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Shear lugs and anchors in anchor plates: Shear distribution

Decembre , 3th 2020 | Author: Prontubeam (@Prontubeam_en) Read: 1824 times

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When the anchor plates are subjected to significant shear forces, an I-shaped, rectangular or tubular profile, also known as a shear lug, is usually welded to their lower part. The objective of this shear lug is, as it seems logical, to resist the shear, thus unloading the anchors that will already be working in tension. However, the question arises as to whether the shear lug is going to resist the entire shear as it is more rigid than the anchors, or if on the contrary, the anchors will resist a part of this shear. In many calculations, it is assumed that the shear is transmitted entirely through the shear lug, thus working the anchors only in tension. The objective of this article is to study whether this hypothesis is correct.

 

Shear lugs and anchors shear distribution

 

We note that in the EC-2 there is an important absence in terms of shear lug information in general, and a complete absence of the shear distribution discussed in this article. There is no information of how to deal with the transmission of shear when we have shear keys. However, the American code, ACI 318-19, does go into more detail on this topic. ACI 318-19 reads in its section §17.11.1.1.3:

 

§17.11.1.1.3 – For anchors welded to the attachment base plate, tension and shear requirements of 17.8 shall include a portion of the total shear of the anchor

 

And explains, in its version with comments, the following about this point §17.11.1.1.3:

 

§R17.11.1.1.3 – Although neglected in the bearing strength evaluation in 17.11.2, welded anchors resist a portion of the shear load because they displace the same as the shear lug. The portion of the applied shear, Vu, that each anchor carries, Vuad, is given by

ACI 318-19 shear distribution formula

Where n is the number of anchors and Aef,sl is the area of ​​the shear key that is going to transmit the shear to the concrete and that we define later.

This means that, indeed, we have to take into account that a certain part of our shear is going to be transmitted through the anchors, invalidating the hypothesis that the shear lug resists the entire shear.

We are going to verify, using a finite element calculation model (FEM), the veracity of the previous formula. To do this, we have modelled a 35mm thick anchor plate with 4 M16 anchors of 200mm length. A 110x115x7.5 square tubular shear lug (mm - Height x Width x Thickness) is welded onto the bottom face of the plate, embedded in the concrete. An I-shaped profile has been welded to the top face of the plate, on which we will apply the shear load. Its dimensions do not have an important weight in the calculation; we only ensure that it is consistent with the size of the other elements of the plate (210x120 with a 14mm web and a 17mm flange) so that it distributes the efforts in a representative area of the plate:

 

FEM Model Shear lug Mesh

Figure 1. Finite Element Model (FEM) - Mesh 

Vertical supports (Y direction) have been modelled at the top of the I profile to simulate the effect of the rest of the structure over it. It is also modelled vertical supports at the bottom of the anchors to simulate the anchor head of the anchor blocking the vertical displacements. The following image shows these boundary conditions:

FEM Model Shear lug Vertical support

Figure 2. Boundary conditions – Vertical support

The four sides of the concrete block are fixed to represent the continuity of the structure where our plate is anchored as shown in the following image:

 

FEM Model Shear lug Concrete boundary condition: fixed

Figure 3. Boundary conditions – Concrete

The interaction between the plate and the concrete has been modelled by means of frictionless contacts, that is, they allow only contact in compression and have no tangential resistance (no friction). The following image shows the contacts used:

FEM Model Shear lug Contact definition

Figure 4. Boundary conditions – Plate – Concrete frictionless contacts

We apply an increasing horizontal force on the flange of the profile. As a function of this force, we are going to obtain the reaction in the shear lug and in each anchor in order to compare them with the value obtained applying the formula of ACI 318-19.

 

FEM Model Shear lug Load applied

Figure 5. Cargas aplicadas – Fuerza dirección +X

First, we are going to calculate theoretically, following the formula presented in ACI 318-19, how much shear the shear lug would transmit and how much the anchors for this particular case we are studying.

To apply the formula presented above we have to define Aef,sl, which according to ACI 318-19 is defined as follows:

Shear force on shear lug

      Aeff,sl ACI 318-19 area definition

Figure 6. Aef,sl – ACI 318-19

Applying the previous image, we obtain an Aef,sl = 6000mm² (which represents approximately 50% of the surface of our shear lug). For the moment, we use this value in the formula, but later we are going to check it with the FEM model. We apply it in the formula of ACI 318-19 to obtain the (Shear per anchor-Vua,i) / (Total Applied Shear-Vu) ratio:

ACI 318-19 shear distribution formula applied

We are going to check this theoretical number with what we would obtain when we apply the increasing shear load in the finite element model that we have presented. The following image shows, depending on the applied load, how much of this load is transmitted to the concrete through the shear lug and how much through the anchors:

Shear distribution Anchor Shear lug

Figure 7. Shear distribution – Anchors and shear lug

We are going to translate this into %, that is, what percentage of the load is transmitted by the anchors compared to the total applied load in order to quickly compare it with the 6.4% value obtained previously. The following image shows us these percentages:

 

Anchor force compared to the total shear force

Figure 8. Porcentaje de carga en pernos comparado con la carga total

We analyse the images presented above:

·         Until the 350kN load is reached, the shear lug resists the entire applied shear and the anchors practically nothing. Note: Anchor 4 seems to resist initially more than the others but it is due to modelling circular anchors with finite elements, corners are created producing a contact between the concrete and the Anchor 4 a few microns of a millimetre before the rest. Under this load, 350kN, the concrete begins to plasticise producing a displacement in the upper part of the shear key. When this displacement occurs in this area, the entire plate tends to move solidly, the anchors enter in contact with the concrete, and the load on the anchors increases:

Concrete stress behing shear lug small area

Figure 9. Concrete stresses for a total load of 350kN

 

·         The bigger the concrete plasticised area in front of the shear key is, the more the anchors are loaded. From a certain load, 590kN, it also plasticises the concrete in front of the anchors, at this moment the ratio Anchor shear/Total shear decreases a little, but the anchors continue to take load as we increase the applied shear load.

Concrete stress behing shear lug

Figure 10. Concrete stresses for a total load of 590kN

 

·         Once the concrete has plasticised, when the loads begin to be important, the participation of the anchors in the shear load reaches values of 4%, with a maximum of 6.3%. This point is studied in detail below.

 

We are going to study the veracity of the ACI 318-19 formula. According to this formula, 6.4% of the total shear load is resisted by each anchor and the rest is transmitted through the shear key. As stated in the ACI 318-19, this distribution occurs when a movement is produced in the anchorage system, since is this movement that produces the distribution. Based on these results, in the two most loaded anchors, under high loads, close to the rupture of the system, we get distributions of 6.0%-6.3%, which is almost the exact value given by the ACI 318-19. For lower load values, having already reached the state of plasticization in several areas, we have distributions of 3%-5%. In conclusion, well agreement is found between the ACI 318-19 formula and our calculations.

 

We need to check, using the results of the model calculation, the theoretical area used, Aef,sl = 6000mm², calculated based on ACI 318-19. The following image shows the area of the shear lug in contact with the concrete whose pressure exceeds 10MPa. Using this criterion it is defined an approximately effective area Aef,sl=7151cm², which is not very far from the theoretical value proposed by ACI 318-19. Using this value the previous formula gives us 5.6%, which is in the same order of magnitude.

 

 

 

 Aeffsl ACI area FEM calculation

Figure 11. Aef,sl calculated using shear lug FEM results

 

The following images show the evolution of our model as we increase the loads:

 

X displacement evolution

Figure 12. FEM model under shear force – Displacement in X direction (mm)

Von-Mises stresses evolution

Figure 13. FEM model under shear force – Von Mises stresses (MPa)

 

Conclusions:

·         It is checked that the hypothesis that the shear lug resists all the shear is false

·         The EC-2 does not give much information about this topic. However, ACI 318-19 in its section §17.11.1.1.3 explains how to assess the contribution of the anchors to the shear resistance when we have a shear lug

·         Our calculations show that the values ​​proposed by ACI 318-19 are very similar to those obtained using our finite element model.

·         The effective area proposed by ACI 318-19 (area of ​​the shear key in contact with the concrete under shear loads) is quite realistic. It is noted that we did some hypotheses to define this effective area using our finite element model. It is considered for this effective area only those areas under compression stresses greater than 10Mpa. This has been an arbitrary value, with no theoretical basis behind it.

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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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