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  1. prex

    Interesting ponding/deflection problem

    Sorry guys, my bad, I'm decidedly too old to come back to differential equations. Anyway a solution to the equation ΔIV=(Bgγ/EI)Δ , where y is kg/m3 and g=9.81 m/s2, can be found only when (π/L)4=Bgγ/EI (and it is a sine function) . So, for any L less than the value defined by the latter...
  2. prex

    Interesting ponding/deflection problem

    If you consider a beam (so not a plate) in bending, then your equation (d4Δ/dx4)=(Bγ/EI)Δ(x) is correct, but the solution is not in the form of a sine curve, it is instead a polynomial of the fifth order, so no critical case can exist.
  3. prex

    Interesting ponding/deflection problem

    Not sure to understand your setup: in (1) you show the plate/membrane held (supported and held, I suppose) in only one direction. If that is true, then the problem becomes really complex, as the level of the retained water will depend on the deflection of side L, and won't be as depicted in (3)...
  4. prex

    Stacking an object

    IMO this problem is the same as the one for the stability of a column under its own weight. In fact, as long as the (equal) objects composing the stack are in contact with each other, the stack stays continuous due to its own weight. Now for a prismatic column under its own weight...
  5. prex

    Theoretical Question - Planar Truss Problem

    There's a quite simple proof of the original problem statement. As this proof is based on simmetry, it proves also that the same statement won't be generally true in the lack of simmetry. 1) Assume the angle alpha is zero: because of simmetry, the statement is true 2) Assume the angle alpha is...
  6. prex

    Calculating welds - Second moment of area

    The second moment of area, as the word iteself says, is area x distance squared. Pls post this kind of questions in the students forum
  7. prex

    Thick Walled Cylinder Question

    sigma_theta+sigma_r is not almost constant, it is exactly constant. To me the elongation due to end pressure only is 30 in, the contraction due to Poisson effect id 27 in, for a total elongation of 3 in
  8. prex

    Thick Walled Cylinder Question

    If you look at your equations, you'll find that sigmatheta+sigmar=const, so the longitudinal elongation (negative, it is a contraction) is, of course, independent of r and is easily found from the strain eq. for epsz (sigmaz being, of course, null everywhere for a free ends pipe). Pls post this...
  9. prex

    The physics of Bungee Jumping

    Sorry guys, I need to make amends. I now see where is the point: Newton's law only holds, for an isolated system, if the mass in F=ma is constant. This problem has something in common with the well known phenomenon of ice skaters, when they spin on the spot at varying speeds by narrowing or...
  10. prex

    The physics of Bungee Jumping

    btrue, I fully respect civil engineers, but I am not one of them. ;) And an inextensible chain is not that unreal, we engineers should be accustomed to the concepts of nearly..., substantially... etc. In our case an actual metallic chain would behave as inextensible, because the strain that it...
  11. prex

    The physics of Bungee Jumping

    Look at it from another perspective. If you want the jumper to experience an acceleration greather than g, then you need to exert a force on the jumper, additional with respect to its weight. This force can't be the weight of the cord, as this one is used to accelerate the cord itself. This...
  12. prex

    The physics of Bungee Jumping

    Greg, read their conclusions, and you'll see that they are (were) not positive on the demonstration of the calculated accelerations by the tests.
  13. prex

    The physics of Bungee Jumping

    The energy argument is used incorrectly IMO. Take an inextensible chain suspended at one end, as in the bungee, falling under its own weight. When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential...
  14. prex

    How Does Polarity Influence Two Part Epoxy Bonding to Neodymium Magnets?

    It is an intriguing question, the manufacturer of the resin won't disclose the details of the resin content, but could be interested in giving some advice. The only idea that comes to mind is that the steel powder in the mix could be from a hard magnetic steel that acquires some magnetic...
  15. prex

    How to solve kinematic system with spring and pulleys?

    The answer to a) should simply be FV/c=r/2 The answer to c) should come from b) by calculating x from v(x)=0 Your solution to b) is not far from being correct. The energy stored in the spring is c x2/8, as the spring elongates by x/2. By replacing J1 and ω1 with their expressions you'll be...
  16. prex

    Orifice Plate Bending - Mystery Calculation

    The original formula can't be correct in general. Letting a=Dpipe/2, b=dn/2 and ρ=b/a, it may be written as [ΔPa4/(64D]plate)(1-ρ2)2. Calling P the total load acting on the plate, P=ΔPπ(a2-b2), that formula may be rearranged as [Pa2/(64D)](0.318-0.318ρ2). The right parenthesis may be considered...
  17. prex

    Rectangular plate; two edges simply supported, two edge free

    You can find it here. prex http://www.xcalcs.com : Online engineering calculations https://www.megamag.it : Magnetic brakes and launchers for fun rides https://www.levitans.com : Air bearing pads
  18. prex

    Statics Problem with 3 supports but only 2 Unknowns (because 2 reactions are known to be equal)

    Yes, it is indeterminate, according to the accepted definition. About reinventing the wheel: when I was a student, long long ago, there was a story that was told to engineering students who took the monster exam on Theory of elasticity. The story read: Do you know who was the student who...
  19. prex

    Statics Problem with 3 supports but only 2 Unknowns (because 2 reactions are known to be equal)

    Owing to symmetry, if you cut the beam at B, you end up with a beam on two supports, one fixed and one simple (pinned). It's a statically determinate problem that's solved in many engineering books (remember: an engineer should never reinvent the wheel [wink]). With P midway of A and B the...
  20. prex

    Joint torques coupled to motor torque in cable-actuated robotic finger

    1) Think of a common belt drive: you have two pulleys with a tight side under tension and a slack side with nearly zero tension, excluding pretension. This explains how is it that the different sections of your cable have different tension forces: the moment applied to each pulley determines the...

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