BASIC METHODS OF ANALYSIS FOR BRIDGES

Transcription

1 BASIC METHODS OF ANALYSIS FOR BRIDGES Bhumika B. Mehta M. E. CIVIL CASAD. B-2, Kalindi Flats, Opp. Kadwa Patidar Boarding, C. G. Road, Ahmedabad Ph. No. (079)

2 CONTENTS 1. INTODUCTION 2. PURPOSE OF DYNAMIC ANALYSIS 3. AVAILABILITY AND USEFULNESS OF ANALYSIS TOOLS 3.1 Static elastic analysis 3.2 Dynamic elastic analysis 3.3 Static inelastic analysis 3.4 Dynamic inelastic analysis 4. SELECTION OF TYPE OF ANALYSIS FOR BRIDGES

3 BASIC METHODS OF ANALYSIS FOR BRIDGES 1. INTRODUCTION Any structure is analysed with static method or dynamic method. Selection of an appropriate analysis method depends on a number of factors. These factors are purpose of analysis, importance of structure, methods available for analysis, type of bridge or structure and soil conditions. Ideal purpose of analysis is to obtain an accurate measure of expected structural response for a given earthquake. To solve this purpose, method used for analysis is also affect significantly. Also importance of structure plays an important role. Static elastic analysis is done for all the structures. For ordinary structures static analysis is sufficient, but for important structures particularly for bridges dynamic analysis should be carried out. Also structures have irregular configuration and varying subsurface condition is analysed by dynamic analysis. 2. PURPOSE OF DYNAMIC ANALYSIS Dynamic analysis can be carried out for following purposes. a) Dynamic analysis provides an accurate measure of expected structural response for a given earthquake event or class of earthquakes. If an accurate structural model can be developed, the calculated global displacements can be used directly to establish seat widths and separations, and local deformations and ductility requirements can be used directly to determine required details. These models must be developed with the understanding that no level of sophistication in structural modeling can overcome the basic uncertainty in seismic loading. b) The dynamic analysis can be used to provide a nominal measure of expected responses, which (if falling within certain prescribed bounds) will ensure adequate behavior of the structure.

4 c) The third purpose of analysis is to ensure that a simple and direct load path is provided for each frame. In addition to ensuring that each frame is capable of supporting its own earthquake actions without having to rely excessively on adjacent frames, a secondary motive for this type of analysis may be to verify a design based on more complex analysis models. 3. AVAILABILITY AND USEFULNESS OF ANALYSIS TOOLS The availability of analysis tools and the availability of professionals skilled in their use impose limitations on analysis. The following comments are needed to help designers select the appropriate analysis methods. 3.1 Static elastic analysis Static analysis can be carried out by hand or using a computer program. The tools and skills are generally available to the bridge design community. Unfortunately, static elastic analysis is suitable for only a limited class (but significant number) of bridges. This class includes short bridges with monolithic abutments. 3.2 Dynamic elastic analysis Multimode dynamic analysis is generally carried out using a computer program. Numerous programs are available, and many engineers possess the skills necessary for their operation and interpretation. Some programs permit input motions along three orthogonal directions and combine responses according to an appropriate modal combination rule; others permit only one component of input motion at a time and require that responses from orthogonal input motions be combined using an algebraic rule (e.g. 1.0L + 0.3T). Both the response time-history option and the modal spectral response option are available. The latter is recommended for routine analysis. Response time-history analysis requires selection of ground motions that envelop the expected input motions. Because of the extra effort involved, elastic response timehistory analysis should probably only be used in cases where it is important to consider spatial and temporal variations in ground motion.

5 Techniques exist for handling multiple-support inputs (including spatial variation of input motion) using response-history or response-spectrum analysis. The techniques are not widely understood, and computer programs for their implementation are not generally available. If properly carried out, dynamic elastic analysis can provide important insights into dynamic response of a bridge. Perhaps of greatest value, a dynamic elastic analysis sheds some light on expected displacement amplitudes. With these in hand, estimates of design requirements are possible. However, elastic dynamic analysis does not provide good insight into local deformation or the distribution of forces, because the effects of nonlinear response on these quantities are not properly represented by the elastic analysis. 3.3 Static inelastic analysis Computer programs for static inelastic analysis have been available for many years. Programs specially suited to analysis of bridge structures have been developed in recent years, although, at present, they lack the ability to handle lateral and vertical loads simultaneously. Proper application of these programs requires advanced skills. When coupled with knowledge of displacement amplitudes obtained from elastic dynamic analysis, static inelastic analysis can be used to great advantage to establish local deformation demands and internal force distributions. 3.4 Dynamic inelastic analysis Developments in recent years have made it possible to carry out dynamic inelastic analysis on bridges. However, the analysis is not routine. Special skills are required for selecting ground motions, carrying out the analysis, and interpreting the results. Special purpose programs have been devised that allow nonlinearities only in selected elements (e.g. in the superstructure hinges); these are probably the most straightforward in their use and interpretation. Other programs allow more generally distributed material nonlinearities as well as geometric nonlinearities. Competent use of these analysis tools requires a significant level of expertise regarding the inner workings of the program as well as the material behavior of the bridge components. Properly used dynamic inelastic analysis has great potential for providing detailed information on global response displacements, local deformations, and internal forces.

6 These may be of particular value in analyzing irregular structures and important bridges. 4. SELECTION OF TYPE OF ANALYSIS FOR BRIDGES a) One or two-span bridges with monolithic abutments The superstructure is likely to respond effectively as a rigid body. Furthermore, lateral stiffness is likely to be controlled by the abutments. A moderately sophisticated dynamic analysis model will not provide more response insight than may be obtained by simple static analysis. b) Long, straight, non-skewed, continuous bridges with uniform supports Although static analysis is likely to provide an adequate measure of expected response, an elastic multi-mode analysis may be preferred for the purpose of assessing lateral displacements and effects of higher modes. The abutment stiffness is likely to dominate response for many of these structures; it is essential to model the abutment stiffness and strength properties correctly if the objective is to obtain a measure of actual seismic response. c) Skewed bridges, curved bridges, and bridges with intermediate hinges Static methods are not likely to provide realistic measures of expected response. Response-spectrum analysis of an elastic model including all significant vibration modes is preferred as a minimum. Tension and compression modes are recommended. d) Long-span bridges and bridges with outriggers or C-bents Vertical response may be significant for these bridges, and it should be considered directly in a response-spectrum analysis of an elastic model that includes all significant vibration modes. The preferred approach is to require that vertical input be considered for all bridges and to combine responses in individual modes using an appropriate combination rule. As described later, vertical input can be included without increasing the analysis effort.

7 e) Bridges with dissimilar supporting elements For bridges with dissimilar adjacent supporting elements, a response-spectrum analysis may be useful for gauging global displacement responses. However, the elastic analysis may lead to incorrect estimates of ductility demands. The estimates may be improved by requiring that element stiffness values be properly based on cracked-section properties rater than gross-section properties, as allowed by current practice. Nonetheless, accurate estimates of local ductility demands cannot be obtained consistently by this approach. For structures of this sort, the elastic analysis should be augmented (improved or better) by a non-linear static analysis that can be carried out by hand or by a computer program. f) Bridges with unbalanced spans These structures may be prone to global torsional responses that result in increased flexural deformation demands on some elements. Dynamic analysis is encouraged for such bridges. Studies on buildings suggest that inelastic behavior may result in significant amplification of torsional responses in comparison with quantities obtained by elastic analysis. These findings should applicable to bridge structures as well. g) Long bridges These structures may be subjected to spatial variations of ground motion along the length. Traveling waves also affect response of the long bridges. At first analysis, the assumption of uniform ground motion appears conservative because it forces the entire bridge to vibrate in phase. Spatially varying ground motion produces out-of-phase dynamic response, which tends to cancel the energy. However, for long structures with intermediate expansion joints, the advantages of out-of-phase dynamic response are commonly lost because outof-phase movement is taken up in the expansion joints, so that the assumption of uniform ground motion is reasonable. The spatial variation of the support

8 displacements does produce so called pseudo-static stresses; however, the stresses do not appear to be significant for bridges with a large number of relatively short spans. In contrast, a suspension bridge or a cantilever bridge with only four supports may be sensitive to spatially varying ground motion, because this motion induces vibration modes, such as rocking of the piers, not excited by uniform ground motion.