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Concreting in phases – Shear forces

October , 28th 2018 | Author: Prontubeam (@Prontubeam_en) Read: 1168 times

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Introduction

When a stop is made in the concreting of an element that continues later, also called concrete joint, the calculation must ensure the shear transmission between the two phases of the concreting. The EC-2 proposes for the concreting by phases, in chapter 6.2.5 “Shear at the interface between concrete cast at different times”, a formulation to calculate this effect. The formulation is a function of the roughness of the surfaces, the compression / tension existing between the two faces (perpendicular to the sections in contact) and the reinforcement that crosses the section. In this article we will deal with the following points:

• Formulation of the concrete’s strength

• Formulation of the acting force

• Constructive provisions

• Other considerations / doubts 

Formulation of the concrete’s strength

The EC-2 [Ref - 2], besides asking us to comply with the provisions of sections 6.2.1-6.2.4, (which are not the subject of this article) in section 6.2.5 proposes the following formulation for the shear strength between the two concreting phases (concrete cast at different times):

Where:

C and μ are values that depend on the roughness of the surface. The EC-2 proposes the following for these values:

Beta values for concrete joints

And σn is defined as the pressure (positive or negative) that can act simultaneously with the shear force. This pressure acts perpendicular to the contact surface between concreting faces. It is considered positive in compression but its value should not exceed 0.6fcd. If it is a matter of tension, in addition to considering it as negative, the first term of the equation c.fctd must be taken as null.

 is defined as the relationship between the steel reinforcement that crosses the two concreting phases and the area between these two phases. Any reinforcement that crosses this section is valid (also the shear one) as long as it is well anchored between the two parts to be joined: 

Image 1 – Shear reinforcement tying the contact surface

The alpha parameter is, as in the shear case, the angle formed by the reinforcement that passes through the two concreting phases and the contact face plane of the concreting phases.

Acting forces formulae

For the acting forces, Eurocode 2 also provides a formulation to follow that depends on the existing shear, the level arm and the contact section width. In this formulation we also take into account a beta factor that decreases the acting shear that we will explain later.

shear force formula for concrete joints

VEd is defined as the transversal shear force

In the following image, we will try to explain the values of z and bi of the previous formula

concrete section stress distribution

Image 2 - Terms of the proposed formulation. Extracted from [Ref 1]

In my opinion,  is not 100% clear, the code EC-2 defines it as follows:

 is the ratio of the longitudinal force in the new concrete area and the total longitudinal force either in the compression or tension zone, both calculated for the section considered

What is it trying to tell us with this? What are we exactly calculating? I will try to clarify it.

We know, from the elasticity theory, that shear stress in a section is defined through the formula below

Shear stress beam distribution

We also know that:

If we look at these two equations and the one given by the EC-2, what it tries to represent is the relationship between the stresses in the concrete interface / joint and the maximum shear stress in the section.

Imagen 3 – beta coefficient explanation

 

Following the nomenclature of Image 3, this coefficient   could be understood as:

The EC-2 does not specify in which cases we should / can use this coefficient. In case of doubt, it is advisable to leave it equal to the unit since, as we will see now, it can lead to erroneous results.

In the presentation of [Ref 1] the application of this beta coefficient is studied in 3 different cases. As we know, when we pour concrete in several phases and creep and retraction come into play, it appears in the concreting joint some "jumps" or "discontinuities" in the stress diagrams that can distort the interpretation of this beta factor that we are calculating. The following image shows the study of this beta factor in 3 possible stress distributions and calculates the acting shear in 3 different ways:

Figure 4 - Comparison of the beta coefficient in different stress distributions [Ref 1]

Is this [Ref 1] it is also proposed an alternative method that we copy here for the convenience of the reader:

Imagen 5 – Alternative method for beta calculation [Ref 1]

As it is shown, the result may vary depending on the hypothesis used, and not always in a “conservative manner”.

Constructive provisions

The EC-2, in section 6.2.5 (3) tells us that in the case that the joint between the two phases is carried out with the reinforcement, the joint can be divided into smaller areas along the beam according to the shear force diagram to dispose more steel in the most requested areas and less in those less requested. The EC-2 proposes the following explanatory image:

Image 6 - Shear diagram representing the steel requirements to join the concreting two phases [Ref 2]

Further thoughts

The problem, which has prompted me to write this article, has been the need to apply this section to structures other than a beam.

First, for a beam it is easy to interpret the formulation, although in my opinion it is not 100% clear. For the beam case, my first impulse was to calculate the shear stress as we do in the case of T sections, in the union of the flanges with the web as proposed by the EC-2:

Image 7 – Shear calculation between the web and the flanges according to EC-2 [Ref 2]

My proposal was to forget the “beta” and “z” values and calculate everything as shown in Figure 5. Finally, I understood for the beam case what we were doing and it is, in fact, what I have tried to explain throughout the article.

When I tried to apply the same philosophy proposed by the EC-2 to the case of a retaining wall that was concreted in several phases, it was not so clear neither which value I should take as z nor what values should I consider to calculate the value of beta (and it is not clear to me yet).

Image 8 – Wall example

In the wall example that I propose, the question arose as to how I could now calculate the value of beta or what we call z (mechanical arm) in this case. It is very possible that it is because some concept is a bit unclear to me, but it would not apply the shear values that I would have used in the beam nor I would be able to calculate a coefficient beta. I would be forced to apply a value of 1.

I encourage readers to comment in the comments area or to publish their own article in Prontubeam about how to interpret the values to be used, and an explanation of why in the beam the considered shear force is perpendicular to the concreting joint and in the wall case it seems more logical to take the following formula:

Is this correct? How would you calculate this shear force in the case of the wall?

References:

 [Ref 1 ]  - Shear in joint – standard EN - https://es.slideshare.net/jogijbels/eurocode-2-design-of-composite-concrete

[Ref 2] – NF-EN-1992-1-1 – Eurocode 2 – Design of concrete structures. Part 1-1 – October 2005

 

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Carlos Corral . MEng Civil Engineering from the Politécnica university of Madrid. Speciality: Structural engineer. Owner and programer of Prontubeam.com and Prontubeam.com/en.
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