Design methodology

In the typical roofs of steel industrial type buildings cold-formed purlins, as secondary structures, are used to support the load-bearing elements of the cladding system. The main characteristics of the behaviour of the typically used C-, Z- or ∑-sections are coming from the coupled plate and distortional buckling and lateral torsional global buckling modes. These phenomena are highly influenced by the structural arrangements of the purlin and cladding system [44]. The lateral and torsional supporting effect of the cladding to the purlin is influenced by several structural parameters what can be hardly considered without experimental studies.

In the existing design codes the application rules use semi-empirical formulations with significant simplifications. It is proved that the purlin design method of Eurocode 3 [60] is conservative and benefits can be gained by improving the analysis model [56].

5.4.1. Design method based on beam model

The design method proposed by the Eurocode 3 is built in the PurlinFED program. The internal force distribution is calculated on a self-developed beam model. The rotational restraint of the cladding system is taken into account by the application of the Eurocode 3 procedure [60].

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The more sophisticated design method – use the research results of the dissertation – is under development. The determined inertia factors in the overlap zone by the overlap tests (Chapter 3.5.4) to be implemented in the internal force calculation of the beam model. This modification takes into account the real distribution of the internal forces. The design of the end of overlap and end support resistances are based on the proposed design methods in Chapter 3.6.

Figure 93. FE model details of the floating roof 5.4.2. Design method based on shell finite element buckling modes

In this case the same procedure is used as detailed previously, except that the calculation of rotational effect of the cladding system is based on the shell FE model. The full model of the roof systems takes into consideration the real rotational rigidity of the cladding system. The slenderness of lateral torsional buckling can be determined by instability analysis of the shell FE model. The automatic buckling mode classifications – detailed in Chapter 2.4 – help to choose the pure lateral torsional buckling mode. The reduction factor for stability checking is calculated from the numerically determined slenderness.

Overlap Bridge Bridge feet

Spring element at the end of anti-sag bar

Purlins

Support

Anti-sag bar

Seam

5.4.3. Design method based on nonlinear simulation on imperfect model

The most complex design method is the nonlinear simulation of imperfect shell finite element models. In the Eurocode 3

application of shell finite elements, the size of the equiva material models and other details of the modeling

case the nominal yield stress has to be applied and the ultimate load can be directly compared to the design loads. The proble

that there is no equivalent geometrical imperfection is specified, experimentally verified imperfection sensitivity analysis is needed what is presented in

same cases.

To illustrate the applicability of the proposed algorithm qualitatively to the ultimate b

scale experimental program [47]

here, only two failure modes are illustrated by In the nonlinear analyses four

first failure is the upper flange elastic distortional buckling. This mode occurs if the upper flange is slender due to the high lip or flange width to thickness ratio, or to the long lateral supporting distance (1200 mm)

If the upper flange is supported laterally in smaller distances (600 mm) but slender enough to initiate the buckling, plastic distortional buckling occur, as in case of structural arrangement, Figure 94b.

If both the upper flange suppo

distortional buckling cannot be occurred. In this case the phenomenon is plastic failure with high horizontal displacement of the lower flange, as it can be seen in

The local failure mode is the web buckling at the end of the overlap near to the middle support. If the length of the overlap is relatively small (300 mm), the shear becomes dominant.

The experienced failures of the full

qualitative comparison of the results it can be concluded that the full FE model of the roof system built up by PurlinFED is can follow the behaviour of a full

Figure 94. Simulated failure modes

flange distortional buckling with plastic defomations tension stress

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Design method based on nonlinear simulation on imperfect model

ost complex design method is the nonlinear simulation of imperfect shell finite Eurocode 3 [61], design methods can be found, which details the application of shell finite elements, the size of the equivalent geometrical imperfections, the material models and other details of the modeling for welded and hot-rolled

case the nominal yield stress has to be applied and the ultimate load can be directly compared The problem of the Eurocode 3 1-3 standard for cold

that there is no equivalent geometrical imperfection is specified, experimentally verified imperfection sensitivity analysis is needed what is presented in the previous chapters for the To illustrate the applicability of the proposed algorithm, the results are compared ultimate behaviour of a special purlin-cladding system studied by a full

[47]. The details of the experimental research are not presented here, only two failure modes are illustrated by photos and the FE model.

In the nonlinear analyses four failures types occur, as they are presented in

s the upper flange elastic distortional buckling. This mode occurs if the upper flange is slender due to the high lip or flange width to thickness ratio, or to the long lateral supporting distance (1200 mm) Figure 94a.

pper flange is supported laterally in smaller distances (600 mm) but slender enough to initiate the buckling, plastic distortional buckling occur, as in case of structural If both the upper flange supporting is efficient and the flange slenderness is small, the distortional buckling cannot be occurred. In this case the phenomenon is plastic failure with high horizontal displacement of the lower flange, as it can be seen in Figure 94

The local failure mode is the web buckling at the end of the overlap near to the middle support. If the length of the overlap is relatively small (300 mm), the shear becomes dominant.

failures of the full-scale tests are presented in Figure 95

qualitative comparison of the results it can be concluded that the full FE model of the roof system built up by PurlinFED is can follow the behaviour of a full-scale experimental test.

ailure modes: (a) upper flange distortional buckling

flange distortional buckling with plastic defomations, (c) lower flange deformation with high tension stress, (d) web buckling at the end of overlap

ost complex design method is the nonlinear simulation of imperfect shell finite , design methods can be found, which details the lent geometrical imperfections, the rolled sections. In this case the nominal yield stress has to be applied and the ultimate load can be directly compared for cold-formed sections is that there is no equivalent geometrical imperfection is specified, experimentally verified the previous chapters for the results are compared cladding system studied by a full-f the experimental research are not presented types occur, as they are presented in Figure 94. The s the upper flange elastic distortional buckling. This mode occurs if the upper flange is slender due to the high lip or flange width to thickness ratio, or to the long lateral pper flange is supported laterally in smaller distances (600 mm) but slender enough to initiate the buckling, plastic distortional buckling occur, as in case of structural rting is efficient and the flange slenderness is small, the distortional buckling cannot be occurred. In this case the phenomenon is plastic failure with

Figure 94c.

The local failure mode is the web buckling at the end of the overlap near to the middle support. If the length of the overlap is relatively small (300 mm), the shear becomes dominant.

Figure 95. By the qualitative comparison of the results it can be concluded that the full FE model of the roof

scale experimental test.

a) upper flange distortional buckling, (b) upper c) lower flange deformation with high

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Figure 95. Observed failure modes: (a) elastic distortional buckling and (b) plastic distortional buckling