A wire strain gage can effectively measure strain in only one direction. To determine the three independent components of plane strain, three linearly independent strain measures are needed, i.e., three strain gages positioned in a rosette-like layout.

Consider a strain rosette attached on the surface with an angle a from the x-axis. The rosette itself contains three strain gages with the internal angles b and g, as illustrated on the right.

Suppose that the strain measured from these three strain gages are ea, eb, and ec, respectively.

The following coordinate transformation equation is used to convert the longitudinal strain from each strain gage into strain expressed in the x-y coordinates,

Applying this equation to each of the three strain gages results in the following system of equations,


These equations are then used to solve for the three unknowns, ex, ey, and exy.

Note: 1. The above formulas use the strain measure exy as opposed to the engineering shear strain gxy, .
To use gxy, the above equations should be adjusted accordingly.
2. The free surface on which the strain rosette is attached is actually in a state of plane stress, while the formulas used above are for plane strain. However, the normal direction of the free surface is indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be applied.

Special Cases of Strain Rosette Layouts
Case 1: 45º strain rosette aligned with the x-y axes, i.e., a = 0º, b = g = 45º.





Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e., a = 30º, b = g = 60º.

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Are you thinking about buying a used truck at a Phoenix truck auction? This article is designed to provide you with the details on how auto auctions work and how they can get you the best deal on a great used truck. Specifics may vary from auction to auction; however, the following information includes helpful and important guidelines from which everyone can benefit.


Phoenix truck auctions are one of the best places to pick up a used truck, especially high end luxury trucks at a fraction of its original retail price. Have you ever pulled up next to a fully loaded Escalade at a stop light, glanced over and noticed that the driver is barely out of high school? How could they possibly afford the truck payment on that kind of ride? Well, they probably purchased the vehicle at a Phoenix truck auction and got a great deal.

If you have ever dreamed about owning a high-end luxury truck or a customized vehicle loaded with aftermarket parts and accessories, you’ve probably done just that – dreamed about it. Paying retail price for a truck like that can put a huge dent in your wallet or your savings account. However, you can get a truck like that for much less.

There are many different kinds of Phoenix truck auctions, but two of the most popular happen to be police confiscated auto auctions and government surplus auto auctions.

Police confiscated auto auctions feature trucks that have been seized due to asset forfeiture in addition to surplus vehicles that have been used by the local police department. Police truck auctions are one of the best places to pick up a used truck. Many people think that the only vehicles available at police truck auctions are actual police trucks. Well, they’re right – but only partially!

Government auto auctions get their supply from criminals. When someone is convicted of a crime, like drug trafficking, the government can seize their assets, including their vehicle. Bad for the criminals but good for you! Government seized automobiles are usually luxury vehicles – BMW, Cadillac, Mercedes, Infiniti, Lexus – and sometimes you may even come across and exotic import! Not many people can afford a truck like this, but it’s possible if you attend a Phoenix truck auction.

Government auto auctions may also feature their own surplus vehicles, or those no longer needed. These can be passenger vehicles, decoy trucks, heavy equipment or even motorcycles, bicycles and ATVs. Other trucks featured at government auctions are retired fleet vehicles. These kinds of automobiles are replaced regularly by their respective agencies and are usually domestic trucks with high mileage that have been meticulously maintained. You are much more likely to receive vehicle history with a government-owned and operated vehicle than you are a seized vehicle. Keep this in mind if vehicle history is important to you. However most vehicles can have a carfax report run to check on any potential ownership problems or maintenance issues.

Please remember: Inspecting trucks being sold at a police seized truck auction is a must! Trucks sold at police seized auctions are sold “As-Is” with no warranty or guarantee unless still under manufacturers warranty. In an “As-Is” auction, there is no warranty on the merchandise and the bidder is responsible for removal from the auction location. This means that the bidder must rely on their own inspection and knowledge to make bidding decisions. Some auction houses, however, allow bidder to bring their own mechanic for vehicle inspections.

Regardless of the frequency of a Phoenix truck auction, you can usually find the event in the local newspaper or published on an online auction site that works with the police departments in your area. The advertisement or listing will give the date, time and place of the auction as well as a synopses of the trucks that will be auctioned off. They may also give a date in which interested parties are invited to inspect the trucks so that they can make decisions about what to buy and how much to spend.

If you're in the market for a good deal on a used truck, it's definitely worth your time to see what's available at your next Phoenix truck auction.

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Finding auto sound systems that can keep up with the constantly evolving technology of today is a real challenge for many car and sound enthusiasts not only around the nation but also around the world. There was a time in the not so distant past when car stereos that had CD players or CD disc changers where the cutting edge of technology. New technology however has nearly rendered the CD players in cars as obsolete as long forgotten 8-track players. The sad news is that many carmakers are clinging to the old days and only offer something as modern as cassette players as standard equipment for auto sound systems.

I think those days will soon be forgotten, as cassettes are no longer even in mainstream production. You should also find that as CDs are rapidly becoming replaced by MP3s that take up very little space in our cars and homes, one day very soon we may see that music companies have decided it is no longer cost effective to produce CDs and render all music to digital formats. So, what does this mean for auto sound systems? It's actually good news for savvy manufacturers are well as savvy consumers who have their eyes on the future and the growing role technology is playing in our lives and as well as our commute to work.

We've seen a recent introduction of satellite radio to our selection of auto sound systems. These stations offer the allure of no commercial interruptions to your music play in exchange for the price of a monthly subscription. At the moment there are two major companies that offer this service to consumers and each have rather proprietary equipment for their use and installation into your car. They are actually offering some rather tempting offers in order to encourage subscribers. Among those wonderful offers are auto sound systems for your vehicle at less than $100 with a prepaid year of subscription services.

For the satellite radio companies this indicates a constantly growing pool of prospective subscribers and the cost of the equipment is a drop in the bucket when compared to customer loyalty and being on the cutting edge of sound technology. The drawback is that you must decide which service you wish to go with before making the purchase. Also while they offer a very nice auto sound system (bare bones kind of kit that only allows for the radio reception in most cases) at a very sweet price, if you want upgrades such as MP3 compatibility, CD players, CD changers, DVD players, GPS, or any number of other new and advanced technology you will still have to purchase those for your sound system at an upgraded price. There are a few packages that come with these things, but the price is a little on the hefty side. Oh the sacrifices we will make for a more enjoyable daily commute.

Know what your expectations are before you decide to purchase the auto sound system of your dream or you could find that it is more the stuff that nightmares are made of than sweet dreams. Do not live in constant fear that if you buy today you will find something you like better 6 months from now, that is a reality. Technology is growing and evolving at a frightening pace. Find the auto sound system that you like best today and make that your purchase. This is a much better option than waiting around indefinitely and purchasing one just as your warranty expires on your car and it's time for a trade in and another auto sound system.

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