Elastic Analysis of Slab Structures

1. Introduction.- 1.1 Aim of the book.- 1.2 State of the art. Main research trends.- 1.2.1 Theoretical approaches of plates.- 1.2.2 Classical approaches to flat slabs with capitals.- 1.2.3 Modern approaches to flat slabs without capitals.- 1.2.4 Early studies on surface couples. The effective plate width.- 1.2.5 Early approaches to the elastic analysis of slab structures.- 1.3 Scope of the book.- 2. New mathematical models for the deflected middle surface of plates.- 2.1 Preliminarics.- 2.1.1 Basic assumptions.- 2.1.2 General computation formulae.- 2.1.3 Characteristics of the categories of plates investigated.- 2.1.4 Characteristics of the types of design loads.- 2.2 Equations of the middle surface of plates deflected by loads of type P, M and q.- 2.2.1 The infinitely long plate.- 2.2.1.1 The locally distributed load P.- 2.2.1.2 The surface couple of vector $$overrightarrow M left| {Oy} right.$$.- 2.2.1.3 The surface couple of vector $$overrightarrow M left| {Ox} right.$$.- 2.2.1.4 The uniformly distributed load q.- 2.2.2 The rectangular plate with two parallel free edges.- 2.2.2.1 The locally distributed load P.- 2.2.2.2 The surface couple of vector $$overrightarrow M left| {Oy} right.$$.- 2.2.2.3 The surface couple of vector $$overrightarrow M left| {Ox} right.$$.- 2.2.2.4 The uniformly distributed load q.- 2.2.3 The rectangular plate simply supported along the entire boundary.- 2.2.3.1 The locally distributed load P.- 2.2.3.2 The surface couple of vector $$overrightarrow M left| {Oy} right.$$.- 2.2.3.3 The surface couple of vector $$overrightarrow M left| {Ox} right.$$.- 2.2.3.4 The uniformly distributed load q.- 2.3 Algorithms for computing elastic displacements, sectional stresses and boundary reactions.- 2.3.1 Systematization of numerical computations.- 2.3.2 Expressions for dimensionless coefficients.- 2.3.2.1 The infinitely long plate.- 2.3.2.2 The rectangular plate with two parallel free edges.- 2.3.2.3 The rectangular plate simply supported along the entire boundary.- 3. Behaviour of plates subjected to a surface couple.- 3.1 Aim of the numerical study. Computation parameters and grid.- 3.2 Factors influencing the magnitude and distribution of elastic displacements of plates subjected to a surface couple.- 3.2.1 Magnitude and distribution of elastic displacements along the plate width.- 3.2.2 Magnitude and distribution of elastic displacements along the plate length.- 3.3 Factors influencing the magnitude and distribution of stresses in plates subjected to a surface couple.- 3.3.1 Magnitude and distribution of bending moments along the plate width.- 3.3.2 Magnitude and distribution of bending moments along the plate length.- 3.3.3 Magnitude and distribution of torsional moments.- 3.3.4 Influence of Poisson's ratio on the values of bending and torsional moments.- 3.4 Accuracy of numerical computations.- 3.4.1 Influence of the number of summed terms in the series on the accuracy of numerical computations.- 3.4.2 Checking the accuracy of computations by use of the reciprocity theorem of unit displacements in the case of plates.- 3.4.3 Checking the accuracy of computations by reference to the results obtained by other authors.- 4. Elastic plates as structural members.- 4.1 Slab structures subjected to transverse loads. Effect of M- and P-type loads.- 4.1.1 Symmetrical and antisymmetrical sets of surface couples M.- 4.1.1.1 The infinitely long plate.- 4.1.1.2 The square plate.- 4.1 2 Symmetrical and antisymmetrical sets of locally distributed forces P.- 4.1.2.1 The infinitely long plate.- 4.1.2.2 The square plate.- 4.1.3 Associated loads of type M and P applied on partially symmetrical or unsymmetrical slab structures.- 4.1.3.1 Unsymmetrical sets of couples M and of locally distributed forces P.- 4.1.3.2 Sets of couples vM and forces vP of different value and sign.- 4.2 Slab structures subjected to lateral loads. Evaluation of the effective slab width.- 4.2.1 The effective width of the plate subjected to only one surface couple M.- 4.2.1.1 Definition. Calculation procedure.- 4.2.1.2 Comparative values of the effective plate width.- 4.2.2 The effective width of the plate subjected to sets of surface couples M associated in a simple row.- 5. A new method for the elastic analysis of slab structures.- 5.1 Use of the general force method. Transverse and in-plane loads.- 5.1.1 General scheme.- 5.1.1.1 Basic systems and condition equations.- 5.1.1.2 Calculation of the elements included in the matrices d and D in the general case.- 5.1.1.3 Systematization recommended in the case of associated unknowns.- 5.1.1.4 Expressions for the elastic displacements and stresses in the initial statically indeterminate slab structure.- 5.1.2 Influence of the relative slab-column stiffness on the value of displacements and stresses in slabs and columns.- 5.1.2.1 Transverse loads.- 5.1.2.2 In-plane loads.- 5.1.3 Effect of failure of supports on slab structures.- 5.2 Use of the general displacement method. In-plane loads.- 5.2.1 Basic scheme.- 5.2.2 Use of the design procedure in the analysis of symmetrical multistoried slab structures.- 6. Introduction to the dynamic analysis of slab structures.- 6.1 Calculation elements for the dynamic analysis of slab structures.- 6.1.1 Elements for the study of free vibrations.- 6.1.2 Elements for the study of forced vibrations.- 6.2 Behaviour of slab structures subjected to dynamic action. Comparative numerical studies.- 6.2.1 Determination of natural circular frequencies.- 6.2.2 Dynamic deflected shape and stresses induced by disturbing forces.- 6.2.3 Comparative dynamic analysis of a multistoried slab structure.- Conclusions.- Reference.- Author index.