In some situations, the stress within an object can be described by a single number, or by a single vector (a number and a direction). Three such simple stress situations are the "uniaxial normal stress", the "simple shear stress", and the "isotropic normal stress".
Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress.
Therefore in a uniaxial material the length increases in the tensile stress direction and the other two directions will decrease in size. In the uniaxial manner of tension, tensile stress is induced by pulling forces. Tensile stress is the opposite of compressive stress.
Structural members in direct tension are ropes, soil anchors and nails, bolts, etc. Beams subjected to bending moments may include tensile stress as well as compressive stress and/or shear stress.
Tensile stress may be increased until the reach of tensile strength, namely the "limit state" of stress.
All real objects occupy three-dimensional space. However, if two dimensions are very large or very small compared to the others, the object may be modelled as one-dimensional. This simplifies the mathematical modelling of the object. One-dimensional objects include a piece of wire loaded at the ends and viewed from the side, and a metal sheet loaded on the face and viewed up close and through the cross section.
Pericyclic reaction
In organic chemistry, a pericyclic reaction is a type of chemical reaction between organic compounds. In the case of pericyclic reactions, the transition state of the molecule is a ring (has a cyclic geometry), and the reaction goes forward in a concerted way. Pericyclic reactions are usually rearrangement reactions. The most important groups of pericyclic reactions are:
In general, pericyclic reactions are equilibrium processes. However, it is possible to push the reaction in one direction if the product is at a significantly lower energy level. This is applying Le Chatelier's principle to a reaction involving a single molecule.
Many pericyclic reactions have similar stepwise radical processes connected with them. Chemists disagree whether some reactions are pericyclic reactions. For example, it is not definitively known whether the [2+2] cycloaddition mechanism is concerted (or may depend on the reactive system). Many pericyclic reactions have similar reactions that are metal-catalyzed. But these metal-catalyzed reactions are also not really pericyclic. The metal catalysts stabilize the reaction intermediates. So the reaction is not concerted, but rather metal-stabilized.
A large photoinduced hydrogen sigmatropic shift was utilized in a corrin synthesis performed by Albert Eschenmoser containing a 16π system.
Due to the principle of microscopic reversibility, there is a parallel set of "retro" pericyclic reactions, which perform the reverse reaction.
Pericyclic reactions also happen in several biological processes:
2011–12 Manchester United F.C. season
The 2011–12 season is Manchester United's 20th season in the Premier League.
Manchester United signed a £40 million four-year deal with DHL.
In November, Sir Alex Ferguson celebrated 25 years in charge of the club.
Manchester United started their season with a tour in the United States. United finishing the tour with a game against Barcelona in Washington on 30 July.
Manchester United will face Benfica, Basel and Otelul Galati in Group C.
Manchester United were drawn against Crystal Palace in the quarter-finals of the League Cup.
The Annoying Orange
The Annoying Orange is a comedy web series created by Dane Boedigheimer. The main character is an orange who annoys other fruits. The episodes are uploaded to the YouTube channel "realannoyingorange" weekly, with now over 200 videos. , The channel had almost 3 million subcribers. At that time, it was 43rd in terms of how many people are subscribed to it.
Orange is the main character. He is described as really annoying, but sometimes funny. He warns others about a knife and other items ready to kill them.
Pear is described as a normal/bad/lying/negative/abusive character. He was Orange (Annoying Orange)'s best friend and normally tells Orange to stop being annoying and shut up, but it is discovered in the episode "Wishful Thinking" that Pear would not be friends without Grapefruit. Pear is in Grapefruit's gang and was making fun of Orange.
Midget Apple is a small apple in the series. He does not like being called "Midget Apple", prefering the term "Little Apple".
Apple is Orange's former best friend and current rival (bully). Apple is in Grapefruit's bullying gang.
In 2012, Cartoon Network made a 2012-2014 high fructose adventures TV show based on the YouTube series.
Cycloaddition
A cycloaddition is a chemical reaction between reactants with double bonds that get replaced by a ring structure. It is a pericyclic chemical reaction where "two or more unsaturated molecules (or parts of the same molecule) combine with the formation of a cyclic adduct in which there is a net reduction of the bond multiplicity." It is a cyclization reaction: it makes new ring of atoms.
Cycloadditions are named by the basic size of the molecules that are being brought together. This would make the Diels–Alder reaction a [4 + 2]cycloaddition, and the 1,3-dipolar cycloaddition a [3 + 2]cycloaddition. This type of reaction is a non-polar addition reaction.
Heat can cause the double bonds to form a ring. Thermal cycloadditions usually have (4n + 2) π electrons participating in the starting material, for some whole number "n". Because of orbital symmetry, most cycloadditions are suprafacial-suprafacial. Rarely, they are antarafacial-antarafacial. There are a few examples of thermal cycloadditions which have 4n π electrons (for example the [2 + 2] cycloaddition). These proceed in a suprafacial-antarafacial sense. For example, the dimerisation of ketene has a orthogonal set of p orbitals. Those p orbitals allow the reaction to proceed using a crossed transition state.
Light can also cause the double bonds to form a ring. Cycloadditions in which 4n π electrons participate can also occur as a result of photochemical activation. Here, one component makes an electron move from the highest occupied molecular orbital (HOMO) (π bonding) to the lowest unoccupied molecular orbital (LUMO) (π* antibonding). After the electron is promoted to the higher orbital, orbital symmetry allows the reaction to proceed in a suprafacial-suprafacial manner. An example is the DeMayo reaction. Another example is shown below, the photochemical dimerization of cinnamic acid.
Note that not all photochemical (2+2) cyclizations are cycloadditions; some are known to operate by radical mechanisms.
Some cycloadditions instead of π bonds operate through strained cyclopropane rings; as these have significant π character. For example, an analog for the Diels–Alder reaction is the quadricyclane-DMAD reaction:
In the (i+j+...) cycloaddition notation i and j refer to the number of atoms involved in the cycloaddition. In this notation a Diels-Alder reaction is a (4+2)cycloaddition and a 1,3-dipolar addition such as the first step in ozonolysis is a (3+2)cycloaddition. This notation uses parenthesis. The IUPAC preferred notation however, with [i+j+...] counts electrons and not atoms. It uses square brackets. In this notation, the Diels–Alder reaction and the dipolar reaction both become a [4+2]cycloaddition. The reaction between norbornadiene and an activated alkyne is a [2+2+2]cycloaddition.
The Diels–Alder reaction is a [4+2]cycloaddition reaction.
The Huisgen cycloaddition reaction is a [2+3]cycloaddition.
The Nitrone-olefin cycloaddition is a [3+2]cycloaddition.