Shear Lag Effect
Plane Beam theory assumes plane section before the bending remains plane after the bending which implies structure should have infinite lateral stiffness or there is no shear force acting at the beam section. Hence bending stress diagram for a beam has to be in a linear pattern.
In the event of earthquake and extreme wind pressure slender structures (The term Slender has a different meaning for box girder, it means ratio of width to span of a box girder,) often experience tremendous amount of lateral load, because most of the mass being lumped primarily at the first degree of freedom. When slender structures, of which span to width ratio is high, experience larger lateral loads they become prone to non-linear bending and shear stress distribution across the cross-section (Fig. 01). In a box girder, a large shear flow is transmitted from vertical webs to the horizontal flanges, which causes in-plane shear deformation of the flanges and results in unpredicted extra longitudinal displacement at the web-flange junction [1]. Due to which central portion of the flange lag behind that of the web for the response quantities. This phenomenon of lagging is called as Shear Lag. Shear Lag effect is relevant to any slender box element that is loaded laterally such as airplane wing structure and box girder bridges.
Figure 1: Schematic Showing Shear-Lag Effect in Box Girder (a) Shear Stress Distribution Across the C/S of Box Girder (b) Non-uniformity of Longitudinal Stress (c) Out-of-plane Warping
While relying on plane beam theory which underestimates shear lag effect in box girder, gives unre- liable response quantities (Shear, Moment, Displacements etc.).
Figure 2: Negative Shear Lag
It has also been observed that there is another phenomenon exist which can be named as "Negative Shear Lag" (Fig.02). For a cantilever box girder researchers observed that for the one fourth the cantilever span length stress at the edge of the box girder is less as compared to stresses at the central flange portion [2].
In the event of earthquake and extreme wind pressure slender structures (The term Slender has a different meaning for box girder, it means ratio of width to span of a box girder,) often experience tremendous amount of lateral load, because most of the mass being lumped primarily at the first degree of freedom. When slender structures, of which span to width ratio is high, experience larger lateral loads they become prone to non-linear bending and shear stress distribution across the cross-section (Fig. 01). In a box girder, a large shear flow is transmitted from vertical webs to the horizontal flanges, which causes in-plane shear deformation of the flanges and results in unpredicted extra longitudinal displacement at the web-flange junction [1]. Due to which central portion of the flange lag behind that of the web for the response quantities. This phenomenon of lagging is called as Shear Lag. Shear Lag effect is relevant to any slender box element that is loaded laterally such as airplane wing structure and box girder bridges.
Figure 1: Schematic Showing Shear-Lag Effect in Box Girder (a) Shear Stress Distribution Across the C/S of Box Girder (b) Non-uniformity of Longitudinal Stress (c) Out-of-plane Warping
While relying on plane beam theory which underestimates shear lag effect in box girder, gives unre- liable response quantities (Shear, Moment, Displacements etc.).
Figure 2: Negative Shear Lag
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NBM&CW December 2010
