One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

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On generalized Cosserat-type theories of plates and shells: a short review and bibliography

The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comite Euro-International du Beton (or Comite Euro- International du Beton—Federation internationale de la precontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50-77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46-56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II. DOI: 10.1061/(ASCE)ST.1943-541X .0000487. © 2012 American Society of Civil Engineers. CE Database subject headings: Creep; Shrinkage; Box girders; Serviceability; Deflection; Span bridges. Author keywords: Prestressed box girder; Bridges; Segmental erection; Shear lag; Design standards; Concrete; Relaxation.

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Excessive Long-Time Deflections of Prestressed Box Girders. I: Record-Span Bridge in Palau and Other Paradigms

The present paper is devoted to a state-of-the-art review on the computational treatment of laminated composite and sandwich panels. Over two hundred texts have been included in the survey with the focus put on theoretical models for multilayered plates and shells, and FEM implementation of various computational concepts. As a result of the review, one could notice a lack of a single numerical model capable for a universal representation of all layered composite and sandwich panels. Usually, with the increase of the range of rotations considered in the particular model, one can observe the decrease of the degree of complexity of the through-the-thickness representation of deformation profiles.

https://www.degruyter.com/downloadpdf/j/eng.2011.1.issue-1/s13531-011-0005-x/s13531-011-0005-x.xml

A literature review on computational models for laminated composite and sandwich panels

W artykule przedstawiono przegląd modeli obliczeniowych stosowanych w analizie laminowanych powlok kompozytowych i sandwiczowych. W przeglądzie uwzgledniono ponad 200 pozycji literatury traktujących o modelach teoretycznych dla plyt i powlok wielo-warstowych oraz/lub o implementacjach numerycznych roznych modeli obliczeniowych. Jako podstawową konkluzje z dokonanego przeglądu, nalezy uznac, ze nie istnieje jeden uniwersalny model matematyczny zdolny do efektywnego reprezentowania ogolu konstrukcji warstwowych. Praktyczna przydatnośc roznych sformulowan teoretycznych zalezy istotnie od specyfiki analizowanego problemu. Przy oczywistych ograniczeniach zdolności obliczeniowych, glownie natury sprzetowej i ekonomicznej, calkiem naturalnym zjawiskiem jest zauwazalna tendencja do zmniejszania rzedu dokladności opisu deformacji profilu poprzecznego wraz ze wzrostem stopnia nieliniowości analizowanych zagadnien.

As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder’s formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Bazant’s exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation.

Excessive Long-Time Deflections of Prestressed Box Girders. II: Numerical Analysis and Lessons Learned

METHODS FOR THE ANALYSIS OF SHEAR LAG IN WIDE FLANGES ARE REVIEWED AND A TREATMENT IS PRESENTED WHICH INCORPORATES THE EFFECT OF THE WEB UPON THE STRESS DISTRIBUTION IN THE STIFFENED FLANGE OF A BOX GIRDER BY REPLACING THE WEB WITH AN EDGE STIFFENER ON THE FLANGE. ATTENTION IS DRAWN TO THE EFFECT OF SEVERE SHEAR LAG IN THE CURVATURE AND DISPLACED SHAPE OF A CANTILEVERED BOX GIRDER. A SERIES OF TESTS ON MODEL GIRDERS IS DESCRIBED AND THE RESULTS ARE COMPARED WITH AN APPROXIMATE "STIFFENER-SHEET" ANALYSIS, A MORE RIGOROUS ORTHOTROPIC PLATE ANALYSIS, AND A PLANE STRESS FINITE ELEMENT ANALYSIS; THE LATTER IS USED TO ANALYSE FLANGES UNDER MORE COMPLEX CONDITIONS. A THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS CONFIRMED THE OBSERVED CURVATURES AT THE SECTION OF HIGH SHEAR LAG. /ASCE/

Shear Lag in Stiffened Box Girders

An examination is made of the stability of a cylindrical air-supported membrane supporting a central line load and subject to ponding by a fluid in the hollow so caused. A critical value of the central load is shown to exist and its value is obtained by a numerical analysis. Results from the analysis indicate that low profile air-supported structures should be less liable to failure by this mode of collapse than inflatables with a semi-circular profile. However, under normal operating pressures even the latter require loads of the order of 400 N/m (27 lb/ft) in the presence of water to cause collapse of structures with a span of 50 m. Nevertheless designs should be examined carefully in view of possiblee pressure reductions coinciding with internal or external roof loadings.

Collapse by Ponding of Air-Supported Membranes

The nonlinear deformation of sandwich shells with a weak core and similar membrane facings is investigated by means of a variable director field. Using previously obtained equilibrium equations, a virtual work principle for such sandwich shells is derived and suitable stain measures defined which are analogous to those of Cosserat surface theory. Compatibility equations between these strain measures are derived and compared, where possible, with corresponding equations of classical nonlinear shell and linear Cosserat surface theories.

Nonlinear Sandwich Shell and Cosserat Surface Theory

A theory is presented to predict the critical central weight which, in the presence a ponding medium, will lead to collapse of an inextensible air supported spherical membrane. Results are developed for a range of radii, pressures and ponding medium densities. Also explored is the manner in which these results will be effected by meridional action only, such as would be caused by a system of cables converging at the apex. A description is given of a series of tests carried out on two laboratory models to confirm the theoretical results. The experimental results indicate that the theory may lead to under design and that this instability is particularly sensitive to surface irregularities near the apex.

Collapse by Ponding of Air-Supported Spherical Caps

The equations of equilibrium for a deformed element of a sandwich shell with a weak cord and similar membrane facings are derived and compared with corresponding equations for a Cosserat surface. The two sets of equations are identical in form which permits a physical interpretation of those concepts which are special to a Cosserat surface theory. Upon specialization, the equations derived are shown to be in agreement with previous results for sandwich shells.

David J. Malcolm

Papers

Shear Lag in Stiffened Box Girders

Collapse by Ponding of Air-Supported Membranes

Nonlinear Sandwich Shell and Cosserat Surface Theory

Collapse by Ponding of Air-Supported Spherical Caps

Cosserat Surface and Sandwich Shell Equilibrium