THE COMPARISON OF THE SIMPLE AND DETAILED APPROACH TO THE STRESS ANALYSIS OF THE STEEL BEAM SUPPORT

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1 XXI RUSSIAN - SLOVAK - РОLISH SEMINAR, MOSCOW - ARKHANGELSK ТHEORETICAL FOUNDATION OF CIVIL ENGINEERING MOSCOW STATE UNIVERSITY OF CIVIL ENGINEERING INSTITUTE OF CIVIL ENGINEERING AND ARCHITECTURE, NORTHERN FEDERAL UNIVERSITY FACULTY OF CIVIL ENGINEERING, UNIVERSITY OF ŽILINA FACULTY OF CIVIL ENGINEERING, WROCLAW UNIVERSITY OF TECHNOLOGY FACULTY OF CIVIL ENGINEERING, WARSAW UNIVERSITY OF TECHNOLOGY THE COMPARISON OF THE SIMPLE AND DETAILED APPROACH TO THE STRESS ANALYSIS OF THE STEEL BEAM SUPPORT Ján KORTIŠ *, Juraj KOŇÁR ** 1. Introduction The right design of details influences the durability and serviceability of structures. However, engineers have only limited tools for right analysis of them. One of them is an expensive and complicated software which uses the theory of finite element method. Applying of this requires powerful computers and well-experienced engineers. In addition this analysis takes a lot of time and usually has to be combined with some experiments on the model or on the real construction which confirm the result of the numerical analysis. This could be done effectively only for details, which are used for prefabricated structures, where the expensive development of the elements will be paid by manufacturing and selling amount of the elements. It is not profitable for design of non-usual types of structures. Applying of some approximated approaches is more effective in these cases. The article describes comparison of two approaches which were used to design the steel structure of the floor which is supported by concrete beams. The differences between the results which were obtained from both types of analysis shows that maximal value of the effective stress could be different.. Description of the analysed structure The additional part of the floor structure was designed to change the interior of the uilding. The floor structure is made of concrete but the additional part is made of steel. The first reason is the length of the span between the beams which support the steel beams of the * ) Ján Kortiš, Ing.PhD., Department of Structural Mechanics, Faculty of Civil Engineering, University of Žilina, Univerzitná 815/1, Žilina, Slovakia. **) Juraj Koňár, Ing., Department of Structural Mechanics, Faculty of Civil Engineering, University of Žilina, Univerzitná 815/1, Žilina, Slovakia.

2 additional part. The next reason why the steel beam was designed is that changes of the structure were requested after the construction of the floor was done. So the connection of the original floor structure and new concrete structure could not be done effectively. The designed floor structure consists of the beams 5.5 m long on which are layered trapezoidal metal sheets. The upper part of the floor is made as concrete deck on the steel sheets. Fig. 1. Longitudinal view on a half part of steel beam Obr. 1. Pozdĺžny pohľad na polovicu oceľového nosníka The steel beams are supported by concrete beams. The support consists of horizontal steel plate 4 mm thin which is welded to the vertical plates. These are welded to the edge of the beam. The upper horizontal plate is layered on the concrete beam. The gap between the surface of the vertical steel plate and concrete beam could have maximal value 0 mm. This gap was accepted during the analysis. Fig.. Longitudinal view on a half part of steel beam Obr.. Pozdĺžny pohľad na polovicu oceľového nosníka

3 . Comparison of two approaches Fig.. Detail of the support of the steel beam Obr.. Detail uloženia oceľového nosníka The steel sheets and concrete plate is not added to the analysis model because we wanted to analyse only the support of the beams. They are only the loading of the beams. The support of the floor structure was analysed because the simple approaches could not show the right distribution of internal forces. The first analysis was done by the simple approach where the boundary conditions of the steel beam are considered as simple supports and the plate which is layered on the concrete beam and connection plates between this plate and steel beam is described like beams with cross sections which are showed on the next figure. Fig. 4. Cross sections and half part of the beam model Obr. 4. Vybrané prierezy a polovičný model nosníka

4 The geometry of the beam model was used to determine the values of internal forces and these were used to verify the cross sections. The results of the verification and maximal value of the stress on all beams are described in the next formulas. The loading consists of the imposed loads and self weight of the floor structure. Computation of inner forces Intensity of the distributed line load is q11kn/m Vertical reaction in the support: R ql 11.,75& 0, kn z t Elastic verification - cross section "a" Cross section parameters: A( 8,4.10 m ; I 4,0.10 m ; W, m M,19.10 Rz 0,.10 σ 94,997MPa τ, 607MPa 6 W,58.10 A 8,4.10 ( Maximal stress on the beam with cross-section "a" σ σ + τ 94,997 +.,607 95,MPa Elastic verification - cross section "b" 6 4 Cross section parameters: A( 7, m ; I 9, m ; W 7, m M Rz, ,.10 σ ,89MPa W A 7, , τ ( Rz 0,.10, 88MPa A 7, ( Maximal stress on the beam with cross-section "b" σ σ + τ 45,89 +.,88 46,MPa Elastic verification - cross section "c" 6 4 Cross section parameters: A( 6, m ; I 9, m ; W 8, m M,5.10 Rz 0,.10 σ 4,77MPa τ 4, 997MPa W 8,04.10 A 6, ( Maximal stress on the beam with cross-section "c" σ σ + τ 4,77 +.4,997 44,6MPa 4. Numerical analyses of the beam support Adina software which uses the theory of finite element method was used to solve the spatial model. Eight nodes solid elements were chosen to generate the mesh of the model. We did not use a very powerful computer so we were not able to solve a model with a lot of elements. As a result the quality of the mesh was only refined in places where we wanted to know the results of stress analysis. The area of the contact between the steel plate and the concrete beam was refined too. The shape of the elements was modified to meet requests of the convergence. The zero displacements in vertical direction were prescribed on the bottom surface of the concrete beam because it was not modelled with full length. The boundary

5 conditions on the steel beam were prescribed in the centre of the span with the respect of symmetry. Two kinds of model were done to compare the results of the spatial models with the results of the simple beam model. The first one has the part of the concrete beam like a support and the next one is supported only on the line where are prescribed zero displacement. This line is placed on the horizontal steel plate with the same distance as the point support of the simple beam model is assumed. Fig. 5. The numerical model of the beam Obr. 5. Výpočtový model oceľového nosníka The highest value of effective stress is in the place where the horizontal steel plate is welded with vertical plate. However, this value is different and depends on the approach which is used. The lowest value is identified on the model where the horizontal steel plate is supported by the part of the concrete beam which was modelled like a cube with the same width and high like the cross section of the concrete beam. The highest value of the stress was identified in the same place when the horizontal steel plate was supported on the line which is in the same distance as is considered in the simple beam model. Fig. 6. The detail of the support of the steel beam Obr. 6. Detail uloženia oceľového nosníka

6 The next table shows the maximal values of the effective stress for both kinds of support. These values are compared with the values of stress obtained thanks simple beam model described previously. The values in the place where is the cross-section C on the beam model is not compared because the quality of the mesh in this area is low and the values of the stress is not crucial. Tab. 1. The maximal values of the effective stress Tab. 1. Maximálne hodnoty výslednice napätí Simple beam model [MPa] Model supported by the part of the concrete beam [MPa] Model supported on the line [MPa] Cross-section A 95, 5,5 198,40 Cross-section B 45,8 16,5 108,0 5. Conclusions Comparison of the results shows that the values of effective stress are different for beam model and spatial model. The values of effective stress on the model which is supported by part of the concrete beam are lower than the values on the simple model. However, the values of effective stress on the model which is supported only on the line are two times higher than for the simple beam model. This shows that the support of the spatial model influences significantly the quality of the results. The simple beam model seems like a good choice because the results are higher than the results of model supported by the part of the concrete beam which could be assume to have better results than the spatial model supported on the line. The support on the line is not good assumption for the spatial model. 6. Literature [1] Adina theory and reference quide, [] ELLIS H. DILL: The finite element method for mechanics of solids with ANSYS applications, CRC Press 011, ISBN POROVNANIE JEDNODUCHEJ A DETAILNEJ NAPATOSTNEJ ANALÝZY ULOŽENIA OCEĽOVÉHO NOSNÍKA Ján KORTIŠ, Juraj KOŇÁR Pri návrhu neštandardných detailov sa stretávame s problémom pri voľbe správneho výpočtového modelu. Vzhľadom na zjednodušenie celého výpočtu sa najčastejšie volí alternatíva zjednodušeného prútového modelu. Ten však nedokáže vystihnúť celkové správanie konštrukcie a preto bola spracovaná porovnávacia štúdia napätostnej analýzy v mieste uloženia oceľového nosníka na železobetónový trám. Z výsledkov vyplynulo, že jednoduché modely sú menej efektívne a nedokážu úplne presne vystihnúť správanie konštrukcie. Pri ich správnom využití však dostávame lepšie výsledky ako pri zle vytvorenom zložitom výpočtovom modeli a to najmä z pohľadu zadávania okrajových podmienok. V prípade ich zlej interpretácie môžeme dostať diametrálne odlišné hodnoty napätí.

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