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Young's modulus of a material doesn't depend on geometry. It is a mechanical property of material and depend on its structure. But, we cannot determine Young's modulus of a material by its structural properties experimentally. We (in your case) want to determine $E$ (Young's modulus) by using $E=\large{\frac{PL}{A\delta}}$ in a tension test ($P$ is the ...

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Yes, $ν$ being always less than 0.5 would be a consequence of $ΔV$ always being negative with traction. Would be, if it were true, which it is not. Citing the Wikipedia article, The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than −1.0 or greater than 0.5 (...) Some anisotropic materials (...) have one or more ...

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Take a piece of string (I just use cheap yard twine) and soak it im rubbing alcohol. Then wrap the soaked string around the glass tube along/in the score mark you made. Then light the alcohol soaked string on fire. let it burn for a few seconds then dip the gloss tube in cold water and it will break along you score line.. I personally use this method in ...

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I think @Joce has the correct answer in his comment, but I'm going to expand their answer a little bit to provide some more detail. The stress power is specified per unit volume, but you have to specify which unit of volume. The stress power integrated over an entire body in the current configuration $\Omega_t$ is given by: \begin{align} \int_{\Omega_t} ...

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The answer is "it depends". If you have a very thin and light "rod" (for example, a piece of fishing wire), the material from which that is made has a shear modulus, and it is in principle possible to have a piece of fishing wire vibrate without being held in tension. However, if you pull both ends tight, like the string of a guitar, then waves will travel ...

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All of these resources are saying the same thing, but you have to pay extremely close attention to the definitions of their differential operators. Specifically, in the brown.edu link, they define the divergence of a tensor $\mathbf{A}$ as $$\nabla \cdot \mathbf{A} = \frac{\partial A_{ij}}{\partial x_i}$$ with summation over the first index of ...

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A cantilever beam is a determinate structure: http://theconstructor.org/structural-engg/analysis/determinate-and-indeterminate-structures/3483/ If the beam has a length $L$ and a point load $P$ acts in it's end, the moment $M$ in it's fixed support is equal to $M=P*L$. So yes, the bending stress will be linearly proportional to the applied load.

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From what I've learnt, this relative strengthening,of cloth when wet, and weakening of paper is due to two factors. First up:The cloth - google fibre structures of cloth, and you will notice that cloth fibers are uniformly but relatively less interlocked, and addition of water causes further attraction via hydrogen bonding. For the paper, it has relatively ...

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Think of it in this way: If there exists a couple on the center of mass by exerting shear stresses on AB and CD, then shouldn't the block rotate? However, we know from experiment that the block will tend to deform (by a very small amount) as shown in Figure A, so there exists no rotation, which means the system is in rotational equilibrium. The couple ...

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