Timoshenko Beams with Rotational End Constraints

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Abstract
Recent experimental evidence shows that the roof elements of reinforced concrete box‐like structures fail in a direct shear mode when subjected to transverse, uniformly distributed, near impulsive pressures. These failures are typically characterized by excessive shear deformations near the roof supports. The Timoshenko beam theory is applied to study the failure of these one‐way slabs by assessing the importance of the shear deformations and the importance of the support constraint. The Timoshenko equations are altered to account for variable rotational end‐constraint and the resulting normal mode solution is illustrated with a numerical example.