We propose a new tamed Milstein-type scheme for stochastic differential equation with Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate of convergence is shown to be equal to 1.0 under mild regularity (e.g. once differentiability) requirements on drift and diffusion coefficients. Novel techniques are developed to tackle two-fold difficulties arising due to jumps of the Markov chain and the reduction of regularity requirements on the coefficients.

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A simple and direct Strut-and-Tie Model (STM) is proposed here to predict the ultimate shear strength of the reinforced concrete bridge pier cap for shear span to depth ratio of 0.4 to 2.4. The model is based on the Kupfer-Gerstle Biaxial Compression-Tension failure criterion which includes the concrete softening effect produced by the presence of transverse tensile stress. The earlier models consider the stress distribution factor for the varied stress distribution across the section by assuming it as linear function which is derived by satisfying equilibrium conditions. In this study the principal stresses have been evaluated by satisfying the compatibility condition at the time of impending failure which has been accounted for the effective area of concrete resisting tension. Also the softening effect has been included by using the formula for tensile strength of cracked concrete proposed by Belarbi and Hsu. The proposed model has been validated with 43 experimental results by author and from literature which confirm the coherency and conservativeness of the predicted results. The parametric study on ultimate shear strength is done so as to infer the relation between various abstract quantities such as compressive strain, shear capacity, span depth ratio and other material properties and get a deeper insight into the behavior of the Pier cap. Thus this paper tries to extend the practical application of Strut-and-Tie Model for reinforced concrete bridge pier cap in understanding the actual behavior of the structure on various dimensional and material parameters.

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