China
Africa
Explore chapters and articles related to this topic
Testing of Composites and Their Constituents
Published in Manoj Kumar Buragohain, Composite Structures, 2017
The short beam shear test works on the three-point beam bending principles [43]. Typically, under three-point loading, a beam is supported at the two ends and loaded in the middle; both bending as well as shear stresses are generated in the beam. The bending stresses are the maximum at the top and bottom faces of the beam—compressive at the top face and tensile at the bottom under the loading point. For an elastic material, the bending stresses vary linearly through the thickness and, by definition, they change sign on the neutral plane. In other words, the bending stresses are zero on the neutral plane. On the other hand, the interlaminar shear stresses, which vary parabolically through the thickness, are zero at the top and bottom faces and maximum on the neutral plane. Thus, the neutral plane is in a state of pure shear.
Sheet and plate metalwork
Published in Roger Timings, Fabrication and Welding Engineering, 2008
As the bending force is gradually increased these stresses, both tensile and compressive, produced in the outermost regions of the material, will eventually exceed the yield strength of the material. Once the yield strength of the material has been exceeded, the movement (strain) which occurs in the material becomes plastic and the material takes on a permanent set. This permanent strain occurs only in the outermost regions furthest from the neutral plane (neutral axis). The neutral plane is an imaginary plane situated between the tension side and the compression side of the bend of the material where the metal is neither stretched or shortened but maintains its original length. Its position will vary slightly due to the differing properties of different materials, their thickness and their physical condition. Therefore, there is a zone adjacent to the neutral plane where the strain remains elastic.
Structural members
Published in William Bolton, Engineering Science, 2020
When a beam bends, one surface becomes extended and so in tension and the other surface becomes reduced in length and so in compression (Figure 25.1). This implies that between the upper and lower surface there is a plane which is unchanged in length when the beam is bent. This plane is called the neutral plane and the line where the plane cuts the cross-section of the beam is the neutral axis.
Variational-based modeling of a piezoelectric/elastic bilayer beam with flexoelectricity
Published in Mechanics of Advanced Materials and Structures, 2023
Generally speaking, the neutral plane is not the geometric middle plane for the beams composed with inhomogeneous or different materials. In this work, the position of neutral plane is expressed by h0, which is the distance between neutral plane and the upper surface of the piezoelectric layer. It can be determined by the force balance equation of the cross section [39, 40].
A consistent shear beam theory for free vibration of functionally graded beams based on physical neutral plane
Published in Mechanics of Advanced Materials and Structures, 2023
Shi-Lian Sun, Xue-Yang Zhang, Xian-Fang Li
It is well known that when the Timoshenko and higher-order shear deformation beam theories are taken into account, the shear stresses over the cross-section do not vanish and are related to the warping shape of the cross-section. Usually, for inhomogeneous beams, both the shear stress and the shear strain arrive at its maximum at the physical neutral surface and vanish at the surfaces of the beams. Nevertheless, the previous studies on FG beams do not consider this feature (e.g. [15–17]). In other words, the warping shapes are still assumed to be the same as those for homogeneous beams. This is only valid for a symmetrically distributed gradient. For asymmetric thickness-wise FG beams, the position of the physical neutral plane does not coincide with the geometrical middle plane. So far, based on the Timoshenko beam theory, there have been many studies focusing on the influence of the position of the physical neutral plane. However, they do not consider the neutral plane on the influence of the shear stress [30–33]. The reason is that the shear stress in Timoshenko beams is not accurate, or the shear stress on the surface of beams cannot be guaranteed free. However, when the higher-order shear deformation is applied, Liu et al. [34] analyzed the thermal-mechanical coupling buckling analysis of porous FG sandwich beams based on the physical neutral plane. The exact solutions for coupled responses of thin-walled FG sandwich beams with asymmetric cross-sections were derived [35]. Fazzolari [36] established exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Hadji and Bedia [37] presented a simple n-order refined theory based on the neutral surface position. A special warping shape with trigonometric functions has been proposed by Larbi et al. [38] to treat the variation of FG beams. AlBasyouni et al. [39] have proposed a simple sinusoidal beam theory to study size-dependent bending and vibration for functionally graded micro beams. A similar treatment can be found for bending and vibration of FG plates [40]. In these papers, the presented higher-order warping shape functions only satisfy the condition of free shear stress on the surfaces of beam. The shortcoming is that the shear stress/strain does not take its maximum at the neutral plane. So far, though many shear beam theories have considered the physical neutral plane, their warping shape functions still make the maximal shear stress/strain at the geometrical middle plane, not the physical neutral plane. We need a more suitable warping shape function to make the shear stress/strain be maximal at the physical neutral plane and vanish on the surfaces of the beam, simultaneously. In other words, for the higher-order shear beam theory available, one gets two incompatible positions of the neutral plane. In fact, owing to the warping of the cross-section, the shear stress on the cross-section varies and must satisfy two basic assumptions: one is that the shear stress vanishes on the surfaces of beam and the other is that the shear stress/strain arrives at its maximum at the physical neutral surface.