## Shear Lag Phenomenon

Consider Fig 3.35, in which columns of a tubular building are noted as T and C. T denotes a column in tension while C denotes a column in compression. The primary resistance to lateral loads comes from the web frames with the T columns in tension and the C columns in compression (Fig. 3.35). The web frames are subjected to the usual in-plane bending and racking action associated with an independent rigid frame. The primary action is modified by the flexibility of the spandrel beams, which causes the axial stresses in the corner columns to increase and those in the interior columns to decrease.

The principal interaction between the web and flange frames occurs through the axial displacements of the corner columns. When column C, for example, is under compression, it will tend to compress the adjacent column C1 (Fig. 3.35) because the two are connected by the spandrel beams. The compressive deformations of C1 will not be identical to that of corner column C since the connecting spandrel beam will bend. The axial deformation of C1 will be less, by an amount depending on the stiffness of the connecting beam. The deformation of column C1 will, in turn, induce compressive deformations of

the next inner column C2, but the deformation will again be less. Thus, each successive interior column will experience a smaller deformation and hence a lower stress than the outer ones. The stresses in the corner column will be greater than those from pure tubular action, and those in the inner columns will be less. The stresses in the inner columns lag behind those in the corner columns, hence the term shear lag.

The difference between stress distribution as predicted by ordinary beam theory, which assumes that plane sections remain plane, and the actual distribution due to shear lag is illustrated in Fig. 3.35. Because the column stresses are distributed less effectively than in an ideal tube, the moment resistance and the flexural rigidity are reduced. Thus, although a framed tube is highly efficient, it does not fully utilize the potential stiffness and strength of the structure because of the effects of shear lag.

Figure 3.35. Shear lag in framed tube. Observe that the axial stresses are distributed quite differently from those predicted by engineer's bending theory.

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