Introduction
Strain energy theory is most of the time categorized as one of the theories of yielding. This is usually done when expressed in terms of principles stress. The main proposers of this theory were Beltrami and their attitude to Haigh. In addition to that, the strain energy theory is mainly focused on an elastic material in that it is based on the most significant value based on the total energy stored in the material. It is for this reason that many research analysts have classified it as a stress and strain product considering that the main focus of the theory is a product of stress and strain in any given elastic material (Jain 2002).
During the calculation of the total strain energy in a 3-dimensional state using the equation above, one will be able to foretell any failures which may occur in an elastic material just in case it is exposed to any type of load. When an elastic material is being exposed to any type of load, it can either be subjected at a quick pace which may occur suddenly in that load in question is exposed to the elastic material in a quick manner (Negi 2008). On the other hand, the load in question may be exposed to an elastic material in a slow manner which may occur gradually in that the load is exposed to the elastic material in small bits. In the two cases, the load has been exposed to the elastic material in two different ways which will be discussed further in this research paper.
Thesis Statement
With reference to the given questions, this research paper will conduct research to find out how the strain energy theory applies when a load is applied on an elastic material suddenly and gradually. In addition to that, this research paper will discuss how the strain energy theory has been developed mathematically with the use of helical springs using their performance under loaded and unloaded conditions.
The application of a load on an elastic material can be done gradually or can also be done suddenly. In both cases of the application of a load on an elastic material, there have been always stress and deformation but the result of the stress and deformation that is caused when a load is exposed suddenly is usually higher that when a load is exposed gradually (Mubeen 2009). This is due to the sudden change in the size and weight of the load in that when a load is exposed suddenly, there is always a sudden change in size and weight which will cause a higher result of stress and deformation. As opposed to this, when a load of the same size and mass is exposed gradually on an elastic material, the change in size and weight is usually gradual which will in turn translate to less result of stress and deformation (Staab 2009).
Discussion
When a load is exposed suddenly to an elastic material, there is always a structural response which may result in complete damage of the structural positioning of the elastic material (Ratner 2003). A very good example of this case is when a load of 1 ton is exposed on a truck that can be able to carry over 5 tons of load. When the 1 ton load is exposed suddenly on the truck, this may result in the destruction of the shock absorbed considering that there was a sudden change in the weight, size and structure of the truck. Research analysts have been able to prove that when a load is exposed suddenly to an elastic material, it may lead to the destruction of the structure considering that the shock absorbers which in this case will be the springs will not be able to hold this weight thereby leading to their elastic limit and thereafter their breakage.
The equation for the Total Strain Energy when under a load
Using the same example as above, when a load of 1 ton is exposed gradually to a truck that may be able to carry over 5 tons worth of weight, no breakage of the shock absorber will result. This is due to the fact that the shock absorbers which in this case are the springs will absorb the shock that will be released by the small amount of weight and size that is being applied on them gradually and will thereby be able to hold the whole amount of load when exposed on a gradual pace (Christensen 2010). Research analysts have proven that most of the mechanical machinery that are being developed today can only be able to hold any amount of load which does not exceed its elastic limit but for this to happen, the load must be applied gradually to the elastic material to prevent the breakage of the mechanical machinery.
Helical springs are wires that are coiled to make a helix (Jindal 2010). The helical springs that are developed through the coiling of the wires are square, rectangular or circular in manner and are used to act as shock absorbers in that the coiling of the wires will be able to make the wire absorb more and more weight without having to break (Gdoutos 2010).
Discussion
When applying a load on a helical spring, it is very important to consider several facts that may include; the nature of the load that is being applied in that the more the weight of the load that is being applied, the more the springs so as to be able to handle more shock that is being released from the application of the load. Another very important aspect to look out for is cost and environmental conditions in that the helical spring that will be made must be able to adapt to the environmental condition of where the load is being applied thus to reduce cases of breakage (Vadlamani 2007).
Helical spring under compression and torsion
A very good example of the use of the helical springs is the brake controllers in vehicles (Karwa 2002). In this case, the driver of the vehicle will step on the brake pedal which will apply load on the helical springs that are used in the development of the braking system (Young 2008). This will then translate to the amount of pressure that will be applied by the helical springs of the brake pads which will then be able to result in the stoppage of the vehicle which was in motion (Jain 2004). To be able to come up with a suitable application for the helical springs, there is always the use of mathematical models in that the model will convey very important information that will be considered very relevant to the designs of the springs (Rao 2008).
Research analysts have been able to use mathematical modeling in a bid to trying to conveying the important messages from the helical springs (Barnett 2001). There is also the recent development of the audio modeling where analysts will be able to hear the message that is being conveyed by the helical springs through an audio enhancement. The stiffness and deflection of the spring will be mainly determined by the number of coils that are used in that helical springs in that the higher the number of springs in the helical spring, the higher the deflection and stiffness in that the spring will be able to carry more load without reaching its elastic limit (Jones 2008).
Conclusion
In conclusion, strain energy theory can be categorized as a theory of yielding and is considered a product of stress and strain. In addition to that, the strain energy theory is mainly focused on an elastic material in that it is based on the most significant value based on the total energy stored in the material. In the strain energy theory, when a load is exposed to an elastic material, it can either be subjected in a quick pace which may occur suddenly in that load in question is exposed to the elastic material in a quick manner. On the other hand, the load in question may be exposed to an elastic material in a slow manner which may occur gradually in that the load in exposed to the elastic material in small bits. Research analysts have been able to prove that when a load is exposed suddenly to an elastic material, it may lead to the destruction of the structure considering that the shock absorbers which in this case will be the springs will not be able to hold this weight thereby leading to their elastic limit and thereafter their breakage.
References
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