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CONCEPTS case (Or The above quantitics associated with elasticity were defined for the lincar stretcaing (a) area suraln; tensile case). Explain the meaning of the ...

Question

CONCEPTS case (Or The above quantitics associated with elasticity were defined for the lincar stretcaing (a) area suraln; tensile case). Explain the meaning of the following similar "Coptateibilytt) & or related (f) shear stress_ (B) (6) volume strain (c) pressure , (d) bulk modulus_ shear strain_ (h) shear modulus elasticity: (@) Hooks law, () Explain the meaning of the following quantities associated with proportional limit () yield point (d) elastic limit (e) brcaking stress (f) Pois

CONCEPTS case (Or The above quantitics associated with elasticity were defined for the lincar stretcaing (a) area suraln; tensile case). Explain the meaning of the following similar "Coptateibilytt) & or related (f) shear stress_ (B) (6) volume strain (c) pressure , (d) bulk modulus_ shear strain_ (h) shear modulus elasticity: (@) Hooks law, () Explain the meaning of the following quantities associated with proportional limit () yield point (d) elastic limit (e) brcaking stress (f) Poisson '5 ratio_ PTOpobovc thermal expansion cquation represents the linear Case Write te correspoolding equation for () the area case and () the volume case; (C) How is the coefficient of volume expansion related t0 the cocfficient of lincar expansion? When solid object expands thcrmally; what happens to any holes contained within it? Do the holes expand contract? By how much? wire of length L and coefficient of linear expansion is bent into circle and then beated untl it expands by an amount AL; (0 What happens to the enclosed area? @) Express the change in arca AA in terms of AL. (c) Show that the coefficient of arca expansion for this loop equal t0 2a (a) What is thermal stress? () Express the thermal stress of & wire not allowed t0 contract upon cooling in terms of its Young' modulus, coefficient of linear expansion _ and cbange temperature



Answers

Review. The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of $4.00 \times 10^{-6} \mathrm{m}^{2}$ is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is $35.0^{\circ} \mathrm{C}$ (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to $-10.0^{\circ} \mathrm{C}$ , what is the tension in the wire? Take Young's modulus for steel to be $20.0 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}$ . (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of $3.00 \times 10^{8} \mathrm{N} / \mathrm{m}^{2}$ . At what temperature would the wire reach its elastic limit? (c) What If? Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.

For the given problem in about a force is given by oh young windowless times they area across actually dental divided by more. Oh, substituted reading for the Delta l. We have a Delta L Series. Oftentimes all more times Don't t divided by El marred somewhat cancel out sort of formal we get here is white answer a call for guilty substituting the values We get the force here so believes we have 20 times gentle power 10 times four times tinkle on minus six found 11 times gentle are minus six times 45 This gives us the force off 3 96 Newt, this is not a I mean about me. The stress is even by stress. Nous is given by force over India. So force me a reason why all four times Delta he derided by a cancels out we are left with why all for Delta t so substrate the railings and swollen from delta t So don't the team get here ese stress minus this derided by why also So we have stresses three Thompson, our eight divided by y times over why we have 20 times and then also he's 11 constant or minus six. So so did you find this? We get identity to be minus 1 36 deliveries in part C. We found. Sorry. That's from Beit from Delta T find filed under pressure, so file temperature will be called to Delta T plus T nard. So, uh, I'll temperature we have I said student body with minus one on one. Agrees Farsi of the results from A and B are independent off the initial went off the wire. So you found that from the courage and given the creations in part, it would be so. This is, um, um, independent off the initial lens off the wire.

In this problem. Considered a road off original length Ellen and cross Saxon area off this road is A and Tencent in this road is F no. So solving part effort the frictional changes the frictional changes in land is due toa both dancing as well as hitting process. Yeah, so Dale l by l not is equal to deal l by l note thermal plus they led by l note Danson. So they'll l by and not is equal toe Alfa dlt plus air by a y. So they'll l by l not Minus Alfa dlt is equal toe f by a white multiplying both sides Bye bye. So we can write it like this after multiplying both sides by y so just solving it further we can write the test by a is equal toe. Why in tow del el by l not minus Alfa dirty So Alfa is coefficient off linear expansion here And why is equal Toe Young's modelers here now solving part B? I will use this formula to solve part B here Did not is not zero Yeah, but it is the amount alp obras and not into dlt that the brass expense so daily El by l not is equal toe by a by so on. Further going we have by a is equal to deal l by and not in tow. Why? So why yes, still in tow. Alfa bra's minus Alfa Still into dirty is the formula. So I am just putting the value off. Why? Still as well as Alfa Brush and Al five Steel as well as dirty here. So on solving this calculation, we will get AB by A is equal to two into 10 power 11 in 20.8 into 10% minus five into 1 20 which is coming as 1.92 into 10 power eight p a.

So mhm B equals negative fee D P D. V and doing the math, it will come out to be five be over three. Number density is 8.45 times 10 to the 28 bar cubic meter. And using that, B will come out to be 6.33 I understand to the 10 basket.

In the first part of this question, we want to find the tension in terms off the ah change in the size and the tempter. We can do that because, ah, stress and temperature changes the length off objects we have here. How the object changes given the changing temperature and how the object change given the change in this dress. So the tension invitation being asked here and the total change delta l will be the stump off. This true that l the first the l huh? We can sum this true. So don't the l is a photo l zero Oh, fuck. L t plus, uh l z o right about a bye now. If we divide both sides by l zero and is only f over a This gives us the equation that they want. That f over a is equal to Why, but deploying down the l divided by l minus Alpha male 30. So this is the first part of the equation. The 2nd 1 we have this system. Here we have ah, brass Ah, a brass bear bar and two steel wires. And we have the system at 20 degrees. The two treaty Think fine steel wires. Ah, have zero tension. So they want to know what is the potential stress in the steel wires when the temperature of the system erase 140 degrees. In this case, we can consider that because the breast Boris have it and the wires are fine. They're stressing the bar is only due to the wires and and due to their wires, doesn't do not affect the the amount by wisdom bar expense do that the temperature increase. So they are the variation off the length that is no. Zero comes from temperature only. So all delta l That's right here All that l comes only from oh, from breasts. Well, zero delta t. Now, if we use the equation that we got before half over a here, you got that f over a is equal to why off this deal, times offer breasts minus out still times Delta T. And we have everything here we have. Why we have Alfa brides and office too. And Delta t Dr T is the difference here. 100 20 degrees. This give us 1.92 terms too. The eight twice go. So in this case, the stress and this still is the tension by the by the area. It's 1.92 times 10 today thing Bhaskar.


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