Chapter 7 Transverse Shear

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Presentation transcript:

Chapter 7 Transverse Shear

Shear Stress in a Beam A typical element removed from an interior point on a cross section of a beam is subjected to both transverse and longitudinal shear stress

Distortion of the Beam Due to Shear Shear strains resulting from the shear stress will tend to distort the cross section in a complex manner, causing the cross section to warp (not to remain plane) In the development of the flexure formula it was assumed that cross sections remained plane and perpendicular to the longitudinal axis of the beam after deformation It can generally be assumed that the cross-sectional warping caused by the shear is small enough that it can be neglected (particularly for the common case of a slender beam, one that has a small depth compared to its length)

An Element Taken from a Beam Consider the horizontal force equilibrium of a portion of an element taken from a beam

Development of the Shear Formula Cutting the element along the section plane

The Shear Formula The shear formula, Consider a rectangular cross section Problems, pg 374

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