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Handbook on Plastic Analysis in Engineering

by Leonid Belenkiy
isbn 0-9742019-2-8
US$299 :: Hardbound
7.5" x 10" :: ©2005
1055 pages
534 fig :: 332 tables

This is a comprehensive reference source, a unique combination of a handbook, a
textbook, and a guide on practical applications of plastic analysis for a wide scope of
structures used in many industries. The use of plastic analysis and its advanced tool,
the limit analysis, can markedly enhance structural design as compared to what can be
done using traditional methods and standards based on the theory of elasticity.
However, practical applications of plastic analysis have been limited due to a very
narrow base of the existing closed-form solutions for elementary cases only. The lack
of closed-form solutions has been a significant obstacle in implementation of plastic
analyses and criteria, which are usually more suitable for reliability assessment and
optimization of material distribution in a structure, thus increasing reliability and

This handbook with all existing and many newly derived formulas is as significant for
plastic analysis applications as many finest handbooks (such as the famous Roark's
Formulas or Kleinlgel's Rigid Frame Formulas, to name a few) have been for elastic
analysis. The book is skillfully organized to provide its reader with all pertinent
theoretical background, simply worded and richly illustrated by numerical examples in
using the formulas and deriving more formulas. This makes it also a convenient
textbook and an advanced theoretical monograph. In this book, virtually every table of
formulas and every discussion topic is stand-alone with all vital information included
and with references to appropriate definitions and/or detailed explanations throughout
the book.

All necessary definitions and background of the theory of plasticity and limit analysis
are presented in Part 1 without proofs. Parts 2 through 6 are focused on determining
limit loads of a great number of structures. Simple formulas are derived, most for the
first time ever, for a great majority of commonly used structures. They are presented
in systematically organized tables with all necessary how-to-use information. Parts 7 &
8 present closed-form solutions for more sophisticated models of material and
structural behavior taking into account geometric non-linearity, elastic and
elastic-plastic compliance of supports, strain hardening of material, buckling of
compressed structures, load-bearing capacity of compressed-bent structures, and
shakedown under variable loads. As a result, formulas for maximum displacements and
deflections, critical loads, and shakedown loads are presented, also mostly for the first
time ever. Accurate solutions are presented where possible; in other cases their upper
and lower bounds or approximate formulas are given with detailed specific information
on their application ranges and error margins. Derivation procedures are explained in
detail for all groups of formulas and numerous examples are given throughout the book
to help the reader in practical applications.

The book is addressed to virtually all who are interested in studying and involved in all
kinds of practical applications of plastic analysis, from engineers in structural design
and stress analysis to those involved in research, rule development, and advanced
academic studies of the theory of plasticity, and from undergraduate students to
professors. Structural engineers in civil, mechanical, shipbuilding, aircraft & space,
ocean, oil & gas, chemical and other engineering industries may need this book. Its
table of contents is self-explanatory.

Table of Contents

Pt. 1. Background: 1.1. Theory of Plasticity; 1.2. Bars, Beams, Plates, and Shells; 1.3.
Limit Analysis; 1.4. Geometrically Non-Linear and Combined Problems; 1.5 Other

Pt. 2. Limit State of Cross Section: 2.1. Pure Bending; 2.2. Pure Bending with
Tension/Compression; 2.3. Pure Torsion and Combined Loading; 2.4. Lateral Bending;
2.5. Restrained Torsion of Thin-Walled Beams

Pt. 3. Limit Loads of Straight Bars and Beams: 3.1. Tension/Compression, Pure Torsion,
and Pure Plain Bending; 3.2. Combined Loading; 3.3. Lateral Bending of I-Beams; 3.4.
Restrained Warping Torsion of Thin-Walled Beams

Pt. 4. Limit Loads of Frames Made of Straight Beams: 4.1. Beams with Broken Axis;
4.2. Rectangular Frames; 4.3. Non-Rectangular Frames; 4.4. Grillages

Pt. 5. Limit Loads of Curved Beams and Frames: 5.1. Background and Simple
Problems; 5.2. Parabolic Arches; 5.3. Circular and Elliptic Arches; 5.4. Rings; 5.5.
Curved Frames

Pt. 6. Limit Loads of Plates and Shells: 6.1. Exact Solutions and Bilateral Estimates; 6.2.
Approximate Kinematic Solutions for Plates and Panels; 6.3. Shells and Plane Stress

Pt. 7. Geometrically Non-Linear and Combined Problems: 7.1. Large Deflection of
Beams; 7.2. Beams on Elastic and Elastic-Plastic Supports; 7.3. Large Deflections of
Plane Curved and Broken-Axis Beams; 7.4. Large Deflections of Plates and Shells; 7.5.
Flexible Structures

Pt. 8. Elastic-Plastic Problems: 8.1. Beams in Elastic-Plastic Stage; 8.2. Determination
of Displacements in Elastic-Plastic Problems; 8.3. Load Bearing Capacity of
Compressed-Bent Structures. Buckling; 8.4. Residual Stresses and Shakedown
Subject Index.