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# Introduction to Unified Strength Theory

By

,

## Shu-Qi Yu

ISBN 9780367246822
Published June 3, 2019 by CRC Press
114 Pages

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## Book Description

Strength theory deals with the yield or failure of materials under complex stress state. It is very important in mechanics of materials, strength of structures, and mechanical and civil engineering. Unified strength theory is a series of yield criteria and failure criteria other than a single strength theory. The unified strength theory can be adopted for various kinds of materials, such as metallic materials, geomaterials, polymers etc. It is the solution to the Voigt-Timoshenko Conundrum. Its limit surfaces cover all regions of the convex strength theory from the lower bound to the upper bound. This book gives a clear and brief description about the unified strength theory both in figures and text. Some applications of unified strength theory are also given in this book. This book is suitable for undergraduate students, who are studying the mechanics of materials and engineering mechanics, as well as for graduate students who are interested in this field. Researchers and engineers can also benefit from this book.

1 Introduction
1.1 Strength of materials in tension and compression
1.2 Strength of materials under complex stress
1.3 Single strength theory
1.4 Voigt-Timoshenko conundrum
1.5 The development of unified strength theory
1.6 Applications of the Yu-UST
1.7 Summary 1
References

2 Stress state and elements
2.1 Introduction
2.2 Stresses on the oblique plane
2.3 Cubic hexahedron and octahedron
2.4 Mohr stress circle
2.5 Stress space
2.6 Summary
References

3 Yu-unified strength theory (Yu-UST)
3.1 Introduction
3.2 The Yu-unified strength theory
3.3 Special cases of the Yu-UST for different parameter b
3.4 Limit loci of the Yu-UST by varying parameter b in the π-plane
3.5 Variation of limit loci of the Yu-UST when α = 1/2
3.6 Limit surfaces of the Yu-UST in principal stress space
3.7 Limit loci of the Yu-UST in plane stress state
3.8 Limit loci of the Yu-UST under the σ τ combined stress state
3.9 Experiment verification of Yu-UST 46 3.10 Summary 49 References 49 Readings

4 Yu-unified yield criteria for metals
4.1 Introduction
4.2 The Yu-unified yield criterion (Yu-UYC)
4.3 Special cases of the Yu-UYC
4.4 Experimental determination of parameter b
4.5 Yu-UYC in the plane stress state
4.6 Yu-UYC in the σ τ stress state
4.7 Yield surfaces of the Yu-UYC
4.8 Summary
References

5 Applications of the Yu-UST and Yu-UYC
5.1 Introduction
5.2 Strength design of a thin-walled pressure cylinder
5.3 Thickness design of a thin-walled pressure vessel
5.4 Strength design of a gun tube of trench mortar
5.5 Strength design of an oil pipe
5.6 Strength design of an automobile transmission shaft: maximum allowable torque
5.7 Strength design of an automobile transmission shaft: outer diameter design of drive shaft
5.8 Strength design of a transmission axle
5.9 Unified solution for elastic limit pressure of a thick-walled cylinder subjected to internal pressure
5.10 Analysis of plastic ultimate pressure for a thick-walled cylinder with internal pressure
5.11 Unified solution of plastic limit internal pressure for a thick-walled cylinder with the same tensile strength and compressive strength materials
5.12 Unified solution of plastic limit internal pressure for a thick-walled cylinder with different tensile strength and compressive strength materials
5.13 Barrel strength design of artillery
5.14 The economic significance of the use of Yu-unified strength theory
5.15 Procedure of the applications of the Yu-UST and Yu-UYC
5.16 Summary
References