## 6 Shear-Lag Effect in Diagrid Tubes  
One of the most important problems in external tubes composed of beams and conventional vertical columns is the shear-lag effect, which undermines their efficiency in high-rise buildings. As shown in Figure 15, for a framed tube subjected to later loads the actual axial force distribution in the vertical columns does not follow the Euler-Bernoulli distribution, i.e., linear and constant trend in the web and flange, respectively [1]. Conversely, due to the nature of the framed tube with closely-spaced columns, both distributions are non-linear and result in higher stresses in the corner columns, compared to the ones in the middle of the flange. This phenomenon is known as the shear-lag effect. Shear-lag coefficients can be defined based on the non-linearity of the stress distribution in the web and flange facades. In the design of a framed tube, limitation of the shear-lag effect often drives the design of the structural elements. Diagrids are known to be stiffer than traditional framed tubes. However, being external tubular systems, they might experience the shear-lag phenomenon as well. For the first time, [PERSON] investigates the influence of the shear-lag in a 60-story tall square diagrid building, in comparison with the conventional framed tube solution [38]. It is found that the diagrid  
Figure 15: Shear-lag effect in framed tubes. Used with permission of Taylor & Francis Ltd. (www. tandfonline.com), from [PERSON] and [PERSON] [1]. terms of lateral deflection and shear-lag effect, compared to the framed tube. However, the shear-lag effect strongly depends on the external diagonal pattern. Steeper diagonal angles can increase the severity of the shear-lag effect, whereas the number of the diagonal bays on the building perimeter does not have a significant influence. Interestingly, it is also found that no direct correlation between the shear-lag effect and lateral deflection appears in diagrids. Sometimes, the solutions with higher shear-lag coefficients provide quite small lateral deflections [38]. This mainly derives from the different mechanical behavior of the diagrid, with respect to the conventional framed tube: the former exploits the axial deformation of the external bracings, while the latter is dependent on the flexural and shear deformation of vertical columns and horizontal beams. As a consequence of the different mechanism, the shear-lag is less severe in diagrids than in conventional framed tubes. The shear-lag effect is also analyzed for hybrid structures, where frame and diagrid tubes act together in different parts of the building [39]. In this study, it is still observed that the shear-lag effect in conventional framed tubes is much more significant than in diagrid systems. However, in hybrid diagrid-frame tubes, the shear-lag coefficients depend on the specific geometrical combination of the two systems over the height of the building, and might not be negligible. The previous studies investigate the shear-lag effects by means of FE calculations [38; 39]. In a more recent work, [PERSON] and [PERSON] [40] propose an analytical formulation for a quick evaluation of the shear-lag effect in diagrid tubes. To this purpose, the diagrid tube is equated to an elastic orthotropic membrane, where the material properties are derived based on the stiffness equivalence. Simple equations allow computation of the internal stresses in the equivalent tube under horizontal loads. From the non-linearity of the distribution of web and flange stresses, a measure of the severity of the shear-lag effect is provided. The suggested methodology is applied to a 52-story tall, rectangular diagrid building, and validated against FE calculations. Different diagrid tubes, with different aspect ratios and diagonal angles, are also investigated. It is found that, for shorter buildings, the shear-lag effect obviously increases; moreover, increasing the steepness of the external diagonals leads to greater shear-lag coefficients.