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...
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
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...
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...
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...
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...
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...
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...
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...
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...
You can find it here.
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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...
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...
