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## Finite element analysis of steel structures – a review of useful guidelines

Your message has been sent, thank you. There was an error sending your message. Your name. Nonlinear calculations usually require a higher effort than linear calculations. Con- cerning the nonlinearity, we need to distinguish between physical and geometric nonlinearities. Regarding physical nonlinearity, the assumption of a linear elastic material behaviour is renounced and the plastifications in parts of the construction are considered in order to obtain more economic structures, i. As far as the plastification is only considered regarding the bearing capacity of the cross sections, this approach is to be assigned to the verification method Elastic- Plastic in Table 1.

Internal forces and moments are determined according to the elastic theory elastic calculation of the system and only load cases are permitted where a maximum of one plastic hinge occurs.

In comparison to that, the plastic 1. While the physical nonlinearity is mainly considered for economic reasons, the geometrical nonlinearities for structures susceptible to losing stability are indispensable for safety reasons. In comparison to linear calculations, relatively large deformations lead to higher internal forces and moments. For that reason, verifications against flexural, lateral torsional or plate buckling have to be executed.

In conjunction with geometric nonlinear calculations, it should be mentioned that the verifications according to the valid standards and codes, as for instance DIN Part 2, rely on a linearisation according to second order theory. This approximation is therefore the basis for the determination of deformations, internal forces and moments as well as critical loads eigenvalues in conformity with the codes. As a general rule, the accuracy of calculations according to second order theory is sufficient in terms of applications in engineering practice since deformations for steel structures are usually relatively small.

In exceptional cases, it may be necessary to perform precise geometric nonlinear calculations. This is always the case when large or even very large deformations occur.

## Advanced Nonlinear Simulations and Structural Design in CivilFEM 2017

For the calculation of the static system a linear elastic material behaviour is assumed with which the internal forces and moments as well as the corre- sponding stresses are determined. Using these stresses, the verification can be executed. With this procedure, the bearing capacity can be increased until reaching the first plastic hinge.

This linearisation is also used for the determination of critical loads eigenvalues. Some also apply for plates and the FE analysis of cross sections. In the Chapters 10 and 11, other terms and assumptions are added relating to these topics. Moreover, all global deformations and loads at the nodes relate to this COS. For reasons of clarity, the subscript k has been neglected for these values in Figure 1.

The deformations in the global COS are marked by an overbar horizontal line above the variable. This designation will also be used for vectors and matrices if they apply to the global COS. The axes y and z are the principal axes of the cross section. According to Figure 1. For warping torsion a standardised warping ordinate 03 is used.

With the sign definition II, the direc- tions of actions at both beam intersections are in compliance with the ones in Figure 1. In Figure 1. For that reason, geometric correlations may be linearised. The longitudinal displacement u s refers to the centre of gravity S and the displacements v M and w M describe the displacement of the shear centre M. The second and the third components result from the bending moments and describe the displace- ments as a consequence of cross section rotations cp y and cp z. Here Formula 1. According to [25], the following relations are valid for the linear beam theory.

For the displace- ments, Formulas 1. It must be pointed out that the axial force and the bending moments act at the centre of gravity, while shear forces, the torsional moments as well as the warping bimoment are re- lated to the shear centre - see Figure 1. For the applica- tion additional information is given in the standards e.

DIN [8], EC 3 [10]. In this context, the bearing capacity of a structure characterises the ability of the car- rying members to resist all loadings which may occur during the erection work and the service life. The ultimate limit state describes a load situation of the structure where a violation of the limit would lead to a calculative collapse or a comparable failure, for example a rupture or a loss of stability and stable equilibrium, respec- tively.

The demands on the ultimate limit state are related to the safety of people and the safety of the building including its equipment and facilities.

In general, the states which may have to be observed cover the loss of the position stability lifting, over- turning, buoying upwards , the failure of the structure or its members including the foundation rupture, changeover in a kinematic chain, loss of stability and the failure due to fatigue influences on the material and other time-related effects.

With regard to steel structures, the ultimate limit state to be verified depends on the verification method see Table 1. The demands on the serviceability are related to the function of the building, the safety of people and the structural appearance.

It has to be verified that the design value of stress at the serviceability limit state does not exceed the design value of a serviceability criterion e. Limit states for the serviceability are not specified in DIN and they are usually arranged and agreed on individually if they are not specified in other basic or engineering standards. Design loads and resistances The safety concepts of the German and European standards are very similar. Both use so-called partial safety factors y F and y M for the determination of the design loads and resistances. The factor y F considers a possible unfavourable deviation of the load in terms of the statistical spatiotemporal spread and, in addition, possible insecurities in the mechanical and stochastic model.

## Rolf Kindmann, Matthias Kraus Steel Structures Design using FEM - PDF

The factor y M includes the spread of the particular resistance value and also covers inaccuracies in the mechanical model related to the calculation of the resistances. The design value of the resistance parameters M d is calculated by dividing the char- acteristic value of the resistance M k e. It should be mentioned that additional rules are specified in the standards concerning the reduction of stress due to parts of the permanent loads.

In contrast to Formulas 1. If the stability of members is not decisive, the factor y M may be taken as 1. In doing so, the main focus is set to the ultimate limit state. Due to the significance of this state as the basis of a safe design, as mentioned previously, it is the main focus of this book. The distributed load is considered to consist of two components, one due to the dead load and one component including the snow loads, as shown in the figure.

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The mid support plays a key role for the verification of the bearing capacity since here the internal forces and moments are at maximum see Figure 1. Using the internal forces and moments, maximum stresses can be calculated, leading to the following verifications: V Using the Elastic-Plastic procedure, the internal forces and moments are calculated according to the elastic theory - see Figure 1.

For the verification of a sufficient load-bearing capacity the interaction conditions e. DIN or the partial internal forces method can now be applied see Chapter 8. The use of the interaction conditions according to DIN requires knowledge of the internal forces and moments at the perfectly plastic state. However, after the bearing capacity is reached at that position, a plastic hinge will develop and the system will still be able to carry additional loads since it will not be kinematic at that load stage.

It now has to be checked whether the arising internal forces and moments within the beam span can be carried by the cross section.