# LINEAR STRUCTURAL ELEMENTS

The **linear structural elements in concrete** they are the pillars and the beams. The concrete columns work mainly with compressive forces and the beams with flexural forces

Compression and flexion are often combined and we have two cases: one in which compression predominates throughout the section (compound compression), and another in which there are tensed and compressed fibers (compound flexion).

If the axes of the columns do not coincide vertically (those above with those below) due to execution errors, an eccentricity of loads would occur that would cause a bending moment.

The bending moments can arise on both sides of the column section, and if they occur simultaneously on both sides, we would call it skewed bending.

A beam works structurally in flexion. Flexion causes traction and compression, especially in the lower and upper chords respectively, where they are maximum.

The shear forces take place close to the supports. There can also be torsional moments, especially in the perimeter beams of the exterior of a floor.

**PRE-DIMENSIONING OF LINEAR STRUCTURAL ELEMENTS: BEAMS AND PILLARS.**

It is the procedure that is carried out before the calculation of the necessary dimensioning in structures hyperstatic before you can accurately calculate the stresses on them.

With the predimensioning, indicative dimensions of the cross sections of the beams and pillars that serve for a calculation of verification and readjustment of the final dimensions of the sections.

A series of aspects intervene in the pre-dimensioning that involve the criteria to be considered, for which it must be taken into account that these parameters may vary depending on aspects such as the quality of the material or the workmanship.

**Pre-dimensioning uses different values depending on the length of the elements:**

*h*=

*L*/9,

*h*=

*L*/ 12, where

*h*the total height or depth of the section, and

*L*the span or free length between supports of the beam. Is considered

*L*/ 9 when it is certain that the reinforcement of the beam is correct, and

*L*/ 12 when there is no certainty of the correct assembly of the beam, although an average can also be made between the two previous ones if the criteria are moderate. For the base (B) of the beam, it will be considered

*B*=

*h*/2.

*h*=

*L*/ 14 and

*B*=

*h*/ 2, where

*h*is the height of the beam cross section,

*L*beam length and

*B*the base of the beam cross section.

*b*x

*d*as long as:

Where *b* is the smallest dimension of the column cross section, *d* is the largest dimension of the cross section, *P* it is the weight of the building, a factor that depends on the type of column, *F _{ck}* the compressive strength of the concrete used. The factor according to the type of abutment can be taken from:

Guy | P | \ phi \ |
---|---|---|

C1 | 1.1 | 0.3 |

C1 | 1.1 | 0.25 |

C2 and C3 | 1.25 | 0.25 |

C4 | 1.5 | 0.3 |

The NTE gives approximate formulas for the predimensioning of beams and columns that are part of frames within structures whose beams and columns form orthogonal three-dimensional trusses.

- If the beam is part of an intermediate floor or of the upper floor, and if the beam is a beam adjacent to the facade or an interior beam of a portico.
- Once the above data is known, there are simplified formulas for calculating the bending moment maximum over the beam.
- From the maximum bending moment, the NTE recommends a width and a height for the rectangular section of the beam.

The procedure is similar for columns, although here the pre-dimensioned section will ultimately depend on the axial stress and the maximum bending moment.

**PANDING PROBLEMS.**

Buckling is the curved lateral deformation of a linear element (beam or column) compressed by an excess load. The buckling depends on the section, the length of the bar, and the type of knot.

The shorter a beam is, the less it will deform. All rectangular beams would deform about the direction of the minor side of the rectangular section, that is, about the minor plane of inertia.

The buckling length of a linear element is determined according to whether the joint is articulated or rigid, considering the deformation caused in an isostatic beam as unitary. In this way, the actual length of the linear member would match the buckling length.

In the event that the linear element is embedded, the deformation would be twice that of an articulated beam, therefore we have realized that the buckling stiffness is greater when the nodes are more hyperstatic.

**EXECUTION OF PILLARS.**

- Stakeout: with azulete the column is marked on the concrete slab or foundation from where it starts.
- Before the placement of the armor, the wait was checked.
- The spacers are placed in a staggered fashion, leaving a separation of less than 1 m for the same bar.
- The pieces concreted against the ground must be covered by at least 7 cm.
- The correct tying of the reinforcements will be verified so that they do not move during concreting.
- Provide stiffeners and legs to ensure the separation between grates.
- Place spacers to ensure the coverings provided for by the project.
- Formwork: check its good condition, without deformation or breakage, and clean the surface. They are elbowed with struts and all faces are checked with a plumb line.
- If the form support does not seat evenly, a cement grout is poured to fill the gaps.
- The level of the concreting is marked on the formwork.
- Assembly of a scaffold to allow easy access for operators to the crown of the abutment.
- The concreting is carried out avoiding disintegrations and displacements. The concrete is placed continuously or in layers.
- Compaction of concrete: it is produced by the use of needle vibrators.
- After concreting, the plumbness of the pillar is checked, allowing approximately 30 minutes to pass to verify that there have been no displacements.
- Remove formwork after 24 hours and check the condition of the concrete.
- If the pockets leave the reinforcement exposed, they must be covered with a specific repair mortar, and if they are very deep, the column must be rebuilt again.

*From left to right and from top to bottom: stakeout, waiting, concreting, unconfused pillars in perfect condition without voids.*

**ARMOR.**

- Rectangular sections work better because they adapt their inertia to the bending forces to which they are subjected.
- Longitudinal reinforcement: It is composed of n bars that act against traction.
- Transverse reinforcement: it is composed of fences separated at a certain distance.
- The stirrup reduces the slenderness The steel absorbs the tensions that the compressed fibers of the concrete cannot withstand.
- The tractions and compressions of the fibers are usually generated in the same plane of the gantry, for this reason the reinforcement of the section is asymmetric.
- If the piars are subjected to skewed bending, they must be armed in each plane according to the compressions and tractions of their fibers.
- The two sides of the section must not have the same reinforcement.
- There may be an error at the time of placing the column on the plan by executing the section with asymmetric reinforcement.
- To avoid errors, the assembly symmetrically, keeping the same quantity on both sides of the section.
- of the compressed bar, avoiding the loosening by buckling of the material that covers it.
- The steel rods must be held by the branches of the stirrup.

The concrete columns work under compression and bending and the forces are transmitted by the girders.

Compression and flexion are often combined and we have two cases: one in which compression predominates throughout the section (compound compression), and another in which there are tensed and compressed fibers (compound flexion).

If the axes of the columns do not coincide vertically (those above with those below) due to execution errors, an eccentricity of loads would occur that would cause a bending moment.

The bending moments can arise on both sides of the column section, and if they occur simultaneously on both sides, we would call it skewed bending.

A beam works structurally in flexion. Flexion causes traction and compression, especially in the lower and upper chords respectively, where they are maximum.

The shear forces take place close to the supports. There can also be torsional moments, especially in the perimeter beams of the exterior of a floor.

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