Learn to Pre-Dimension a Reinforced Concrete Structure

Casa de fim de semana em São Paulo / spbr arquitetos. Image © Nelson Kon

It’s fundamental that architects know about structures, not only to bring their designs to reality but also to be able to discuss their projects with engineers in order to find the best solutions for construction. Structural pre-dimensioning is crucial to the initial design of the structural components, revealing the restrictions and the possibilities of the spaces.

One of the main loads that a structure must support is its own weight, so it’s essential to know this information so that the different parts of the building can be dimensioned. When starting a structural project, the engineer doesn’t yet know the dimensions of the different pieces that make up the structure, and therefore, can’t know their own weight. A paradox appears without a solution: to know the weight it’s necessary to know the dimensions, but, to know the dimensions, it’s necessary to know the weight.

During the development of the project the architect finds himself in the curious situation of having to design without necessarily knowing the size of each of the parts of the building (such as the size of the pillars, for example). These important elements directly affect functionality and aesthetics of the project.

Casa e Estúdio na Vila Romana / MMBB Arquitetos. Image © Nelson Kon

In order to resolve this impasse, rapid processes of pre-dimensioning were developed that, although they don’t present exact results, are pretty accurate. Obviously, it’s necessary to perform subsequent structural calculations with all the care and accuracy required by technical standards, but at least pre-dimensioning provides a starting point for the project to be carried out.

The objective of this text is to present one of the methods of pre-dimensioning slabs, beams, and pillars of buildings built with reinforced concrete. There are several other methods, but this is probably one of the most common. All the spans cited in this text can be considered as the distance –center to center– between the supports.

Casa das duas vigas / Yuri Vital. Image © Nelson Kon

Pre-dimensioning of slabs

The spans, length W₁ and width W₂, of the slabs, are determined by the beams that normally define the perimeter. The only dimension that is not known about the slab is its height H. To have an idea of the preliminary height alternatives in a solid slab, you can divide its smaller span by 40, avoiding slabs that are thinner than 7 cm (in common floor slabs) and 12 cm (in slabs that support vehicle traffic). In prefabricated and ribbed slabs, the initial height can be calculated by dividing the smaller span by 20.

Pre-dimensioning of beams

In beams, what is known a priori is its span W₁ (in beams with two supports), or its spans W₁, W_{2, … ,}W_n (in the case of beams with multiple supports). If the beam is cantilevered, the length of the cantilever W_b is known. Beam thickness Bw, which must always be equal to or greater than 12 cm, can be considered as the thickness of the wall that the beam supports, without cladding. Similarly to the slab calculations, it is still necessary to determine the height h of the beams, which should not be less than 20 cm.

In beams with 2 supports and without cantilevers at their ends, the height can be calculated by dividing the span W₁ by 10, rounded to the multiple of 5 (higher).

In beams with multiple supports, the height will be calculated by dividing the major span (W₁, W_2,orW_n) by 12, also rounding to the multiple of 5 (higher). This height H can be used on the whole beam, even in the smaller spans.

The height of the cantilever beam can be estimated by dividing the cantilever length by 5.

Pre-dimensioning of pillars

For pillars, only the height is known, so it is necessary to determine the area of the pillar’s cross-section (A x B). Brazilian technical standards, for example, recommend that dimensions A and B be equal to or greater than 19 cm, but in special cases, it can be 14 cm, provided that the area of the section is greater than or equal to 360 cm2. It’s recommended that the largest dimension of the cross-section be not much greater than twice the smallest dimension: B ≤ 2A.

The load of a pillar changes on each floor and can be estimated using ‘influence areas,’ which is determined by half the distance between neighboring pillars. Each m2 of influence area of each slab will contribute 1000 kgf of load to the pillar, including the weight of the slab, the weight of the walls and claddings, and the accidental loads. It’s possible that the contribution of the first slab, which is in contact with the ground, and of the last slab, in the highest part of the building, is only 500 kgf/m2.

Obviously, the load will accumulate in the pillars from the top down, so, the lower the pillar is located, the greater the area of its cross-section will be, depending on the load it’s supporting on its top and the admissible tension of the concrete used (without taking into account its possible and probable flexo-compression). Only for the purposes of pre-dimensioning, a low resistance concrete is considered in the calculation of the initial area of the pillar, with allowable calculation tension, considering a safety factor of 10 mpa, or 100 kgf/m2, in favor of safety resulting in more robust pillars.

Each pillar must be calculated individually. Below is an example of pre-dimensioning one of the pillars of a 5-story building. It is assumed that the influence area of the pillar was constant at all levels and equal to 40 m2.

We clarify that what is presented in this article is only a pre-dimensioning process for auxiliary effects in the elaboration of an architectural project. It must never be adopted as a final structural project. All the calculations for the construction of the building must be rigorously tested for compliance with the technical norms.