Typologies of building structures
The typologies of building structures can be classified according to the predominant tensions
developed under the design loads in forms with uniform stresses (a) and forms with variable stresses (b).
Shapes with uniform stresses
These typologies of building structures stand out for presenting a homogeneous distribution of stress throughout the cross section of the longitudinal elements or throughout the thickness of the surface elements. This category includes cable structures, arches, hinged knot structures, membranes and sheets.
Cable structures represent a highly effective way of supporting loads. Their great flexibility makes them incapable of resisting bending or compression forces, so they must support loads through tensile forces. To fulfill this function, these structures must adopt the geometry of the funicular polygon corresponding to the loads. Which generally involves significant changes in their geometry and makes them less suitable for certain applications.
Arches are structures that operate exclusively under compression if they are given the shape corresponding to the funicular polygon of the loads to which they are subjected. When in this form, the arches can be considered as inverted cables. However, unlike cables, archwires typically have some bending rigidity. Due to this rigidity, when a change in the applied forces occurs, the arch cannot adjust its geometry and adapt to the funicular polygon of the new forces without developing bending stresses. Therefore, the change in geometry will be smaller compared to cables and bending stresses will be generated in conjunction with compression stresses.
Articulated knot bar structures
The bar structures of articulated nodes, both flat and spatial, have the capacity to withstand any state of loads applied to the nodes through tensile or compression forces in the bars that compose them. Although the uniform distribution of stresses in the cross sections of the bars is only achieved in the ideal structure, in reality, due to the imperfection of the joints at the nodes, secondary bending stresses arise when the structure deforms.
Flexible membranes are surface structures that, in a first approximation, can be considered as a set of cables. Due to their superficial nature, membranes experience shear stresses between adjacent elements, which allows them to withstand variations in distributed loads without experiencing significant changes in their geometry, except those due to elastic deformations of the material.
However, point loads generate discontinuities and can only be supported with strong changes in geometry in the application area, similar to what happens in cables. These characteristics make flexible membranes especially suitable for distributed loads, but require special consideration in the case of point loads.
Sheets are surface structures similar to membranes, but have flexural strength and rigidity. Like membranes, sheets can support distributed loads developing uniform stresses with slight secondary bending due to small membrane deformations. As long as certain boundary conditions are met.
However, when there are strong variations in the load distribution or when point loads are applied, the considerable local changes in geometry that occur in the membranes translate into strong local bending stresses in the sheets. This means that the slats can handle distributed loads more efficiently. But they must be approached with caution when faced with concentrated loads or extreme variations in load distribution.
Shapes with variable tensions
These typologies of building structures are characterized by presenting variations in tension along the cross section of the longitudinal elements or along the thickness of the surface elements. These structures include beams, rigid joint structures and plates.
Shapes that have uniform stresses make more efficient use of the strength of the available material, compared to shapes that have variable stresses. In structures with variable stresses, the material located between the two faces experiences lower stresses under elastic conditions, except in areas where there are high tangential stresses.
Beams represent the simplest case of structures with variable stresses. In a straight beam, the axial forces do not contribute to resisting the load components that are perpendicular to the directrix of the piece. These components must be balanced by shear forces and bending moments. Therefore, variable normal and tangential stresses develop in the cross section of the beam.
With the aim of improving the use of the beam, various geometries have been devised for the cross section. One of the most common is the double T section, where most of the material is placed in the wings (where normal stresses are maximum). Leaving in the core (where the tangential stresses are maximum) the amount of material necessary to resist said tangential stresses.
Another way to optimize the use of the beam is through plastic design, which consists of considering the ultimate resistance of the piece when the material works at maximum tension at all points. This approach allows the material to be used more efficiently and ensure that the beam has optimal performance against the applied loads.
Plates are surface structures that have the ability to transmit loads in two directions. Like beams, plates resist transverse loads through shear stresses. However, torsional moments in addition to bending moments also occur in a section of a plate.
The rigidity of a plate is greater compared to that of a set of beams with the same span and thickness due to its ability to transmit loads in two directions and its significant torsional rigidity. This greater rigidity makes the plates more efficient and versatile structures to support loads in different directions and offer greater overall resistance.
Rigid knot bar structures
Rigid knot bar structures are one of the typologies of building structures. They are composed of linear elements that are subjected to axial forces, shears and bending moments. Since the elements that make up these structures are mainly subject to bending forces (except in pillars of very tall structures). Some provisions are used to improve the use of the material, such as haunches and semi-rigid knots, among others.
In addition, plastic design methods are used that pursue the same objective. These strategies seek to make better use of the material and optimize the resistance of the structure to the different types of loads it may face. By implementing these provisions and design methods, greater efficiency and performance of rigid knot bar structures are achieved.