Abstract
The definition of Timoshenko beam elements, which allows for the consideration of transverse shear effects, is summarized in Table 4.1. The derivation in lectures normally starts with the introduction of an elemental coordinate system (x, z) where the x-axis is aligned with the principal axis of the element and the z-axis is perpendicular to the element. Based on the definition of this element, displacements \((u_{1z},u_{2z})\) can only occur perpendicular to the principal axis while the rotations \((\phi _{1y},\phi _{2y})\) act around the y-axis.
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Notes
- 1.
This assumption is taken if a cross sectional area A is specified in the first geometry data field. If \(A=0\) is entered in the first geometry field, Marc uses the beam section data corresponding to the section number given in the second geometry field \((I_x)\). This allows specification of the torsional stiffness factor unequal to \(I_x + I_y\) as well as the shear areas \(A_{\text {s},x}\) and \(A_{\text {s},y}\) unequal to the area A or the specification of arbitrary sections using numerical section integration, see [7].
- 2.
This element uses a one-point integration rule for the stiffness matrix.
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© 2016 Springer Science+Business Media Singapore
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Öchsner, A., Öchsner, M. (2016). Timoshenko Beams. In: The Finite Element Analysis Program MSC Marc/Mentat. Springer, Singapore. https://doi.org/10.1007/978-981-10-0821-4_4
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DOI: https://doi.org/10.1007/978-981-10-0821-4_4
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