# Real Geometrical Imperfection of Bow-String Arches--Measurement and Global Analysis
## 2 Imperfections  
### Application of Imperfections in Bridge Arch Analysis  
The use of arch member models opens the way for the use of calculation according to the second order theory with specified imperfections also in commonly available commercial software. So, if a more sophisticated approach is needed, the imperfections should be incorporated directly into the global arch bridge models. For local imperfections, the equivalent initial deformation of the members in the shape of sinusoid or quadratic parabola are defined in EN 1993-1-1. Initial global imperfections due to the inclination of frame systems can also be applied in the analysis of the bowstring arches, especially in the case of rigid hangers, or as imperfections of vertical or inclined portals. However, the full consideration of local and global imperfections in the global analysis puts great demands on the complexity of the computational model and cause difficulties in entering imperfections. Therefore, the method where the second order effects are taken into account, partly through global analysis and partly through the individual assessment of the members, is now more widely used.  
Alternatively, the assumed shape of the global and local imperfections may also be derived from the shape of the elastic buckling mode of the structure in the considered plane. The advantage of this procedure is that the first buckling mode of the structure can be calculated. It represents the most effective initial shape of the deformation. Moreover, this procedure presented by the authors of [3,4] can be advantageously incorporated into the computer programs. The so-called unique global and local imperfection is calculated by a stability calculation within the global analysis. However, the use of shapes of critical buckling modes of the structure as equivalent imperfections encounters the problem of determining the amplitudes of buckling modes [5, 6, 7]. In the case of a spatial structure subjected to compression and biaxial bending, but structurally designed such that the buckling in one of the planes is minor, the authors of the paper [8] have already proposed a procedure for calculating the amplitude of the imperfection in the dominant plane. This procedure was used by the authors of [9] for their analyses and comparisons. To date, the most comprehensive approach in this area was probably presented in the works of authors [10,11], which extend the knowledge of applying unique global and local imperfections to more complex spatial tasks taking into account not only flexural buckling but also the lateral torsional buckling.  
However, the aforementioned works deal with theoretical analysis using design equivalent geometric imperfections. Works where real imperfections would be included and a comparison of their impact on the loss of the out-of-plane stability of the arch are not available. For this reason, it is necessary to identify the real geometric imperfections of the arches on real bridge objects and to analyse their influence on the stability and resistance of arches [12]. Then, the outputs of these measurements should be applied into the geometrically and materially nonlinear analyses (GMNIA) of spatial arch bridges with imperfect arches by introducing real geometric and structural imperfections. Alternatively, the geometrically nonlinear analyses (GNIA) of these systems can be executed with equivalent geometric imperfections derived from measured deformations and scaled to reflect both real geometrical and structural imperfections, respectively.