ON A CLOSED-FORM SOLUTION TO OFF-AXIS FOUR-POINT BENDING EQUATION OF A SIMPLY SUPPORTED BEAM
This paper aims at performing a closed-form solution to off-axis four-point bending equation of a statically determinate beam, the cross-sectional area of which is assumed to remain invariant.The phenomenon of off-axis four-point bending is investigated for high rates of the beam’s curvature.In this context, a rigorous analytical method to evaluate the deflection of the beam is performed.The novelty of this work is that the deflection is explicitly expressed as a combination of elementary single-valued continuous functions and thus no special functions or elliptic integrals appear, in opposition with other analytical approaches to this problem.Consequently, the proposed explicit solution is useful to extract firm qualitative information about the linearly elastic behavior of a large category of simply supported continuum beams under this specific asymmetric loading.
simply supported beam, off-axis four-point bending, deflection, closed-form solution.