Elastic Analysis of Slab Structures

Any practitioner who takes his profession in earnest, such that daily work is not a heavy duty but part of their life, will recognize in this book the rigorousness of the analysis and the comprehensive presentation of the problems. This professional attitude is solely able to make the research and design engineer deal with strength structures and their behaviour. Indeed, the computational means that are nowadays available permit the numerical computation of whatever problem; the pro­ gram libraries are extremely rich and programs themselves have developed intensively. Howeyer, though computers are available at any moment without restrictions on the frequency with which they are employed, they finally impoYerish the creative compe­ tency of the civil engineer. Thus, he will calculate increasingly more while devising increasingly less. He will draw less and less on the experience gained in devising and implementing bearing structures because the computational process can be repeated as often as desired over a minimum time-period by means of the available programs. \Ve note that nowadays structures are no longer investigated or economically designed to comply with the requirements of the topic of interest. :Much to the contrary, the solutions are chosen so as to comply with the capabilities of the programs. A bearing structure lives as is prescribed by its initial con­ structive data.

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.