The bonded electrical resistance strain gage : an introduction

422 Pages·1992·11.693 MB·English

by  William M Murray, William R Miller

The Bonded Electrical Resistance
Strain Gage
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The Bonde d
Electrical Resistanc e
Strain Gag e
An Introduction
WILLIAM M . MURRAY
Professor Emeritus
Massachusetts Institute of Technology
WILLIAM R . MILLE R
Professor Emeritus
The University of Toledo
New York Oxfor d
OXFORD UNIVERSITY PRES S
1992
Oxford Universit y Press
Oxford Ne w York Toront o
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Copyright ; 1992 by Oxford Universit y Press, Inc.
Published by Oxford University Press, Inc.,
200 Madison Avenue. New York 10016
Oxford is a registered trademark of Oxford University Press
All rights reserved. No part of this publication may be reproduced,
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Library of Congress Cataloging-in-Publication Data
Murray, William M.
The bonded electrical resistance strain gage :
an introduction / by William M. Murray and William R. Miller.
p. cm. Include s bibliographical references and index.
ISBN 0-19-507209-X
1. Strain gages. 2 , Electric resistance Measurement .
I. Miller. William R. (William Ralph), 1917- . II . Title.
TA413.5.M87 199 2 624.1'76'028 7 dc2 0 91-4136 9
2 4 6 8 9 7 53 1
Printed i n the United States of America
on acid-free paper
PREFACE
Experimental stress analysis is an important tool in the overall design and
development of machinery and structures. While analytical techniques and
computer solutions are available during the design stage, the results are still
dependent on many assumptions that must be made in order to adapt them
to the problems at hand. Only when the design is fixed, the prototypes are
constructed, and testing is underway, can the problem areas be realistically
determined, and this must be done through experimental means.
One method o f finding the weaknesses, and a method whic h is used
extensively, is through the use of the electrical resistance strain gage. Strain
gages ar e relativel y lo w i n cost , easil y applie d b y a reasonabl y skille d
technician, do not require extensive investment in instrumentation (for the
general user), and yet they yield a wealth of information in a relatively short
time. The information and its validity is, of course, dependent on the training
and knowledg e of the engineer who plans the tests and reduces the data.
The latter statement becomes painfully apparent when one finds a user trying
to interpret data from a single strain gage applied i n an unknown biaxial
stress field.
In 1988 , the authors decided t o edit Dr. Murray's notes, which were
developed ove r his extensive career, and to write an introductory text on
electrical resistance strain gages. The text is directed at senior and first-year
graduate student s in th e engineerin g disciplines , although student s fro m
other fields (geology, engineering physics, etc.) will also benefit.
The prerequisites for a strain gag e course are the following: (1) The
basic courses in resistance of materials. (2) An elementary course in electrical
circuits. (3) At least one course in mechanical or structural design is desirable.
It follows that the more experience students have in analysis and design, the
more they will benefit from an experimental course. It is in the laborator y
and in experimental courses that students really develop a sense of security
in, and a better understanding of, the theory they have been exposed to in
their analytical studies.
The development of stress and strain transformation equations and the
corresponding Mohr' s circles, as well as the stress-strain relationships, are
covered in Chapter 2. Depending on the student's preparation, the instructor
may use this chapter for a rapid review or eliminate it entirely. The authors,
however, have found it beneficial to spend a t least several periods o n the
material.
Basic electrica l circuit s ar e examine d i n Chapter s 3 through 5 . An
elementary circuit consisting of a single strain gage and its response to strain
is first considered, followed by the potentiometric circuit and the Wheatstone
vi PREFAC E
bridge. In the development of the expressions for output voltage, as the strain
gage's resistance change s wit h increasing loading , i s the effec t o f circuit
nonlinearity. The equations are developed so that th e student ca n easily
handle the intervening algebra between steps and thereby see the nonlinearity
terms unfold. It is important that students recognize this and understand ,
when recording large strains, how to correct the indicated strains to obtain
the actual strains . The effec t o f resistance i n both th e power supply an d
indicating meter is also accounted for.
Lead-line resistance is considered in the Wheatstone bridge circuits. The
circuits are the full bridge, the half bridge with four wires, the half bridge
with three wires, the quarter bridge with three wires, and the quarter bridge
with two wires. The equations are developed so that the nonlinearity effects
are apparent.
Sensitivity variation in order to obtain a desired output is next discussed
in Chapter 6. Equations are developed, including nonlinearity effects, for the
desensitization of single gages, half-bridge circuits, and full-bridge circuits.
Chapter 7 is devoted to the lateral, or transverse, effect on strain gages,
along with a discussion of the methods used to determine the gage factor
and th e transvers e sensitivity factor o f strain gages . This i s followed by
Chapters 8 and 9 on strain gage rosettes and data reduction. It is shown
how t o reduc e rosett e dat a b y bot h analytica l method s an d graphica l
methods. This is followed by considering transverse effects, using information
from Chapte r 7 , in rosette data reduction.
Chapter 1 0 discusses how strain gages may be used t o measure both
normal stresse s and shearin g stresses directly, while Chapter 1 1 considers
the effec t o f temperature o n strai n gag e readings . Temperature-induce d
strains ar e discussed , followe d b y a n examinatio n o f self-temperature-
compensated gage s an d thei r thermal output curves when the gages ar e
bonded t o severa l different materials . One ca n se e how t o correc t th e
indicated strain not only for the temperature-induced strain, but also for the
gage factor variation resulting from temperature change.
Several type s of strain-gage transducer s are covere d i n Chapte r 12 .
Among them are the axial-force load cell, the torque meter, the shear meter,
and th e pressure transducer . The purpos e i s to introduce the student t o
several types of transducers that could be made and calibrated for his use
in the laboratory.
At the time of Dr. Murray's death on August 14, 1990, the major portion
of the manuscript had been completed. If there are errors or discrepancies,
the fault i s not his but mine. In completing the text, I gathered together all
of the source material in order to give proper credit; I sincerely hope none
has been overlooked.
A textbook is not the work of one or several people alone. All of us are
influenced not only by our contemporaries but by those who have preceded
us (one has only to think of Professor Otto Mohr to realize this). Therefore,
I want to acknowledge our debt to all of these people, not the least of whom
PREFACE vi i
were our students. I want especially to thank Martha Watson Spalding of
Measurements Group, Inc. for her cooperation in furnishing a considerable
amount o f material. I als o wan t t o acknowledg e the assistanc e o f th e
following companies: BLH Electronics, Inc.; Eaton Corporation, Transducer
Products; Electri x Industries , Inc.; Hartru n Corporation ; Measurement s
Group, Inc.; Stein Engineering Services, Inc.; and Texas Measurements, Inc.
W. R. Miller
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CONTENTS
1. Fundamental Concepts for Strain Gages, 3
1.1 Introduction, 3
1.2 Characteristics Desired in a Strain Gage, 4
1.3 General Considerations, 5
1.4 Analysis of Strain Sensitivity in Metals, 14
1.5 Wire Strain Gages, 24
1.6 Foil Strain Gages, 29
1.7 Semiconductor Gages, 32
1.8 Some Other Types of Gages, 33
1.9 Brittle Lacquer Coatings, 36
2. Stress-Strain Analysi s and Stress-Strain Relations, 42
2.1 Introduction, 42
2.2 Basic Concepts of Stress, 43
2.3 Biaxial Stresses, 45
2.4 Mohr's Circle for Stress, 54
2.5 Basic Concepts of Strain, 61
2.6 Plane Strain, 62
2.7 Mohr's Circle for Strain, 68
2.8 Stress-Strain Relationships, 72
2.9 Application of Equations, 77
2.10 Stress and Strain Invariants, 81
3. Elementary Circuits, 90
3.1 Introduction, 90
3.2 Constant- Voltage Circuit, 91
3.3 Constant-Current Circuit, 94
3.4 Advantages of the Constant-Current Circuit, 96
3.5 Fundamental Laws of Measurement, 97