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The rigid beam is supported at its ends by two A-36 steel

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

Solution for problem 4-21 Chapter 4

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 4-21

The rigid beam is supported at its ends by two A-36 steel tie rods. If the allowable stress for the steel is sallow = 16.2 ksi, the load w = 3 kip>ft, and x = 4 ft, determine the smallest diameter of each rod so that the beam remains in the horizontal position when it is loaded.

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Wesley Fowler ASTR Chapter 7 The Earth’s Structure Earth is the most massive of the terrestrial planets, it has very dense materials in its interior, it is the only planet with liquid water on its surface. • Inner Core: 0 - 1300 km (solid) • Outer Core: 1300 – 3500 km (liquid) • Mantle: 3500 – 6350(ish) km • Crust: 5 – 50 km thick – Oceanic Crust: ~5 km thick – Continental Crust: ~ 30 – 50 km thick • Hydrosphere: All water • Atmosphere: Crust – 100 km (Point at which flight is not possible) • Magnetosphere: >100 km The Earth’s Atmosphere The outgassing of water vapor, methane, CO , and2nitrogen compounds from the Earth’s surface is the origin of the atmosphere. These compounds are altered by the Sun’s UV light in a process called photodissociation, which breaks up nitrogen compounds, isolating nitrogen. Nitrogen clumps together to form N gas2 which is very inert and hard to break up. - Remaining compounds absorbed into rocks Oxygen enters the atmosphere from photosynthetic organisms in the ocean. Nitrogen 78% Oxygen 21% Argon 0.9% CO ~ 0.03% 2 Troposphere: Lower level of atmosphere. All weather occurs here. (0-17kn) Stratosphere: Where the ozone layer is, and where planes fly. (17-50km) Mesosphere (50-80kn) Ionosphere/Thermosphere: Ionized molecules and free electrons here. (80+km) Temperature Inversions define the boundaries between layers - Temperature increases in ozone layer with ascension due to o 3 absorbing sunlight, Troposphere: Air is constantly being moved around through convection, which is driven by Erath’s warm surface due to sunlight. - Convection is the transfer of heat from one pace o another through the movement of a gas or liquid. Astrosphere: Ozone layer is an excellent absorber of UV radiation, why there is the temperature inversion The ozone hole: Large hole in the ozone layer above Antarctica, caused by pollution of chlorofluorocarbons (CFCs) in Antarctica, which kills ozone cells. The sky is blue because blue light is scattered in the atmosphere of of air molecules. Blue light is scattered more than red light due to its shorter wavelength (400nm), and appears to come from all directions as a result. Most red light is not scattered in the atmosphere. “Rayleigh scattered” 9.8 times more efficiently scattered than red light Mie scattered 1.75 more efficiently than red light At sunrise and sunset, the sunlight has more atmosphere to travel through, and blue light scatters out of line of sight along with greens and yellows, leaving mostly red light to be seen. Surface Heating Earth’s surface absorbs about 70% of the incident solar radiation. - Were it not for the atmosphere, the surface temperature would be 250K or -23C Greenhouse gases are molecules and compounds that efficiently absorb the infrared radiation. Include CO 2 methane, and water vapor. Warms up the -23C to 14C (57.2F) Wesley Fowler ASTR Chapter 7 Climate Change Climate: Long timescale characteristic of the environment (i.e. a dessert, a rainforest) Weather: Temporary condition (it is raining) - Climate change: The change of the average condition of the Earth. Human activity is increasing the amount of CO in t2e atmosphere, thus increasing the amount of the atmosphere’s greenhouse gases which trap thermal radiation. Thus the temperature of the world is increasing with the rise of CO emission because less and less thermal radiation is escaping 2 through the atmosphere. Possible outcomes of climate change: - Increased surface and ocean temperatures - Rising sea levels - Longer and more intense periods of severe weather - Changes in atmospheric and oceanic circulation patterns - Increase of desert area in equatorial regions - Increase in ocean acidity and larger and more numerous “dead zones” The Earth’s Interior In order to determine the internal structure of the Earth, scientists use seismic waves generated during earthquakes. - P-waves (Primary Waves) Pressure waves that travel fastest, causing vibration in the direction of motion. These can travel through solid, liquid and gases. - S-waves (Secondary Waves) Shear waves that travel slower, causing vibration perpendicular to the direction of motion. These can only travel through solids, and be absorbed by liquids and gases. By observing the difference between these two wave speeds, scientist can determine the density of the rock in the Earth’s interior. - Since S waves cannot pass through liquids, we know that there is a liquid outer core surrounding the inner core with a radius of 3500 km. Surface Activity Plate Tectonics: The oceans and continents are floating on top of a highly viscous convective mantle of in a series of plates - Earth is the only planet known to have plate tectonics. Lithosphere: The Earth’s crust and upper solid mantle made up of the Earth’s plates. - 100 km thick on average Asthenosphere: Upper mantle below the Lithosphere, a highly viscous convective mantle. - Not molten, but flowing Tectonic Motion: Plates floating on top of convection cells in the mantle. - Magma seeps to surface at cracks between plate boundaries. Volcanoes are very common in these areas. - Plates grinding or colliding against each other produces earthquakes. Pangaea Pangaea refers to the Supercontinent that housed the current continents. It explains fossil evidence, and the breakup of Pangaea explains why the continents drift about 2cm ever year. Earth’s Magnetic Field Requirements for a planetary magnetic field: 1. Convection of conducting liquid in interior - Needs to be large enough 2. Sufficiently fast rotation rate - Lower than ~25 days Dynamo Theory: The combination of these two requirements creates an electrical generator which produces an electrical field. - Earth fits this theory, and has the strongest field of all the terrestrial planets Magnetosphere: The region in space influenced by Earth’s magnetic field - Charged particles of the Solar Wind are deflected by Earth’s magnetic field Van Allen Belts: Regions in the magnetosphere perfect for trapping charged particles, which send them into the upper atmosphere, creating the aurorae (northern lights) Tides Earth’s tides are caused primarily by the moon’s gravitation force, as well as by a force from the sun that is twice as weak due to distance. There are two low and two high tides per day. - Tides are a differential force, meaning that the gravitational force from the moon is stronger on the closer side of Earth, and weaker on the farther side. (a) Tidal Bulge: The near-side’s ocean is lifted towards the moon, while on the far side the land is being pulled away from the far side’s ocean. This is why we have low and high tides. (b) - High tide is the side closest and farther from the moon, low tide in on the caps of the bulge. Determined by the tidal bulge. Spring tides are the strongest tides, and occur at a new or full moon. Neap tides are the weakest tides, and occur at a 1 or 3 quarter moon. Tidal locking: The moon’s motion is causing the Earth’s rotation to gradually slow, making the days longer by +2.3 milliseconds per century - Furthermore, the moon is retreating from Earth at a rate of 4cm per year

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Chapter 4, Problem 4-21 is Solved
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Textbook: Mechanics of Materials
Edition: 10
Author: Russell C. Hibbeler
ISBN: 9780134319650

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The rigid beam is supported at its ends by two A-36 steel