Bending moment

About: Bending moment is a research topic. Over the lifetime, 14577 publications have been published within this topic receiving 158834 citations. The topic is also known as: bending moment.

Bending and buckling of inflatable beams: Some new theoretical results

Abstract: The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.

Effect of plate position relative to bending direction on the rigidity of a plate osteosynthesis. A theoretical analysis.

Abstract: Mechanical unloading of the plated bone segment is observed after plate osteosynthesis because the implant takes over a part of the physiological loading. Strain reduction in the bony tissue depends on the rigidity of the plate (cross-sectional area, geometrical form, and modulus of elasticity). The aim of the present study was to calculate theoretically the effect of plate position relative to bending direction on the overall bending stiffness of the composite system plate-bone. To calculate the rigidity, a cylindrical bone model with mechanical characteristics similar to a sheep tibia and a rectangular plate cross-section corresponding to a DC-plate with either a modulus of elasticity of steel or titanium was used. Calculations under different bending directions were performed according to the laws of the linear bending theory and the composite beam theory. The bending stiffness of a plate osteosynthesis reaches a minimum and a maximum respectively, in cases in which the bending moment acts in the direction of the main axis of the area moment of inertia of the plate. The minimum is present with the plate bent vertically, the maximum with the plate bent horizontally, e.g. on the tension side of the composite system--on the assumption that the bone structure opposite the plate is capable of withstanding compressive loading. For steel and titanium plates, factors of 2 and 2.25 respectively were calculated between the minimum and the maximum bending stiffnesses of the osteosynthesis. The bending rigidity of the plate alone has only a minimal effect on the total stiffness of the osteosynthesis. With a plate bent vertically, the difference between steel and titanium plates was 18%, with the plate bent horizontally (situated on the tension side), it was only 7%. The bending stiffness of a plate osteosynthesis depends on the cross-section, the geometrical form, and the modulus of elasticity of the plate, as well as on the plate position relative to the bending direction of the composite system. The modulus of elasticity of the plate is relatively unimportant, while with a given plate the individual plate position relative to the bending direction is of crucial importance. Thus, changing the modulus of elasticity of the plate cannot solve the problem of implant induced unloading of the bone cortex because the bending stiffness of the composite system depends much more on the plate position relative to the bending direction.

Failure Mode Analyses of Reinforced Concrete Beams Strengthened in Flexure with Externally Bonded Fiber-Reinforced Polymers

Abstract: As existing structures age or are required to meet the changing demands on our civil infrastructure, poststrengthening and retrofitting are inevitable. A relatively recent technique to strengthen reinforced concrete ~RC! beams in flexure uses fiber-reinforced polymer ~FRP! strips or sheets glued to the tension side of the beam. A number of researchers have reported that the failure mode of an FRP-strengthened RC beam can change from the desired ductile mode of an underreinforced beam to a brittle one. This paper analyzes the effects of this strengthening technique on the response and failure modes of a reference RC beam. A nonlinear RC beam element model with bond-slip between the concrete and the FRP plate is used to study how the failure mechanism of simply supported strength- ened RC beams is affected by the following parameters: plate length, plate width, plate stiffness, and loading type. The beam geometry is kept constant. The parametric studies confirm the experimentally observed results according to which the most commonly observed failure modes due to loss of composite actions are affected by the plate geometric and material properties. In addition, distributed loads ~difficult to apply in an experimental test! may not be as sensitive to plate debonding in the region of maximum bending moment as are beams subjected to point loads.