Behavior of Materials in Tension

Understanding the behavior of materials when loaded is a vital part of creating safe and reliable structures. Of the various stresses a given structural element may be subjected to, tensile stress is perhaps the most concerning. - Not that materials are necessarily always that much stronger in compression and shear, given an equal force per unit area.

It doesn't take a genius to see that beams are weaker to bending than columns are to buckling. This is due to the direction and position of the primary loads and not because of the material's tensile properties. This becomes apparent when both the beams and columns are of the same material, length, and cross section, yet the beams will exhibit major deflection long before the column comes even near buckling.

Due to this phenomenon, a beam must be carefully designed, with its second moment of area and material make-up ultimately deciding its resistance to deformation and failure. Rather than only tension, a horizontal structural member will more likely experience both tension on the upper face, and compression on the lower face, as it bends downward when loaded.

Stress-Strain Curve

Generally speaking, there are two kinds of material-types, ductile and brittle. By using a stress-strain curve one can graph the behavior of these materials starting from its original state to its point of rupture. Ductile materials will exhibit both an engineering or apparent stress-strain curve as well as a 'true' or actual stress-strain curve.

The difference is that the engineering curve bases its stress on the initial cross section of the material in question, whereas the true curve takes instantaneous ratios as the cross sectional area decreases due to Poisson's contractions. So with the engineering curve, the stress decreases with the decrease in cross section, whereas stress in the true curve will continue to rise.

Under normal test conditions, the true stress-strain curve is difficult to determine without continually monitoring the cross section. This is why the engineering curve is commonly used to make quick analysis of materials, even though the true curve is a better representation. As long as you don't get the two mixed up, they both have their individual pros and cons.

Strain-hardening and Necking

Ductile materials also exhibit a phenomenon called strain-hardening or work-hardening when its yield point has been crossed and it enters plastic deformation. As the stress increases due to the strain-hardening, it will eventually reach its ultimate strength, at which point it will begin necking.

Necking is when the material's cross section begins decreasing rapidly in a localized point, as opposed to a uniform decrease across the entire member. Once a member begins necking, rupture will soon follow. Necking is strictly a property of ductile materials, as opposed to brittle materials which will fracture before displaying any major cross-sectional reduction.

Brittle materials do not exhibit the discrepancy between true stress-strain and engineering stress-strain, as they neither have a yield point nor strain-harden. What this means is that the stress-strain curve of brittle materials will be linear, and extend in a linear fashion right up to their point of rupture. There is no yield point where the stress decreases, and no necking after ultimate strength.

Explaining the Phenomenon of Time Dilation

Physics is an interesting subject but not necessarily easy for all students. Many times, students find it tough to understand the concepts explained to them in a classroom setting. In such cases, it is vital for the students to seek help from the private Physics tutors who can help you understand the concepts clearly. In this article, we will explain the phenomenon of time dilation.

With the introduction of the special and general theory of relativity, Albert Einstein wrecked two established orders of physics. The special theory of relativity, published in 1905, brought together space and time into a sole entity. On the other hand, in 1915, general theory of relativity showed declared the gravity to be a result of the curve of space time.

First, Albert Einstein delivered a blow to the idea of an absolute time proposed by Sir Isaac Newton. After that, he went on to find flaws with the theory of gravitation by Newton, with his own general theory of relativity. This theory states that the matter warps or bends the space time about it, and the movement of the objects is influenced by this curve.

However, it must be noted that the general and special theory of relativity are the two distinct theories. One of them describes the motion as per the inertial frames of reference, while the other describes the similarity of the accelerated frames and gravity. There is one phenomenon that is quite commonly predicted by both the theories, and it is time dilation.

The special theory mentioned above is actually based, and derived from the two very fundamental postulates, one of which states that the speed of light remains steady in vacuum and other states that the laws of physics stay the same in all sorts of inertial frame. Any frame that moves at steady velocity with deference to a fixed frame is called an inertial frame.

The principle of time dilation states that time will slowdown for space ship with reverence to the time that is related with the fixed frame. If the velocity of space ship is larger, then the time dilation will be slower. The equation brought forward for time dilation is as follows: Δt' = Δt/ √ (1 - v2 / c2). In the formula, Δt' refers to the time interval on the space ship, and Δt refers to the time interval for rest frame of the reference. If you want to know more about time dilation then consider hiring a Physics tutor who can explain the concepts to you with the help of practical experiments.

Reproduction Cycle in Angiosperms


As a student of Botany, you will be interested to gain in-depth knowledge of the plants. However, sometimes students find it tough to understand because there are so many scientific names to deal with. The instruction provided in a classroom may not be enough to clear all your doubts, especially because of the large number of students in a class. In such cases, it is recommended that you take help of a private Botany tutor. In this article, we will discuss about the reproduction cycle of angiosperms, which are the seed bearing flowering plants.

Have you wondered how this world would look like if there were no flowers? There wouldn't be so much of colors in our lives. Thus, the flowers have an important role to play in the master plan of nature, as they execute the reproduction cycle in plants. With the evolution of plant species on the planet, the reproduction from seeds became popular. These seed bearing plants are classified into two divisions, gymnosperms and angiosperms.

It is fascinating to note that the angiosperms came into existence from nearly 240 to 200 million years ago, when they swerved from the gymnosperms. Their reproductive organs are much more modified and advanced than the gymnosperms. The basic difference between the two is that in gymnosperms, the seeds are not enclosed inside a floral structure, but in angiosperms, the unfertilized seeds are enclosed in the ovaries of flowers. After fertilization, the ovaries become swollen and fleshy. They become fruits containing the fertilized seeds, which are ripe for germination under favorable conditions.

Thus, the flowers are the main reproductive units, but they may differ sdxually. It is interesting to note that some plants have separate male and female sexes, how others have both the reproductive organs present in the same flower. Though discovered quite later, angiosperms are the prevailing plant varieties causing reproduction in the planet today.

For the reproduction to take place, the angiosperms are more reliant on humans than the animals, because they are responsible for the dispersal of seeds. We, humans use flowers and fruits for decoration and consumption purposes. There are also several insects and birds that feed on fruits and the nectar of flowers. This is how the pollens and seeds arrive at their destination, through the bipedal, quadrupedal and the avian carriers.

The reproduction cycle of a distinctive angiosperm includes pollination, fertilization, development of fruit and seeds, and the dispersal of seeds. If you wish to know more about each step in detail then consider hiring an expert private Botany tutor.

Characteristics of Kingdom Monera


As a student of Biology, you will study regarding the various living entities ranging from microorganisms to mammals. Though all these sub-branches of biology are very interesting, you may also find it difficult to understand the various characteristics of the several plant and animal kingdoms. Furthermore, classroom instruction may not be enough to clear all your doubts. If you are planning to take up a career in this field then you must have a strong foundation. Hence, you must consider hiring a Biology tutor in your locality to clear all your doubts. In this article, we will discuss about the kingdom Monera.

To begin with, kingdom Monera refers to the microorganisms that are considered as the most ancient living creatures in the world. It includes the single celled organisms known as bacteria. An in-depth study of the Monera kingdom characteristics will reveal that this kingdom is divided into two different groups -Archaea and Bacteria. This classification was included in the three-domain system of taxonomy, established in the year 1991. Here are some important characteristics that will help you understand the kingdom Monera better:

    * They measure about 1 micrometer in length and are complex entities.
    * The cell structure is basically unicellular, and some organisms form certain groups or filaments.
    * They are simplest form of prokaryotic cell structures.
    * The cell structure lacks nuclei, and several other cell organelles.
    * The cell wall is composed of polypeptide cross links and polysaccharides with a chemical known as peptidoglycan.
    * They do not have encircled sub-cellular organelles such as mitochondria, and only contain ribosomes.
    * In this organism, the DNA is enclosed in the cytoplasm known as nucleoid. There are several bacterial species that comprise rings of DNA known as plasmids.
    * The cytoplasm is encircled by the plasma membrane, which lies underneath the cell wall. The plasma membrane of the cell is composed of lipids and proteins.
    * The reproduction usually takes place asexually through binary fission; or sexually by conjugation. The process of circulation as well as digestion is usually carried out through diffusion.

The Monera kingdom actually involves all the bacteria that are known to infect animals, humans as well as plants. However, most of these microorganisms are known as beneficial bacteria, instead of pathogenic bacteria. The examples include actinomyces, bacillus, campylobacter, clostridium, helicobacter, klebsiella, mycoplasma, neisseria, pseudomonas, and staphylococcus. If you wish to learn more about them in detail then consider hiring a private Biology tutor.

Archimedes' Law of Floatation Explained


Students with an affinity for Physics always have a quest for gaining knowledge about the mysteries of this world. Have you wondered how a vast ship sails calmly on the sea? Or, how a hot air balloon happens to go up in the air? Unfortunately, students cannot get all their questions answered in a classroom setting as there are several students seeking the attention of teachers. In such a case, you must consider hiring a private Physics tutor who will not only clear all your doubts but also explain the concepts further with the help of illustrations. In this article, we will discuss about the Archimedes law of floatation wherein the lies the answer to the above questions.

It is known that Archimedes was one of the best mathematicians of his time. He was also a physicist and an inventor. He was Greek by birth and there are several amazing inventions to his credit. He is known for the famous principle of floatation and the screw propeller. His works in the field of math includes discovering infinitesimals, formulas for measuring a circle, spheres, parabolas, cylinders and cones. The principle of floatation remains of his most recognized and popular inventions till date.

You will find it fascinating to know that Archimedes devised with most of his inventions to help his nation during the time of war. However, this principle was invented when a king asked him to verify the purity of a golden crown without harming it in any way. After days of pondering over it, the great scientist came up with an amazing solution and he took to the streets shouting 'eureka, eureka' in joy. The answer that he found was that he can find the density of the crown by measuring the volume of water that the crown displaced when immersed in a tub.

Thus, the Archimedes' law of floatation states that an object, whether wholly or partially submerged in liquid, experiences an upward thrust and the force is equal to the volume of the liquid displaced by the object. It is interesting to note that for any object that is completely submerged in liquid, the amount of fluid displaced is equal to its volume. And for an object that floats on a liquid surface, the volume of the displaced fluid is same as that of the object. This object experiences an upward force known as the buoyant force. If you wish to know more about the various inventions by Archimedes then hire a private physics tutor today.

Chemistry and Thermodynamics

Lost in the woods of science.

The study of science starts for everyone as a small trail in the woods of ignorance, but with effort and experience, that trail becomes our personal highway of knowledge and information, opening many possibilities. Albert Einstein, like everyone else, started out in the woods, and he showed that getting out is worth the effort, not just for him, but for all his knowledge did for Mankind. Science is not for everyone and few Einstein's exist. Sadly many get lost, confused and frustrated, giving up before they can utter their first "Eureka", as a gem of knowledge falls into place. Those "Eureka" moments can excite us to keep going down our particular path.

So the first step is to be motivated and want to know more.

The next important step is to pay attention to the definitions: something that is important in every area: in sports you must know the rules to play the game: it is same for science. Knowing the definitions clears up confusions, and applying them (solving problems) solidifies them. Eventually the scientific method and thinking become a way of life, and gives insight into many situations, even outside your particular area of expertise.

A structure emerges. For example, the life sciences and medicine rest upon biochemistry and pharmacology, which rests upon organic chemistry, and organic depends on physical chemistry. Physical chemistry rests upon physics, and mathematics is the logic that binds them all together.

Along the way there are many sidelines, too numerous to list here: new materials, nano-technology are two important and well known disciplines. Also various areas overlap into multi-discipline fields, like physical chemistry and organic (physical-organic chemistry); organic synthesis and chemical kinetics (organocatalysis), Inorganic and organic chemistry (organometallic chemistry): the list goes on and on.

Clearly no-one can become an expert in all of these areas. However a good foundation in the basic of physical science allows one to at least be in a position to appreciate the work of others in the many areas of scientific endeavor. You might end up as a lawyer, a social worker or in finance. A good background in science will help the lawyer argue his case of, say, patent violation; helps the social worker understand the side effects of medication a client might be taking, and allows the financier to make intelligent decisions about whether to invest in one mining company or another.

On the other hand, you might become a scientist which leads to many interesting careers.

Scientists and engineers

Science can be divided into two broad categories: fundamental science (research), and applying those ideas (engineering: also called Research and Development (R&D)). Today there are about ten times more engineers than there are scientists. It takes more effort and more people to take the fundamental ideas developed by a few, and turn them into technology that we use to improve our quality of life.

Think of the automobile industry. The internal combustion engine, based upon the Otto cycle was developed by a few (who showed it worked), and then many engineers took that basic idea and over the last hundred years developed the cars we have today.

To be a good engineer, you must start with the fundamentals and learn the basics before you can apply them.

The macroscopic and the microscopic

A broad division of science is into the macroscopic (big enough sample that we can measure and examine), and the microscopic (atoms, molecules and collections of these, too small to observe individually).

There are two big cornerstones of macroscopic science: Thermodynamics (the study of heat, work and efficiency), and Classical Mechanics (Newtonian physics that describes the motion of macroscopic objects).

The microscopic is governed by quantum mechanics.

Since microscopic particles have a lot of symmetry, the field of group theory (a mathematical subject) should be mentioned. This helps to visualize molecules and reactions, and has particular relevance in the most fundamental science, which is physics. You do not have to be a mathematician to use group theory. Mathematics is a tool of scientists: logic guides us.

The field of Statistical Mechanics relates macroscopic objects to its microscopic particles.

The example of chemistry

Chemistry is the study of the making and breaking of bonds-that is chemicals react to form different chemicals. A chemical reaction proceeds if the conditions are right: two important conditions are energy and entropy. Both are substances and entropy is as tangible as energy. How did this come about?

Engineers started to notice things a couple of hundred years ago: like horses that walked in a circle and drove the machinery to bore cannons. The horses walked at a constant rate, (constant energy) but a dull bit produced a lot of heat and not a lot of work (boring the cannon was slow), but a sharp bit produced a lot less heat and more boring. This is the First Law of Thermodynamics:

Energy (horse power) = heat (friction) + work (cannon bore).

Clearly energy is not cheap (the horses must be purchased, fed and cared for), so it would be better to reduce the heat loss and increase the work done. That is, the efficiency of the use of energy became an important consideration.

In the 19th century, thermodynamics further evolved motivated by the need to increase efficiency of the steam engine that drove the industrial revolution. The first steam engines were about 3% efficient and so improvements were definitely needed. Adding a second cylinder, for example, improved things lot but they could do more? Could the dream of 100% efficiency come true-i. e. perpetual motion?

This led Sadi Carnot in the 1830's to define a cycle for the steam engine from which entropy was discovered, and the Second law of Thermodynamics was formulated-perpetual motion was shown to be impossible. The Otto cycle was developed for an internal combustion engine about forty years later.

Although alchemy is an old subject, it was only after the First and Second Laws of thermodynamics were developed that chemistry really took off. Many were involved in its development. Besides Sadi Carnot, a few notable names are James Maxwell, Rudolf Clausius, James Joule, Willard Gibbs and Ludwig Boltzmann.

The ideas they developed apply well to chemistry. When bonds are broken, energy must be added to the system; and when bonds are formed, energy is released to the surroundings. Some chemical reactions produce more randomness (higher entropy) and sometimes more order (lower entropy) as the atoms rearrange to form products. Both energy (heat and work) and entropy (randomness) play important roles in the spontaneity of a chemical reaction.

Here is an example. Trinitrotoluene (TNT) can explode (a rapid chemical reaction). From the chemical formula it has three nitrogen bonds. Most chemical explosives contain nitrogen by the way. The combustion of one mole of TNT releases 3,400 kJ mol-1 of energy,

C7H5N3O6(s) + 21/4 O2(g) à7 CO2(g) + 5/2 H2O(g) + 3/2 N2 (g) ∆H = -3,400 kJmol-1

Compare this, however, with the energy of combustion of sugar as sucrose (a slow chemical reaction),

C12H22O11(s) + 12 O2(g) à12 CO2(g) + 11 H2O(l) ∆H = -5,644 kJ mol-1

Sucrose produces a lot more energy per mole that TNT! So why is not sucrose an explosive too? Sucrose burns slowly relative to TNT, with a corresponding slow release of carbon dioxide. TNT burns so fast that a lot of energy is released in a short period of time. Furthermore, solid TNT occupies a small volume, but the final volume is equal to 11 moles of gas (about 250 liters at STP). The destruction is not caused so much by the heat released but the rapid expansion of the gases produced. Using the First Law, the energy released by one mole, (3,400 kJ) goes into some heat but a lot of work is done to the surroundings as the gas expands, and this can cause damage.

This is where entropy comes in. Notice that the right hand side of the TNT combustion has only 21/4=5.25 moles of gas, while the RHS has 11 moles of gas. This means there is more disorder on the RHS than the LHS. Clearly the rapid expansion in the explosive combustion of TNT can lead to destruction (it would knock Humpty Dumpty off his wall) and cause greater disorder and therefore the entropy increases. Both energy and entropy are favorable for this reaction to proceed. This is not always the case, especially biological processes, where entropy, not energy, is the main driving force.

Thermodynamics tells us which chemical reactions will proceed and which will not. Chemical Kinetics tells us how fast those reactions take place, and how much energy is needed to initiate a reaction. TNT is not very sensitive to shock because it has a high activation energy. On the other hand, Nitroglycerine, (NG), another chemical explosive (with lots of nitrogen bonds), explodes with a small shock and cannot be transported in liquid form at room temperature. It has a low activation energy. Alfred Nobel solved the nitroglycerine problem by inventing dynamite: reducing the sensitivity to shock by soaking NG in sawdust, paper or some absorptive material. The patent was so successful that he left us the legacy of the Nobel Prize.

Equilibrium thermodynamics is a closed field today with no new fundamental research being done. It is a beautiful, complete and compact theory that gives the relationship between the macroscopic quantities we can measure: energy, heat capacities, compressibility factors and many more, with wide application.

Thermodynamics is essential knowledge for all chemists. However thermodynamics fails to explain why these relationships exist. This is given by another elegant theory called Statistical Mechanics.

Physical Chemistry covers all these.

There is a lot more to say, but that is a summary. Actually many say that thermodynamics is not a good name because it describes equilibrium properties, not dynamical one. A better name would be thermostatics--but nobody calls it that.

I am a Professor of Chemistry at McGill University (Montreal, Canada), as well as president of MCH Multimedia Inc.

I am also co- author of Physical Chemistry - Laidler, Meiser, Sanctuary. This popular Physical Chemistry Book ( http://www.mchmultimedia.com/store/Physical-Chemistry-ebooks.html ) is widely used in Chemistry Syllabuses around the world.

Also Visit my blog http://quantummechanics.mchmultimedia.com for more information about Physical Chemistry, Quantum Mechanics and more.