Tables For The Analysis Of Plates Slabs And Diaphragms Based On The Elastic Theory Pdf May 2026

I found the book "Berechnungstafeln für Platten und Wandscheiben = Tables for the analysis of plates, slabs and diaphragms, based on the elastic theory" by Richard Bareš (1979). It's available on the Internet Archive (item identifier: berechnungstafel0000bare). Would you like a direct link or instructions to access/download the PDF?

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

The analysis of reinforced concrete structures requires precise calculations to ensure safety, serviceability, and economy. For engineers working with two-dimensional elements, Tables for the Analysis of Plates, Slabs, and Diaphragms Based on the Elastic Theory serves as an indispensable reference. These tables simplify complex differential equations into manageable coefficients for everyday design. 🏗️ Core Principles of Elastic Theory

The elastic theory assumes that materials return to their original shape after unloading. In the context of plates and slabs, this involves: Linear Elasticity: Stress is proportional to strain.

Small Deflections: The displacement is small relative to thickness.

Kirchhoff-Love Hypothesis: Straight lines normal to the mid-surface remain straight and normal after bending. 📘 Why Engineers Use Design Tables

Manually solving the Lagrange biharmonic equation for plate bending is time-consuming. Reference tables provide a shortcut by offering pre-calculated coefficients based on:

Boundary Conditions: Fixed, simply supported, or free edges. Aspect Ratio: The relationship between the length ( ) and width (

Loading Types: Uniformly distributed loads, hydrostatic pressure, or point loads. Key Benefits Efficiency: Reduces calculation time from hours to minutes.

Standardization: Ensures consistency across different engineering projects.

Verification: Acts as a "sanity check" for Finite Element Analysis (FEA) software results. 📐 Components Covered in the Tables 1. Two-Way Slabs Tables provide coefficients for bending moments (

) and shear forces. By selecting the correct ratio of spans, engineers can find the maximum stress points at the center and supports. 2. Rectangular Plates

For plates subjected to transverse loading, tables help determine: Maximum deflection ( Torsional moments at the corners. Support reactions for foundation design. 3. Diaphragms (Deep Beams)

Diaphragms act as structural elements transferring lateral loads to vertical resistive elements. The tables assist in calculating in-plane stresses, which differ significantly from standard beam theory due to the height-to-span ratio. 🔍 Notable References and Authors I found the book "Berechnungstafeln für Platten und

While many seek a "PDF" version of these tables, several classic texts form the backbone of this data:

Richard Bares: Known for "Tables for the Analysis of Plates, Slabs and Diaphragms," a definitive collection of coefficients.

S. Timoshenko: "Theory of Plates and Shells" provides the mathematical foundation for these tables.

Pucher: Influence surfaces for plates, essential for moving loads. 💻 Transition to Digital Analysis

While physical tables are excellent for simple geometries, modern engineering often utilizes software:

FEA Integration: Software like SAP2000 or STAAD.Pro uses the same elastic theories but handles complex shapes.

Hybrid Workflow: Engineers often use tables to verify the "order of magnitude" of computer-generated results to catch modeling errors. 🛠️ Practical Application Example

To find the bending moment in a simply supported square slab with a uniform load ( Identify the Aspect Ratio ( Locate the Coefficient ( ) from the table (e.g., 0.04790.0479 for specific conditions). Apply the formula:

If you are looking for a specific calculation, I can help you further if you provide: The dimensions of the slab or plate.

The boundary conditions (e.g., all edges pinned, or two edges fixed). The type of load (uniform or concentrated).

The work titled " Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory

" is a seminal engineering reference authored by Richard Bareš, first published in 1969.

Before the widespread use of finite element software, this book served as an essential tool for design engineers, providing pre-calculated coefficients to solve complex differential equations of plate bending. Core Purpose and Scope

The book is primarily a collection of design aids that allow engineers to calculate internal forces—such as bending moments, shear forces, and deflections—without performing manual integration of elastic surface equations.

Plates and Slabs: Focuses on elements where thickness is significantly smaller than other dimensions, primarily subjected to loads perpendicular to their surface.

Diaphragms (Wandscheiben): Addresses "deep beams" or wall-like structures where the load acts in the plane of the element.

Elastic Theory Foundation: All tables are derived using the classical linear elastic theory (often referred to as Kirchhoff-Love theory), assuming small deflections and material homogeneity. Content Highlights

Pre-Calculated Coefficients: The book contains extensive tables for various boundary conditions (clamped, simply supported, free edges) and loading types (uniformly distributed, hydrostatic, concentrated loads).

Comprehensive Data: With over 600 pages in later editions, it covers a vast range of geometric aspect ratios for rectangular and circular slabs.

Explanatory Text: Tables are accompanied by formulas and text that outline the basic methods of calculation for specific structural problems. Where to Find it

While physical copies are rare, digital versions and snippets are often hosted on academic and engineering repositories:

"Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory" is a seminal engineering reference by Richard Bares

. It serves as a vital bridge between complex mathematical elasticity theory and the practical requirements of structural design. The Core Premise: Simplifying Complexity At the heart of the book is the Classical Thin Plate Theory

(often referred to as Kirchhoff-Love theory). Analyzing plates and slabs involves solving fourth-order partial differential equations (the Lagrange equation), which is notoriously difficult for everyday engineering practice. Bares’ work provides a comprehensive set of pre-calculated coefficients

that allow engineers to determine bending moments, shear forces, and deflections using simple arithmetic instead of advanced calculus. Key Components of the Analysis The tables are categorized based on three primary factors: Boundary Conditions: Title: Looking for Tables for the Analysis of

Whether the edges are simply supported, clamped (fixed), or free.

Detailed analysis for rectangular and circular slabs, as well as more complex diaphragms. Loading Patterns:

Data for uniformly distributed loads, hydrostatic pressure, and concentrated point loads. Significance in Structural Engineering Before the ubiquity of Finite Element Method (FEM)

software, Bares’ tables were the industry standard. Even today, they remain essential for: Preliminary Design:

Quickly sizing structural elements before running complex computer simulations. Verification:

Providing a "sanity check" to ensure that software outputs are within a logical range. Educational Foundation: Helping students understand how different aspect ratios ( ) affect the distribution of internal forces in a slab. The Role of Elastic Theory By basing the tables on Elastic Theory

, Bares assumes that the material (usually reinforced concrete or steel) behaves linearly—meaning it returns to its original shape after loading and stress is proportional to strain. While modern design also considers "plastic" or "limit state" analysis, the elastic approach remains the primary method for ensuring serviceability

, such as preventing excessive cracking or deflection in floor systems. Conclusion

Richard Bares’ work transformed theoretical elasticity into a functional tool. By condensing thousands of hours of manual calculation into organized tables, he enabled a generation of engineers to design safer, more efficient buildings and bridges with high precision. or a specific coefficient table for a particular slab geometry?

The seminal work Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory Richard Bareš

is a cornerstone of structural engineering literature. Originally published in German as Berechnungstafeln für Platten und Wandscheiben

, this collection provides a comprehensive set of practical formulas and look-up tables used to solve complex problems in plate and slab analysis without the need for manual, high-level calculus. Overview of the Method The book is built upon the classical elastic theory of plates and shells

, primarily focusing on the linear-elastic behavior of structural elements. Unlike the yield-line theory

, which focuses on collapse loads and plastic behavior, the elastic theory ensures that structural elements remain within their serviceability limits, preventing excessive cracking and deflection.

The analysis typically involves solving the governing differential equations of equilibrium, which can be expressed in terms of bending moments ( cap M sub x cap M sub y ), twisting moments ( cap M sub x y end-sub ), and shear forces ( cap V sub x cap V sub y Fundamental Equations

In elastic theory, the bending of a thin plate is often described by the Lagrange-Euler equation (biharmonic equation):

nabla squared nabla squared w equals the fraction with numerator q and denominator cap D end-fraction : Deflection of the plate. : Intensity of the distributed load. : Flexural rigidity, defined as Components of the Analysis

Bareš's tables categorize structural elements based on their primary mechanical function and loading:

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:

Roark’s Formulas for Stress and Strain (Chapter 11 on plates)?
Theory of Plates and Shells by Timoshenko & Woinowsky-Krieger (Appendices with tables)?
Modern software like SAFE, ADAPT, or even FEM tools like SCIA or RFEM?

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. Roark’s Formulas for Stress and Strain (Chapter 11

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.

Key limitations:

Only linear elastic, isotropic material.
Limited to simple support, clamped, free, or elastic edge conditions.
Mostly rectangular or circular plates.

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:

SAFE/ADAPT use finite element methods but often embed these classic coefficients for their “strip method” or “coefficient method” checks.
For diaphragms specifically, the Bares tables are superseded by simple hand methods (e.g., the “strut-and-tie” for deep beams or “cantilever beam analogy” for horizontal diaphragms). But for perforated or L-shaped diaphragms, the tables give you a quick elastic stress distribution without FEA.

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).

"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

Conclusion: A Timeless Toolkit

The request for a PDF containing "tables for the analysis of plates slabs and diaphragms based on the elastic theory" is not a sign of resistance to technology. Rather, it reflects a mature understanding that efficient engineering blends theory, computation, and curated empirical data. These tables represent thousands of hours of past analytical work, condensed into a few dozen pages of coefficients. They empower the modern engineer to move quickly, verify thoroughly, and design confidently.

Whether you are designing a concrete flat slab for an apartment tower, a steel deck diaphragm for a warehouse, or a composite plate for a naval vessel, having a reliable digital copy of these tables is an essential part of your toolkit. Seek out a well-scanned, correctly referenced PDF. Learn its structure. Respect its assumptions. And let it accelerate your work for years to come.

References for further reading (look for these titles in PDF form):

Timoshenko, S., & Woinowsky-Krieger, S. – Theory of Plates and Shells (2nd ed.)
Roark, R. J., & Young, W. C. – Formulas for Stress and Strain
Szilard, R. – Theory and Analysis of Plates: Classical and Numerical Methods
PCA – Slab Thickness Design for Industrial Concrete Floors on Grade (Bulletin)

End of Article

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.

3. Diaphragms (In-Plane Loading)

Plates subjected to in-plane shear or edge forces (membrane action).
Stress concentration factors around openings.
Stiffness coefficients for equivalent orthotropic plates.

2.5 Influence Surfaces for Moving Loads

Particularly valuable for bridge slabs and industrial floors. Tables give ordinates for influence lines of moment and shear at critical points.

4. Continuous Plates & Slabs

Tables for two-way slab strips with multiple spans.
Moment and shear coefficients for interior and exterior panels.
Elastic support conditions (e.g., beams or columns).

Preface

Scope of the book and the application of Elastic Theory.
Definitions of symbols, sign conventions, and coordinate systems.
Assumptions regarding material homogeneity, isotropy, and small deflections.

Step 1 – Identify your case

From the table’s index, find the boundary condition diagram that matches. Each case has a code (e.g., C-12).

Why You Need the PDF (The Limitations of Modern Software)

While FEA software is powerful, it is also fragile. A misplaced boundary condition in a finite element model can yield a 400% error in slab design. The elastic tables act as a sanity check.

The Case for the PDF:

Speed: Finding a coefficient for a simply supported slab ($a/b=1.5$) takes 10 seconds.
Parametric Study: Changing the aspect ratio requires a page flip, not a remesh.
Diaphragm Analysis: For in-plane loaded plates (shear walls/diaphragms), the tables provide stress functions and shear flow distributions without complex modelling.
Historical Reliability: Bridges, bunkers, and skyscrapers built pre-1970 were designed exclusively using these tables.