Development of strut-and-tie models for RC bridge pier caps subjected to asymmetric loading
Reinforced concrete (RC) bridge pier caps are subjected to concentrated loads from the superstructure. These are deep members where strain distribution is non-linear and traditional flexural theory cannot be used. Strut-and-tie method can be used to design and detail such regions which idealises the pier cap domain into struts and ties capable of transmitting the loads to the pier. The loads on pier caps can be asymmetric due the effect of live loads, unequal spans and possible curvature of the superstructure. This paper attempts to develop strut-and-tie models for symmetric pier caps subject to asymmetric loading. The possible strut and tie models (STM) for load cases with one side subjected to a heavier load with respect to the other are presented. The ratio between heavier and lighter load is considered as a parameter in this study. The optimised strut and tie model is chosen from the possible models for a particular load case based on minimum tension load path (sum of product of force and corresponding length of the tension members). A solution algorithm is presented for the development of strut and tie models.
Assessment of shear strength of circular reinforced concrete beams
Reinforced concrete (RC) members with circular cross sections are sometimes preferred over rectangular cross sections in members such as columns, piers, and piles, because of their identical strength properties in all directions. In practice, the shear strength of a circular section is generally based on an equivalent rectangular section, using the formulation provided in ACI 318-14. This paper establishes the need to introduce an additional correction factor of 2/π to the shear strength estimation of circular stirrups, using the formulation applicable for rectangular stirrups. Use of this modified formula is validated in the experimental results of 30 tests on RC circular beams, reported in this paper, as well as 27 test results reported by Ang et al. (1989) and Jensen (2010). The theoretical predictions of shear strength have been based on ACI 318-14 and IS 456-2000.
Behaviour of glass fibre reinforced gypsum wall panel under cyclic lateral loading
Glass fibre reinforced gypsum (GFRG) wall panel, a composite walling product, is made essentially of formulated gypsum plaster, reinforced with glass fibres. The behaviour of such wall panels under earthquake loading merits investigation. The hollow cores inside the walls can be filled with reinforced concrete to increase the strength and lateral load resistance. The results of experimental test on a full-scale GFRG wall panel, filled with reinforced concrete, and subjected to axial and in-plane reverse cyclic load, are presented in this paper. The experimental specimen is 1.02 m wide and 2.85 m high. Hysteretic behaviour of the wall panel, acting as a shear wall, is discussed. © 2008 Taylor & Francis Group.
Experimental study on long-term behavior of PSC beams
The present study reports the experimental investigations of the long-term strains in two PSC beams, one bonded and one unbonded, having the same cross-section and concrete mix, subject to the same prestress and environmental conditions. In addition, control specimens in the form of one unloaded prism specimen of the same cross-section, and two standard cylinders, one loaded axially and the other unloaded, were also monitored for the same time duration of 250 days. Electrical strain gauges and fiber optic sensors were used for strain measurement, and the results show that they agree well with each other. The ACI 209 model is found to have the least error in the prediction of axially loaded cylinder creep and shrinkage strains. However, all the prediction models (assuming constant stress) are found, in general, to overestimate the creep and shrinkage strains, and the overall loss in prestress in the two PSC beams. When the loss in prestress is incorporated, using a 3D finite element numerical model, the prediction is found to improve significantly in all the models, and particularly in the case of the GL 2000 and MC2010 models. Alternatively, improved predictions can be obtained by using the compliance from cylinder creep data and the shrinkage strains from a control specimen (having the same volume-to-surface ratio) for predicting the strains in PSC beams; this is found to yield good results.
Simplified method for transverse bending analysis of concrete box-girder bridges
Of the various methods available for the analysis of box-girder bridges subject to vehicular loading, threedimensional finite element analysis (3DFEA) gives accurate results, compared to the other methods. However, 3DFEA is not commonly adopted in practice, and simplified methods of frame analysis are preferred. In this paper, a new simplified method (Modified Fixed Beam Method) is presented for the transverse bending analysis of box-girder bridges without overhangs. The results of extensive three-dimensional finite element analysis have been quantitatively assessed to provide a logical basis for the proposed 'Modified Fixed Beam Method' suitable for design practice. In the proposed method, the top flange of the box-girder bridge is modeled as a beam with fixity at the web-top flange junctions (fixed beam model), and the transverse bending moments so generated are suitably modified to yield the actual distribution of transverse moments. Modification factors are proposed based on extensive numerical studies, to account for the influence of type and location of loads, wheel contact dimensions, spacing of webs and the relative thickness of flange and web. Finally, the application of this proposed simplified method is demonstrated by means of two illustrative examples.
Analysis of the ASTM C512 Spring-Loaded CREEP Frame
The test method of ASTM C512 (ASTM. 2015. Standard test method for creep of concrete in compression. ASTM C512/C512M. West Conshohocken, PA: ASTM) dictates the use of a spring-loaded creep frame to perform a creep test on concrete. The main thesis of the study is that tests performed using these spring-loaded frames is not a creep test in the sense that the force acting on the specimen is not held constant while the specimen undergoes time-dependent strain. Analysis of this frame is performed using a linear viscoelastic model to represent concrete and isotropic Hooke's law to represent the steel rods and springs. The internal force and displacement in concrete and steel rods at any given instant of time is found using equilibrium equations and compatibility conditions. It is observed that the force transmitted to the concrete does not remain constant throughout the test duration but is a function of the spring and rod stiffness and the viscoelastic properties of the concrete. Hence, a drop in the magnitude of the force transmitted to the concrete specimen occurs in experiments when a spring-loaded creep frame is used. Experimental validation is also carried out by comparing the response of a spring-loaded creep frame with theoretical results. In this work, optimal spring and rod stiffness values to minimize the drop in the force transmitted to the concrete specimen are established. Thus, this study could be used to determine the linear viscoelastic properties of concrete in a creep frame.
Improvement of IS 1343 procedure for estimation of ultimate moment capacity of PSC sections with bonded tendons
The prevailing version of IS 1343 (1980) needs improvement with respect to the procedure for estimating the ultimate moment capacity of prestressed concrete (PSC) sections. There is a lack of clarity in the specified typical stress-strain curves for two different types of tendons specified in the code especially with regard to the manner in which the specified partial safety factor has to be applied. The code also suggests a simplified method in Appendix B, as an alternative to more rigorous strain compatibility method for estimating the ultimate moment capacity. However, it is seen that the IS 1343 simplified procedure invariably fails to satisfy the condition of force equilibrium and also overestimates the moment capacity. These shortcomings in the code are examined and reviewed in this paper, and suitable modifications are proposed in the form of modified stress-strain curves and simplified tables for incorporation in the forthcoming revision of the code.
Development of strut-and-tie models for rc bridge pier caps subjected to asymmetric loading
Reinforced concrete (RC) bridge pier caps are subjected to concentrated loads from the superstructure. These are deep members where strain distribution is non-linear and traditional flexural theory cannot be used. Strut-and-tie method can be used to design and detail such regions which idealises the pier cap domain into struts and ties capable of transmitting the loads to the pier. The loads on pier caps can be asymmetric due the effect of live loads, unequal spans and possible curvature of the superstructure. This paper attempts to develop strut-and-tie models for symmetric pier caps subject to asymmetric loading. The possible strut and tie models (STM) for load cases with one side subjected to a heavier load with respect to the other are presented. The ratio between heavier and lighter load is considered as a parameter in this study. The optimised strut and tie model is chosen from the possible models for a particular load case based on minimum tension load path (sum of product of force and corresponding length of the tension members). A solution algorithm is presented for the development of strut and tie models.
Strength assessment of RC deep beams and corbels
The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of disturbed regions (‘D’ regions) of reinforced concrete members such as in corbels and deep beams, where traditional flexure theory does not apply. This paper evaluates the applicability of the equilibrium based STM in strength predictions of deep beams (with rectangular and circular cross-section) and corbels using the available experiments in literature. STM is found to give fairly good results for corbel and deep beams. The failure modes of these deep members are also studied, and an optimum amount of distribution reinforcement is suggested to eliminate the premature diagonal splitting failure. A comparison with existing empirical and semi empirical methods also show that STM gives more reliable results. The nonlinear finite element analysis (NLFEA) of 50 deep beams and 20 corbels could capture the complete behaviour of deep members including crack pattern, failure load and failure load accurately.
Reliability analysis and design of cantilever RC retaining walls against sliding failure
Among the various modes of failure of reinforced concrete (RC) cantilever retaining walls, the sliding mode of failure is invariably seen to be the critical mode governing the proportions of the wall. Traditionally, a constant factor of safety (usually 1.5) is adopted in the design of cantilever retaining walls against sliding and overturning instability, regardless of the actual uncertainties in the various design variables. This paper presents the stability analysis of cantilever retaining walls, accounting for uncertainties in the design variables in the framework of probability theory. The first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo simulation (MCS) method are used as alternative ways to evaluate the probability of failure associated with the sliding failure of retaining walls of various heights (ranging from 4 to 8 m). Sensitivity analysis has shown that the angle of internal friction (Φ) and the coefficient of friction below the concrete base slab (μ) are the most sensitive random variables. It is shown that cantilever retaining walls, optimally proportioned to achieve a factor of safety of 1.5 against sliding failure, can have significant variations in the reliability index (or probability of failure). In order to achieve consistently a 'target' reliability index (β = 2.5 or 3.0), the factor of safety must be appropriately chosen, accounting for uncertainties, especially with regard to Φ and μ. In this paper, easy-to-use design tables have been developed for this purpose.