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The 36-mm-diameter shaft is made of a grade of steel with

Mechanics of Materials | 6th Edition | ISBN: 9780073380285 | Authors: Ferdinand Beer ISBN: 9780073380285 142

Solution for problem 7.85 Chapter 7

Mechanics of Materials | 6th Edition

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Mechanics of Materials | 6th Edition | ISBN: 9780073380285 | Authors: Ferdinand Beer

Mechanics of Materials | 6th Edition

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Problem 7.85

The 36-mm-diameter shaft is made of a grade of steel with a 250-MPatensile yield stress. Using the maximum-shearing-stress criterion,determine the magnitude of the torque T for which yield occurswhen P 5 200 kN.

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Art History 4/4/2016 Chapter 15 th th Chi Rho Iota Page from the Book of Kells: Late 8 or early 9 century Pg. 428 (Figure 15­1)  Painted and drawn on animal skin. This book features the 4 gospels that show the ornamental celebration of Christ’s first appearance in the books.  Swirling patterns and interlaced forms for decoration. The interlacing is normally animals or plants. And this is probably a copy of the small metal work of that day’s art.  These were made as a Codex not scrolls, they were bi­fold sheets sewn together and gathered into a book. This was a large undertaking too. There were 4 people writing the languages 3 painters working on them. Each page took about a month to 6 weeks. 40­50 pages were normally done. 180 calf hides were used. The pigment colors were precious and usually came from other places, and would sometimes take 6 months to trade. The monastery objects were always the most important and precious during this time. Europe of the Early Middle Ages Pg. 430 (Map 15­1)  There were about 9 major different ethnic groups in the area shown in this image.  Roman colonies were all through the west. Christianity was trying to be spread around France, England and Ireland. Jewelry of Queen Arnegunde: 580­590 Pg. 432 (Figure 15­2)  From the early community of franks.  Found in grave sites and excavated at an abbey or monastery complex. Of St. Denis North of Paris, was an area of trade for Franks.  The pin itself from this image was about 8 inches long.  Merovech converted to Christianity in 596 and he was the first Merovingian.  The wealthy people who wore jewelry gave them power, status and wealth. Also some a sign of beauty  Earing’s, necklaces, broach/pin to hold up clothing, rings, there were handbags that would be used to hold some jewelry and other items as well.  There was a red over garment that was gold embroidered thread during the time by the queen and clasped around the waist and neck by some of these objects. The garments helped fasten the clothing together too.  The metals were pounded into shape, chased, and inlaid with glass and semiprecious stones, then mounted into metal compartments. Gummersmark Brooch: 6 Century Pg. 433 (Figure 15­3)  Scandinavians artists made this.  Silver that was gilded with gold also and it was about 6 inches tall. The top was rectangular and there was a medallion plate below that was the cover for the safety pin catch.  Around the frame you see the characteristic pattern changes. Eye and beaks of a bird is represented around the rectangular top.  At the bottom part a man is squeezed between two dragons. There are monster heads and crouching dogs. There was an active area of represented animals.  Design is symmetrical and represents the order of the world. Animals is seen in profile or from the front. Hinged clasp, from the Sutton Hoo Burial Ship: 7 century Pg. 434 (Figure 15­4)  Found in a buried ship with weapons, armor, and other objects for the wealth.  Leather body armor over his shoulders. The two sides were connected with the gold pin.  Gold was fused into the surface of the piece Symbol of the Evangelistic Matthew, Gospel book of Durrow: second half of the 7 century Pg. 435 (Figure 15­5)  Painted with tempera such as in the late Roman Empire.  The owner of it was converted to Christianity.  The gospel book of some sort was needed in each village and each monastery where monks lived.  This book was commonly placed on church alters and placed in ceremonies.  People felt better having a book, they felt protected.  The book contains geometric pages, 4 full pages of evangelist symbols, one page containing symbols of all 4 evangelists, 4 text pages to begin each of the 4 gospel books.  All the evangelists had their own symbol, Matthews was that of an abstract man. It looked very childlike and had no arms. Walks in profile.  Frame of this page shows a copy of metal work decoration. The page looks off white which means it was treated but left in most of the traditional color. Page with the Beginning of the Text of Matthew’s Gospel, Lindisfarne Gospel Book: 715­720 Pg. 436 (Figure 15­6)  Ethewall bound it who was Eadfrith’s successor  There were silver or lead pigments that were added into outlines on the pages. These were aided by devices, straight edges, compasses, oval shapes and everything could be drawn precisely.  The letters were elaborately framed and there was Roman influence which makes it look more naturalistic. Matthew Writing His Gospel, Lindisfarne Gospel Book: 715­720 Pg. 437 (Figure 15­7)  O Agios means saint  The reader was able to specifically identify with the writer when looking at this book. Ezra Restoring the Sacred Scriptures, In the Bible Known as the Codes Amiatinus: 700­715 Pg. 437 (Figure 15­8)  3 copies were made of this writing.  Behind him is a library of books from this time.  This is a better illusion of the Ezra than the image of Matthew from before. Lots of detail like in Roman text. South Cross, Ahenny: 8 century Pg. 438 (Figure 15­9)  High Cross: this one is made out of a local stone from the area. Granite, sandstone and limestone were commonly used to make this type of stone cross.  This specific one is made of sandstone and is on a monastery ground for a boundary marker.  These could also be places where some miraculous event happened or could have been identified for local saints to find.  They do not make a special burial place, but mostly special effects and boundaries.  Metal work influenced the shape of this piece Maius Woman Clothed with the Sun, the Morgan Beatus: 940­945 Pg. 439 (Figure 15­10)  Copies of original manuscript on vellum.  Represents the triumph of the church over its enemies.  There are definitive columns of color here. Emeterius and Ende, with the scribe Senior Battle of the Bird and the Serpent, Commentary on the Apocalypse by Beatus and Commentary on Daniel by Jerome: 975 Pg. 440 (Figure 15­11)  Tempera on parchment  Both of the artists took responsibility for the arts and shared the work.  This is the representation of a triumph over Satan.  Text states the bird represents Christ that covers itself with mud to trick the saint and then the snake decides the bird is harmless and then he conquers over the snake/Satan and kills him. 4/6/16 Pg. 428 (Map 15­1) Gripping Beasts, Detail of Oseberg Ship: 815­820 Pg. 441 (Figure 15­12)  Made to float into inter coastal waters, steady waters. For kings and queens or leaders.  Leaders were buried on ships and floated to sea. Sometimes set on fire.  Intricate work was done on this and it looks like a snake curled up at the end.  Furnishings were on a ship, sled, bed, and other materials were carved and the sides of the sled was carved. Their ship and burial was their work of art.  The fantasy imagined in these ships were part of their world and their artwork. Royal Rune Stones, Right­Hand Stone Ordered by King Harald Bluetooth: 983­985 Pg. 442 (Figure 15­13)  Ordered this stone and it had a quote: Made for Gorm and Thyra his father and mother. He won all demark and Norway making the Denmark into Christians. These were his accomplishments. Exterior (A) and Cutaway Drawing (B) of Stave Church, Borgund, Norway: 1125­1150 Pg. 443 (Figure 15­14a)  Staves are stakes made of tree trunks and they are rounded on one edge.  The frame of this building is made of timber. Made with Slot construction. The horizontal sections lock into place with the vertical sections. The shingles were square and covered in bark pieces. The roof is set at 45 degree angles. All the angels of the roof were 45 degree angles to keep snow from sitting on top.  The work was open inside. You can see the cris­cross boards and eves. Equestrian Portrait of Charles the Bald: 9 Century Pg. 444 (Figure 15­15)  Charlemagne went to Rome. Living between the eastern or saline franks.  Charlemagne was crowned as Roman Emperor. He brought back the title for himself. Was crowned by a pope.  This is a portrait of himself.  Head of a Frankish King was not the last bullet style.  They were trying to recreate the Roman Empire look, their ancestors of Romans had lived in Italy. They came from that area to this Franks region. Interior View (A) and Section Drawing (B), Palace Chapel of Charlemagne: 792­805 Pg. 445 (Figure 15­16a)  8 sided building and on one side there was a tribute.  Charlemagne was a co­equal of the spiritual leader of the empire.  His throne was across from the chapel.  There was a huge atrium outside of the temple and there was a giant gate entering into it. It was the gate to a giant courtyard. The second floor of the building had a throne and porch. He could have addressed the people either in the atrium or inside the building.  The king combined the spiritual and secular. Interior view (A) and Section Drawing (B) Palace Pg. 445 (Figure 15­16) Westwork, Abbey Church of Corvey: 9 Century Pg. 446 (Figure 15­17)  Western entrance of the church.  This was a model of a huge entrance at the west. Two towers, elevated second section where there is a gallery. This was developed in the Carolingian times and carried to the next time period also.  This is where one of the bishops came, religious and secular titles were held by them at the same time. There was their own chapel in here for them to go by themselves and stay on trips here. Local saints also might have had special chapels. The Bishops, kind or emperor could have resided on the west side of these churches. Saint Gall Plan (Original and Redrawn with Captions): 817 Pg. 447 (Figure 15­18a&b)  Benedict order was established in this time.  Early people were like monks and deprived themselves and were alone.  These people devoted themselves to God and were wealthy the complex was protected like a castle. This was a place of safety, peace and security. Some of them were wealthy people. This is a blueprint of a monastery. There is an abbey inside it called St. Gall.  The claustrum is important, place usually a courtyard and set off from a busy street. A lot of big churches have areas like this where it is a place of contemplation and meditation. Right in the center of this blueprint and the dormitory is right outside of that. There was a craft center for clothing and goods and for others goods like leathered materials. This actually became an enterprise.  The church is connected into the claustrum. The abbey churches built up the area in front of the alter. There was a wall built to shelter the quire away from the church. There was a naïve they could enter into separately. Page with St. Matthew the Evangelist, Coronation Gospels: 9 Century Pg. 448 (Figure 15­19) Page with St. Matthew the Evangelist, Ebbo Gospels (Fig 15­20)  This style is different because the figure has no halo and the figure is rendered differently with turbulent. The lines that were drawn are going back and forth franticly. This is an inspired drawing, a lot of agitation in the drawing. The blue colors are spiritual and exciting. A Closer Look: Psalm 23 in the Utrecht Psalter: 816­835 Pg. 450  These started to be used in services and read from during service.  There is a drawing of the psalm and a literal image of it. The 23 psalm shows that the psalmist is in it. All of these images show references into communion and the religion. The imagery was represented in this image. Crucifixion with Angels and Mourning Figures, Lindau Gospels: 870­880 Pg. 451 (Figure 15­21)  There is concordances in these. Ornate pages and then the Gospels are covered.  There is a jeweled cover with precious stones and gilded.  This book is about the crucifixion, evangelism and angles, also figures in morning of the crucifixion. These books house a precious work. Gero Crucifix: 970 Pg. 454 (Figure 15­24)  Huge sculpture, over 6 feet tall.  Not idealized Christ like shown in the last image. This is the suffering Christ and a physical image of him suffering. In the back the communion was held on this sculpture. Plan (A) and Interior (B), Church of St. Cyriakus, Gernrode: 961 Pg. 453 (Figure 15­23b) Doors of Bishop Bernward: 1015 Pg. 455 (Figure 15­25)  Bronze doors. This is the biblical narrative from the very beginning scenes from Genesis, Exodus.  Giant bronze knockers.  This is a whole casted piece of bronze. The sculptors used the lost wax method. This allowed them to model these figures in 3 dimensions and allowed the background to be characterized.

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Chapter 7, Problem 7.85 is Solved
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Textbook: Mechanics of Materials
Edition: 6
Author: Ferdinand Beer
ISBN: 9780073380285

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The 36-mm-diameter shaft is made of a grade of steel with