K.A. Patel

Explicit expression for effective moment of inertia of RC beams

Deflection is an important design parameter for structures subjected to service load. This paper provides an explicit expression for effective moment of inertia considering cracking, for uniformly distributed loaded reinforced concrete (RC) beams. The proposed explicit expression can be used for rapid prediction of short-term deflection at service load. The explicit expression has been obtained from the trained neural network considering concrete cracking, tension stiffening and entire practical range of reinforcement. Three significant structural parameters have been identified that govern the change in effective moment of inertia and therefore deflection. These three parameters are chosen as inputs to train neural network. The training data sets for neural network are generated using finite element software ABAQUS. The explicit expression has been validated for a number of simply supported and continuous beams and it is shown that the predicted deflections have reasonable accuracy for practical purpose. A sensitivity analysis has been performed, which indicates substantial dependence of effective moment of inertia on the selected input parameters.

Analytical-numerical procedure incorporating cracking in RC beams

Purpose – The purpose of this paper is to develop, for use in everyday design, a procedure that incorporates the effect of concrete cracking in reinforced concrete (RC) beams at service load and requires computational efforts which is a fraction of that required for the available methods. Further for ease of use in everyday design the reinforcement input data is minimized. The procedure has been demonstrated for continuous beams and is under development for tall building frames. Design/methodology/approach – The procedure is analytical at the element level and numerical at the structural level. A cracked span length beam element consisting of three cracked zones and two uncracked zones has been used. Closed form expressions for flexibility coefficients, end displacements, crack lengths, and mid-span deflection of the cracked span length beam element have been presented. In order to keep the procedure analytical at the element level, average tension stiffening characteristics are arrived at for cracked zon...

An element incorporating cracking for reinforced concrete skeletal structures at service load

An element has been proposed to take into account cracking in the reinforced concrete skeletal structures subjected to a service load. A typical skeletal member is modeled as a single element and is visualized to consist of at most five zones (cracked or uncracked). Closed-form expressions for the flexibility and stiffness coefficients and end displacements have been obtained. Furthermore, for use in everyday design, a hybrid analytical–numerical procedure has been developed using the proposed element. The procedure is analytical at the element level and numerical at the structural level. To keep the procedure analytical at the element level, the average tension stiffening characteristics are arrived at for the cracked zones. The developed procedure has been validated in limiting cases by comparison with the experimental results reported elsewhere and by comparison with the finite element method results. The proposed element would lead to a drastic reduction in computational time for large reinforced concrete structures, for example, tall reinforced concrete building frames.

An automated computationally efficient two-stage procedure for service load analysis of RC flexural members considering concrete cracking

An automated computationally efficient two-stage procedure has been proposed for service load analysis of reinforced concrete (RC) flexural members considering concrete cracking and tension stiffening. The proposed procedure yields cracked lengths, redistributed bending moments and inelastic deflections. The computation of final state, including cracked lengths and interpolation coefficients for tension stiffening, is automated by the initialization of second stage from the results of first stage. The procedure combines the analytical–numerical procedure developed by authors and the neural networks methodology. The cracked lengths and corresponding interpolation coefficients are rapidly estimated in the first stage using the closed-form expressions which are obtained from the trained neural networks. Eight separate neural networks are trained for the estimation of final cracked lengths and interpolation coefficients at in-span locations and supports. The use of estimated cracked lengths and interpolation coefficients of the first stage, in the beginning of second stage, significantly reduces number of iterations in the second stage. The deflections and bending moments obtained from the two-stage procedure are compared with those from the analytical–numerical procedure for a number of beams. The analytical–numerical procedure requires around six analyses to yield results with sufficient accuracy for design purpose (within 2–3%); whereas, in the two-stage procedure, only two analyses, one in each stage, are required to yield results with similar accuracy. The developed two-stage procedure requires a significantly small computational effort as compared to similarly accurate methods available in literature.