Topic
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.
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TL;DR: In this paper, the higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties, and a general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions.
Abstract: The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates that the method is simple and efficient. Moreover, the gradient variation of Young’s modulus and Poisson’s ratio may be arbitrary functions of the thickness direction. Functionally graded Rayleigh and Euler–Bernoulli beams are two special cases when the shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation of material properties.
104 citations
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TL;DR: In this article, the authors used a 1:20th scale 3-bladed horizontal axis TST at a large towing tank facility to measure rotor thrust and torque whilst one blade was instrumented to acquire blade root strain, azimuthal position and rotational speed all at high frequency.
104 citations
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01 Dec 1995TL;DR: In this paper, a summary about the present process understanding of the laser bending technology is given, three different bending mechanisms are distinguished, and a bending mechanism is suggested which explains the stability behaviour.
Abstract: A summary about the present process understanding of the laser bending technology is given. Three different bending mechanisms are distinguished. Experimental results showing that at certain parameters an instability behaviour can occur are discussed. A bending mechanism is suggested which explains the stability behaviour. It is shown that laser bending can be extended in order to generate convex shapes, which means a bending away from the laser beam. The possibility of bending towards the laser beam or of bending away from the laser beam opens new ranges of applications, two of which are introduced in this paper.
104 citations
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TL;DR: In this paper, the expected extreme base moment is computed by multiplying the mean base moment by the proposed GLF, which is then distributed to each floor in terms of the floor load in a format similar to the one used to distribute the base shear in earthquake engineering practice.
104 citations
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TL;DR: In this article, the effects of contact stiffness on the impact behavior of reinforced concrete beams were investigated experimentally and numerically, and extensive numerical simulations were carried out to confirm the findings from the experimental results and to perform parametric studies.
104 citations