Assessment of bending solution of beam with arbitrary boundary conditions: an accurate comparison of various approaches

Abstract

Bending responses are the important characteristics of structures. In this paper, the bending solution of the thin and thick beams which are elastically restrained against rotation and translation are presented using various theories. Hence, accurate and direct modeling technique is offered for modeling of the thin and thick beams. The effect of the values of the span-to-depth ratio and type of the beam supports are assessed to state accurate comparison of various theories. Finally, the numerical examples are shown in order to present the evaluation of the efficiency and simplicity of the various theories. The results of the theories are compared with the results of the finite element method (ABAQUS). Based on the results, using the Timoshenko beam theory, the obtained values are in good agreement with the Finite Element modeling for the values of the span-to-depth ratio (L/h) less than 3. On the other hands, due to ignoring the shear deformation effect, the Euler-Bernoulli theory underestimates the deflection of the moderately deep beams (L/h=5).

Hysteretic behaviour of uniaxially thermoformed auxetic foams under 3-point bending low-frequency vibration

“…The support span is constant as 100 mm. The span/depth ratio of the beam specimen is 10, within the limit of Euler beam theory [59,60]. The mass of the middle holder is 68.4 g.…”

“…The beam used in this work has a support span of 100 mm and thickness of 10 mm; therefore, the span to depth ratio is 10. A direct comparison between Euler and Timoshenko beams with different span to depth is done by Ghannadiasl et al by using theoretical modelling [59], and Gaur et al by using finite elements [60]. The two models provide very close results, with a * 2% difference of stiffness, when the span to depth ratio reaches 10 and the beam is simply supported at two ends.…”

Parameter Identification of Frame Structures by considering Shear Deformation

“…The classical Euler-Bernoulli beam theory is usually used to analyze the behavior of structural elements because it can properly simulate the behavior of slender beams [21][22][23][24]. For slender beams, various studies have suggested that using Timoshenko beam theory can improve the accuracy of structural analysis.…”