Mechanical Engineering: Ch 10: Forces on Cables (23 of 33) Catenary

Mechanical Engineering: Ch 10: Forces on Cables (23 of 33) Catenary - Example 1

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7 жыл бұрын

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In this video I will find s=? (length of the cable), T0=?, Tmax=? of the catenary hanging cable (c=? is found by using the iterative process.): example 1.
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Пікірлер: 42

@mohammedalhaloul9685 2 жыл бұрын

You are a great teacher . I ha ve watched many videos on KZfaq explaining how to derive catenary curve equation but for the first time ,I have a chance to relate the many complicated concepts and see the bigger picture . Thanks a lot

@MichelvanBiezen 2 жыл бұрын

Yes the catenary is a mysterious object until you can connect all the dots.

@timgrant1796 2 жыл бұрын

These are fair approximations, suitable for most practical applications with relatively small loads and strong cables, with negligible cable stretch. A little numerical analysis yields: To= 3279.3129 N, Tb= 4279.3129 N & y= 65.586259 cosh(50 * x/3279.3129 -0.76235481) -85.586259, with a cable length of 109.972m and an angle at the supports of 39.975643 deg wrt horizontal, all to an unnecessary level of precision for this example.

@MichelvanBiezen 2 жыл бұрын

In the real world that level of "precision" has no practical purpose. The level of precision should reflect the accuracy of the measurements that go into the problem. (I actually take points off if my students give me answers like that)

@timgrant1796 2 жыл бұрын

@@MichelvanBiezen As well you might, for we don't need people wasting time and reducing economy of effort. I was once happy to guide my own students to a better understanding of orders of magnitude and useful analysis in matters of accuracy and precision (e.g. the difference between stringing transmission lines and guiding a radio telescope to an area subtending a thousandth of an arc second of the sky), but am now also happy to watch angels dancing where they may.

@karimkhan1312 5 жыл бұрын

YOU R THE BEST ON EVERY TOPIC

@hoangdong6327 4 жыл бұрын

c satisfies c(e^(d/2c)-e^(-d/2c))=s, where d= distance 2 poles and s=length of the rope

@krithikp9741 5 жыл бұрын

Thank you Mr.van Biezen ☺️

@thalysonbrito6971 3 жыл бұрын

What an amazing lecture. Thank you!

@MichelvanBiezen 3 жыл бұрын

Glad it was helpful!

@AJ-et3vf 6 ай бұрын

Great video sir. Thank you

@MichelvanBiezen 6 ай бұрын

You are welcome

@jessiep.manlapas577 3 жыл бұрын

Well explained and done 🤗 it made mo understand it more. Thanks a lot.

@MichelvanBiezen 3 жыл бұрын

Glad it helped

@havinchung0119 3 жыл бұрын

Thank you so much

@MichelvanBiezen 3 жыл бұрын

You're most welcome

@lesross4442 7 жыл бұрын

Mr. van Bieze, Your explanation is clear and delivered well. However, for my needs I would like to change the problem. It seems that the distance Y is arbitrary and in this problem, the distance h is given. Can you rearrange the equations to make the reference line (Y) at the location of the connections (Y=0) and show how to calculate h given L and s? Looking forward to your reply. Les Ross

@MichelvanBiezen 7 жыл бұрын

If you watch the other videos as well you'll see that the location of the y reference is a very specific location. For the equations to work you must maintain that convention.

@lesross4442 7 жыл бұрын

Yes, I am trying to do just that, but KZfaq does not list all of the videos in order. Perhaps if we had a play list of just the chapter 10 videos. But I did watch (16 of 23) and saw that you concluded that X=sinh(y) and y=sinh-1(x). In this case y is the sag. But doesn't the (X,Y) relation depend on the cable length s? My application is for a cable on a space vehicle, so Y above the ground is not useful except as an arbitrary datum. I really need to calculate the sag (h). I know L and S. Can we assume that C = -h and start from there?

@MichelvanBiezen 7 жыл бұрын

Y is an particular point below the lowest point on the cable and it is related to the other parameters as shown in the videos.

@nicholasprovencher7360 3 жыл бұрын

@@lesross4442 y=0 doesn't technically mean "ground level" either. I work in lighting, and have designed systems where the y coordinate is roughly 170ft below ground level. Assume y is arbitrary and ignore it having a position in real life.

@lesross4442 7 жыл бұрын

Mr. van Biezen, I think I worked out an understanding of the catenary in my sleep last night. The pieces started coming together in the shower this morning. Please tell me if I am on the right track or am I completely delusional? The catenary is a particular shape of a curved line just like a circle, an ellipse or a parabola. Each of these shapes have a general formula (r^2=x^2+y^2 for the circle) and a characteristic that describes the particular example (r=10). In the case of the catenary, that characteristic is the distance you are calling C. It is like the focus of a parabola or the distance between the foci of an ellipse. But each of these general shapes is infinite in length without another characteristic describing the arc length. For the catenary I think there are 5 parameters, the characteristic C, the sag h, the distance L, the arc length S and the angle at the fixed end of the arc. One of these parameters may be redundant. I think that with any 2 of these parameter known and knowing the formula for the catenary, the others may be found. This relationship to other curves may have been presented in another Chapter 10 video, but You Tube will not present them in order. If I am correct, I would appreciate a video presenting the generalized catenary math as it relates to other curves. The thing that tripped me up is that the catenary is ALWAYS presented like a telephone wire curving down. This makes me think that C is the ground. I think it could be presented more generally to avoid confusion. With respect, Les Ross

@teodoroabdo3137 3 жыл бұрын

How do you calculate h if you only know s? That is problem you have to solve.

@riyadh921 3 ай бұрын

Hi teacher, thanks for this. But what is C? why do we need to solve this?

@MichelvanBiezen 3 ай бұрын

C is a bit mysterious in the calculations, but it represents the horzontal tension in the cable. By increasing C, you increase the tension, and reduce the sag in the cable.