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44 CHAPTER 5 Regional and Local Response Analysis Studies Three types of actions, as shown in Figure 5-1, have been were developed to perform parameter studies, investigate considered in the analysis work for this project. capacities and damage modes, and prescribe a methodology to prevent such damage. Detailed 3-D, nonlinear analyses 1. Global or overall girder action of the bridge together with were performed using ABAQUS Version 6.5 "damaged plas- its supporting piers and abutments. ticity" concrete cracking model. Such models provided tendon 2. Regional beam action of each web supported at the top horizontal force plots versus deformation, and these, in com- and bottom flanges as a beam. bination with strain contour and crack pattern plots show the 3. Local action of the concrete cover over the tendons, evolution of damage with increasing force. Comparison of and/or local lateral shear/breakout failure adjacent to the such plots among different geometries and reinforcing schemes ducts. This is sometimes referred to as Lateral Tendon provides quantitative and qualitative parameter sensitivity Breakout (LTB) evaluation. The FE analyses were used to provide insights into where Global or overall girder action of the bridge together with damage first accumulates and develops, but these parameter its supporting piers and abutments is covered in Chapter 4. sensitivity comparisons are not exhaustive, and there are This chapter focuses on "regional" and "local" action. limitations to what can and cannot be reliably predicted by Regional beam action considers each web as a beam sup- FE analysis. A limitation of the parameter studies, for exam- ported at the top and bottom flanges. The regional moments ple, is that, for cases with reduced cover, the web thickness can be determined from a 2-D frame analysis of the cross sec- was held constant, and this tends to increase the moment arm tion. The prestress lateral force is determined individually for to the web stirrups, which partially offsets the reduction in each web with due consideration for the allowable variation in strength associated with reduced cover. prestress force between webs. The compressive reactive forces Limitations on the FE simulations, for example, include on the concrete are applied as distributed loads on the webs and the fact that ultimate failures caused by discrete crack propa- as concentrated loads at the centerlines of the slabs. The system gation are difficult to predict. FE analysis practitioners (e.g., is in static equilibrium and the support reactions will be zero. members of ACI/ASCE Committee 447 "Finite Element Local slab action of the concrete cover over the tendons has Analysis of Reinforced Concrete") have a range of opinions been identified as a major cause of failure in several curved on how best to predict the propagation of individual cracks post-tensioned bridges that did not have duct or web ties. For in a structure component with a lot of rebar. Some advocate a web without duct or web ties, the cover concrete is the only the use of fracture-mechanics-based algorithms shown to element restraining the lateral prestress force. The cover predict propagation of single cracks in plain concrete reason- concrete acts as a plain concrete beam to restrain the lateral ably well. But for practical FE analysis of concrete with a lot prestress force, F, as shown in Figure 5-2. The "local slab" is of rebar and a lot of cracks, the industry standard approach is subject to lateral shear and bending from the lateral prestress to use smeared crack models, as was used here. force. The web is subject to regional transverse bending which What these models do reasonably well is predict "zones of results in tensile stresses on the local slab. likely crack formation" and strain distributions in concrete Detailed local analysis models were used to evaluate the and rebar, which provide insight into causes and triggers local stresses resulting from longitudinal tendons generating for failure. Experience and judgment is required for the transverse forces on curved webs. Finite element (FE) models interpretation of the results. The work herein is based on