Virtual and Rapid Prototyping Methods Applied in Civil Engineering . Snow , Wind and Earthquake Simulations on a Five Storey Building

The paper presents a virtual model of a building with five levels, which was subjected to virtual testing. The results are shown in the figures and diagrams. Also, the finite element method for building simulation for the snow load was used. Based on the 3D model of the building and the digitalized displacement diagram the kinematics and dynamics simulation of the building was made similar to the earthquake on March 4, 1977 in Vrancea, Romania, felt throughout the Balkans. Also, the action of the wind in front of building was simulated with Flow simulations analysis module. The results were shown in the maps of pressures, speeds or temperatures. To obtain real similar calculations, the simulations of the building for the situations were made when we have multiple loads (snow, earthquake, wind). Also, the rapid prototyping method was presented, applied on the scaled building using Prusa Mendel I3 3D printer.


INTRODUCTION
The safety of construction ensured since the design phase is provided by Euro Codes, that are valid for most classical types of buildings.The question is whether they are valid for buildings with a special or spectacular configuration.In this paper, a building with five levels was subjected to virtual testing using primary requirement, starting from the known principles of verification and testing.The results of these tests were compared with the results obtained by classical calculations given by Euro Codes.Also, we know the importance of checking the calculations of the earthquake.The dynamics of construction, analyzed by the finite element method, a solution seems generally valid for any type of construction, even with a futuristic architectural configuration [1].
The finite element method (FEM) is a numerical technique for analyzing continuous structures, developed especially for the two and three dimensions (2D and 3D), mainly engineering applications (for the study of formability, heat transfer, fluid flow, a.s.o.).
FEM is based on the idea that a continuous structure, based on geometry and some complex boundary conditions, the exact solution cannot be found, and if it can be found, the computational effort is unjustified.If we can find an approximate solution, easier to reach and with a reasonable approximation engineering degree, this becomes the solution to the original structure.In other words, the analysis of a FEM structure consists of replacing it with another solution which is easier to find.The results approximate initial structure, but are acceptable from the engineering point of view [1].
Our study tried to demonstrate and find a general computational method, using main mechanical principles and formulation, which can verify any kind of structures used in civil engineering.Euro Codes give us complicated methods available only on classical structures.For complex, futuristic, non-linear or composite structures we do not believe these Codes works very well, or the calculation become too complicate to be applied.
In this paper we want to test various FEM techniques on a classical structure and compare to the results given by Euro Codes.If the results are similar, the FEM method can be extended and used for nonconform and futuristic structures.

THE 3D MODEL OF THE FIVE LEVEL OFFICE BUILDING
First, the entire reinforced concrete structure of the building was modelled [2].The steps of the that operation are common for any type of CAD software (Figure 1) [3,4].
Using similar CAD operations the first and second floor brickwork structures were defined (Figure 2) [2,5].
Also, the woodwork elements as doors and windows were defined (Figure 3).
It was also defined, an element that will simulate soil that is placed around the basement concrete structure.This component is shown in Figure 4 [6-8].These elements, as outlined above, were reunited in the assembly module using specific constraints [2]. Figure 5 shows the final model of the office building.

DETERMINATION OF AN EQUIVALENT ELASTI-CITY MODULUS FOR THE ENTIRE REINFORCED CONCRETE STRUCTURE
It is known that for determining the modulus of elasticity in a mechanical element, it is subjected to experimental testing, so by measuring the elongation for different strengths, we determine specific normal stress σ and strain ε which are known components in the relationship (1).
Obviously, these two components can be expressed by equation (2) where ∆l is the elongation (measurable) l 0 is the original length (measurable) F is the force (known) Initial section A 0 is the element area under virtual test operation (measurable).
The intention is to test different virtual concrete items for different loads, underlying the idea of determining a medium modulus that can be used for the whole structure of the building.Subsequently, we plan to suppose this structure to various loads: • static load; • snow load; • equivalent loads similar to earthquake from Vrancea, Romania on 4 March 1977; • wind loads; • different combinations of these primary loads.

Simulation of the behavior of different reinforced concrete elements at different loads
The model shown in Figure 6 is a composite column made of concrete and metallic bars, columns being placed at the distance specified in the project [1].

Figure 6. The model of a column made by concrete and metallic elements
This model was the subject of a simple loading scheme.Also, in Figure 7, it is presented the mesh structure of the column used to test to different forces.This model was successively loaded with traction forces between 100000 and 900000 N. The results for the extreme loadings are shown in displacement maps in Figure 8. Reinforced concrete elements were all tested using different loading schemes to determine the main characteristic parameters of the material as elastic modulus and Poisson's ratio [1].For two reinforced concrete elements we obtain the diagrams presented in Fig. 9.That value and other average parameters were used in the following simulations.

FEA SIMULATION MADE FOR SNOW LOADING [9]
In Romania, determining of the snow loading for the structure calculus was done using the map with the maximal values as shown in Figure 10.
To achieve the simulation the model presented in Figure 11 was used, where the pressure of snow of 2 kN/m 2 and the weights caused by the action of gravity were taken into account.Also, in that figure the load scheme and the finite elements structure was presented.
The results are composed by three types of maps: stress, strain and displacement maps.In Figure 12 the map results obtained after the snow loading simulation (only stress and displacement maps) are presented.The model is shown in the deformed shape, magnified by 1392 times.The earthquake also affected Bulgaria.In the town of Svishtov, three apartment buildings were destroyed and over 100 people died.The earthquake's epicenter was located in Vrancea, the most active seismic area in the country, at a depth of about 100 km from the earth sur-face.The shock wave was felt in most of the Balkans [11,12].
Based on the records made by INCERC Laboratory we obtained a digitalization of the March 4, 1977 earthquake in Excel format, and based on the data obtained, a chart in Figure 13 was made.

Figure 13. The digitalized diagram of displacement for the analyzed earthquake
To obtain the system analysis, during the earthquake, two main elements were considered: reinforced concrete structure of the building and the soil with dimensions of 50x50x5 m.These two elements were connected virtually through a linear motor, whose action was on the values from digitalization of the earthquake [10].
The action of the virtual motor that acts between the ground and the building is given by the displacement and acceleration shown in Figure 14 and are similar to Vrancea earthquake of March 4, 1977 [13-16].
After running the application, the determined ground reaction force during the 40 seconds of the virtual earthquake is shown in Figure 15.
Also, was obtained the building structure behaviour, based on FEM maps, for the north direction of the virtual earthquake (Figure 16).Using other directions, the results are almost similar.

SIMULATION OF WIND ACTION OVER THE FIVE LEVEL BUILDING
To determine the effect of wind on a five level building, Flow Simulation Analysis module was used.It studied the effect obtained for air movements with a velocity of 150 km/h perpendicular to the south facade of the building [17].
We have obtained the results materialized in maps pressures, velocities, temperatures a.s.o.Ambient temperature was considered 20 օ C.These results maps were presented in Figures 17-20.

First combined loading simulation
The analysis of the situation that combined load consists of the following : • Type Vrancea action earthquake from west direction; • Wind with the velocity of 150 km/h from west direction ; • Snow pressure load of 2 kN / m 2 .
Figure 21 presents the map results obtained after the first combined loading simulation.

Second combined loading simulation
The analysis of the situation that combined load consists of the following: • Type Vrancea action earthquake from west direction ; • Wind with velocity of 150km / h from east direction ; • Snow load pressure of 2 kN/m 2 .
Figure 22 presents the map results obtained after the second combined loading simulation.

THE RAPID PROTYPING OF A SCALE MODEL FOR THE STUDIED BUILDING [18-21]
In the past decade, a new concept of manufacturing called "Rapid Prototyping" physical coating or without solid preform manufacturing became popular in the world.The operations included in Rapid Prototyping (RP) became relatively popular about twelve years ago with the advance of stereo lithography technology.Stereo lithography has a significant impact, in particular, on designing new products.The process started from a 3D CAD model involving ultraviolet sources, photosensitive polymers, melted plastic, metallic fine powders or laser systems [18][19][20][21].
The basic technique of this new method of rapid prototyping consists of a 3D model divided in thin layers, followed by physical realization of layers and their arrangement "layer upon layer".The materialization of 3D objects using stratified techniques is an idea as old as science and technology (the pyramids of Egypt were built block over block and layer over layer).
Using this printer we obtained fragments of levels building at the scale 1: 100 represented in the figures below.These elements were assembled with special glue, were completed using an air drying polymer clay and acrylic paint was used.Figure 23 presents different images with the scaled printed building.We obtained the printed model to test our 3D printing device for scale building model.Also, this device is available to produce plastic shapes for complicated or futuristic scaled models.During the printing operations the problems were identified and new methods were determined for complicated shape 3D printing used for any kind of building.

DISCUSSIONS
The five_level building was analyzed using both methods: with calculation given by the Euro Codes and using FEM techniques.The results were similar because a classical type of structure was used.For the earthquake calculation, the Euro Codes give only general verification calculus based on a supplementary average soil acceleration given by a map of values.For example, in our region, the Euro Codes give the calculation value for soil acceleration a=0.16 g.As we presented in Figure 14 the maximum acceleration (green map) is a≈1000 mm/s 2 or a≈0.1 g and it is reached after 6 seconds after the initiation of the virtual earthquake.The Euro Codes give only a supplementary calculation static load to be used in different cases, but FEM techniques give dynamic loads and parameters calculated in every moment of the virtual earthquake.Also, virtual simulation gives all the parameters in any location of the building during the earthquake.Very easily, the building can receive virtual verification for every kind of earthquake.
The Euro Codes calculation for wind gives only a supplementary load, but the FEM wind analysis can give a lot of parameters as pressure, temperature, velocity of the wind in any location on the virtual building.In addition, all the initial parameters can be changed and can be adapted to any values, very easily.
All these advantages recommend the FEM techniques to be used for all building structures, classical or futuristic.

CONCLUSIONS
Analyzing the two combined loading situations the following conclusions can be drawn: The method presented in this paper is a viable tool for the analysis of complex situations encountered in practice.This method can replace or complete the Euro Codes design calculation, which encounter difficulties to use in complicated or futuristic structures, increasingly used in practice.
Also, a scaled model was 3D printed and methods for complex shapes were determined.

Figure 5 .
Figure 5.The final model of the building including ground element

Figure 7 .Figure 8 .
Figure 7.The loading scheme and the mesh structure of the column

Figure 9 .
Figure 9.The elastic modulus diagrams for two reinforced concrete elements Analyzing many elastic modulus diagrams made for different elements and loadings, we obtained an average value E average = 70913621431.34N/m 2 = 7.091ˑ10 10 N/m 2 .

Figure 19 .
Figure 19.The velocity of air mass [m/s]

Figure 21 .
Figure 21.The FEM results for the first combined loading simulation (stress and displacement maps)

Figure 22 .
Figure 22.The FEM results for the second combined loading simulation (stress and displacement maps)

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In both analyzed combined loading situations, displacements are very high, reaching 164.3 mm when wind acts in the direction of the earthquake from the west and to the value of 163.4 mm when the earthquake and wind have different directions ; • Values of stress reach in the first case 153.8 MPa and 157.2 MPa in the second case ; • Strain values are low, between 2.53ˑ10 -3 and 2.47ˑ10 -3 for the two analyzed situations; • It is found that both conditions are unfavorable causing large displacements.