Bo Edlund

Shear capacity of plate girders with trapezoidally corrugated webs

Abstract In this paper, the shear capacity of plate girders with trapezoidally corrugated webs is numerically studied using a non-linear finite element method. Effects of large deflections are taken into account and a perfectly elastic-plastic material model obeying a von Mises yield criterion is assumed. The following geometric parameters that influence the shear capacity of such girders are investigated: (1) the overall dimension of the web panel; (2) the web thickness; (3) the corrugation depth of the web; (4) the corrugation angle; and (5) the width of the plane sub-panel of the web. More specifically, the influence of these parameters both on the ultimate shear capacity and on the remaining shear capacity in the post-buckling range, as well as on the buckling modes, are reported. Based on the numerical results, empirical formulae that were proposed earlier for the prediction of the shear capacity are examined and suggestions for an optimal design of such girders in shear are given.

Ultimate strength of girders with trapezoidally corrugated webs under patch loading

This paper deals with the buckling and postbuckling behaviour of plate girders with corrugated web under a concentrated load on the top flange. A couple of design models and experiments from earlier studies are briefly reviewed. Further, six additional experimental tests have been performed on a girder with thin corrugated web. A FE-model of this girder is then developed and the behaviour of the girder is validated through comparisons with the girder used in the tests. The ultimate load and the postbuckling behaviour were determined by both laboratory tests and finite element simulations for three different positions of a narrow load strip across the flange, namely at: (1) an inclined fold, (2) the junction between two folds, (3) a longitudinal fold. Finally, a parametric study is performed using the FE-model where the influence of certain parameters on the ultimate load and buckling behaviour is investigated. The results from this parametric study are compared and evaluated together with two design models chosen to be the most suitable.

Nonlinear FE analysis of longitudinally stiffened girder webs under patch loading

Abstract The ultimate load behavior of longitudinally stiffened girder webs under patch loading is studied here by means of a nonlinear finite element analysis. Large-deflection effects and initial shape imperfections are taken into account. The influence of the slenderness of the directly loaded web panel on the patch loading capacity is studied in depth, together with the size of the loaded flange. In addition, the influence of stiffener rigidity is also analyzed. This study was aimed at finding an optimum position of longitudinal stiffeners for patch loading. Currently, designers use the value recommended for bending, i.e. one-fifth of girder depth. The results presented here show that a stiffener located closer than one-tenth of the girder depth significantly increases the load carrying capacity of the plate girder due to a decrease in the slenderness ratio of the web panel between the loaded flange and the longitudinal stiffener.

Failure mechanism of slender girder webs with a longitudinal stiffener under patch loading

The failure mechanism of slender girder webs stiffened by a single longitudinal stiffener under patch loading is addressed. Experimental results have shown that failure is due to crippling in the web panel formed between the loaded flange and the stiffener. This mechanism is similar to the one for unstiffened webs, which is characterized by the presence of elastoplastic deformations in the compression flange (plastic hinges) and in the web (yield lines). A longitudinal stiffener with normal position, b1<0.3hw, and rigidity restricts the size of the buckle in the upper web panel, and in some cases the distance between the outermost plastic hinges in the loaded flange is reduced. Based on the upper bound theorem of plastic collapse an expression for the patch loading resistance of webs stiffened by a single horizontal stiffener is presented. Theoretical predictions are in good agreement with experimental results.

Buckling analysis of trapezoidally corrugated panels using spline finite strip method

Abstract Buckling of trapezoidally corrugated panels under in-plane loading is analyzed by a spline finite strip method. The influence on the elastic buckling load of various parameters, such as geometry. loading forms and boundary conditions, etc., is studied. It is found that: (1) for longitudinal compression the buckling load increases with the corrugation angle α, and for a given α the highest buckling load is achieved when the ‘proportion parameter’ γ = 1 ; (2) for shear loading the buckling load increases as α increases, and for a given α the highest buckling load is obtained when γ = 2 ; and (3) for a combined loading of compression and shear, interactive curves can be approximated by unit circles when α = 15°, 30°, 45°, 60° and 90° . However, when α = 75° a parabola seems to be a better approximation. Based on the numerical experiments, simplified formulae and interactive curves are suggested for practical design.

I-shaped steel girders subjected to bending moment and travelling patch loading

Abstract In this paper results are presented from numerical simulations of a travelling patch load on the flange of I-shaped plate girders of three different dimensions. The FEM modelling aims at simulating the load case of bridge launching over multiple supports. The girders have typical bridge girder dimensions, and they were subjected to both patch loading and bending moment. Analyses were made at the load levels of approximately 48% and 67% of the ultimate load-carrying capacity due to patch loading and a constant applied bending moment. At the higher load level damage in the form of accumulating plastic deformation appeared in the girder models.

Computer simulation of the scatter in steel member strength

Abstract A Monte Carlo method for digital computer simulation of the strength of (steel) members and structures is presented and is applied to rolled steel beams and columns, and thin-walled cylinders. Input data are cumulative distribution functions (histograms) for the geometric and strength variables. The output (i.e. the scatter in structural strength) is printed as histograms and is statistically analysed. Each output histogram is compared with the Gaussian normal distribution. Using the nonparametric test of homogeneity a number of histograms may then be compared. The case studies presented deal with the plastic strength of steel beams and the maximum load of axially loaded steel columns and thin-walled cylinders. Mathematical models for beams subject to pure bending moment, moment and axial force, moment and shear, or uniform torsion are presented. For the initially straight, centrally loaded column a tangent modulus theory which considers residual stresses is used. The simulations have been carried out for one HEA beam, four HEB beams and three IPE beams. Comparison of the simulation results show that the scatter in load carrying capacity of the simulated beams and columns can be regarded as normally distributed, that the load carrying capacity of beams and columns of the same group (HEB or IPE) and beams and columns of the groups HEA and HEB have distributions which differ very little from each other, and that the scatter in simulated beam strength, and in simulated column strength for short and medium length columns, is much more affected by the variation in yield strength of the material than by the variation in cross sectional data. This conclusion holds for ordinary distributions in yield strength of structural carbon steel. Comparisons of simulation results and test results show good agreement for the beams. The agreement is not so good for the columns mainly because in the tangent modulus theory it is assumed that the columns are initially straight. For the cylinders excellent agreement was achieved. The experience gained with the simulation system presented here shows that a medium size computer can be economically used to simulate a relatively large number of plays.

FATIGUE CRACKING IN A STEEL RAILWAY BRIDGE

The railway between Lulea, Sweden, and Narvik, Norway, was completed in 1902, and renewed in the early 1960s. Several of its old riveted bridges were replaced by welded plate girder bridges. After only a few years, cracks appeared, then gradually spread in some of the plate girders. The cracks were arrested by drilling a hole at each crack tip. In the early 1990s, a bridge replacement programme began. Five similar bridges showed 100-200mm-long fatigue cracks at the ends of vertical stiffeners. They were constructed of two parallel, simply supported welded steel I-beams, with sleepers set directly on the top flange. One bridge was selected for detailed computer analysis. It has a span length of 11.6m, and its track lies on a horizontal curve with radius 600m. Its two main girders, 1900mm apart, are straight, 1000mm deep, and connected by cross framing approximately every 2.6m. The web plate of both girders is strengthened by a vertical stiffener at every cross frame. Preliminary analysis was made on the assumption that the cracks resulted from transverse bending of the web plate. A linear static analysis was performed, by modelling the bridge using a finite element analysis program. Four alternative bracing systems were also analysed. It was found that the simplest remedy was to attach the web stiffener to the flange.

Bridge Expansion Joints – Design for Movements, Performance and Durability

Expansion joints in medium-size and long bridges should be regarded as important bridge components.There is a trend to minimize the number of joints, and design each joint to permit large movements. It is therefore important to develop suitable joint types that function smoothly for such large movements during a long time without damages or malfunctioning. A widely used, modern joint type for large joint movements is the Modular Bridge Expansion Joint (MBEJ). The paper mainly deals with different aspects of MBEJs (function, fatigue, durability, maintenance, noise etc). Traffic forces on MBEJs as well as quality requirements and assessment are discussed.

Robustness and Resilience -- Two Key Concepts for a Sustainable Built Environment

The first item is Robustness of structures, which has drawn much attention during the past decade. In this paper special interest will be paid to accidental loading and extreme events like natural hazards. The part dealing with Resilience is related to Natural Hazards and Disasters and their influence on the built environment and society. One section deals with vulnerability and resilience of communities, especially in urbanized areas. The paper is of conceptual character and contains some critical review of some past work. It will show the importance of using relevant and clear concepts.