Chapter iv of the research paper embodies the summary, conclusion and recommendation.

What is the purpose of Chapter 4 or the Findings or Results Chapter?

This chapter should provide the product of your analytic process. Think of it as a “stand alone” chapter that you could hand to a friend and just by reading it, they would know exactly what you discovered through your study. The chapter should reveal the “answers” to your research questions and reflect the design you put forward in Chapter 2. It should also align to the purpose of the study you offered in Chapter 1 as well as demonstrate why the study was important to conduct in the first place. Your findings or results should connect to your literature review and especially your conceptual framework. In some quantitative dissertations the results section presents only the products of statistical analyses that have been conducted. In other quantitative dissertation, the results section also provides a discussion that connects the results to the relevant literature and conceptual framework.

The chapter represents the best thinking of the student and the advising committee about how to answer the research questions being posed. So you can see that an incomplete understanding of the role of Chapter 3 can lead to a methodology full of gaps, creating the potential for the study to go off track, and not answer the research questions.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

47 4.1 Summary The rotational response of elastomeric bearings was studied using testing and analysis. The program concentrated on steel- reinforced elastomeric bearings. The test bearings were pur- chased from the four largest manufacturers in the country. The test program included static and cyclic rotation tests on full bearings, and material tests and diagnostic tests on full bearings to evaluate their instantaneous state of damage. Many of the tests were conducted in a specially constructed test machine capable of applying to a bearing independently controlled, constant axial force, constant shear deformation, and cyclic rotation. In the static test series, the parameters investigated were combinations of axial load and rotation. In the cyclic load tests, they included the effects of axial load, rotation angle and num- ber of cycles, bearing geometry (aspect ratio and shape factor), materials, shim plate edge treatment, and manufacturer. The behavior of the bearings was modeled in three ways. An approximate linear model, based on small deflection theory, was used to investigate basic behavioral phenomena and to derive design equations. FEAs also were conducted using large deformations and special constitutive laws for nonlinear, nearly incompressible materials. The goals were to evaluate the suitability of the simpler linear models, to investigate behaviors that could not be studied in the labora- tory and to determine the relationship between local deforma- tions, which could not be measured, and global displacements, which could. Finally, empirical models were developed to predict the fatigue behavior of the bearings under cyclic loading. The results of the tests and analyses were combined and used to develop design procedures. 4.2 Conclusions The following conclusions were drawn from this research. 4.2.1 Conclusions on Behavior Measured in Tests 1. Steel reinforced elastomeric bearings are extremely robust. In tests, bearings that had been subjected to loads approx- imately 10 times their design value and had suffered con- siderable visible damage were still able to carry the vertical load. While this ability is useful because it would prevent immediate collapse of the bridge, the vertical deflection and the damage to the bearing would seriously impair the bridge’s serviceability. 2. The bearings tested in this study came from the four largest manufacturers in the country. All were of high quality. The test results showed that the quality of bearings today is higher than it was 20 years ago. No one manufacturer stood out as universally superior to the others. 3. No clear and unique definition of failure exists for an elas- tomeric bearing. The first form of damage is typically local tension debonding of the edge cover from the edge of the shims. More intense static loading, or continued cyclic loading, may lead to delamination, characterized by the propagation of a horizontal shear crack back into the elas- tomer layers. It typically runs in the rubber, close to the steel-rubber interface. At very high axial loads, the steel shims yield and fracture. The debonding and delamination mechanisms tend to be progressive and occur more readily under cyclic loading. Shim fracture occurs only in response to very high axial load, either static or cyclic. 4. The tension debonding of the edge cover from the vertical face of the steel shim has no adverse effect on the perfor- mance of the bearing. However, it presages the start of shear delamination from the horizontal surface of the shims, which will change the bearing’s stiffness, and will eventually cause the bearing to tear apart. These behaviors will have a negative impact on the bridge superstructure. 5. The lack of a unique definition of failure makes development of design specifications difficult, because the demarcation C H A P T E R 4 Summary, Conclusions, and Recommendations

between acceptable and unacceptable behavior is not binary but rather requires judgment over the level of dam- age that is acceptable. Furthermore, the difficulties are aggravated by the facts that the quality of the manufactur- ing influences the loading required to cause a given level of damage, and damage accumulates as a fatigue process. Fatigue data typically show considerable scatter and the process is difficult to characterize reliably. 6. In this study, tension debonding of the rubber cover from the shim edge was used as the critical damage measure. 7. The fatigue resistance of the rubber did not show a clear correlation with any obvious material property such as tension strength or elongation at break. 8. Sharp edges on the shims promote debonding. If they are deburred with a special tool, or rounded with a belt sander, debonding is delayed. More precise rounding of the edges than that (for example, with machine tools) provides little additional benefit. 9. Adding shear deformation of 30% causes no noticeable change in the number of cycles required to reach a given level of debonding. 4.2.2 Conclusions on Analytical and Numerical Modeling 1. Bearings made from 60-durometer elastomer performed better under comparable loads than did nominally identical 50-durometer bearings, because the increased stiffness reduced the maximum shear strain. The observation that they performed even better than predicted by theory sup- ports the view that shear strain rather than stress is an appropriate measure of fatigue demand. 2. Bearings with shape factors of 9 and 12 performed better than did bearings of shape factor 6 under loading that caused similar total shear strains in each. Theory suggests that, when the induced shear strains are the same, the perfor- mance should be the same. This finding supports the use of bearings with large shape factors. 3. The approximate linear theory originally developed by Gent and his coworkers provides a reasonable estimate of the rotational stiffness. The compressive stiffness was harder to match, because it displays significant nonlinearity and because determining the point of zero displacement is difficult. 4. FEA in general confirmed, at low loads and rotations, the validity of the small displacement analyses. In particular, they showed that superposition of load-cases was valid, that the stiffness and strain coefficients developed by Stanton and Lund using linear theory were accurate enough for use in design, and that the value of internal hydrostatic stress predicted by the simple linear theory was valid. 5. FEA also showed several behaviors that would otherwise have been very hard to observe. First was the existence of a small local region of high hydrostatic stress at the outer, vertical edge of the shim, which, in combination with the very large local strains there, appears to be responsible for the tension debonding observed in almost all the tests. Second was the lateral movement of the shims at mid- height, when pure rotation is applied to the bearing. If the bearing is thought of as a very short column, this effect is analogous to the lateral deflection at mid-height of the column when end moments are applied. This shim dis- placement alters the strain field in the critical region at the edge of the shims, and may affect the debonding behavior there. 4.2.3 Conclusions on Development of Design Procedures 1. Obtaining reliable laboratory measurements of local shear strains in the rubber is impossible. Therefore it was neces- sary to use computed strains in the models for predicting debonding. 2. Initial debonding under static load occurred at a total shear strain that was nearly the same in a range of tests with different load and rotation combinations. This finding was used to develop a total shear strain limit for mono- tonic load. 3. Analyses of trucks passing over typical bridges showed that the cyclic axial load effects of the loading create shear strains in the elastomer much larger than those caused by the rotation. 4. An empirical but rational fatigue model was developed to predict the level of cyclic debonding as a function of the constant axial load, the amplitude of the cyclic rotation, and the number of cycles. It is referred to here as the Nonlinear Model because it made use of a nonlinear axial load-displacement relationship. It was able to predict well the fatigue life of the bearings, even though the dataset included a wide variety of loadings and bearing geometries. However, it had to be abandoned because it predicted extensive debonding in a class of bearing that is widely used for freeway overpasses, whereas such damage is not seen in practice. A description of it is retained in Appendix F so that, if suitable cyclic axial test data become available, it could be developed for use in a specification. 5. An alternative and simpler design method was developed. It is referred to herein as the Linear Model. It was based on a linear relationship between axial force and deflections, and did not attempt to link the progress of damage con- tinuously to the number of cycles of load. It fitted the test data by relating the total applied shear strain to the number of cycles at a specific level of damage (25% debonding). 48

When applied to bearings commonly used for typical freeway overpasses, it predicted that very little debonding should occur. This prediction is in agreement with field observations. 6. The Method B design procedure based on the Linear Model is simple to use. The major changes from the present spec- ifications are: the permissible combinations of load and rotation are controlled by an explicit total strain approach; lift-off is allowed if no external bonded plates exist; and a check is required for rupture by hydrostatic tension if external plates do exist. The limit on absolute axial stress has been removed, but a limit in terms of GS remains. 7. Method A design procedure was developed from Method B by computing a maximum probable rotation on the bear- ing, and finding the corresponding axial stress that would be allowed under the Method B rules. In order to optimize the usefulness of Method B (by keeping the allowable stress as high as reasonably possible) some restrictions on its use proved necessary. Only seldom are these restrictions likely to provide active constraints. 4.3 Recommendations 4.3.1 Recommendations for Implementation 1. The design methodology proposed in Appendix G for both Method A and Method B is written in language and a format suitable for direct adoption in the AASHTO LRFD Specifications. Those design requirements provide better correlation with behavior observed in the tests than do the existing ones, they are more transparent to the user, and they are simpler to implement. They also address combinations of loading, including light axial load and large rotations that prove problematic under the existing specifications. 2. The criteria for additional, more stringent, testing presently required for Method B bearings should be reconsidered, and an alternative is proposed. Design by the existing Method B triggers the need for more rigorous testing. The cost of that testing acts as a disincentive to the use of Method B. That in turn inhibits the use of high shape factor bearings, which are encouraged under the proposed Method B and were shown in the test program to be very effective in inhibiting the initiation and propagation of damage due to debonding and delamination. More rigorous testing is most urgently needed for large bearings, partic- ularly thick ones, because they are more difficult to fabricate. Consequently, it is proposed that bearing size, and not the design method used, be used as the criterion for more rigorous testing. This raises the practical problem that suitable testing facilities with enough capacity to load such a bearing may not be available. Several approaches are proposed for resolving that problem. 3. The edges of all steel shims in all bearings should be deburred or otherwise rounded prior to being molded in the bear- ing. Doing so reduces the stress concentration in the rubber at the critical location at the edge of the shim. The proposed strain limits in Appendix G are contingent on this being done. 4.3.2 Recommendations for Further Research 1. Average axial strains measured in the tests were found to differ from those calculated by both linear elastic methods and nonlinear elastic FE models. An approximate, semi- empirical, nonlinear model was developed, but an improved understanding of axial load effects and their nonlinearities is desirable. 2. The fatigue effects of axial loading should be investigated experimentally and analytically, so that they can be incor- porated into the design method in a rational way. 3. Creep of the rubber should be investigated and included in the design method. The axial load tests showed significant continued displacement after the load was reached and held constant, resulting in increased strains for a given stress. For a design method based on shear strain limits, it is important to know the actual strains. The effect of load duration on strength should also be investigated. 4. The effects of aspect ratio should be further investigated. For the limited number of tests in this research, the bearings with smaller aspect ratios performed much better than expected on the basis of maximum shear strains calcu- lated using theoretical models. 49

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What should be included in a chapter 4 research?

How do you summarize a chapter 4 in research?