Parametric study results

Optimization results are summarized in Table A-5. In the first and second columns, the dimensions of cross sections can be found for both column and beam elements, respectively, while the D/C column shows the demand-to-capacity ratio in ULS of persistent design situation related to the critical failure mode. βopt is the reliability index related to the optimum safety level that results minimum life cycle cost value (CLC in Fig. 2-1). C0 contains the cost of purlins, sheeting- and bracing system, as well. In order to take into account the whole frame’s cost in the calculation the outer frames have been considered with the following dimensions: 300-300x6+200x8 (columns) and 300-300x6+200x8 (beams).

First of all, general conclusions can be drawn related to data presented in Table A-5. Not surprisingly, in case of design situations where the considerable gravity load is high the resulted optimal solutions have thicker elements and they are more expensive because the seismic forces are higher (e.g. compare case #1 to #3 or case #4 to #6, etc.). Due to the increase in the level of

a) b) c)

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seismic forces, the resulted optimal reliability indices are lower because the strengthening of the structure becomes more expensive and it may become not economical.

It can be seen from the parameters of the fitted lognormal distributions (Table 5-1) that the seismic effect is characterized by high degree of uncertainty irrespectively to the seismicity of the investigated site. During the consideration of historical earthquakes in PSHA high uncertainty is partly coming from the evaluation of statistical data set containing from a number of sites. In case of low and moderate seismicity (e.g. Hungary) typically there is no dominant site in investigated set and large number of different sources influence the site’s hazard curve contrary to sites characterized by high seismicity where few sources may affect dominantly the uncertainty in the hazard curve. For this reason, significant difference may be realized between hazard curves of Komárom and Râmnicu Sărat; the hazard curve related to Komárom site is much more uncertain (Table 5-1) than the curve that characterizes the seismicity of Râmnicu Sărat. This uncertainty highly influences the results of reliability analysis. It might be surprising and interesting for the reader that a certain configuration is characterized by similar reliability indices for the both sites (only slight differences can be observed). The 90^th percentiles are very close to each other, nonetheless, the mean of PGA distributions are significantly different.

Contrary to the optimized solutions for fire effects, the results (Table A-5) of seismic design optimization show that the D/C ratio in persistent design situation is very low by a number of cases.

It shows that seismic design situation may be the leading design situation when the seismic mass or/and the target reliability index is high regardless to the moderate seismicity of the site. Regarding to cross section dimensions, strong conclusions cannot be drawn compared to the original structural configuration; both stockier but smaller and thinner but higher sections may be appropriate in order to find optimal configurations.

According to the opinion of many designers, sheeting system decreases the structure’s safety because its stiffness increases the global structural stiffness; therefor it increases the seismic forces acting on the building. Nevertheless, based on the results of this study sheeting system has beneficial effect on the structural safety and the cost of resulted configurations by the industrial frames with similar function, size and configuration to the investigated frame. This statement is confirmed (Table A-5, Fig. 7-11) for high and moderate seismicity, for low and high vertical forces, as well. The tendency is clear in the results; the same structural safety can be achieved beside 0-15% less superstructure’s cost with the consideration of sheeting system in the structural analysis

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depending on the consequence class, on the severity of seismic action and on the intensity of vertical loading; the saving is higher in case of higher intensity of horizontal actions. It is important to note that sheeting system has to be designed and checked against seismic effects in order to ensure its contribution to the global behaviour during the earthquake.

Fig. 7-11 – The cost of the superstructure and the resulted reliability indices for high seismicity,

In fact, the contribution of sheeting system decreases the vibration period of the building thus it increases the base shear force (as the results of HighPerFrame RDI project showed) (Table 7-5).

It seems that the contribution of sheeting system is not beneficial and it may decrease the structural safety through increasing the seismic load on the building. Nonetheless, different beneficial effects may be developed during seismic excitation due to the sheeting system. These beneficial effects decrease the level of internal forces in the main elements; resulting cheaper and safer solutions.

Considered sheeting LTP45+Z200 LTP20+Z200 none

Transversal period 0,5932 s 0,6371 s 0,7462 s

Longitudinal period 0,2912 s 0,3102 s 0,3660 s

Design acceleration in transversal direction 5,6407 m/s² 5,3119 m/s² 4,5356 m/s² Design acceleration in longitudinal direction 5,6407 m/s² 5,6407 m/s² 5,6407 m/s² Transversal base shear force 225,89 kN 212,72 kN 181,63 kN Longitudinal base shear force 225,89 kN 225,89 kN 225,89 kN Table 7-5 – The effect of sheeting system’s stiffness on the base shear force; case RLTP4502 for ~ 0.3g PGA [BT9]

According to previous results [79] [BT9] [BT12], the sheeting system decreases the value of internal forces in the main frame elements (Fig. 7-12) through developing a spatial contribution together with the wind and side braces. These parts compose a box-like structure; a part of the horizontal forces is transferred to the ground through the braces at the end of structure similarly to a simple supported beam (Fig. 7-13). Furthermore, it helps a global response being developed where adjacent frames help to each other in resisting the seismic forces. Another advantage is that the sheeting behaves as a chord of main frame elements thus it increases their bending stiffness and it contributes in resisting the bending moments. As the results of the example in [BT9] showed the bending moments in the structure may be decreased by cca. 5-25% (Fig. 7-12).

40 60 80 100

2 2,5 3 3,5

C0+ C1[1000€]

β

without sheeting with sheeting

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Fig. 7-12 – Bending moment diagram of the main frames after SRSS sum (0.3g PGA; continuous blue – outer frames, continuous red – inner frames, dashed blue – second and fifth frames): a) LTP45+Z200; b) no sheeting system is

considered [BT9]

Fig. 7-13 – Base shear forces [N] of the frames after SRSS sum (0.3g PGA): a) LTP45+Z200; b) no sheeting system is considered [BT9]

In order to consider the contribution of sheeting system in the global behaviour, spatial 3D structural model need to be applied together with realistic modelling of the stiffness and the properties of connections of trapezoidal sheeting and purlins in the analysis. This model need to able to describe the internal forces and stresses in the main elements, in the braces and in the sheeting system as well. The beneficial effect of the sheeting system can be utilized only if the sheeting’s and connections’ failure is avoided. By many of the investigated cases the base shear forces are higher than possible resultant horizontal forces coming from wind actions. If the D/C ratio related to the failure of sheeting, purlins or connections is not significant due to wind forces,

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the contribution of sheeting system in seismic design situation may be utilized without additional costs.

Panels between frames that subjected to significantly different horizontal actions due to their different loading conditions may be designed against higher internal forces. In case of the investigated structure, panels that are subjected to high seismic forces are the second and the fourth panels. By longer industrial halls that consist of large number of frames the contribution of sheeting system may be lower because the braced bays are situated far from the middle and the panels are not capable to transfer the loads to the braces.

Based on the results of 28 optimized cases, a table with possible values for target reliability indices is presented in Table 7-6, similarly to Table 7-4 that shows possible target reliability indices for fire design. It can be seen that this table is in better agreement with the recommendations of JCSS and ISO 2394 than with EC0. The target values are also influenced by the acceptance ability of the society and global economy of the country.

50 years service life: calculated target reliability indices Seismic mass Seismic effect

severity

Minor consequences

Moderate

consequences Large consequences

High High 2.2* 2.5 – 2.7 2.8 – 3.0*

Moderate Medium 2.3* 2.6 – 2.8 2.8 – 3.0†*

Low Low 2.6* 2.8 – 3.0 3.0 – 3.5*

* based on limited number of cases, further investigation is necessary; † assumed value, there is problem with the convergence Table 7-6 – Calculated possible target reliability indices in seismic design situation for tapered portal frames with

storage function

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