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    Two extensions towards practical applications of a paradox in curved beams

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    For particular sections of a rectilinear beam subjected to bending it is possible to simultaneously lower the bending stress and reduce the beam mass, by wisely removing material from zones far from the neutral axis. It has recently been shown that an analogous paradoxical behaviour occurs in a curved beam subjected to bending, by laterally removing material from section zones close to the neutral axis. The bending stress diminution is often of the order of a few %, whereas the mass diminution may reach 10 %. To get practically more interesting results, in this paper the demanding achievement of a concurrent stress and mass reduction is relaxed in favour of two weaker requests: a) for a general section, the intrados stress is assumed as the reference stress, and the maximum mass reduction achieved by laterally removing material is sought under the condition that the intrados stress equals such reference stress; b) the intrados stress of a particular section is assumed as the reference stress, and material is laterally removed from the adjacent sections until their intrados stress equals the above reference value. Analytical applications of the two above approaches to a crane hook are carried out and compared to FE forecasts

    Advancing contact of a 2D elastic curved beam indented by a rigid pin with clearance

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    A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming an incomplete ring in frictionless and unbonded contact with a rigid pin loaded by a point force and in the presence of clearance. The circular beam is modelled as an incomplete elastic thick ring, constrained at both ends and in a plane stress state. The stress and displacement fields within the beam are derived from a biharmonic Airy stress function, according to the Michell solution in polar coordinates. The mixed boundary value problem is reduced to a set of dual series equations and then to a non-homogeneous linear system of infinite equations, which is then solved by truncation. The non-linear relations between the applied load and the contact angle or the pressure distribution are obtained by using an inverse method. The analytical results are compared with finite element predictions for a pin-lug connection and a reasonable agreement is observed for several typical geometries. The peaks of contact pressure and von Mises equivalent stress and their location within the curved beam are evidenced
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