C11. Modeling the loading

As explained in chapter E, it is important to always verify for each loading case (permanent, accidental, and thermal), by computing manually the summation of the loads, the global torsor of the loads: reaction forces and moments. (Most of the software enable outputting the global torsor).

C.11.1 Thinking about the test load cases

It is important, as soon as the modeling is completed, to plan test load cases that allow validating the good overall behavior of the model.

For example, unit forces uniformly distributed in the 3 directions, unitary punctual loads, or even temperature variations. For these load cases, the deformations (usual orders of magnitude in civil engineering, kinematics, or mesh discontinuities, ...) and the reactions at the support (all forces supposedly applied must be found in the reactions) will be examined.

Therefore, these tests enable verifying the stiffnesses, boundary conditions, and internal connections. They can also be used to verify more complex load cases (order of magnitude of the effects).

C.11.2 The case of dead load

Most software automatically consider the self-weight deduced from the cross-sections of the elements and the volumetric weight of the material.

This direct method must be systematically verified. Indeed, the geometrical simplifications necessary for modeling may induce a self-weight that differs from the one calculated with the drawings. A rigorous manual approach of the measurements should not lead to a discrepancy of more than 5%. In any case, any deviation must always be justified.

As soon as the net cross-sections deviate from the gross cross-sections of the structure (e.g. if cracking, shear drag, or oversize are considered), the self-weight considered as dead load must be redefined, so the automatic option should not be used. Another option would be to modify the characteristics of the materials that are being considered, element by element.

C.11.3 Surface loads and linear loads

Surface loads are generally applied to the average fiber of the plate element. When considering the intensity and perimeter of the surface load, the diffusion of the loads up to the average fiber, including possible diffusion through the thickness of the concrete cover, must be taken into account.

Furthermore, one must verify whether the surface load is applied according to the normal of the element (local reference) or according to the general reference of the model.

Some loads (e.g. snow) are defined according to a reference surface (the horizontal for snow), which must be considered when applying to surfaces that are not parallel to this reference plane (e.g. a sloped roof for snow). Often in software, it is necessary to explicitly specify whether a load is projected or not.

Other types of loads (wind, hydraulic pressure, ...) are always perpendicular to the surfaces.

Finally, the orientation of the loads should always be verified as well as the deformations and reactions at the supports, just like for the self-weight case.

See the examples below.

Example of the nozzle with earth thrust loading

Problem: model a linear load on an inclined surface.

The software offer options when defining the load, which are sometimes not very explicit.

Case 1: Load defined in the user global reference frame

The load applied to the bar is defined as a horizontal load per linear meter of the element.

Case 2: Load defined in the projected reference frame

The load applied on the bar is defined as a horizontal load per linear meter measured perpendicular to the direction of the load (vertically in this case).

Tip: Always check, on a simple example, that the option used corresponds to the desired load model.

Linear loads are also affected by these problems of diffusion and coordinate system.

Note: in the case of earth thrust, the best modeling technique is the second one, i.e. a projection of the loads on a vertical plane.

C.11.4 Thermal loads

Thermal loads are made of two types of loads:

Linear variations: a very common special case is the uniform variation,

Temperature gradients that result from a temperature difference between the extreme surfaces of a structure.

It is essential to use test cases to verify the correct consideration of thermal phenomena in coherence with the clamping of the structure.

It should be noted that thermal loads only create efforts (or stresses) if the structure is not free to deform (clamping, hyperstatic structures, ...).

Concrete cracking can play an important role in stress distribution (see 11.5 below).

C.11.5 Shrinkage and Creep Modeling

In the absence of a specific software option, concrete shrinkage modeling can be performed by applying equivalent thermal load cases.

Creep modeling can be performed by applying thermal load cases or reduction of the elastic modulus of materials.

It is important to verify that the imposed deformations are consistent with the expected phenomenon.

If there is any doubt, it is always possible to perform range calculations, to frame the short and long term (case of compound bridges, foundations, ...).

Detailed description: modeling of shrinkage in compound bridges

Link to shrinkage modeling in compound bridges

C.11.6 Live loads

Understanding the concept of influence lines is fundamental for a good apprehension of the positioning of convoys, it avoids designing for too many load cases.

In the case of complex structures, the concept is not easily applicable, however, influence lines can always be generated by placing unitary forces at different nodes of the structure. After post-processing the results, with a spreadsheet, for example, both surface and live loads can be positioned to produce the most undesirable effect.

The codes frequently define load models that combine loads of different natures with concomitance rules and specific geometric configurations. They should be read fully and carefully. It then allows, thanks to the influence line, to apply the loads at the position that is most undesirable for the studied effect (deflections, forces, ...).

Loading according to the influence lines.

Case of distributed loads that can be broken up and of convoys with variable vehicle spacing.

To our knowledge, all the regulations require to load the structures along the influence lines. Common practices or the phase in which the project is in (preliminary studies, pre-design, or even Executive design) can lead to simplifications: loading of two adjacent spans, loading of complete spans alternately ("one out of two”) ...

Link to the ECAM website

In the case of engineering structures, more specifically for Execution design calculations, loading by influence lines is mandatory, and it is not enough to load complete spans or to make vehicles drive uniformly close to one another.

It is therefore necessary to make sure that the software used is capable of performing influence line (IL) calculations, i.e. adapting the loaded lengths or adapting the number and spacing of vehicles in a convoy to obtain the most unfavorable situation for the desired effect, for example, the bending moment, the reaction of support or the deformation, ...

Eurocode uniformly distributed loads. We are looking for the maximum shear force (i.e. positive or negative) at mid-span of a bridge with two equal spans (2×25 m) and a constant section. We know that the influence line of the shear force at mid-span has the following shape:

For lack of a better solution, one might be tempted to fully load one or both spans.

The diagram below shows, for a unit load of 10 kN/m, the shear envelope for the cases:

Span 1 loaded

Span 2 loaded

Spans 1+2 loaded

At mid-span 1, one gets |V|_max = 31.3 kN:

The diagram below shows the same shear diagram, but with a beam loaded according to the IL:

Zone IL upper curve

Zone IL lower curve

One gets |V|_max = 53.7 kN, which is a significant difference.

The exercise could be repeated for all sections.

The latter is particularly true for the loadings in fascicule 61 title II, which we must still use when recalculating for example:

Distributed charges A(L) similar to uniformly distributed loads, but which have the characteristic of varying in intensity according to the loaded length L,

B or Mc convoys, whose spacing can vary, sometimes with a required minimum distance. Convoy Bc is described below.

2) Illustration on the previous bridge for the case of convoy Bc for the reaction bending moment

The influence line of the reaction moment looks like this:

A refined study would have to be carried out to find the precise position of the trucks, but it can be easily observed that (here for 25m spans - reminder) the trucks must be separated to obtain a maximum effect:

Application: we run two convoys on the bridge, the first one with the two trucks very close to each other, as drawn in the codes, and the second one with a distance of about 28.80m (determined graphically).

The results:

Trucks very close to one another, envelope, and unfavorable position.

Separate trucks, envelope, and unfavorable position.

The difference concerning the reaction moments is about 13%. However, the load case used to obtain the maximum reaction bending moment is not the one to be used for the spans.

Practically speaking, one quickly realizes that finding the loaded lengths and/or positions and the spacings of trucks, for all sections and all values of interest, is incredibly difficult by hand. Thus, using a software becomes evident - again for Executive desing level calculations. For the other phases, simplified calculations, with a certain margin on justifications and quantities remains possible by studying certain judiciously chosen sections of the structure, but this is beyond the scope of this document.

Set of load cases and results for distributed loads. Span 1, span 2, and spans 1+2:

Loading according to the IL:

C.11.7 Thrust modeling and land abutment

Generally, the actions generated by the soil (thrust for example), water pressures, or seismic actions are modeled by loads. The reactions (pressures on the ground, which can go up to a plastic threshold, the abutment, ...) are represented by linear or non-linear springs.

Linear seismic approaches are allowed if the foundation uplift is limited to 30% of the foundation surface. Be careful: no reaction forces are applied on a face blocked by springs... we let the springs do the work.

Note: a displacement approach is also possible to model the thrust loads and can lead to a reduction of the overall loading (see AFPS / AFTES Guide. GUIDE "Conception et protection parasismiques des ouvrages souterrains").