# 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.

While relying on plane beam theory which underestimates shear lag effect in box girder, gives unre- liable response quantities (Shear, Moment, Displacements etc.).

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].

Significant points about Shear Lag:-

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 |

Significant points about Shear Lag:-

- Conventional Plane Beam Theory underestimates the shear lag effect.
- Shear Lag results in non-linear displacement distribution across the cross section.
- Due to shear lag longitudinal displacement of the Fig. 02 Negative Shear Lag box girder increases.
- It also leads to stress concentration at web-flange junction and results in out-of-plane warping.
- In cable stayed bridges, forces due to shear lag effect observed maximum at pylon and reduces away from it [3].
- Shear Lag effect increases with the width of the Box Girder i.e. slender section has increased.

- Number of the shells in the box girder would be increased.
- Slenderness ratio of the bridge would be reduced.
- Height of the pylon would be reduced. It has been observed that extra-dosed bridges attract lesser lateral forces and hence minimizes shear lag effect.

## References

- Bazant, P., Vladimir, K., “Shear lag effect and uncertainty in concrete box girder creep”, ASCE
- Leonard, J., “Investigation of shear lag effect in highrise building with dia-grid system”, Thesis report,
- Gao-feng, WU., Hong, XU., “Theoretical and experimental study on shear lag effect of partially cable stayed bridge”, Journal of Zhejiang University Science.