studiot

There are two types of 'things' in our universe. English calls them concrete nouns (such as brick) and abstract nouns (such as happiness). We do not know if any concrete things can or do go on forever (I have never heard of an infinite brick) - we do not even know if the whole universe is infinite or not. But all concrete things we know of (except perhaps the universe) of have a beginning and an end, which is how a brick is 9 inches long. But we have found abstract things that have a beginning (or they would not exist at all), but have no end The difference between 0.9 inches and 0.9 recurring is exactly this. And 9, 0.9 0.3 are abstract things. /Edit In respect of Zeno's paradoxes, The path and time are concrete things with start and finish lines so are finite. The division is an abstract thing which has a start but may have no finish, although obviously you can stop dividing at any point if you wish /Endedit Does this help?

In the derivation of a wave equation from Maxwell's 3rd and 4th equations [math]\nabla \times E = \frac{{ - \partial B}}{{\partial t}}[/math] [math]\nabla \times H = \frac{{\partial D}}{{\partial t}}[/math] Use is made of substition of the so called constitutive equations stating the properties of transmission media in general. [math]D = \varepsilon E[/math] [math]B = \mu H[/math] [math]J = \sigma E[/math] In the last of these sigma is zero, hence J is zero in free space, which affects the magnetic equation. Substituting these and doing some algebra leads to The electric wave equation. [math]\frac{{{\partial ^2}{E_x}}}{{\partial {z^2}}} = {\varepsilon _0}{\mu _0}\frac{{{\partial ^2}{E_x}}}{{\partial {t^2}}}[/math] The constant on the RHS is equal to the reciprocal of the wave speed, hence [math]{c^2} = \frac{1}{{{\varepsilon _0}{\mu _0}}}[/math] Now consider what would happen if [math]\varepsilon [/math] and [math]\mu [/math] became infinite. The solution of the equation would become undefined and not a wave. So for any wave that does exist these must be finite.

Agreed but instead of the word travels doesn't this sound better? You are still thinking of it as a classical wave that travels spreads away from the source. The point of a wave packet is that it doesn't spread. That is how it models a travelling particle. I thought the moving graphics on Wiki described this rather well. A travelling EM (classical) wave takes its field along with it as it goes. That is how it spreads. The quantum field always occupies all the space available to it. Perturbation is another word for excitation and one mathematical way of approaching this is perturbation theory. But like everything else about quantum theory it is hydra like - multiheaded so no single one of our methods covers it all.

Why not?

Clasically yes indeed. Wiki is good on this. https://en.wikipedia.org/wiki/Impedance_of_free_space I think the finiteness comes form the fact that in the classical wave equation we are equating a function of space to a function of time (as a second order differential equation) and we would not have a wave if the constants were not finite. Note that the correct term for the excitation of the field representation is a wave packet not a wave. Again Wiki has a good picture. https://en.wikipedia.org/wiki/Wave_packet

Thank you. You obviously know a lot of shipyard types. (No doubt the salt of the earth and all that) But you also know a lot of good high level Physics. Do you never find non scientists using speed when they mean velocity or velocity when they mean speed, or mixing force and energy or power? water movement is even more general and covers even more cases, so what. Science needs to be specific so we can all agree what we are talking about.

Would you like to elaborate in this, perhaps with a simple worked example? In particular I am interested in this part of the statement What exactly do you mean by it and how does it fit with the idea that the wavelength = distance between adjacent wavefronts?

Like I said, the correct term is tidal stream and you will find them on Admiralty Charts, the Admiralty Tidal Stream Atlas and the Admiralty Manual of Tides. https://www.admiralty.co.uk/publications/miscellaneous-tidal-publications/admiralty-tidal-stream-atlases Since the Admiralty did almost all the work, mostly in the 19th century, they are entitled to set the terminology. But as a more pragmatic justification for differentiating between currents and tides. The tidal horizontal movement of water is the result of the vertical movement of the water surface as the rotation of the Moon moves it above the surface, its gravity causing a moving local 'hump'. Note that the gravitational interaction between the Earth and Moon means that the hump is not directly below the Moon. Water is drawn in from all directions to service this hump. So you cannot say the water is moving in a particular direction in quite the same way as a thermally or concentraction (salinity) driven current, which does not in any case lift the surface of the water.

Flutes and recorders act as open pipes. Reeded instruments like the clarinet act as closed pipes. A pipe has a node at a closed end and an antinode at an open one. https://www.google.co.uk/search?source=hp&ei=GinnWoSGNYakwAL816mgCg&q=is+a+flute+open+or+closed+at+the+end&oq=is+a+flute+open+or+closed+at+the+end&gs_l=psy-ab.3..33i22i29i30k1l5.1682.8680.0.9153.36.35.0.1.1.0.124.3295.24j11.35.0....0...1c.1.64.psy-ab..0.34.3130...0j46j0i131k1j0i46k1j0i131i46k1j46i131k1j0i3k1j0i10k1j0i22i30k1.0.Hg4WwcekEgc

You will be telling me that there are both direct and alternating ocean currents next. If you look on an Admiralty chart you will find the tidal streams marked. Tidals treams are the correct hydrographic term for the horizontal ( component of the) movement of water as a result of tidal action. Currents would exist, even if you took away the Moon and thus the tides and even if you took away the Earth's rotation. In fact that is a good place to start considering the movement of terrestrial waters.

+1 Nah, not a phantom. It mustha bin a Sassenach.

Perhaps your difficulty is in failing to distinguish between Mathematics and Physics. No thing in the physical world is quite a different concept from zero in Mathematics. Numbers and equations are in the province of Mathematics, which deals in mathematical objects as precisely defined as we can make them. Zero is such an object and therefore can be said to exist mathematically. The mathematical object 'zero' follows certain rules (yes Peano's are as good as any) which require 1*0 = 0*1 = 0

Well on the subject of a failure investigation here are the four areas that I would investigate. (one more than usual due to the construction technique). 1) Inadequate design. 2) Inadequate materials. 3) Inadequate Workmanship. 4) Misadventure during construction. As to calculations, I was simply looking for some dimensions, without which calculation cannot proceed. That was too much to ask huh? Despite the rules of this forum, I must wade through a 110 page doc? Thus I have been using your calculated forces. As such it is clear to me that even without any reinforcement at all the concrete of M11 was capable of surviving the maximum load you calculated. However you calculated a fancy spreadsheet that omitted two vital pieces of information. Firstly no mention of the links was made. These are provided to prevent bursting, which is the normal mode of compressive failure of short compressive members. The links also aid construction. Secondly no mention of length was made. This is required to determine the actual amount of reinforcement necessary to prevent bending and to satisfy the codes. But you have put in a lot of work and somewhere in those drawings I saw a note about the "shear failure at the connection". I have already queried the possibility of shear failure, and no connection details have been provided. But the big question is torsion. I note the form of the bridge is an inverted T. As such imbalanced loads (perhaps due to failue area 4) would introduce significant torsion in the members, which may not have been allowed for in the detailing. As I'm sure you are aware, the combination of torsional effects with shear and bending stress can be many times that of direct stresses from normal (=standard) loading.

This is still avoiding the point I made / question I asked which was How is it possible for a particle to change its energy if no force acts on it?

Torsion is the effect produced by two opposing (but separated) couples. A single couple will produce rotation. This similar to two opposing (but separated) forces combining to produce a couple.

At molecular level there is something called a screw dislocation in materials science theory. https://www.google.com/search?q=screw+dislocation&ie=utf-8&oe=utf-8&client=firefox-b At a larger scale it is responsible for the ocean gyres, due to the Coriolis force. Yes, this is a plastic behaviour and is used in soil mechanics to determine what is known as the Atterberg limits. https://www.google.com/search?client=firefox-b&ei=2GDkWqXwOcmZgAbE7LSAAw&q=atterberg+test&oq=atterberg+&gs_l=psy-ab.1.0.0l10.85674.87388.0.90364.10.10.0.0.0.0.178.1110.0j8.8.0.foo%2Ckpnr%3D200%2Ccfro%3D1.3..0...1.1.64.psy-ab..2.8.1102...0i67k1j0i131k1j0i131i46k1j46i131k1j0i10k1.0.l92DHmCneDg The simplest form is rolling a plastic material like dough or soil or plasticine between the fingers. Yes indeed torsion can be very destructive. This is often because very high stresses can be developed when it is combined with other forms of stress, which direct, shear and bending. I am going to be proposing this as a possible reason for the recent Florida Bridge collapse in the current thread on that subject here.

So are you now saying that you didn't mean this claim you made, so big and bold? Are you , in fact, now saying these are not the actual forces involved? For example a post tensioning force is not applied 'factored' . You jack until the required force is physically as measured. Incidentally ,code minimum steel is 0.4% here, if the Florida state code is anything like ours, and up to a maximum of 6%. So unless substantially greater loads than 1927 KIP were applied M11 was not technically under-reinforced.

These are your figures, so I'm glad you 'agree' them. Again this is your figure, so I'm glad you 'agree' it. I am quite capable of working out the forces in a relatively simple lattice girder like this one. I did, however, ask you a question about the necessary information and I would have thought the least you could do would be to point me to the right page instead of being sarcastic. I also understand the working of ~RC struts and in particular their failure modes, something you seem abnormally reluctant to discuss. So no more half lectures please. You are presumably aware that the ultimate strength of grade C60 steel is half as strong again at 90,000 psi? You have however claimed that the actual stress applied to member M11 exceeded then concrete strength of 6000 psi, when the calculation you accepted shows it to be only 2/3 of that figure. Since you obviously missed it last time I will repeat this. We do not expect a component to come near to failure under normal working loads, which is why we derate things by applying factors. So consideration of factored loads is not appropriate in a failure investigation. Have you ever conducted any failure investigations? I have and I can assure you that the procedure is quite different from the normal design one. We are not asking does it conform to the code (although that question will inevitably be asked as well) when we are trying to determine what happened.

Better let's keep the discussion professional shall we? I'm trying to make sense of your calculations, but have not yet tried to wade through the 110 page pdf you linked which presumably has the information required to make my own calcs? At the moment I am at the following stage with your figures. Area M11 = 24 x 21 = 504 sq ins Area steel = 8 x 0.6 = 4.8 sq ins Aread duct = 14 sq ins area concrete = 485.2 sq ins Applied load = 1927000 lbs force If this was applied to the concrete alone compressive pressure = 1927000 / 485.2 = 4000 psi (just under) Granted I have not applied any factors, but a failure investigation must investigate ultimate conditions of collapse.

You have said this twice, but that doesn't make it either true or an explanation/amswer to my question. I don't know is that is because you are entirely missing the point, or what. Potentials act over space not time. But you mentioned forces, not potentials and forces change the energy of a body by doing work on it. I do not need a fancy differential or integral equation to know that if no work is done on a free body the energy of a body does not change.

So are you suggesting there is a solution to the circumstances presented whereby the energy can change? At last, thank you for answering the OP question. Can I take it your answer is No, Copenhagen is inappropriate? You could have said that a long time ago. I would certainly agree with you that many of physical phenomena are also described or inherent in the maths. But all this does is demonstrate what a jolly good model that particular piece of mathematics is. (and therefore why we use it). As to Mathematics itself, yes every differential equation can be remodelled as an integral equation - I have several books on the subject. But I would also council two things "Beware of all or nothing statements" They have a habit of tripping themselves up. "Beware of saying that it is a consequence of the maths and nothing more" There is more to the mathematical modelling of physical processes than that. Take 'centrifugal force' for example. This is physically evident from some points of view (models) but not others.

Basically yes. That is why the Sun's gravity was used for the test.

You have described member 11 as under-reinforced. How does (by what mode) an underreinforced concrete member fail? Edit, further why was it in so much compression? Ties are usually much longer than struts so it looks like a tie in the diagram, not a strut?

No I think the question being asked is equivalent to greedy shipowners in the past asking How many sacks of coal will sink my boat?

That is not what I asked, sorry.