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.

Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames

Abstract: The potential energy expression and the (14 by 14) stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived. The transformation matrix relating the forces and displacements (including bimoment and warping parameter) at the adjacent end cross section of two elements meeting at an angle is deduced as the limiting case of a transfer matrix of a curved beam. To cope with asymmetric cross sections, some element displacements and forces are referred to the shear center and others to the cross-sectional centroid and the matrix for transformation from shear center to centroid is set up. The incremental larger-displacement analysis is formulated using the Eulerian coordinate approach with updating of the local coordinate systems at each load increment. The deformed beams are imagined to be composed of straight elements. Results of lateral post-buckling analysis of various beams are presented.

Analysis of Piled Raft Systems in Layered Soil

Abstract: This paper presents a method of analysis for piled raft systems constructed in layered soils. The method presented takes account of the interactions of the raft, piles and soil without the cost of a full three-dimensional rigorous analysis. This is done by the use of finite layer methods for the analysis of the soil and finite element methods for the raft. Examples are provided in the paper for piled rafts constructed on layered soils, and results are presented for bending moments in the raft and loads in the piles.

Modelling of shear hinge mechanism in poorly detailed RC beam-column joints

Abstract: Recent experimental investigations on the seismic performance of existing reinforced concrete frame buildings, designed for gravity loads only as typical of seismic-prone countries before the introduction of seismic oriented codes, underlined a significant vulnerability of the joint panel zone region ([1-4]). Inadequate structural detailing (i.e. total lack of transverse reinforcement in the joint region), deficiencies in the anchorage (use of plain round bars with end-hooks) and the absence of any capacity design principles can lead to the development of brittle failure mechanisms, particularly in exterior joints where additional sources of shear transfer within the joint region cannot develop after first diagonal crack. Local and global damage and failure mechanisms might be significantly affected by the consequent peculiar non-linear behaviour of the joint. When assessing the seismic performance of existing under-designed or designed-for-gravity-only buildings, an adequate modelling of the inelastic behaviour of the joint panel zone appears, therefore, to be essential. Alternative approaches for modelling the RC beam column joint, ranging from simplified empirical to refined finite elements models, are available in literature ([5-9]). Multi-node or multi-spring macro-models typically require the definition of a high number of input-parameters as well as appropriate constitutive-laws for the materials. The excessive complexity discourages them from being used as predictive tools in extensive parametric numerical studies. Furthermore, due to relatively scarce information based from experimental tests on gravity-load-designed frame systems and subassemblies, there is a general lack of appropriate modelling solutions for poorly designed beam-column joint system. In this paper, a simplified analytical model for joint behaviour is presented and proposed as a viable tool for extensive parametrical studies on the seismic response of existing frame systems. Based on the experimental results on gravity-load-designed beam-column subassemblies and on a frame system, the concept of a shear hinge associated with the joint damage mechanism is introduced as an alternative to flexural plastic hinging and the observed implications at local and global level response are described. According to a concentrated plasticity approach, an equivalent rotational spring, governing the relative rotation of the beams and columns, is adopted to represent the joint behaviour in the linear and non-linear range. The monotonic moment-rotation characteristics of the spring can be directly derived from equilibrium considerations on the bending moments of the adjacent elements, corresponding to principal tensile stress levels in the mid-depth of the joint panel zone. An appropriate hysteretic rule with “pinching” behaviour to take into account both bar slipping mechanisms or shear cracking in the joint region should be adopted to model the cyclic behavior. Preliminary numericalexperimental comparisons with the cyclic tests on beam-column subassemblies designed for gravity only as typical of the Italian construction practice between the 1950s and 1970s are also provided.

Exact solutions of inflected functionally graded nano-beams in integral elasticity

Abstract: The elastostatic problem of a Bernoulli-Euler functionally graded nanobeam is formulated by adopting stress-driven nonlocal elasticity theory, recently proposed by G. Romano and R. Barretta. According to this model, elastic bending curvature is got by convoluting bending moment interaction with an attenuation function. The stress-driven integral relation is equivalent to a differential problem with higher-order homogeneous constitutive boundary conditions, when the special bi-exponential kernel introduced by Helmholtz is considered. Simple solution procedures, based on integral and differential formulations, are illustrated in detail to establish the exact expressions of nonlocal transverse displacements of inflected nano-beams of technical interest. It is also shown that all the considered nano-beams have no solution if Eringen's strain-driven integral model is adopted. The solutions of the stress-driven integral method indicate that the stiffness of nanobeams increases at smaller scales due to size effects. Local solutions are obtained as limit of the nonlocal ones when the characteristic length tends to zero.

Crashworthiness design of multi-corner thin-walled columns

Abstract: This paper presents a crashworthiness design of regular multi-corner thin-walled columns with different types of cross-sections and different profiles, including straight octagonal columns and curved hexagonal columns. In this paper, the straight octagonal section columns are first optimized, which mainly take axial crash loads during crashes. Next, the curved hexagonal section columns are optimized following the same approach, which are subject to bending moment when impact occurs. During the design optimizations, specific energy absorption (SEA) is set as the design objective, side length of the cross-sections and wall thickness are selected as design variables, and maximum crushing force (Pm) is set as the design constraint. Both the objective and constraint are formulated using the response surface method (RSM) based on sets of finite element (FE) results obtained from FE analyses (FEA). After obtaining the optimal designs, parametric studies are performed to investigate the influences of the design variables on the crash performance of such multi-corner thin-walled columns.