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    <subfield code="a">Yii, Sui Kui</subfield>
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    <subfield code="a">The vibration of elastic beams is discussed and consideration is  given to the effect of warping deformation due to the presence of shear  stress. The elementary and Timoshenko beam theories assume that plane  cross sections remain plane after deformation. In this study, the govern ing equation of transverse vibration is derived taking into consideration  the out-of-plane deformation of cross sections caused by shear distortion.  The governing equation of torsional vibration is similarly derived.  Numerical examples are presented for beams with simply supported  boundary condition. Narrow rectangular, thin-walled tube and box sections  are used to illustrate transverse vibration, wide flange sections are used  to illustrate torsional vibration.</subfield>
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