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Solved: The solid shaft of radius c is subjected to a

Mechanics of Materials | 10th Edition | ISBN: 9780134319650 | Authors: Russell C. Hibbeler ISBN: 9780134319650 134

Solution for problem 5-48 Chapter 5

Mechanics of Materials | 10th Edition

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Mechanics of Materials | 10th Edition | ISBN: 9780134319650 | Authors: Russell C. Hibbeler

Mechanics of Materials | 10th Edition

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Problem 5-48

The solid shaft of radius c is subjected to a torque T at its ends. Show that the maximum shear strain in the shaft is gmax = Tc>JG. What is the shear strain on an element located at point A, c>2 from the center of the shaft? Sketch the shear strain distortion of this element.

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3/22/16 Lecture 13 Groundwater and Rivers Hydrology  Why do we care o Water is resource we cannot survive without o There is a fixed amount of water on Earth (limited resource)  Hydrologic Cycle o Notice how much water is in each step…  Ocean is the main major reservoir  Glaciers is second major reservoir  Groundwater supply is the third major reservoir  Notice how much smaller the water source is in rivers and lakes Groundwater  Runof: water runs of the surface of the earth  Infiltration: water soaks into the ground and makes its way deeper and deeper Infiltration Properties  Porosity: how much void space is present in an area (measured in percentage) o 3 main types  Intergranular porosity happens when the pores all intergranular pores or pore spaces in-between grains that water can seep into accumulate with water and creates a decently large porosity  Fractures: cracks rock that water can seep into and fill  Vuggy porosity happens when vugs or a part of the rock dissolved away and allows water storage in the hole created Controls on Porosity  Determined by sediment/rock properties: o Sorting: well sorted sediment tends to have high porosity, poorly sorted sediment has lower porosity o Cementation: higher cementation, lower porosity and vice versa (cementation is when a new mineral fills the gaps between grains of the other material) o Permeability: measures how easily the water can flow through the sediment material, higher permeability  higher porosity Groundwater (GW)  Water Table (WT): water goes deeper and deeper until it can’t go any further, than begins to fill up the pores from the base up (why the base is the saturation zone) o Above water table, pores spaces are mainly empty o Below water table, pores spaces are mainly full  Aquifer: any layer of sediment/rock that will holds a water supply **Recover for human use via wells o Unconfined aquifer: body of water below the water table that o Aquitard: impermeable layer that acts as a barrier to keep the water in aquifer from sinking lower o Confined aquifer: an aquitard above and below the aquifer makes a barrier that doesn't allow water to be added to the aquifer o Artesian well: confined aquifer on slope has more pressure at the base of the slope, so drilling into the aquitard at the base of the slope will have enough pressure to push the water up (no need to building a pump thus a cheaper well) o Perched Aquifer (Perched WT): secondary aquifer perched halfway up a hillside because of an impervious layer that keeps is from reaching an aquifer down below (relatively small) Question: Where should town build a new mall Site A or B 10 km A TOWN B Answer: Water needs a recharge area; so do not build over the recharge area b/c that will prevent the water from reaching the aquifer below. o People will want site A b/c it’s closer to town so to settle dispute, look for third option (site C could be in-between A an B on the right edge of town) Water Supply o Recharge: the amount of water added back into aquifer o Discharge: the amount of water is flowing out of aquifer (natural or man- made discharge) o If Recharge > Discharge, water table rises  Can cause difficulty with construction when building foundations o If Recharge < Discharge, you’re overdrafting Efects of Overdrafting o Cone of depression: depressed the surface of the water table close to the well so the well can run dry even if there is water left o Cone stops growing when flow from the well balances water pumped from well o Subsidence: ground level sinking Dates on the pole show how much the ground level has changed over the years. Change is not from erosion but from subsidence o Salinity Contamination: salt water can contaminate the aquifer o Desalinization: filtering the salt out (expensive, requires a large plant)  Water bills higher for residence who live near places that deal with salinity contamination GW Movement  Typically GW moves very slowly o Good: groundwater tends to stay in one spot for a long time so the water supply will be around for while o Bad: when water gets contaminated, it sits and stays contaminated for a long period of time (no water flow to flush contamination out)  Erodes even at slow speeds o Groundwater carries dissolved substances  CO2 and SO2  Dissolve carbonate rocks o Threat of sink holes Case Study: Groundwater Contamination  Love Canal, Niagra Falls NY  Early 1900s: a canal system was started to connect to a river but never was finished o Canals lined with cement  1940s: chemical plant bought canals to dump their chemical waste product o Buried it with fine grain sediment o Fenced if of an called it a day  1960s: love canal had a lot of house development o The people bought the land from the chemical company decided to build on the property despite it was where the chemical waste had been dumped o Sold for $1 o Wet rainy season caused the water table to rise, so the contaminated water started moving closer to the surface  1970s: health issues increased for the people living in the love canal area o Birth defects, asthma, cancer, etc.  1978: local homeowners learn there’s 21,000 tons of chemical waste underground o Who’s responsible o Situation was so bad that children would get chemical burns from playing in the grass  Aug. 7, 1978: Federal declaration of emergency to evaluate the people in some of the neighborhoods (same declaration as 9/11  very serious situation)  1980: Superfund Act allowed for government money to go to the cleanup of contaminated area  1994: legal proceedings drug out until for 16 years until finally the chemical company was held responsible, and everyone promised never all this situation to happen again  2008: YET survey of 4 states found 500,000 kids are in schools less than ½ a mile from waste dumps, including one on top of a PCB dumpsite (PCB has high correlation with cancer) 3/29/16 Geology Lecture 14 Coastlines Geology in the News  Mt Pavlof in Alaska is erupting  Ash being spewed 37,000 ft high  3 eruption in 3 years Rivers and Streams Why should we care  Major agent of weathering and erosion Forming a River  Drainage basin: area on either side of river where water is flowing down into that particular river o Water has to flow downhill – duh  Channels: carved out path that water will flow o Water likes the flow the easiest path it can  V-shaped valley: V shape of a valley that was formed by a river flowing through  Tributaries: a river or stream flowing into a larger river or lake. o Branching/dendritic: branches of tributaries that all flow into one larger river o Radial: hill/mountain that tributaries are flowing down, the white area in the center is the peak of elevation o Rectangular: fractures/joints in the rock that the tributaries follow  Levee: naturally raised area on the banks of the river made by natural sediment deposits  Floodplain: flat plain where the water will go if it floods over the banks of a river Channels  Braided streams (or braided channel): multiple channels that have been molded together o Causes:  Variable discharge: the amount of water flowing through the area changes a lot, multiple channels added to help obtain any extra water  Large sediment supply: too much sediment will clog the river, and the water will have to find another route around the natural made dam  Easily erodible banks: water continually erodes its banks and spreads out  Steep elevation gradients o Channels tend to be straighter with steep elevation gradients b/c the amount of water/the speed of the water increase the energy and allows the river to cut/erode through the rock  Lower gradient o Channels start to meander with lower gradient (each loop called a meander) b/c lost velocity/energy so it has to flow around rocks/obstacles instead of eroding through them o Meanders  Cut bank: in a curve of river, water on the outer side of curve moves faster and causes erosion  Point bar: water on the inner part of the curve that is moving slower and cannot cause erosion  Compare this concept to race cars going around the bend o Meanders migrate over time    Oxbow lakes (oxbows): as the meander migrates, a meander can be cut off from stream/river and left to dry (seen in time 4 of diagram above) o Meander vs. Man  Meandering causes problems for people  Artificially straighten, but that also causes problems  Can increase water velocity and eventually causes flooding Floods  How much water moves part a point in a given amount of time o Discharge = velocity * area  If Discharge increases until channel cannot contain all the water, flooding occurs Floodplain development  Floods deposit lots of fine-grained sediment o Good for farms b/c sediment is nutrient rich o Bad for developed areas b/c the damage that comes with flooding “How often and how big are the floods here”  Recurrence interval: probability that a flood of the given size is going to hit that area in any given at time o Probability in a given year = 1 / interval Example:  Q: What is the probability of a 5-yr flood happening this year  A: 1 / 5 = 0.2 20% o Caveats about interval (warnings):  Probability calculation, not a guarantee  Varies from river to river  Practice Problem: You buy a house along the Honey Badger River. Your property would be affected by a 50-year flood event. What is the probability of a 50-year flood event occurring this year along the Honey Badger River o 1/50 = 0.02 ~ 2% The End of the River • Mouth: where the river is emptying out into a body of water • Erosion ends, deposition starts • Distributaries: when the main channel breaks into many smaller channels • Deltas: distributaries/mouth all create the delta of a river Delta Processes  Subsidence: excess weight of the sediment causes area to sink lower than sea level o Ex: Venice built on a delta, weight of sediment + weight of construction has caused flooding Water Quality and Availability  An average adult can survive on 2-3 Liters/day  For cooking, bathing, sanitation, we need about 50 L/day/person  Average per capita use in US ~ 6,000 L/day o Agriculture influences that 6,000 o Manufacturing does too Water Quality  Potable: water that is safe to drink and tastes good o Almost all water supplies contain some dissolved material o Question is whether a given amount of the material is safe Biological Contamination • Microbes can enter drinking water supplies • Fecal Coliform Count: o # of coliform bacteria per 100 ml o Coliform bacteria used as a proxy o Drinking water = 0 o Swimming/etc = 200 Chemical Contamination • Chemicals commonly added to water via infiltration and runoff o Pesticides o Fertilizers  Radiation can also enter water supplies o Mines o Waste disposal Water Quality Clean-Up • Clean-up possible but difficult o takes time & money • Faster recharge = easier to clean once contaminant source is isolated o ‘Fast’ recovery = matter of years Water Availability • Legal fights among states over who gets how much water from a reservoir • ‘Downriver’ states suing ‘upriver’ states for taking too much • Upriver states say old water use agreements are outdated CASE STUDY: SC vs NC • 10 million gallons from the Catawba River annually • Catawaba R accounts for about half the water supply to the SC low country • Taken before US Supreme Court • SC & GA are in contention over the Savannah River CASE STUDY: GA vs TN  GA state legislature has proposed legislation to move the state border about 1 mile north  Claim is based on an 1818 surveying error placing the border at the wrong location CASE STUDY: Everyone in the SW US vs Everyone else in the SW • Colorado River lawsuits date back to 1931 o CA, AZ, NV, NM, UT, & Native American groups Colorado River Overuse • Providing water to 30 million people • 70% of its water diverted to irrigate 3.5 million acres • 10 years of drought • Water level down 130 ft since 2000 in some areas • Flow est. to drop 5-20% in next 40 yrs due to climate change • Ends 50 miles before even reaching the Pacific Ocean • Delta reduced from 3,000 acres to 250 acres in < 100 years Future Case: Water Wars • What happens in areas where courts aren’t available to settle disputes 3 o 2000: 36 nations are defined as ‘water stressed’ (< 1700 m H 2/person annually) o 2010: 1 billion people in water stressed regions (16% of pop-) o 2050: Est to be 2 billion (22% of pop-)

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Chapter 5, Problem 5-48 is Solved
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Textbook: Mechanics of Materials
Edition: 10
Author: Russell C. Hibbeler
ISBN: 9780134319650

This full solution covers the following key subjects: shaft, strain, shear, element, radius. This expansive textbook survival guide covers 14 chapters, and 1373 solutions. The full step-by-step solution to problem: 5-48 from chapter: 5 was answered by , our top Engineering and Tech solution expert on 11/10/17, 06:06PM. Mechanics of Materials was written by and is associated to the ISBN: 9780134319650. This textbook survival guide was created for the textbook: Mechanics of Materials, edition: 10. Since the solution to 5-48 from 5 chapter was answered, more than 329 students have viewed the full step-by-step answer. The answer to “The solid shaft of radius c is subjected to a torque T at its ends. Show that the maximum shear strain in the shaft is gmax = Tc>JG. What is the shear strain on an element located at point A, c>2 from the center of the shaft? Sketch the shear strain distortion of this element.” is broken down into a number of easy to follow steps, and 55 words.

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Solved: The solid shaft of radius c is subjected to a