Basic Principles of Plates and Slabs : For Safer and More Cost Effective Structures

by LOWE P. G. (ED)

• ISBN13: 9781870325448
• ISBN10: 1870325443
• Format: Hardcover
• Copyright: 2004-04-01
• Publisher: Whittles Pub
• More Book Details
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Summary

Floor structures account for the majority of all the structural material incorporated into a typical building and plate theories provide the information required to design them. This comprehensive book provides a wide-ranging account of the theoretical aspects of plate and slab theory - in essence structural floors - followed by a discussion of the construction and design of real plate and slab elements.

Author Biography

Peter Lowe is Emeritus Professor of Civil Engineering, University of Auckland, New Zealand and an Honorary Professor of Civil Engineering, University of Sydney, Australia

Table of Contents

Preliminaries
Motivation	1	(1)
The aim of the work	2	(1)
Acknowledgements	3	(2)
Review---The Change From One To Two Dimensions
Introduction	5	(1)
Vectors---algebra	5	(4)
Vectors---calculus	9	(2)
Matrices	11	(2)
Statics---equilibrium	13	(2)
Summation convention and index notation	15	(1)
Beam bending	15	(8)
Conclusions	23	(1)
Statics and Kinematics of Plate Bending
Introduction	24	(1)
The stress resultants	24	(4)
Principal values	28	(3)
The moment circle	31	(2)
Equilibrium equations---rectangular coordinates	33	(3)
Plate bending kinematics---rectangular coordinates	36	(4)
Equilibrium equations---polar coordinates---radial symmetry	40	(2)
Plate bending kinematics---polar coordinates---radial symmetry	42	(3)
Conclusions	45	(1)
Elastic Plates
Introduction	46	(1)
Elastic theory of plate bending---moment/curvature relations	46	(4)
Elastic theory of plate bending---the governing equation	50	(1)
Circular plates---radial symmetry	51	(2)
Some simple solutions for circular plates	53	(5)
Simple solutions for problems in rectangular coordinates	58	(3)
Further separation of variable features---rectangular plates	61	(3)
Solution by finite differences	64	(10)
Some other aspects of plate theory	74	(5)
Stability of plates	79	(4)
Further exercises	83	(1)
Conclusions	84	(1)
Plastic Plates
Introduction	85	(1)
Solid metal plates	85	(1)
Yield criteria	85	(3)
The bound theorems	88	(3)
The normality rule	91	(1)
Circular plates---square yield locus	91	(6)
Circular plates---Tresca yield locus	97	(5)
Plates of other shapes---square and regular shapes	102	(3)
Reinforced concrete slabs---upper bounds	105	(1)
Yield line theory---I. Fundamentals---mainly isotropic	105	(10)
Yield line theory---II. Further isotropic examples	115	(3)
Yield line theory---III. Orthotropic problems	118	(5)
Strip method---Hillerborg's proposals	123	(1)
Plates and slabs---the comparison method and lower bounds	124	(1)
The comparison method---general principles	124	(5)
The comparison method---lower bounds on the collapse load	129	(2)
Finding the rmin---a geometrical problem	131	(5)
Affinity Theorem---orthotropic plates---associated isotropic equivalents	136	(2)
Other edge conditions	138	(1)
Conclusions	139	(1)
Optimal Plates
Introduction	140	(1)
Problem formulation	140	(2)
Constant curvature surfaces and principal directions	142	(2)
Basic results---corners	144	(7)
Some complete results	151	(2)
Moment volumes	153	(2)
Some theory	155	(4)
Conclusions	159	(1)
Exercises	160	(1)
Construction and Design---A Case for New Technology
Introduction	161	(3)
A case for new technology in construction	164	(3)
Some ``ideals'' to be aimed for in construction	167	(5)
Externally reinforced concrete---the preferred system of reinforcement and construction	172	(7)
Section design for externally reinforced concrete members	179	(7)
Conclusions	186	(1)
Exercises	187	(1)
Bibliography and Concluding Exercises
Bibliography	188	(4)
Notes on the development of structural mechanics	192	(10)
Further Exercises	202	(6)
Concluding remarks	208	(1)
Appendix GEOMETRY OF SURFACES
A.0 The need for geometry	209	(1)
A.1 Geometry of a plane curve---curvature	209	(3)
A.2 Length measurement on a surface---first fundamental form	212	(3)
A.3 The normal to a surface	215	(2)
A.4 Normal curvature---second fundamental form	217	(2)
A.5 The derivatives of n---the Weingarten equations	219	(1)
A.6 Directions on a surface	220	(1)
A.7 The principal curvatures	221	(1)
A.8 Principal directions	222	(2)
A.9 Curvature and twist along the coordinate lines	224	(4)
A.10 The curvature matrix	228	(2)
A.11 The curvature circle	230	(6)
A.12 Continuity requirements	236	(3)
A.13 Special surfaces	239	(4)
A.14 Summary---the geometrical quantities required for the construction of a plate theory	243	(2)
Index	245