Basis

Mass concrete is a moldable material with good mechanical and durability properties and, although it resists appreciable tensions and compression efforts, it has a very low tensile strength. To adequately resist tensile stresses, it is necessary to combine concrete with a steel skeleton. This skeleton has the mission of resisting the tensile stresses that appear in the structure, while the concrete will resist compression (being cheaper than steel and offering adequate durability properties).

The proper selection of the characteristics of the type of concrete and corrugated steel, in addition to the dimensions and quantities of the materials, allows the collapse of the structural elements to be controlled. For example, an appropriate combination of these variables can allow the steel to yield and thus confer greater ductility so that it deforms enough to be visible before collapse. However, an element with too much corrugated steel inside may present a brittle break, since the bars do not allow that certain ductility and will not show obvious signs of deformation. This is why, in general, the regulations relating to this issue limit the maximum amount of steel that can be placed in the most critical points of the structures.

Longitudinal steel bars, called main or longitudinal reinforcement, are placed in elongated linear elements, such as beams and columns. These steel bars are sized according to the magnitude of the axial force and bending moments, while the shear force and torsional moment determine the characteristics of the transverse or secondary reinforcement.

• - Tracción: Un elemento está sometido a tracción cuando sobre él actúan fuerzas que tienden a estirarlo; los tensores son elementos resistentes que aguantan muy bien este tipo de esfuerzos.

• - Compresión: Un elemento está sometido a compresión cuando sobre él actúan fuerzas que tienden a aplastarlo. Los pilares son ejemplos de ello.

• - Flexión:[7]​ Un elemento está sometido a flexión cuando actúan sobre él cargas que tiendan a doblarlo. A este tipo de esfuerzo se ven sometidas las vigas de estructuras.[8]​.

Calculation of reinforced concrete beams and columns

The Euler-Bernoulli beam theory is not suitable for the calculation of reinforced concrete beams or columns. Resistant elements with these characteristics present a more complex resistance mechanism due to the concurrence of two different materials, concrete and steel, with very different Young's moduli. The moments of inertia are variable according to the size of the cracks in the elements. The different mechanical properties of both materials present in a reinforced concrete element mean that the equilibrium equations that link the internal forces introduced by the forces and tensions of the concrete and the steel are not as simple as those of homogeneous sections, which are those used in the Euler-Bernoulli theory.

In the Spanish Structural Concrete Instruction, mandatory regulations for reinforced concrete structures in Spain until 2021, the mechanical balance equations for the axial force N and the bending moment M of a rectangular section can be written very approximately as:

Where:.

If the normalized rectangle diagram is used to represent the stress-strain relationship of concrete then the tension and compression reinforcement stresses can be expressed in the above functions as:.

On the other hand, the forces supported by the compressed concrete block are given by:.

Section sizing

The problem of section sizing arises when determining the minimum amount of steel to guarantee the adequate resistance of the element. Generally, a reduction in cost is sought, which implies considering various shapes for the section and calculating the reinforcement for each of these possible sections, in order to establish an indicative cost for each section.

A section of a beam subjected to simple bending necessarily requires tension reinforcement (set of bars) placed in the tensioned part of the section, and depending on the bending moment it may also require reinforcement in the compressed part. The area of ​​both reinforcements of a rectangular section can be approximately calculated using the following sets of formulas:.

Where:.

With the same notations, the tensile reinforcement is calculated as:.

Checking sections

The verification problem consists of, given a section completely defined by its geometric dimensions and a certain number of bars with a well-defined arrangement, to verify by calculation whether said section will be capable of supporting the stresses induced in it by the action of known loads.

• - Main (or longitudinal) reinforcement: That required to absorb tensile stresses on the lower face in beams subjected to compound bending, or longitudinal reinforcement in columns.

• - Secondary (or transverse) reinforcement: Any reinforcement transverse to the axis of the bar. In beams it absorbs shear forces, maintains the position of the longitudinal reinforcement when the concrete is still fresh and reduces their effective buckling length.

• - Stirrup: Open reinforcement, currently out of use, used to resist shear forces in a structural element; generally, bars, wires or electrowelded wire mesh (smooth or ribbed), either without kinks or bent, in L-shaped, U-shaped or rectangular shapes, and located perpendicularly or at an angle, with respect to the longitudinal reinforcement. The word "stirrup" is normally applied to the transverse reinforcement of elements subject to bending and the term "mooring" to those in elements subject to compression. It should be noted that if there are torsional forces, the stirrup must be closed.

• Fence: Stirrup closed by a bent wire. A fence can be made up of several reinforcing elements with seismic hooks at each end.

• Strap: Continuous stirrup rolled in the shape of a cylindrical helix used in elements subjected to compression forces that serve to confine the longitudinal reinforcement of a column and the portion of the bent bars of the beam as anchorage in the column. The free space between spirals must be uniform and aligned, not less than 80 mm nor more than 25 mm from each other. For elements made in situ, the diameter of the straps should not be less than 10 mm.

• - Distribution reinforcement: In general, these are those steel meshes intended to maintain the distance and proper functioning of the main reinforcements in reinforced concrete floors.

• - Negative reinforcement: These are those bars installed in unidirectional slabs, in the compression layer, whose objective is to absorb part of the tensile stresses caused by the bending of the element.

• - Seismic hook: Hook of a stirrup, fence or lock, with a bend of 135° and with an extension of 6 times the diameter (but not less than 75 mm) that links the longitudinal reinforcement and projects towards the interior of the stirrup or fence.

• - Lock: Continuous bar with a seismic hook at one end, and a hook no less than 90°, with a minimum extension of 6 times the diameter at the other end. The hooks must link peripheral longitudinal bars. The 90° hooks of two consecutive transverse locks that link the same longitudinal bars must have alternate ends.

• - The Spanish regulations Spanish Structural Concrete Instruction EHE-08 of 2008 were definitively repealed on August 10, 2021. The Structural Code is currently in force.[9]​.

• - The European regulations, although not mandatory, are Eurocode 2: Concrete Structures Project.

• - The reference Argentine regulation is CIRSOC Regulation 201-2005, which replaces the old CIRSOC 201-1982. The new regulations are based on the American ACI regulations, as opposed to those of 1982, which were based on the old German DIN regulations.

• - The aforementioned American regulation is ACI 318-05 (American Concrete Institute).

• - Aluminosis.

• - Corrugated steel.

• - Formwork.

• - SS Faith.

Literature

• - Valenzuela, Armando. "Reinforced concrete patents. From big business to great technological development. The antecedents of the Modern Movement" rita_ Indexed Magazine of Academic Texts, 3, pp. 134-145. doi: 10.24192/2386-7027(2015)(v3)(10)(v3)(10) "doi:10.24192/2386-7027(2015)(v3)(10)").

• - Educational videos on the history of reinforced concrete in Spain.

• - CIRSOC 201, Argentine regulations for reinforced concrete construction.

Basis

Mass concrete is a moldable material with good mechanical and durability properties and, although it resists appreciable tensions and compression efforts, it has a very low tensile strength. To adequately resist tensile stresses, it is necessary to combine concrete with a steel skeleton. This skeleton has the mission of resisting the tensile stresses that appear in the structure, while the concrete will resist compression (being cheaper than steel and offering adequate durability properties).

The proper selection of the characteristics of the type of concrete and corrugated steel, in addition to the dimensions and quantities of the materials, allows the collapse of the structural elements to be controlled. For example, an appropriate combination of these variables can allow the steel to yield and thus confer greater ductility so that it deforms enough to be visible before collapse. However, an element with too much corrugated steel inside may present a brittle break, since the bars do not allow that certain ductility and will not show obvious signs of deformation. This is why, in general, the regulations relating to this issue limit the maximum amount of steel that can be placed in the most critical points of the structures.

Longitudinal steel bars, called main or longitudinal reinforcement, are placed in elongated linear elements, such as beams and columns. These steel bars are sized according to the magnitude of the axial force and bending moments, while the shear force and torsional moment determine the characteristics of the transverse or secondary reinforcement.

• - Tracción: Un elemento está sometido a tracción cuando sobre él actúan fuerzas que tienden a estirarlo; los tensores son elementos resistentes que aguantan muy bien este tipo de esfuerzos.

• - Compresión: Un elemento está sometido a compresión cuando sobre él actúan fuerzas que tienden a aplastarlo. Los pilares son ejemplos de ello.

• - Flexión:[7]​ Un elemento está sometido a flexión cuando actúan sobre él cargas que tiendan a doblarlo. A este tipo de esfuerzo se ven sometidas las vigas de estructuras.[8]​.

Calculation of reinforced concrete beams and columns

The Euler-Bernoulli beam theory is not suitable for the calculation of reinforced concrete beams or columns. Resistant elements with these characteristics present a more complex resistance mechanism due to the concurrence of two different materials, concrete and steel, with very different Young's moduli. The moments of inertia are variable according to the size of the cracks in the elements. The different mechanical properties of both materials present in a reinforced concrete element mean that the equilibrium equations that link the internal forces introduced by the forces and tensions of the concrete and the steel are not as simple as those of homogeneous sections, which are those used in the Euler-Bernoulli theory.

In the Spanish Structural Concrete Instruction, mandatory regulations for reinforced concrete structures in Spain until 2021, the mechanical balance equations for the axial force N and the bending moment M of a rectangular section can be written very approximately as:

Where:.

If the normalized rectangle diagram is used to represent the stress-strain relationship of concrete then the tension and compression reinforcement stresses can be expressed in the above functions as:.

On the other hand, the forces supported by the compressed concrete block are given by:.

Section sizing

The problem of section sizing arises when determining the minimum amount of steel to guarantee the adequate resistance of the element. Generally, a reduction in cost is sought, which implies considering various shapes for the section and calculating the reinforcement for each of these possible sections, in order to establish an indicative cost for each section.

A section of a beam subjected to simple bending necessarily requires tension reinforcement (set of bars) placed in the tensioned part of the section, and depending on the bending moment it may also require reinforcement in the compressed part. The area of ​​both reinforcements of a rectangular section can be approximately calculated using the following sets of formulas:.

Where:.

With the same notations, the tensile reinforcement is calculated as:.

Checking sections

The verification problem consists of, given a section completely defined by its geometric dimensions and a certain number of bars with a well-defined arrangement, to verify by calculation whether said section will be capable of supporting the stresses induced in it by the action of known loads.

• - Main (or longitudinal) reinforcement: That required to absorb tensile stresses on the lower face in beams subjected to compound bending, or longitudinal reinforcement in columns.

• - Secondary (or transverse) reinforcement: Any reinforcement transverse to the axis of the bar. In beams it absorbs shear forces, maintains the position of the longitudinal reinforcement when the concrete is still fresh and reduces their effective buckling length.

• - Stirrup: Open reinforcement, currently out of use, used to resist shear forces in a structural element; generally, bars, wires or electrowelded wire mesh (smooth or ribbed), either without kinks or bent, in L-shaped, U-shaped or rectangular shapes, and located perpendicularly or at an angle, with respect to the longitudinal reinforcement. The word "stirrup" is normally applied to the transverse reinforcement of elements subject to bending and the term "mooring" to those in elements subject to compression. It should be noted that if there are torsional forces, the stirrup must be closed.

• Fence: Stirrup closed by a bent wire. A fence can be made up of several reinforcing elements with seismic hooks at each end.

• Strap: Continuous stirrup rolled in the shape of a cylindrical helix used in elements subjected to compression forces that serve to confine the longitudinal reinforcement of a column and the portion of the bent bars of the beam as anchorage in the column. The free space between spirals must be uniform and aligned, not less than 80 mm nor more than 25 mm from each other. For elements made in situ, the diameter of the straps should not be less than 10 mm.

• - Distribution reinforcement: In general, these are those steel meshes intended to maintain the distance and proper functioning of the main reinforcements in reinforced concrete floors.

• - Negative reinforcement: These are those bars installed in unidirectional slabs, in the compression layer, whose objective is to absorb part of the tensile stresses caused by the bending of the element.

• - Seismic hook: Hook of a stirrup, fence or lock, with a bend of 135° and with an extension of 6 times the diameter (but not less than 75 mm) that links the longitudinal reinforcement and projects towards the interior of the stirrup or fence.

• - Lock: Continuous bar with a seismic hook at one end, and a hook no less than 90°, with a minimum extension of 6 times the diameter at the other end. The hooks must link peripheral longitudinal bars. The 90° hooks of two consecutive transverse locks that link the same longitudinal bars must have alternate ends.

• - The Spanish regulations Spanish Structural Concrete Instruction EHE-08 of 2008 were definitively repealed on August 10, 2021. The Structural Code is currently in force.[9]​.

• - The European regulations, although not mandatory, are Eurocode 2: Concrete Structures Project.

• - The reference Argentine regulation is CIRSOC Regulation 201-2005, which replaces the old CIRSOC 201-1982. The new regulations are based on the American ACI regulations, as opposed to those of 1982, which were based on the old German DIN regulations.

• - The aforementioned American regulation is ACI 318-05 (American Concrete Institute).

• - Aluminosis.

• - Corrugated steel.

• - Formwork.

• - SS Faith.

Literature

• - Valenzuela, Armando. "Reinforced concrete patents. From big business to great technological development. The antecedents of the Modern Movement" rita_ Indexed Magazine of Academic Texts, 3, pp. 134-145. doi: 10.24192/2386-7027(2015)(v3)(10)(v3)(10) "doi:10.24192/2386-7027(2015)(v3)(10)").

• - Educational videos on the history of reinforced concrete in Spain.

• - CIRSOC 201, Argentine regulations for reinforced concrete construction.