# SimEx: A Tool for the Rapid Evaluation of the Effects of Explosions
## 3 Example of Application: Facade of a Building under Blast Loading
### Estimation of the Equivalent SDOF System Response  
To study the structural response to an explosive charge, it is necessary to know in detail the type of construction. However, when using a simplified SDOF model, the study  
Figure 10: Interface of the Blast Wave calculation assistant for a charge weight of 150 kg of TNT at the ISA mean sea level, showing the variation of the blast parameters with the standoff distance from the front facade (top table). The lower part of the assistant shows the blast parameters calculated at a point located at \(d=20\) m standoff distance and \(h_{0}=5.5\) m above the charge. can be simplified and generalized for many different cases. In the present example, we will analyze a facade structure like the one in Figure 9b, composed of equally spaced pillars and an outer enclosure wall. The first element that receives the blast wave is the enclosure of the facade. This, in turn, transmits the load to the rest of the structure. In most constructions, the facade is only an enclosure without structural function (glass facades, brick, etc.). In first approximation, it can be considered that the exterior enclosure transmits the full load received directly to the pillars. The pillars are structural elements whose integrity is considered critical. It will therefore be the first element to be studied since the protection of the supporting structure is pivotal to avoid the potential collapse of the building. The enclosure can be considered as a secondary element in most constructions and therefore a significantly higher level of damage than in primary elements can be allowed. Figure 9c shows the simplest element in which the facade is to be divided. Each pillar receives loads from a part of the facade corresponding to the distance between pillars and the height between floors. The load generated by the explosion is applied to the pillars crosswise, so they behave in first approximation as bending elements. For the calculation of the equivalent properties, the beam assistants available in SimEx are employed. Either for metal or concrete beams, the length corresponds to the height between floors, while the span is the spacing between pillars. In the case of pillars, the boundary condition between floors is that of embedment on both sides, whereas a free condition is preferred at the roof. As a result, we use fixed-fixed conditions for Levels 0 and 1 and cantilever (or fixed-free) for Level 2. The presence of a roof diaphragm element may require additional considerations regarding the boundary condition at the roof top, but we prefer to use a fixed-free boundary condition for the second floor both for simplicity and for illustrating the effect of considering different boundary conditions on different floors. In the case of metal beams, it is only necessary to indicate the standard shape of the profile and the size. SimEx uses European cross-section profiles HEB, IPE, and IPN in accordance with Euronorm 53-62 (DIN 1025) [41]. Figure 11 shows the result for a HEB 340 profile with a length of 3 m and a separation between pillars of 5 m. The assistant uses standardized profiles, so if a non-existent measure is introduced, it corrects down to the nearest lower normalized profile. However, it is also possible to select custom profiles and materials. In this case, the area, first moment of area about the bending axis, moment of inertia about the bending axis, density, Young's modulus, and resistance must be provided by the user. Once the structural properties have been introduced, closing the assistant incorporates the computed data into the main SimEx interface. Figure 2 shows the result for the case under study. It should be noted that the additional enclosure mass supported by the pillar when flexed must also be included in the mass of the equivalent SDOF system in the main interface. If a rectangular reinforced concrete pillar is considered, SimEx requires that the external measurements \(b\) and \(h\) (perpendicular and parallel to the direction of application of the load, respectively) be introduced.