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problem one steel rod OC of diameter D.and yield strength 370 7.2 mega pascals.is subjected to the external loads as.shown below rod.Oh see Nova diameter D and it has these.loads he determined the diameter D for.the rod to have a factor of safety of.two for normal stresses caused by.bending moment so only for the bending.moment the stresses caused by the.bending moment draw shear and a bending.moment underneath the Freebody diagram.and you know before substituting any.values show the expression you found for.the diameter as a function of n m and s.so that last sentence is basically a.problem on its own so I'm gonna do that.first which is very very easy and it's.what the design course is focused on.more than the shear and bending diagrams.so I know that my factor of safety is.the strength over the stress and they're.telling me the stresses we're only going.to consider the ones due to the bending.moment so this is s over em Y over I and.I know that I is for rod is high over 64.thanks T to the fourth and that Y is the.distance from my neutral axis to where.I'm calculating the normal stresses so.in this case if it's a rod the neutral.axis would be at the center of them of.the rod and the maximum stress which is.where what I used for the for the factor.of safety would be on the surface so.from the center to the surface it's just.a radius for half a damn okay so this is.the expression expression for M and if I.solve for D D cubed would be 64 over 2.32 times M times n over PI over s ok.so basically my answer would be 32 times.n times M over PI s and to the 1/3 ok.solving for for this DQ'd that's that.that's done and it's more than half of.the problem ok now I need em I have N.and I have the strength of them as you I.need the maximum moment so that I can.calculate the correct diameter of the.rod and to do that I need to identify.which where the maximum moment is so for.that is what I'm you're gonna use the.shear and the bending daggers so to do.that I can I'm gonna do a shear.and underneath it a bending moment.diagram these are all in kilonewtons so.my V and IB kilonewtons and the distance.is our meters so my M will be.kilonewtons times major right that's all.I have so far and from the free body.diagram I realized that I don't have r1.or r2 so that's actually the first thing.that I'm gonna do if I do a sum of.forces in the Y direction I would have.the both variable so I wouldn't be able.to solve for that but if I do a sum of.moments about o or B I would eliminate.one of those two and I would be able to.solve for the other one so I'm gonna do.sum of moments about be s the distances.are easier for me so I had a distance of.two point two I have a force of r1 at a.distance of one I have a force of two.and a distance of one I have a force of.four and that has to be equal to zero.r1 would around about B would be.rotating this clockwise which is.negative the two would be counter.clockwise positive and the for clockwise.negative this just means that minus 2.point 2 r1 is equal to 2.so r1 is equal to minus two over two.point two whatever that is and then from.the sum of forces in the y-direction I'm.gonna have an r1 which I know is going.down minus two over two point two minus.two plus r2 minus 4 equal to zero.just that broad is not going up right.now so our two would be equal to 6 plus.two over two point two this is kilo.Newtons and this is Killa yeah I can put.this in the calculator and I have my.values here let's do that is your point.zero point nine zero nine 0.91 0.91 and.negative kilonewtons and then for the.other one would be six plus that so 6.91.kilonewtons positive okay so I know that.for my shear diagram I'm gonna go down.our one is actually going down cuz I got.a negative value I gotta keep going down.to then go up certain amount at B so.that when I reach C I go down four and I.reach a zero so I know that the maximum.value I'm gonna have here is 4 and the.minimum would be that 0.91.plus two so a minus two point ninety one.so I know that closer to a nine point at.to two point ninety one I have my zero.meaning that's where my.as it x-axis is gonna go X and this is.meters so I go down point 91 at a I go.down an extra to add B I go down I go up.6.91 but I know that I have to reach 4.so that when I get to see and I go down.for I reach to 0 ok and I don't even I.don't really care about these values.because I'm not gonna use these four for.what I'm looking for okay and then the.moment so there are no external or.internal moments and oh a B or C.anywhere so my moment diagram is just.gonna be the integral of this meaning.that I'm gonna start at zero and then.I'm gonna have negative slope higher.negative slope and then a positive slope.to reach zero so I'm gonna be on the.negative side of my y-axis for the.moment diagrams I'm gonna do my zero at.the very top X and meters because I.started at zero I have a negative slope.to reach this value and then a higher.steeper negative slope to reach this.value and then a positive slope of 4 to.reach this value and what am I'm.interested in in this value right here.the maximum so that I can replace or.substitute them by that value and.calculate my D and to reach this value.now I need to do is integrate my V.because M is an integral of e so the.area under the curve of this section.that in that shaded region this is one.meter from B to C one meter and this is.for kilonewtons if I multiply one meter.times for killin mutant basically this.shaded area would give me 4 kilonewton.meter.and obviously a negative negative value.so this is a minus 4 and this is exactly.what I needed.kilonewton meter I missed I missed that.meter unit all right so now I go back to.this expression D would be 32 times my.moment 4,000 Newton meter times my.factor of safety 2 over PI and my.strength three seventy seven point two.three seventy seven point two times 10.to the sixth because it's megapascals.and pass codes aren't Newton so over.meter squared so needn't and Newton's go.away and then meter cubed but to the one.third that it's just gonna be meters I.do that in the calculator 32 times 4,000.times 2/3 77.cube root of that and that's zero point.zero six metres meaning 60 millimeters.right done with the first problem second.one draw a Mohr circle diagram properly.labeled find the principal normal into.your stresses and determine the angle.from the x-axis to Sigma 1 which is the.first principle stress draw the stress.element for the principal stresses and.here are my current stress of States so.I'm gonna do a small drawing of what I.have I have a three ksi a -5 and why.okay sigh and a -3 in town so - means.that when I look at the right side of my.square I would have a vector of force.that would make this rotate clockwise so.this one right here is 3 okay as well.okay so easy my average things that I'm.gonna need here for my for my more.circle so it says use only a front of.this page for a properly labeled more.circle so let's do that I'm gonna have.when I used a whole page that it's easy.for me do a good drawing.this is gonna be sickness there's gonna.be towels and I can do the calculations.in the back use them back for the math.so I have 3 minus 5 or minus 3 3 minus 5.and minus three so Sigma X plus Sigma Y.over 2 is the average 3 plus -5 over 2.is my Center at minus 1 and the radius.is gonna be Sigma X minus Sigma Y over 2.squared plus tau XY squared Sigma X 3.minus minus 5 over 2 squared plus -3.squared the square root of that so this.is 8 over 2 4 squared plus 3 squared.square root of that which is a 5 or is.16 plus 9 25 square root of 25 plus or.minus 5 okay that's the radius I know.that that's also the maximum shearing.stress so with that information I know.that my center is at minus 1 and the.radius is 5 my Center is it minus 1 and.I'm gonna move 1 2 3 4 5 for the minimum.or the one on the left and from this.Center 1 2 3 4 5 4 Sigma 1 Sigma 1 Sigma.2 doesn't matter how I label them it's.just the principal stresses and that.same 5 is gonna be the radius 1 2 3 4 5.which is my maximum stress a shearing.stress 1 2 3 4 5.okay so something like this doesn't need.to be perfect but do try to make it as.best as you can.all right so my principle stripe my.original stress states would be 3 and X.1 2 3 and minus 5 minus 3 sorry for the.signal for the hotel so this is my X and.does this make sense yes cuz if I go all.the way to the other side.I get a Y of minus 5 so let's label.these minus 1 minus 5 minus 6 and 0 plus.5 over 4 so I know things like my Sigma.average is minus 1 my Sigma max in this.case would be a minus 6 ksi my Center is.the same as the Sigma average just at.minus 1 comma 0.Mitel max or the radius is a 5 plus or.minus 5 5 K is high and all I need now.is the angle which is the angle from my.original state to going to the principal.stresses this is 2 theta P right how do.I do that I know that tangent of 2 theta.P is equal to this component which is.just my ex from the original stresses.not my sorry my Y the towel of my.original stresses so this has components.of 3 comma minus 3 3 minus 3.and that's what I need three opposite.over adjacent which would be from the.centered to here from minus one to three.which is a 4 or 3 minus minus 1 3 over 4.so 2 theta P is tangent minus 1 of 3/4.and this is a 36 point 9 degrees is it.positive or negative.it's going clockwise from my original.state to the principal stresses means.it's gonna be negative so minus.thirty-six point nine and that's it.

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Scotland unveiled the world's first large-scale tidal energy farm. I am so disappointed in the USA and my home state of California. Why aren't we going all out to have something like this off the coast of California?

A four foot variation in height twice a day is the low energy system and six foot variation four times a day. A cubic meter of seawater weighs about 1027 kg. So lifting it four to six feet two to four times a day generates 24.57 kJ to 73.70 kJ over 24 hours. That’s 284 milliwatts to 853 milliwatts per square meter of ocean water. So, if you can arrange a flat that covers say 10 acres and has a channel connecting it to the ocean, you get between 994.32 MJ and 2983.00 MJ every 24 hours. This is 11.50 kW to 34.52 kW average power. https://www.researchgate.net/post/What_is_a_reliable_electricity_con Continue Reading

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