear strains due to axial load should form a substantial part of the design specification. However, no test data were available to evaluate the relationship between cyclic axial load and debond- ing. For want of a better alternative, it was assumed that all cyclic shear strains of the same magnitude, regardless of their source, would contribute equally to the fatigue damage. This assumption allowed the test data on cyclic rotation to be used to evaluate shear strains due to cyclic compression. The design procedure was developed using the Linear Model and uses a cyclic amplification factor cN that has a con- stant value of 2.0. This is the general approach taken by the European bearing specification EN 1337, although that spec- ification uses different numerical values. The specification proposals are given in Appendix G. 2.4 QA/QC Issues A secondary goal of this research program was to evaluate the QC and QA issues related to steel reinforced elastomeric bridge bearings. This issue was raised in the original request for proposals, because of concerns regarding current test requirements for elastomeric bearings, recent revisions to the M251 material specifications for elastomeric bearings, and the recent recommendations of NCHRP Report 449 (Yura et al., 2001). This was a secondary goal, in that no experimental research was proposed to investigate the issues, but the re- search team addressed it during the research. In particular: ⢠Surveys of state bridge engineers and practicing engineers were performed to determine concerns regarding the qual- ity of elastomeric bearings and the cost and effectiveness of QA testing. Some of these survey issues are discussed in Appendix B. ⢠The researchers held discussions with the four major man- ufacturers to obtain their input on manufacturing and QC of elastomeric bearings. ⢠The researchers had extensive meetings with experts such as Professor Alan Gent on elastomers and common testing requirements. These meetings were held in conjunction with Advisory Group meetings at intervals throughout the research. ⢠The researchers closely monitored the bearings tested in their research program to evaluate the quality and perfor- mance of the bearing, and where possible they attempted to correlate this performance to the tested properties from the QA test results. This evaluation brought to light a number of issues, which are briefly discussed here. 2.4.1 Quality of Current Elastomeric Bearings Researchers tested a large number of elastomeric bearings in this study, however, they also have tested a large number of elastomeric bearings in prior research as reported in NCHRP Reports 298 and 325. A comparison of test results from present and prior studies shows that the quality of elastomeric bearings 28 1.6 1.8 Thermal Effects 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 50 100 150 200 Span (ft) Zone 1 Zone 3 End Rotation due to En d Ro ta tio n (ra d/1 00 0) Figure 2.19. Rotation due to thermal gradient on girder.
today is, on average, higher than it was 20 years ago. This can be seen by comparing the average compressive stress at which initial debonding of elastomeric bearings was observed. That stress was larger in this study than in earlier ones. In addition, the progression of damage was significantly smaller than in earlier studies. This finding shows that the current QA/QC measures are proving effective. 2.4.2 Test Requirements Requirements for testing materials and finished bearings have changed significantly in the last year. Prior to 2006, material tests were specified largely in tables 18.2.3.1.1 (Neoprene) and 18.2.3.1.2 (Natural Rubber) of Chapter 18 of the AASHTO Bridge Construction Specifica- tions. Tests were to be conducted on separate samples of ma- terial that did not have to be taken from the finished bearing. Most manufacturers made special samples for the purpose and cured them according to the same time and temperature history as the bearing. Material test requirements have been moved to the AASHTO M251 Materials Specification. This change is cer- tainly rational. However, two parallel testing regimes have been established, some tests have been eliminated, and some new tests have been introduced. Some problems are evident in the new arrangements. Details of the new testing arrangements are shown in Table 2.3. A major change also was introduced by permitting two dif- ferent test regimes. The first is applicable to all bearings while the second is optional, and may, at the engineerâs discretion, be used for bearings designed by Method A and specified in terms of hardness alone. In the first, universally applicable regime, the bearings are subject to a small number of material tests (the column headed âall bearingsâ in Table 2.3) that must, according to Section 4.2 of M251, be conducted on samples taken from the finished bearing. Some finished bearings from each lot also are to be subjected to further tests, defined in Section 8.8 of M251-06. In the second regime (applicable only to Method A bearings) and specified in Appendix X1 of M251-06, the elastomer is to be subjected to a larger battery of tests (column headed âMethod A onlyâ in Table 2.3), but the tests in Section 8.8 on finished bearings need not be conducted. The wording of Ap- pendix X1 does not make clear whether the material tests specified in Table X1 are to be conducted on material taken from finished bearings, or whether special coupons may be molded for the purpose. These changes constitute a significantly different test system for elastomers and bearings than existed before. Review of M251-06 suggests that the new arrangements need some further massaging, because the changes have introduced some poten- tial problems. The most important issues are summarized here. 1. Section 8.8.4. Shear modulus test. Three methods of de- termining the shear modulus are specified: ASTM D4014, M251 Annex 1 (an inclined compression test) and M251 Annex 2 (the same test rig as the shear bond test in 8.8.3, similar to half of a D4014 quad shear test rig). The follow- ing comments apply: ⢠Specifying three different permissible tests to determine one quantity (the shear modulus, G) is ill-advised. This is particularly true because the acceptable range for the measured G is only ±15%. Especially with natural rubber, which is subject to some variation because it is a natural product, such a tolerance might be hard to maintain even with a single test procedure. (It is worth remem- bering that the shear stress-strain curve is nonlinear, so the section of the curve used affects the outcome. This adds further uncertainty and is another reason for using a single method.) With three different procedures, each using a different shaped specimen and a different testing approach, the situation has a high potential for contrac- tual disputes. Reliance on a single method would be preferable. Fortunately, for bearings designed by Method B only one method (ASTM D4014) is permitted. No rea- sons are given. ⢠The geometric requirements given in M251 A 2.3.1 are inconsistent. The rubber is to be cut from a finished bearing, yet if the internal layer thickness is greater than 1.25 in., no specimen can be cut from it that will meet all the geometric requirements. Such thick layers are not likely, but they are perfectly possible. ⢠The test purports to measure shear modulus and is to be applied to material used in bearing designed by Method A. Yet the LRFD Design Specification now per- mits bearings to be designed using Method A based on hardness alone. If shear modulus is not needed for de- sign and is not specified, the reasons for conducting a test for it remain unclear. 2. It is believed that the tests indicated in Table 2.3 were elim- inated in the interests of economy. However, Section 4.2 of 29 ASTM Subject Pre-2006 ref. (Ch 18 Constr.) All brgs. Meth.A 2240 Hardness 412 Minimum G yes 412 Strength 412 Elongation yes 573 Heat resistance/aging 395 Compression set yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes 1149 Ozone resistance 746 Low temp brittleness yes 4014 Low Temp shear stiffness (crystallization) M251-06 Table 2.3. Material tests.
M251 now states that, âThe properties of the cured elas- tomeric compound material listed in Table 1 shall be deter- mined using samples taken from actual bearings.â Prepar- ing samples from a finished bearing imposes considerable extra costs, both for preparation time of the sample and in destruction and loss of a bearing. Although the changes only are just coming into force and no cost data are yet available, it is likely that the net effect will be to increase overall costs. 3. The M251-06 Specification distinguishes bearings speci- fied by hardness and designed under Method A from all other bearings. The former may be tested under what ap- pears to be a less stringent regime. This choice raises ques- tions, because manufacturers typically have one procedure and one set of quality standards for making bearings. Fur- thermore, they often are unaware of the method used for design. Therefore there is no reason to believe that they will build in higher or lower quality for bearings designed by Method A. By contrast, bearing size and especially thick- ness does influence quality, because of the difficulties in maintaining accurate shim placement and layer thickness when many layers are used, and because of the difficulties in achieving an even cure through the thickness if hrt is large. (The outer layers heat up sooner, and the rubber risks over-curing and reverting before the center has fully cured.) Researchers believe that, if different testing regimes are to be used, they should be differentiated on the basis of bearing size and not design method. This is particularly true because the stresses used in Method A are often, but not necessarily, lower than those in Method B. 4. The material test criteria specified in M251-06 Table 1 (for use with all bearings) and those in M251-06 Table X1 (for Method A bearings only) are inconsistent. For example, in Table 1, the elongation at break for all elastomers must be greater than 400%, regardless of hardness or shear modu- lus. Yet in Table X1, the elongations are specified as 450%, 400%, and 300% for hardnesses of 50±5, 60±5, 70±5 Shore A points. Inconsistency often leads to difficulties, includ- ing contractual disputes. It should be recognized that sig- nificant sums of money may depend on the outcome of a test, because in many cases the lot of bearings is to be re- jected if the test fails. Therefore the tests should be as clear and unambiguous as possible. Clarity in intent also is likely to lead to more competitive pricing. If a manufacturer is unsure about the testing regime, it is likely that money will be added to the bid to cover uncertainties associated with test- ing. This is a standard and understandable risk-management procedure. 5. The AASHTO Design Specifications, Section 14.7.5.2 states the range of shear modulus permissible for use in design. The lower bound now stated in M251-06 for an as-tested value is the same (80 psi), but no upper bound is placed on the as-tested value (14.7.5.2 gives 175 psi for design). The two specifications thus differ in that respect. Note also that the design values are stated in ksi (as are all stresses in the Design Specifications) but those in M251 are in MPa and psi. 6. Section 8.3 of M251-06 requires that the manufacturer â. . . shall certify that each bearing in the lot satisfies the re- quirements of the design specification. . . .â This seems to place an unreasonable burden on the manufacturer. If the manufacturer did not design the bearings, how would he even know what load cases were used for design, let alone how to conduct the necessary stress analysis? Prior to 2006, the AASHTO Construction Specifications required a long-term compression test (15 hours) on bear- ings designed by Method B. The difficulty and expense of conducting this test appeared to be a disincentive to using Method B. The present arrangements, whereby samples have to be taken from finished bearings to construct material coupons for testing method B bearings, might continue to act as a disincentive. For that reason and those discussed in para- graph 3 above, it is recommended that the criteria for more rigorous testing be associated with bearing size and not de- sign method. It is proposed here that the criterion be hrt ⥠8 inches, or plan area ⥠1000 in2. It is worth mentioning that the shear modulus of the elas- tomer and the required shear stiffness of the bearing should not be specified. The existence of end effects at the ends of the elastomer layers and some âbendingâ flexibility in the whole bearing, especially if it is thick, mean the shear stiffness of the bearing is not equal to GA/hrt, where hrt is the total rubber thickness. If the shear stiffness of the bearing is computed on this simple basis and if the shear modulus also is specified, the bearing manufacturer will be placed in the impossible posi- tion of being asked to satisfy two incompatible requirements. Further difficulties may be introduced if the tapered wedge test (Yura et al., 2001) is used and the effect of axial load on the lateral stiffness of the bearing is not correctly accounted for. For similar reasons, hardness and shear modulus should not be specified for a single material. 2.4.3 Number of Tests Required The number of tests required is a concern. The frequency of testing depends on the number of bearings defined to con- stitute a lot, and that frequency therefore depends on the in- terpretation of the words âlotâ and âelastomer batch.â This is discussed in M251-06 Section 8.2. What happens if there are more than 100 identical bearings? Some states purchase bear- ings en masse, store them, and then provide them to the con- tractor as needed. Do the bearings need to be absolutely iden- tical to constitute a lot or is some discrepancy permitted? The 30
definition of a batch also is important, and the definition dif- fers between manufacturers that mix their own rubber and those that buy it premixed. Manufacturers that mix their own batch generally mean one mixer load, so the amount depends on the size of the mixer, whereas those that buy premixed material tend to mean a single purchase. Such a purchase may be very large and, depending on the rubber supplier, it might include many separate mixer loads. The frequency of testing affects the cost, and manufactur- ers have expressed dissatisfaction over the specificationâs lack of clarity on this issue. Because the cost of testing must be in- cluded in the bid price, the latter will depend on the inter- pretation of the wording in the specification. The lack of clar- ity is perceived as causing a non-level playing field, and revision of these definitions is needed. 2.4.4 Material Test Requirements A wide range of material and QA test requirements have historically been employed. These include: ⢠ASTM D2240 Shore A durometer hardness, ⢠ASTM D412 Tensile strength and elongation at break, ⢠ASTM D573 Heat resistance, ⢠ASTM D395 Compression set, ⢠ASTM D1149 Ozone resistance, ⢠ASTM D1149 Low temperature crystallization, and ⢠ASTM D1043 Instantaneous thermal stiffening. Some discussion of these tests is warranted. The hardness test has been in the AASHTO Specifications for many years. It is somewhat imprecise, in that two individuals may measure the same rubber sample and report different hard- ness values. For a finished bearing, it also gives different results when the bearing is loaded or not, and it can be affected by the proximity of a steel shim (for example if it is conducted on a high shape factor bearing with thin layers). Its main virtue is that it can be performed very quickly and easily and, not surpris- ingly, it has a long history of use. However, shear modulus G is a more precise and reliable measure. Hardness can be corre- lated approximately with Youngâs modulus, but the correla- tion contains some scatter. For this reason the AASHTO LRFD Design Specifications specify a range of G values that corre- spond to a particular hardness. Furthermore, the hardness test can be conducted easily on a finished bearing, whereas the shear modulus test requires a special coupon that must either be specially fabricated (and so may have different properties from the bearing itself, due to different curing time) or it must be cut from the bearing, a procedure both difficult and expen- sive and destroys the bearing. The hardness measurement causes problems when an engi- neer specifies both hardness and shear modulus, because the re- lation between hardness and shear stiffness is not precise. From the point of view of accurate measurement of material proper- ties, the hardness test should be eliminated, and the industry should rely totally on shear stiffness. However, in 2006 the AASHTO LRFD Design Specifications changed to permit bear- ings designed by Method A to use material specified by hard- ness alone. It is understood that this change was made in the in- terests of economy (that is, eliminating the need for the shear modulus test), and justified by the fact that some spare bearing capacity exists as a result of design by Method A so that some variation in material properties would not be critical. Whether the perceived economic benefits of this decision warrant the re- duction in quality control is open to question; some of the main manufacturers have reported to the researchers that the cost of preparing and testing shear modulus samples is trivial. The test takes less than five minutes of a technicianâs time. Questions sometimes have been raised about the precise correlation between a particular test and the final elastomer properties. Such precise correlations in general have not been established. For example, Lindley pointed out that an elastomer compound could be changed to improve any one characteris- tic, but only at the expense of another (Lindley 1982). There- fore imposition of minimum requirements for a number of different characteristics is the best way to ensure an elastomer of overall high quality. The temptation to reject a particular test, because a precise link with some characteristic of the fin- ished bearing cannot be seen, should be resisted unless the matter has been studied carefully. Researchers could detect no correlation between bearing performance and the elastomerâs tensile strength and/or elon- gation at break. This finding is consistent with many specifi- cations (for example, EN 1337, BS5400) that treat the total strain capacity as independent of rubber properties, but in- consistent with others (for example, BE1/76) that relate the total strain capacity to its elongation at break. All the bearings supplied for testing satisfied the AASHTO tensile strength and elongation requirements, and none of them performed badly. Some of the materials had strength or elongation sig- nificantly higher than the minimum required by the specifi- cation, but that excess material capacity did not correlate with particularly good bearing performance. The argument in favor of testing for heat resistance and compression is again indirect. No bearings were received that failed these tests, so it was not possible in this study to deter- mine their effectiveness. However, that may well be an indi- cator that the tests are effective in keeping unsuitable material from the market-place. All of these material tests are relatively quick and easy to perform if the manufacturerâs laboratory owns the required equipment, which is the case for the major suppliers. Cost savings that would be achieved by abandoning them appear to be trivial, especially compared to the costs of replacing 31
even a single bearing in a bridge. Current QA/QC procedures are resulting in good quality elastomeric bearings, and relax- ation of the test requirements appears to carry considerable risk without a corresponding price benefit. 2.4.5 Very Large or Unusual Bearings Discussions with design engineers, manufacturers, and state bridge engineers indicate that very large and unusual elas- tomeric bearings have become more common over time. Fur- thermore, any changes in the specifications that allow bearings to be designed for higher loads or more extreme movements are likely to increase that tendency further. Questions exist over ways to ensure good quality and good performance from such bearings. First, the specification provisions are based on design models that have been verified almost exclusively by tests on small- to moderate-sized bearings, and questions remain whether they also apply to larger bearings. (Seismic isolation bearings are often largerâthree or four feet in diameterâ but they typically have shape factors that are much higher than those used for bridge expansion bearings. The com- pression strains are much smaller, and the shear deforma- tions are much larger, than those typically used in bridges, so seismic isolation bearings do not provide a basis for com- plete verification of the design models.) Comparisons of test results on small- and moderate-sized bearings have not sug- gested the existence of a size effect, but without reliable tests on large bearings, it cannot be stated with certainty that one does not exist. Second, the size of the bearing may create special problems in manufacturing that increase the need for testing. Elas- tomeric bearings are made by building up layers of elastomer and steel in the mold. Heat and pressure then are applied to vulcanize the elastomer. However, the heat is applied from the outside and must penetrate inwards by conduction. This takes time, and the outer regions of the bearing inevitably receive more heat and for a longer time than the inner regions. This is particularly true of thick bearings for two reasons. First, the steel shims are good thermal conductors and help to conduct the heat laterally, but this is not particularly helpful because the molding press generally applies the heat from the top and bottom only. Lateral heat flow is relatively unimportant. Sec- ond, vertical heat flow is critical because it occurs perpendic- ular to the steel and rubber layers, and heat conduction is poor in that direction. Consequently, a thick bearing is inher- ently more difficult to vulcanize. If at any location the rubber is not heated long enough, it will not be fully cured, and if it is heated to too high a temperature or for too long a time, it may revert. Either process will prevent achieving the desired mate- rial properties. Some manufacturers use embedded thermo- couples to check the temperature distribution throughout such large bearings. This improves control of the process, but it does not eliminate the difficulties in curing large bearings. Last, it may be difficult to test these large and unusual bear- ings because the required load is larger than the capacity of the available test machinery. This creates a practical problem, as the large bearings are the ones most in need of testing for ver- ification, yet testing them is the most difficult. Some possible alternatives are discussed in Section 3.3 of this report. 32