The work " Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory
" by Richard Bareš is a foundational reference in structural engineering, particularly for designers working with reinforced concrete and steel-plate composite structures. Core Significance and Utility
First published in the 1960s and updated through several editions, this book serves as a bridge between complex mathematical theory and practical structural design. Before the ubiquity of high-powered Finite Element Method (FEM) software, Bareš’s tables were the industry standard for determining internal stresses, bending moments, and deflections in flat structural elements. Report Highlights
Comprehensive Data Library: The text contains over 600 pages of formulas and pre-calculated tables. It covers a vast range of boundary conditions (e.g., fixed, simply supported, free) and various loading scenarios like point loads and uniformly distributed loads.
Theoretical Foundation: The tables are rooted in the Classical Elastic Theory of Thin Plates, which assumes that deformations are small and the material remains within its elastic limit. Practical Application:
Plates and Slabs: Essential for calculating reinforcement requirements in floor systems.
Diaphragms (Deep Beams): Provides methods for analyzing in-plane stresses in vertical or horizontal diaphragms, often used in shear wall or bridge girder design.
Bilingual Accessibility: Many editions, such as the 1979 release by Bauverlag, are published in German and English (Berechnungstafeln für Platten und Wandscheiben), making them a global engineering staple. Availability for Research
While the book is often out of print, it remains accessible through specialized archives and libraries:
Title: Looking for Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory – Any modern alternatives?
User: StructEngineer_87 Posted: Today, 11:42 AM
I keep coming across references to the book Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory by Bares (or sometimes attributed to Czerny/Bares). From what I understand, it’s a foundational collection of influence coefficients and closed-form solutions for elastic plates under various loadings and boundary conditions – essentially the pre-FEA handbook.
Does anyone still use this (or have a PDF they could share)? I’m aware it’s long out of print. I’m particularly interested in the diaphragm tables for lateral load distribution in concrete structures.
Also curious – for those who’ve used it, how does it compare to:
Is there any value left in the Bares/Czerny tables beyond academic/historical interest? I’m trying to avoid blindly trusting FEA for preliminary design of unusual slab geometries.
Reply 1 – Senior Member, PE I’ve got a scanned PDF of the Czerny tables (often mis-titled as Bares). The proper reference is usually: Czerny, F. (1976). Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory. Ernst & Sohn.
Be careful – there are two versions: one for slabs (bending moments) and one for diaphragms (in-plane shear/axial stresses). The diaphragm tables are rare. The work " Tables for the Analysis of
Key limitations:
Why still useful?
They’re excellent for sanity-checking FEA results, especially for moment coefficients in two-way slabs. I’ve caught many modelling errors (wrong boundary conditions, mesh issues) by comparing mid-span moments to Czerny’s coefficients.
Reply 2 – Junior Engineer Why not just use the Eurocode 2 tables for two-way slabs? They’re essentially simplified versions of the same elastic theory.
Reply 1 again – Senior Member, PE Eurocode 2 tables are for ultimate limit state with redistribution. The Czerny tables are purely elastic (serviceability). For example, if you need deflections or crack control in a complex bay, the original elastic coefficients are more accurate. Also, EC2 doesn’t cover irregular shapes or diaphragms.
Reply 3 – Structural Analyst I have a PDF titled “Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory” by Richard Bares (1979, translated from French). It’s ~250 pages. Happy to share a link (mods: is that allowed if it’s out of print/abandoned copyright?).
In terms of modern use:
Honestly, if you do any work with concrete shell roofs or bridge deck slabs, these tables are gold. I keep a printed copy in my office.
OP’s follow-up:
Thanks everyone – especially @Reply3, yes please DM me the PDF link. I’m mainly after the diaphragm tables for a non-rectangular transfer slab. I’ll cross-check with a simple FEA model, but I want the elastic baseline first.
Also, for anyone else looking: I found a partial preview on Google Books, and WorldCat lists it in a few university libraries (signature: TA660.P6 B3713 1979).
Reply 4 – CAE Software User
Worth noting: If you have access to MATLAB or Python, you can generate many of these tables on the fly using Navier’s solution (double Fourier series) for simply supported plates. For clamped edges, Lévy’s method. The Bares tables just saved everyone the computation time in the 1970s.
But for diaphragms (in-plane loading), the governing equation is the Airy stress function – the tables essentially give you coefficients for membrane stresses. Modern FEM is far more flexible.
Final thought from OP:
Sounds like the PDF is worth having for historical reference and quick checks, but don’t rely on it for final design without a sanity check. Thanks all.
If you’d like, I can also summarize the actual content you would find in that PDF (e.g., common coefficient tables for moment and shear).
The manual "Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory" (widely known as the R. Bares tables) serves as a fundamental reference in structural engineering. It bridges the gap between complex mathematical theory and practical design, providing pre-calculated coefficients for engineers.
The Bridge Between Theory and Practice: An Analysis of the Bares Tables Introduction
Structural engineering is defined by the challenge of predicting how complex surfaces—plates, slabs, and diaphragms—will react under various loads. While the Elastic Theory provides the rigorous mathematical framework (primarily through Lagrange’s differential equations) to describe these behaviors, solving these equations manually is notoriously difficult. Richard Bares’ Tables for the Analysis of Plates, Slabs and Diaphragms emerged as an essential tool, simplifying these calculations into a format usable for daily engineering practice. The Core Objective: Solving for Internal Forces Title: Looking for Tables for the Analysis of
The primary purpose of the Bares tables is to provide quick access to values for bending moments, twisting moments, and shear forces. Instead of performing high-level calculus for every project, an engineer can look up dimensionless coefficients based on two primary factors: Aspect Ratio (
): The relationship between the length and width of the slab.
Boundary Conditions: Whether the edges are simply supported, fixed (clamped), or free.
By multiplying these coefficients by the applied load and the square of the span, designers can accurately determine the reinforcement needed for concrete slabs or the thickness required for steel plates. Application to Slabs and Diaphragms
While "plates" and "slabs" often refer to elements subjected to loads perpendicular to their surface (like a floor), "diaphragms" refer to elements loaded in their own plane (like a shear wall resisting wind or seismic forces). Bares’ work is unique because it addresses both, providing a unified approach to two-dimensional stress distribution. This is critical for ensuring that a building acts as a cohesive unit during lateral loading. Methodology: The Elastic Theory
The tables are rooted in the Linear Elastic Theory, which assumes that materials return to their original shape after unloading and that stress is proportional to strain. While modern design often considers "plastic" behavior (the state just before a structure fails), elastic analysis remains the standard for serviceability. It ensures that under normal daily use, floors do not vibrate excessively and ceilings do not crack. Modern Relevance in the Age of FEA
With the advent of Finite Element Analysis (FEA) software like SAP2000 or ETABS, some might view printed tables as obsolete. However, the Bares tables remain vital for two reasons:
Verification: They provide a "sanity check" for complex computer models. If a software output differs significantly from the Bares coefficient, it usually signals a modeling error.
Preliminary Design: In the initial phases of a project, an engineer can use these tables to estimate material quantities in minutes without building a full digital model. Conclusion
Richard Bares’ collection of tables represents a milestone in structural literature. By translating the "pure" physics of elastic theory into a "practical" handbook, it empowered a generation of engineers to design safer, more efficient structures. Even in a digital-first industry, the logic and precision of these tables remain a cornerstone of structural integrity.
Based on standard structural engineering literature, the phrase "feature for tables for the analysis of plates slabs and diaphragms based on the elastic theory" most likely refers to the data presentation style found in classic textbooks, specifically the seminal work by S. Timoshenko and S. Woinowsky-Krieger, titled Theory of Plates and Shells.
However, if you are looking for a software feature or a specific PDF document, the interpretation changes slightly.
Here is a detailed breakdown of what this feature entails and where to find the resources.
Tables allow rapid exploration of aspect ratio effects. For a square plate, ( M_max ) occurs at center; as ( a/b ) increases, moments shift—visible instantly from tabulated values.
The modern engineer should not choose between FEA and tables. Use the Tiered Approach:
"Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory" by Richard Bareš is a foundational 1969 reference work providing over 600 pages of coefficients for structural engineering design. The text simplifies complex differential equations for bending moments and deflections in slabs and plates. Digital versions are available for viewing on Internet Archive Open Library IQY Technical College Basic Theory of Plates and Elastic Stability Roark’s Formulas for Stress and Strain (Chapter 11
The reference you are likely looking for is " Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory
" by Richard Bareš. This seminal engineering handbook provides a comprehensive set of tables and formulas for calculating stresses and deformations in various flat structural elements. Overview of the Book
Purpose: Designed as a practical tool for design engineers to analyze structural components without requiring complex, from-scratch differential equation solving.
Scope: It covers rectangular and circular plates, slabs (plates loaded perpendicular to their plane), and diaphragms (plates loaded in-plane).
Theoretical Basis: The calculations are rooted in Classical Elastic Theory (typically Kirchhoff-Love plate theory for thin plates), assuming small deflections and linear elastic material behavior. Key Technical Contents
The handbook typically categorizes solutions based on the geometry and boundary conditions of the element: Rectangular Plates: Tables for various aspect ratios (
) and support conditions (e.g., all sides simply supported, clamped-clamped, or mixed conditions). Slabs: Focuses on bending moments ( ), twisting moments ( Mxycap M sub x y end-sub ), and shear forces.
Diaphragms: Focuses on in-plane stress distribution (plane stress theory).
Loading Conditions: Includes solutions for uniformly distributed loads, hydrostatic loads, and concentrated point loads. Digital Access and PDF Resources
Physical copies or digitized versions of this handbook can be found through the following platforms:
Internet Archive: Offers a digital version of the 1971 edition, titled Berechnungstafeln für Platten und Wandscheiben.
Scribd: Some users have uploaded full PDF versions of the 1979 English edition for viewing or download.
Google Books: Provides a preview and bibliographic details for the book. Basic Theory of Plates and Elastic Stability
Based on the title provided, this appears to refer to the classic engineering reference text (most notably the work by J.H. Bares or similar standard treatises on structural elastic theory).
Below is a comprehensive Content Outline and Topic Summary structured as if it were the Table of Contents and Chapter Overview for a textbook or technical resource titled "Tables for the Analysis of Plates, Slabs, and Diaphragms Based on the Elastic Theory."