What Is the Shear Modulus Definition and Examples

The shear modulus is defined as the ratio of shear stress to shear strain. It is also known as the modulus of rigidity and may be denoted by G or less commonly by S or  ÃŽ ¼. The SI unit of shear modulus is the Pascal (Pa), but values are usually expressed in gigapascals (GPa). In English units, shear modulus is given in terms of pounds per square inch (PSI) or kilo (thousands) pounds per square in (ksi). A large shear modulus value indicates a solid is highly rigid. In other words, a large force is required to produce deformation.A small shear modulus value indicates a solid is soft or flexible. Little force is needed to deform it.One definition of a fluid is a substance with a shear modulus of zero. Any force deforms its surface. Shear Modulus Equation The shear modulus is determined by measuring the deformation of a solid from applying a force parallel to one surface of a solid, while an opposing force acts on its opposite surface and holds the solid in place. Think of shear as pushing against one side of a block, with friction as the opposing force. Another example would be attempting to cut wire or hair with dull scissors. The equation for the shear modulus is: G Ï„xy / ÃŽ ³xy F/A / Δx/l Fl / AΔx Where: G is the shear modulus or modulus of rigidityÏ„xy is the shear stressÃŽ ³xy is the shear strainA is the area over which the force actsΔx is the transverse displacementl is the initial length Shear strain is Δx/l tan ÃŽ ¸ or sometimes ÃŽ ¸, where ÃŽ ¸ is the angle formed by the deformation produced by the applied force. Example Calculation For example, find the shear modulus of a sample under a stress of 4x104 N/m2 experiencing a strain of 5x10-2. G Ï„ / ÃŽ ³ (4x104 N/m2) / (5x10-2) 8x105 N/m2 or 8x105 Pa 800  KPa Isotropic and Anisotropic Materials Some materials are isotropic with respect to shear, meaning the deformation in response to a force is the same regardless of orientation. Other materials are anisotropic and respond differently to stress or strain depending on orientation. Anisotropic materials are much more susceptible to shear along one axis than another. For example, consider the behavior of a block of wood and how it might respond to a force applied parallel to the wood grain compared to its response to a force applied perpendicular to the grain. Consider  the way a diamond responds to an applied force. How readily the crystal shears depends on the orientation of the force with respect to the crystal lattice. Effect of Temperature and Pressure As you might expect, a materials response to an applied force changes with temperature and pressure. In metals, shear modulus typically decreases with increasing temperature. Rigidity decreases with increasing pressure. Three models used to predict the effects of temperature and pressure on shear modulus are the Mechanical Threshold Stress (MTS) plastic flow stress model, the Nadal and LePoac (NP) shear modulus model, and the Steinberg-Cochran-Guinan (SCG) shear modulus model. For metals, there tends to be a region of temperature and pressures over which change in shear modulus is linear. Outside of this range, modeling behavior is trickier. Table of Shear Modulus Values This is a table of sample shear modulus values at room temperature. Soft, flexible materials tend to have low shear modulus values. Alkaline earth and basic metals have intermediate values. Transition metals and alloys have high values. Diamond, a hard and stiff substance, has an extremely high shear modulus. Material Shear Modulus (GPa) Rubber 0.0006 Polyethylene 0.117 Plywood 0.62 Nylon 4.1 Lead (Pb) 13.1 Magnesium (Mg) 16.5 Cadmium (Cd) 19 Kevlar 19 Concrete 21 Aluminum (Al) 25.5 Glass 26.2 Brass 40 Titanium (Ti) 41.1 Copper (Cu) 44.7 Iron (Fe) 52.5 Steel 79.3 Diamond (C) 478.0 Note that the values for Youngs modulus follow a similar trend. Youngs modulus is a measure of a solids stiffness or linear resistance to deformation. Shear modulus, Youngs modulus, and bulk modulus are modulii of elasticity, all based on Hookes law and  connected to each other via equations. Sources Crandall, Dahl, Lardner (1959). An Introduction to the Mechanics of Solids. Boston: McGraw-Hill. ISBN 0-07-013441-3.Guinan, M; Steinberg, D (1974). Pressure and temperature derivatives of the isotropic polycrystalline shear modulus for 65 elements. Journal of Physics and Chemistry of Solids. 35 (11): 1501. doi:10.1016/S0022-3697(74)80278-7Landau L.D., Pitaevskii, L.P., Kosevich, A.M., Lifshitz E.M. (1970).  Theory of Elasticity, vol. 7. (Theoretical Physics).  3rd Ed. Pergamon: Oxford. ISBN:978-0750626330Varshni, Y. (1981). Temperature Dependence of the Elastic Constants.  Physical Review B.  2  (10): 3952.

Education Differences Have Made A Child s Education

There doesn’t go a day where thinking about education differences have made a child’s education much different than what is expected. Today’s society are suffering from the same injustice that our ancestors have gone through. I personally have experienced a type of segregation of education because of being middle class and because of my race. There is a need for equal education systems that can help children of this generation better understand the curriculum and not have to put behind because of who they are and where they come from. Children suffer the most when they are not taught well enough to their abilities that can be shown. There are ways teachers can help advance the knowledge of students by expanding their abilities and explain things better than they believe is best. When one teacher believes their way of teaching is better than other teachers it is hard to tell when you can’t see it personally. Ones abilities are too limited to what wiser peop le can give to you. â€Å"In Math, when two-digit division was introduced, the teacher in one school gave a four-minute lecture on what the terms are called. The children were to copy these names in their notebooks†¦ the math teacher in the other working-class school followed similar procedures regarding two-digit division and at one point her class seemed confused. She said, ‘You’re confusing yourselves. You’re tensing up. Remember, when you do this, it’s the same steps over and over again- and that’s the way division alwaysShow MoreRelatedA Child s Education Is Vital991 Words   |  4 Pagescharacter of a child’s life and education, especially those children of poverty? These questions are important to consider for educators and all involved in the goal for children to have greater achievement. It s even more important to note that forty percent of the poor, in the United States, are children (Stevenson, 1997). Knowing this is the re ason that finding solutions and studying the effects of parent involvement, both at school and at home, can have on a child’s education is vital. This paper willRead MoreHomeless Child Education : Homeless Children1678 Words   |  7 PagesHomeless Children Education Several factors severely compromise the ability of homeless children to succeed in school, as I discovered in interviews with 277 homeless families in New York City in 1988. Barriers to the success of these children include health problems, hunger, transportation obstacles, and difficulty obtaining school clothes and suppliesà ¢Ã¢â€š ¬Ã¢â‚¬ all of which are linked to low attendance rates (Rafferty and Rollins 1989). Other factors are associated with the nature of the emergency shelterRead MoreAchieving Gender Equality : Education1520 Words   |  7 PagesAchieving Gender Equality: Education in China In Gish Jen’s short story Who s Irish?, the main character is a determined Chinese grandmother who moved to America with her husband when she was a young woman, and now, in her old age, she is nearing her limit when she cannot handle her granddaughter s behavior and how she is being raised. The story was written in 1956 and while reading it a question of interest grew in knowing about gender inequality in China and if it has changed in the last severalRead MoreFor My Research Project, I Will Be Elaborating On Two Main1497 Words   |  6 Pagespeople s actions or does it not make much of a difference. My first research will be focused on does having a college degree help to predict who makes the decision on who brings up children. My main issue that I would be addressed with this data is whether having a degree of a master compared to an associate’s degree makes a difference in who raises a child. The reason behind this is because if a person has finish school with a to p degree, would the parent of whom claim the highest degree have a fullRead MoreWhat Major Policy Changes Has Affected During Educational Provision? England Between 1944 And The Present Day?1694 Words   |  7 Pagespolicy changes that have occurred in educational provision in England between 1944 and the present day in primary education. Introduction A policy is a plan or of action used by the Ministry of education to set out clear rules and expectations for the delivery of programs and services to the public.(BCE ) In this essay I will be discussing two major policy changes that have occurred in educational provision in England between 1944 and the present day in primary education. I will be discussingRead MoreMinority Groups And The Minority Group Within Special Education1698 Words   |  7 PagesDisproportionality refers to the overrepresentation or underrepresentation of a minority group within special education programs and services. The disproportionate representation of minority students in special education has been an ongoing and significant matter in education for decades. More and more minority children are being identified as disabled or having an intellectual disability or learning disability. However, in most cases the children are being misdiagnosed and consequently, are beingRead MoreThe Different Education Exam Systems1266 Words   |  6 PagesIntroductory As we know, different country has diversity style of education system, we cannot say which is better or worse, each one has its own advantages and disadvantages. We can figure out the differences and connections with them, and learn to know the reasons why different countries has different education system. I am going to talk the teaching style and education purpose in three countries, China, America and Japan. As for teaching style, This will determine the interests forRead MoreInequality Can Be Defined As Opportunities Distributed1580 Words   |  7 Pagesindividuals in a society in an unequal distribution. Education is known to be the great equalizer of society, However, unequal distribution of educational resources negates this very concept. In education, a crucial measure of child s performance their socioeconomic status. Difference in social background results in differences in achievement within an academic field. Studies have shown that the higher the socioeconomic status, the more access to better education, and educational resources such as tutoringRead MoreThe Theory Of Developmental Psychology1644 Words   |  7 Pageshuman being to birth to adulthood. It was first made to help infants and children, but now it has expanded to help the adolescence and adults just as well. Paul B. Baltes, has apply the six principles of human development, lifelong, multidimensional, multidir ectional, gains and losses, contextual and historical, and multidisciplinary. There are several fields of developmental psychology like Adolescence, Attachment, Cognitive development, Education, and Parenting that will be address. DevelopmentalRead MoreFactors That Affect The Probability Of An Individual1506 Words   |  7 Pagesprobability of an individual going to college following high school. Using the Sociological Imagination we will examine societal factors that may result in The main subjects that will be explored are how an individual s socioeconomic status , race, gender, and societal norms can have a large impact on them going to college. In this paper we I will be making use of the sociological imagination to interpret the individual issue of chances of attending college. The sociological imagination takes a look

The Effects Of Outdoor Play On Children - 1120 Words

Outdoor Play In today’s society, we have increasing numbers of obesity in children. Researchers are trying to find the answer as to why this is happening. The sad part is, no one has looked at the numbers of how much time a child spends outside has decreased over the last decade. We have increasing numbers of technology being produced on the market and fail to look at how technology has harmed humans in a biological sense. There has been evidence of blue-violet light, produced from smart phones, is related to macular degeneration, where a macula sits in front of the ocular nerve prohibit loss of central vision (Newsbeat, 2014). Why should our world fall into the trap of smartphones and devices and forget about the outdoors? Playing outdoors stimulates many things for children, along with keeping them healthy. One blog promotes playing outdoors and explains the enhancement of development that happens when a child is outside. It’s time our children step away from technolo gy and learn the greatness of the outdoors. Laurie Hollman (2016), a psychoanalyst, wrote an article on Huffington post explaining the positive effects of playing outdoors has on children. When a child is able to play outside, they are first learning to coordinate their body with their surroundings. This can either be through playing with a ball, using a swing, playing on a jungle gym, or even playing hop-scotch. When a child is playing with parent outside they are building a relationship. This relationshipShow MoreRelatedThe Effects Of Outdoor Play On Children1860 Words   |  8 PagesOutdoor Play In today’s society, we have increasing numbers of obesity in children. Researchers are trying to find the answer as to why this is happening. The sad part is, no one has looked at the numbers of how much time a child spends outside has decreased over the last decade. We have increasing numbers of technology being produced on the market and fail to look at how technology has harmed humans in a biological sense. There has been evidence of blue-violet light, produced from smartRead MoreThe Effects Of Indoor Play On Children s Outdoor Play1150 Words   |  5 Pagesover all the aspects of children’s outdoor play [reference? This is a blanket statement that needs to changed or referenced. You need evidence]. Some [factors] that affect outdoor play include risks [such as?], parental concerns about outdoor play and not having adequate play space available for children. Risk is equal to a combination of events/consequences and associated uncertainties (Aven, 2007). Ris k in play refers to any possibility of physical injury during play. Early childhood settings usuallyRead MoreOutdoor Recreation Essay1367 Words   |  6 PagesOutdoor recreation has been around for more than 80 centuries. Throughout the years, outdoor recreation has evolved in many different aspects. Outdoor recreation began as a tool for survival strategies, such as hunting and fishing. As the years have passed, people went on to hunt and fish as a form of recreation. As a population, we can concur that outdoor recreation has many positive attributes such as personal satisfaction and enjoyment, as well as negative aspects that could amount to the costlyRead MoreGardening: Planting SunFlowers in a School Environment Essay1436 Words   |  6 Pageswhich is planting sunflower. I chose this project because my kindergarten’s outdoor environment space is limited. This project involved 5 years old children. The process of growing this sunflower plant took about two months. The p roject has met the objective well. The main objective of this project was experiencing the outdoor environment by the children. Children gain vast benefits from learning outdoors. Being outdoors allows them to move around without many of the restrictions of being insideRead MoreChildren and Technology: Growing Up in the Modern World Can Have Negative Effects on Children1011 Words   |  5 PagesChildren growing up in the modern world of today would rather stay inside and play on the internet, watch television, or play video games than go outside and play. Serious repetitive strain injuries suffered after spending hours glued to game consoles is up 60% since 2002 (Par. 5 Clarke). Technology and modern society have created lifestyle changes that are detrimental to the well being of children. First, this paper will discuss the effects of technology and modern society on the physical and mentalRead MoreImpacts of Video Gaming1704 Words   |  7 Pagesand physical well-being of children. This research report supports the scientific view that although video games are beneficial in terms of improving attention, they negatively affect the children’s social being on a deeper context. The methods employed in the collection of data involved administering of closed questionnaires to the parents and teachers in a small neighborhood. The inherent motive was to establish the beliefs of parents and teachers upon the negative effects of the video games. TheRead More The Crucible - Comparing Play And Movie Essay974 Words   |  4 PagesArthur Millers play, The Crucible, and the movie with the same name have many differences and similarities, all of which contribute to the individual effectiveness of each in conveying their central message. There are several additions and variances in the movie. First of all, the scene where the children and Tituba are dancing in the forest is never seen in the forest; we simply learn of it from dialogue. This scene was most probably added in the movie for a dramatic effect: foreshadowing. Read MoreIs Television Making Your Child Smart Enough? Essay1501 Words   |  7 Pagespaper? Is Sesame Street teaching Little Tommy how to spell â€Å"dog†? When you watch a children s television program you understand most of the content and lessons. Good for you. It’s made for children and you’re an adult. However, are the children able to grasp these lessons and is it affecting their social behaviors? The history of children s programming shows an increase in quality programming and new content for children is constantly being made with networks like Nickelodeon announcing more than 650Read MoreThe Crucible - Comparing Play and Movie1004 Words   |  5 Pages#9;Arthur Miller s play, The Crucible, and the movie with the same name have many differences and similarities, all of which contribute to the individual effectiveness of each in conveying their central message. #9;There are several additions and variances in the movie. First of all, the scene where the children and Tituba are dancing in the forest is never seen in the forest; we simply learn of it from dialogue. This scene was most probably added in the movie for a dramatic effect: foreshadowingRead MoreThe Health Of A Landscape1282 Words   |  6 Pagesphysical surroundings can have an impact on their overall health. With a contemporary cultural emphasis on healthy living, land planners including urban designers and landscape architects have unique opportunities to integrate health into our everyday outdoor spaces. In a publication written by Landscape Institute, a Royal Chartered Institute for Landscape Architects and land planners, there are 5 essential principles that contribute to the success of a ‘healthy landscape’. Principle 1 â€Å"Healthy places

Renaissance Art Essay Example For Students

Renaissance Art Essay As we move into the Renaissance period, artists of the fifteenth-century represented a variety of textures, shapes, and spaces that they experienced around them in their lives. They developed a style of painting called linear perspective which would allow them to reflect simulations of three-dimensional forms arranged in space. This would give the painting a depth and realism not seen until now in the different eras. There was a heavy emphasis placed on the realistic portrait-like paintings giving a life-like sense to the images. This Humanist style of painting placed retreat value on science reason, and the individual while keeping an unwavering religious faith style. One of the techniques developed in Northern Europe was oil painting, unlike the Italian artist, the northern artists painted in oil on canvas. Oil paint takes much longer to dry allowing the painter time to easily make changes. The long drying process would allow the paint to dry smooth erasing the brush strokes. More importantly, oil paint is translucent when applied in thin layers, known as glazes. This method of built up glazes would let the light penetrate to the lower areas and then reflect back which would create the appearance of an interior glow, giving viewers the illusion that they were looking at real objects rather than painted imitations. Italian artists favored tempera, the method of suspending powered pigments in oils like linseed or sometimes walnut. One large difference from the Northern oils was that tempera had to be precisely applied as it dried almost immediately. Also, tempera has an opaque finish which did not allow light to penetrate to the lower layers not allowing the reflections, this resulted in a matte or dull finish unless a layer f varnish is applied to give the painting a sheen. As we notice in figure 12-4 below, we see that the artists stay with some of the Christian features so well known in the Gothic and Romanesque periods except for a much more real or life-like detail. The patrons who funded this pious donation appear on the outside of the polyphonys shutters, much brighter than the rest of the images in the otherwise sober painting, which is only visible when in the closed position. When in the open position however, the upper seven panels are vibrant and colorful depicting God, Mary, John the Baptist, angelic musical ensembles, and ending tit Adam and Eve shown in startlingly lifelike nudes. The lower five panels are shown in almost amazing realistic images of meadows, woods cities and a diverse mixture of apostles, saints, confessors, virgins, martyrs, hermits, pilgrims Assemble to adore the Lamb of God as described in the book of Revelation. Fig. 12-4 (Closed) Fig. 12-4 (open) Italian painters and artists aimed at achieving lifelike figures like their counterparts in the north but focusing on idealized figures in three-dimensional forms set within a rationally organized space using linear perspective. If we look at fugue 12-7, we see the lifeli ke images of Mary, Joseph adoring the newborn Jesus with a host of angels sympathetic expressions on the faces of the on lookers. Fig. 12-7 During this time in the Renaissance era, southern Europe rebirths the nude in the artworks as was a normal in early Greek art. Figure 13-11 below, Michelangelo David, the fugue embodies the antique ideal of the athletic male, the facial expression on the other hand is a stark difference from the earlier arts showing emotional power and a concentrated glaze. Looking at figure 13-12, The Creation of Adam, Michelangelo captures the instance when god tasks him with the spark of life. The facial expressions and the body interaction are extremely evolved from the earlier Greek works and exhibits a more humanistic appearance. Figure 13-10, Interior, Sistine Chapel, Michelangelo painted images depicting the sincere empathetic expressions so well known to the Italian Classicism of Southern Europe. Fig. 13-9 Fig. 13-10 Fig. 13-12 The relationship between the artist and patron appears to have been somewhat comparable to what [the relationship between a ball player and his/her agent. The patron more often than not would be the subject of the painting.