## Computational Methods for Reinforced Concrete Structures

“There are no exact answers. Just bad ones, good ones and better ones. Engineering is the

art of approximation.” Approximation is performed with models. We consider a reality of

interest, e.g., a concrete beam. In a first view, it has properties such as dimensions, color,

surface texture. From a view of structural analysis the latter ones are irrelevant. A more

detailed inspection reveals a lot of more properties: composition, weight, strength, stiffness,

temperatures, conductivities, capacities, and so on. From a structural point of view some

of them are essential. We combine those essential properties to form a conceptual model.

Whether a property is essential is obvious for some, but the valuation of others might be

doubtful. We have to choose. By choosing properties our model becomes approximate

compared to reality. Approximations are more or less accurate.

On one hand, we should reduce the number of properties of a model. Any reduction of

properties will make a model less accurate. Nevertheless, it might remain a good model. On

the other hand, an over-reduction of properties will make a model inaccurate and therefore

useless. Maybe also properties are introduced which have no counterparts in the reality of

interest. Conceptual modeling is the art of choosing properties. As all other arts it cannot

be performed guided by strict rules.

art of approximation.” Approximation is performed with models. We consider a reality of

interest, e.g., a concrete beam. In a first view, it has properties such as dimensions, color,

surface texture. From a view of structural analysis the latter ones are irrelevant. A more

detailed inspection reveals a lot of more properties: composition, weight, strength, stiffness,

temperatures, conductivities, capacities, and so on. From a structural point of view some

of them are essential. We combine those essential properties to form a conceptual model.

Whether a property is essential is obvious for some, but the valuation of others might be

doubtful. We have to choose. By choosing properties our model becomes approximate

compared to reality. Approximations are more or less accurate.

On one hand, we should reduce the number of properties of a model. Any reduction of

properties will make a model less accurate. Nevertheless, it might remain a good model. On

the other hand, an over-reduction of properties will make a model inaccurate and therefore

useless. Maybe also properties are introduced which have no counterparts in the reality of

interest. Conceptual modeling is the art of choosing properties. As all other arts it cannot

be performed guided by strict rules.

A numerical model needs some completion as it has to be described by means of programming

to form a computational model. Finally, programs yield solutions through processing

by computers. The whole cycle is shown in Fig. 1.1. Sometimes it is appropriate to merge

the sophisticated sequence of models into the model.

A final solution provided after computer processing is approximate compared to the

exact solution of the underlying mathematical model. This is caused by discretization and

round-off errors. Let us assume that we can minimize this mathematical approximation

error in some sense and consider the final solution as a model solution. Nevertheless, the

relation between the model solution and the underlying reality of interest is basically an

issue. Both – model and reality of interest – share the same properties by definition or

conceptual modeling, respectively. Let us also assume that the real data of properties can

be objectively determined, e.g., by measurements.

to form a computational model. Finally, programs yield solutions through processing

by computers. The whole cycle is shown in Fig. 1.1. Sometimes it is appropriate to merge

the sophisticated sequence of models into the model.

A final solution provided after computer processing is approximate compared to the

exact solution of the underlying mathematical model. This is caused by discretization and

round-off errors. Let us assume that we can minimize this mathematical approximation

error in some sense and consider the final solution as a model solution. Nevertheless, the

relation between the model solution and the underlying reality of interest is basically an

issue. Both – model and reality of interest – share the same properties by definition or

conceptual modeling, respectively. Let us also assume that the real data of properties can

be objectively determined, e.g., by measurements.

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