Quick and Dirty Mohr’s Circle Solution for the Strain Gauge Rosette A 3 gauge rosette is attached to a simple tension bar. The three gauges of the rosette are at 45 degrees in relation to each other but the rosette is not aligned with the strap. The strap is 1.00 inches wide and 0.25 inches thick and is loaded with 3000 lbs tension with the force aligned with the long axis of the bar. The material is steel with: E = 29E6 psi and ν = 0.3
Theory:
The theory is that the stress in the bar is uniaxial with the principal stresses being equal to P/A and zero. The strains are biaxial with the maximum being P/AE and the minimum being – νP/AE. The first principal stress and strain will be aligned with the force and the long axis of the bar.
Test Data:
When loaded with 3000 lbs tension the three strain readings were: εA = 310 µε εB = 20 µε εC = 26 µε
10/27/2008
Page 1 of 4
Solution:
Gauges A and C are perpendicular and since angles are doubled on Mohr’s circle, they will plot 180 degrees apart on the circle and define a diameter. Since A and C form a diameter of the circle, the center of the circle will be half way between them. Center at (310 + 26)/2 = 168 µε Find the offset from the center to gauges A and B 310  168 = 142 µε 20  168 = 188 µε These can be used to find the radius Radius = [ 1422 + (188)2 ]1/2 = 235 µε Now we can find the principal strains ε1 = center + radius = 168 + 235 = 404 µε ε2 = center – radius = 168 – 235 = 67 µε Using the center and the radius, draw Mohr’s circle and draw three lines to represent the gauge readings. Consider a diameter of the circle connecting A and C. This diameter will have a perpendicular extending to B. There is only one way that this can be arraigned such that the counter clockwise sense, ABC, of the rosette is preserved. In our case the...
...T.C.D 
Measurement of Strain using Electrical Resistance StrainGauges 
3B3  Mechanics of Solids 

Adam McCreevey 
3/15/2013 
This is a laboratory to learn how to make measurements using a straingauge by using different configurations, also to determine experimentally the axial and transverse stress at the surface of the beam and compare them to theoretical calculations 
Introduction
If a length of wire is subject to a stress within its elastic limits, the resulting elongation and change of diameter alters the resistance. The resulting principle is used in the resistance straingauge, which consists of many turns of resistance wire, wound on an insulating former, the straingauge wire is selected for the minimum temperature coefficient of resistivity. They may be used to measure extremely small displacements, of the order of nanometres. Straingauges are classified as bonded or nonbonded. The bonded type has a wire mounted on a paper backing and the paper could be pasted to the surface of the body under strain. The unbonded type is simply wire mounted between two supports which move with respect to each other. For the purpose of this experiment, we use the bonded type of straingauge. In order to convert variations in resistance into recordable...
...TITLE PAGE
Laboratory Title: 2D StrainRosette Analysis
Contents
Page 1 Title page
Page 2 Contents
Page 3 Nomenclature
Page 4 Summary
Page 4 Literature Search
Page 56 Theory
Page 7 Apparatus
Page 8 Procedure
Page 9 Tabulated Experimental Results
Page 1013 Sample Calculations
Page 14 Tabulated Calculated Results
Page 14 Error Analysis
Page 14 Conclusions
Page 15 Group Teamwork Management
Page 15 Safety Assessment
Page 16 Discussion / Analysis
Page 16 References
Page 2
NOMENCLATURE
M = Mass (grams)
[pic] (N/m²)(Pa)
w =Width (M)
h =height (M)
ε1, ε2, ε3 = strains measured along corresponding axes of rosette elements, in/in (m/m)
ν = Poisson’s Ratio
E = modulus of elasticity, psi (N/m )
y = deflection (in)
P = force, lbs
L = distance from clamp to loading micrometer (mm)
x = the distance from the loading micrometer to the rosette centreline
t = the beam thickness, in (m)
b = beam width, in(m)
c = semi thickness of the beam, in (m)
M = bending moment at rosette centreline, psi(Pa or N/m²)
ε p,q = algebraically maximum and minimum principal...
...Technical Paper by R.J. Bathurst, T.M. Allen, and
D.L. Walters
SHORTTERM STRAIN AND DEFORMATION
BEHAVIOR OF GEOSYNTHETIC WALLS AT
WORKING STRESS CONDITIONS
ABSTRACT: The paper reviews geosynthetic reinforcement strain measurement
techniques that have been reported in a database of welldocumented case studies and
more recent fullscale laboratory test walls. Interpretation of strain measurements,
accuracy of readings, and advantages and disadvantages of different techniques are
discussed. In general, properly calibrated straingauges have proven useful to estimate
reinforcement strains at low strain levels (0.02 to 2%). Extensometers are shown to be
accurate at strains greater than 2% and to have marginal reliability at strains between
0.5 and 2%. A strategy to improve confidence with interpretation of strain readings is
to use straingauges and extensometers in the field and to adjust straingauge calibration factors based on in situ measurements from both devices. Corrected reinforcement
strains can be used together with appropriately selected reinforcement stiffness values
to estimate reinforcement loads. Estimated loads can then be compared to predicted
values using current and proposed design methods for the internal stability of...
...5/3/2011
Lecture 1
LECTURE 1 TOPICS
I. Product of Inertia for An Area
Definition Parallel Axis Theorem on Product of Inertia Moments of Inertia About an Inclined Axes Principal Moments of Inertia Mohr’sCircle for Second Moment of Areas
II. Unsymmetrical Bending II Unsymmetrical Bending
Unsymmetrical Bending about the Horizontal and Vertical Axes of the Cross Section Unsymmetrical Bending about the Principal Axes
1
5/3/2011
Lecture 1, Part 1
Product of Inertia for an Area
Consider the figure shown below
y x A dA y x Product of Inertia of A wrt x and y axis: Product of Inertia of Element dA:
2
5/3/2011
Product of Inertia for an Area
Consider the figure shown below
y x A dA y x Unit: length4 – m4, mm4, ft4, in4 g NOTE: 1. Ixy can be positive, negative or zero. 2. The product of inertia of an area wrt any two orthogonal axes is zero when either of the axes is an axis of symmetry. Product of Inertia of A wrt x and y axis:
Product of Inertia for an Area
Parallel Axis Theorem Parallel‐Axis Theorem
y’ y x’ Product of Inertia of A wrt x and y axis: dA C dy x dx y’ x’ ’ Product of Inertia of Element dA:
3
5/3/2011
Product of Inertia for an Area
Parallel Axis Theorem Parallel‐Axis Theorem
y’ y x’
dA C dy
y’ x’ ’
x dx
The product of inertia of an area wrt any two perpendicular axes x and y is equal to the product of inertia of the area wrt a pair of centroidal axes parallel to...
...ES180 : Technological Science 1
StrainGauge
Laboratory Report
By Akash Sherchan
Student I.D. #: 1124433
University of Warwick
Summary
The straingauge laboratory session had a lot of aims and one of the main aims was to provide us with experience in using circuits based on operational amplifiers and examine the characteristics of these circuits when they amplify DC signals. Another aim was to also investigate the use and characteristics of resistive straingauges. The overall objective was to understand the how these widely used transducers are used and how they behave. This will be done through custom prebuilt electronic circuits which will then be used to amplify signals from a resistive straingauge when weighed down with washers.
Table of Contents
Introduction
Method
Results
Graphical Representation
Analysis and Discussion of Results
Conclusion
Bibliography
Appendix
Introduction:
The aim of the laboratory was to gain experience in the use of OperationalAmplifiers and the study of their characteristics. This report will cover the method used to study OpAmps and analyse the results thus explaining and showing the behaviour and OpAmps. This laboratory had 3 sections looking at a noninverting amplifier, inverting amplifier and a straingauge bridge (differential opamp) respectively.
Where:
• V+ :...
...PART A
Courts all over the world have set precedence’s of treating directors as trustees which means in the performance of their assigned legal and corporate duties, they stand in a fiduciary relation to the shareholders of the company. A director as a trustee shall act in the best of his ability to benefit the company and not in furtherance of his own interest.
Each of the four directors of the company stand in a fiduciary position to the company and thus liable for their acts of omission and commission to the shareholders of the company. They did not take adequate safeguards while deciding to invest a relatively huge sum of $20 million in a completely new business venture.
Section 232(2) and (3) of the Corporations Act has provided the followings:
An officer including a director of a corporation shall be duty bound to act with honesty of intentions as well as actions while exercising his powers vested while discharging his duties. This has been well documented in the case of Australian Growth ResourcesCorporation Pty Ltd v. Van Reesma (1988) 13 ACLR 261.Arthur who has already acquired stakes in Weaves Pty Limited should have disclosed his position to the Board of directors of Chance ltd. He was in a position to influence the Board and thus acted with sufficient and provable dishonesty. He is liable to be prosecuted under s.233.
It has been an established fact that if certain business decisions are taken and they don’t serve any rational purpose for the betterment...
...Proposing a Solution
I live outside of a small town of 3,000 people. The water system of our small town supplies drinking water to a population of 3,000 to 5,000. Our water system has been in place for 20 plus years and neglect has been rampant for almost the same period of time.
Public water systems are governed by regulations and monitored by the State of Louisiana. The Town of Ferriday has been under state mandated “boil orders” more times that you could count. One of the more recent events was when the State Inspectors arrived to conduct a regular inspection of the water treatment plant and found that a portion of the top of the water storage tank had collapsed and fallen in. The regulations state that potable water must be stored in such a way to prevent any contamination from outside sources. Inspectors found dead birds and debris in the town drinking water supply. National Guard supplied tankers that were placed all around town and filled with potable water from a nearby town. Our citizens were only able to get drinking water by bringing their own bottles or containers out and filling them at these tanker locations. This went on for months as a new water storage tank was constructed. The town had to bid the construction of the tank and argue about the companies’ bids, then finally award and construct the new tank.
During all of this, the finger pointing was rampant and everyone blames someone else or the prior administration in the...
...CHAPTER 10
CRITICISMS OF ABSORPTION COST SYSTEMS:
INCENTIVE TO OVERPRODUCE
P 101: Solution to Federal Mixing (10 minutes)
[Explaining absorption versus variable costing]
Variable costing writes off to income all fixed manufacturing costs incurred during the year. Absorption costing prorates the fixed overheads between units in inventory and units sold based on machine hours.
Absorption costing net income is higher than under variable costing by $1.2 million. This means that inventories under absorption costing are higher by $1.2 million.
The ending workinprocess inventory contains 20,000 more machine hours than the beginning inventory (90,000 – 70,000 machine hours). From the data given, the fixed overhead rate applied to products is $60 per machine hour. Or,
$1.2 million = (90,000 – 70,000) × fixed overhead rate
Fixed overhead rate =
= $60
P 10–2: Solution to Xerox (15 minutes)
[Incentives to over produce]
By building inventories and using absorption costing, Xerox shifts some of its fixed manufacturing costs from cost of goods sold to inventories. This decreases cost of goods sold and increases net income as long as average unit costs are decreasing. This is a shortterm strategy to boost accounting earnings and earnings will reverse as soon as inventories are depleted. This strategy is unlikely to mislead the stock market. Since the higher inventories must be disclosed as part of the...
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