Figure 1-4. Thermal linear gradient across shell wall.

from Ti to To and the growth of the cube is fully restrained:

where Tj = initial temperature, °F T2 = new temperature, °F a = mean coefficient of thermal expansion in./in./°F E = modulus of elasticity, psi v — Poisson's ratio = .3 for steel AT = mean temperature difference, °F

Case 1: If the bar is restricted only in one direction but free to expand in the other direction, the resulting uniaxial stress, a, would be ct= -Ea(T2-Ti)

Case 2: If restraint is in both directions, x and y, then:

Case 3: If restraint is in all three directions, x, y, and z, then erx = oy = crz = —aE AT/1 — 2v

Case 4: If a thermal linear gradient is across the wall of a thin shell (see Figure 1—4), then:

This is a bending stress and not a membrane stress. The hot side is in tension, the cold side in compression. Note that this is independent of vessel diameter or thickness. The stress is due to internal restraint.

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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