Sensitivity analysis of steel plane frames with initial imperfections

2011 ◽  
Vol 33 (8) ◽  
pp. 2342-2349 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Initial Imperfections ◽  
Plane Frames

scholarly journals GEOMETRICALLY NON-LINEAR FINITE ELEMENT RELIABILITY ANALYSIS OF STEEL PLANE FRAMES WITH INITIAL IMPERFECTIONS / PLIENINIŲ RĖMŲ SU DEFEKTAIS GEOMETRIŠKAI NETIESINĖ BAIGTINIŲ ELEMENTŲ PATIKIMUMO ANALIZĖ

2012 ◽  
Vol 18 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Statistical Analysis ◽  
Carrying Capacity ◽  
Sampling Method ◽  
Latin Hypercube Sampling ◽  
Load Carrying Capacity ◽  
Initial Imperfections ◽  
Load Carrying ◽  
Eurocode 3 ◽  
Non Linear ◽  
Plane Frames

The random load carrying capacity of steel plane frames with bracing stiffness is studied. The load carrying capacity is evaluated using the geometrically non-linear FEM analysis. The incremental stiffness matrix of a slightly curved element utilized in the non-linear incremental analysis is listed. Initial imperfections are considered as random variables. Statistical analysis and Sobol sensitivity analysis are performed using the Latin Hypercube Sampling method. The effect of initial random imperfections on the load carrying capacity is studied, whilst assuming constant slenderness of the columns. The evaluation parameters are the pair of non-random values of elastic bracing stiffness, and system length of the columns. The paper illustrates that the load carrying capacity is very sensitive to initial crookedness of the columns in the event that the non-sway (symmetric) and sway (anti-symmetric) buckling modes coincide. In this case, the design load carrying capacity obtained from statistical analysis according to the EN 1990 (2002) standard is relatively very small (of low safety). Results show that the reliability of design of a steel frame according to EUROCODE 3 (1993) is significantly misaligned. The significance of the first and the second buckling forces as indicators of sensitivity of the load carrying capacity to the imperfections is discussed. Santrauka Tiriama plieninio plokščio rėmo su standžiaisiais ryšiais laikomoji galia. Ji vertinama atliekant geometriškai netiesinę BEM analizę. Aptariama šiek tiek išlinkusio elemento laipsniškai didėjanti standumo matrica, atliekant netiesinį iteracinį skaičiavimą. Atsitiktiniu dydžiu laikomas pradinis defektas. Statistinė ir Sobolio (Sobol) jautrumo analizė atliekama pritaikant LHS metodą (Latin Hypercube Sampling Method). Nagrinėjamas pradinio atsitiktinio defekto poveikis laikomajai galiai darant prielaidą, kad pastovus dydis yra liauna kolona. Vertinimo kriterijus yra ne atsitiktinių didžių pora, t. y. tampriai standus ryšiai ir konstrukcijos kolonų aukštis. Straipsnyje aptariama kolonos pradinio kreivio įtaka laikomajai galiai, atsižvelgiant į klupumo formas, kai nelinksta (simetrinė apkrova) ir linksta (nesimetrinė apkrova). Laikomosios galios projektavimo apkrovos, šiuo atveju gautos iš statistinės analizės pagal EN 1990 (2002) standartą, yra palyginti nedidelės. Gauti rezultatai rodo, kad plieninio rėmo patikimumas pagal Eurocode 3 (1993) labai nesutampa. Nagrinėjama defektų įtaka laikomajai galiai atsižvelgiant į pirmą ir antrą klupimo jėgą.

Nonlinear analysis of steel plane frames with initial imperfections

1986 ◽  
Vol 23 (4) ◽  
pp. 553-557 ◽  
Author(s):  
T.Y. Kam ◽  
F.S. Lee
Keyword(s):  
Nonlinear Analysis ◽  
Initial Imperfections ◽  
Plane Frames

scholarly journals Sensitivity analysis for a problem of optimal structure design

1994 ◽  
Vol 16 (1) ◽  
pp. 36-42
Author(s):  
Ngo Huong Nhu
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Finite Element ◽  
Structure Design ◽  
Optimal Structure ◽  
Effective Algorithm ◽  
The Finite Element Method ◽  
Plane Frames ◽  
Sensitivity Vector

On the basis of theory of structure sensitivity analysis, the gradient – projection method and the finite element method, a detailed and effective algorithm of determination of the sensitivity-vector for the optimal structure design problem is proposed. Numerical results illustrating the program corresponding to this algorithm have been given for some plane frames.

scholarly journals SENSITIVITY ANALYSIS OF THE EFFECT OF INITIAL IMPERFECTIONS ON THE (I) ULTIMATE LOAD AND (II) FATIGUE BEHAVIOUR OF STEEL PLATE GIRDERS

2005 ◽  
Vol 11 (2) ◽  
pp. 99-107 ◽  
Author(s):  
Zdenek Kala ◽  
Jirí Kala ◽  
Miroslav Škaloud ◽  
Bretislav Teplý
Keyword(s):  
Sensitivity Analysis ◽  
Stress State ◽  
Theoretical Investigation ◽  
Carrying Capacity ◽  
Ultimate Load ◽  
The Other ◽  
Load Carrying Capacity ◽  
Initial Imperfections ◽  
Load Carrying ◽  
Plate Girder

The study is divided into two parts: (i) in the first one, the plate girder (Fig 1) is considered to be exposed to quasi‐constant loading (ie to loads which are either constant or repeated in a very small number of cycles), while (ii) in the other one, the girder is assumed to be subjected to repeated loading. Then it is understandable that the objective of the first part should be to look into the influence of initial imperfections on the static ultimate load of the girder related to the formation of a plastic failure mechanism in it, while that of the second part was to study the effect of imperfections on the stress state under considerably lesser loads, viz under such as to correspond to the development of fatigue cracks in the girder and, consequently, to its fatigue limit state. In this case the state of stress was measured by bending stresses developing in the crack‐prone areas (Fig 4) of the web “breathing” under the repeated loads, which ‐as demonstrated by the Prague experiments ‐ occur at the toes of the fillet welds connecting the “breathing” web with the girder flanges and stiffeners. In both parts, the results of the theoretical investigation were compared with the conclusions of numerous tests carried out at the Institute of Theoretical and Applied Mechanics in Prague. The correlation was found to be very good; for example, the experimental load‐carrying capacity of the girders tested in Prague was close to the mean value of the corresponding theoretical solutions performed for the same girders. Thereby the analytical model applied in the theoretical investigation can be regarded as verified. The theoretical analysis was based on a non‐linear variant of the finite element method, the girder being modelled by means of shell elements and the ANSYS program being applied. All input imperfections were considered to be random quantities. The statistical distributions were introduced according to both experimentally obtained results and data given in literature. Random realisations of input random quantities were simulated by the LHS (Latin Hypercube Sampling) method. By way of sensitivity analysis it was studied to what extend the variability of initial imperfections was reflected in the variability of stresses in the crack‐prone areas of the girder. The main conclusion can be formulated as follows: While the effect of (and sensitivity to) the initial out‐of‐flatness of the girder web, in the case studied of a plate girder whose web is subjected to predominant shear, on the static load‐carrying capacity is (see the results of the first part of the study) very small (only a few p.c), the same effect on the stress state occurring in the crack‐prone areas of the “breathing” web under service loads can be (see the other part of the study) very important. This is also one of the main explanations of the large scatter of the results of the fatigue tests conducted in Prague.

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