A Treatise On Statics: With Application to Physics 2
A Treatise On Statics: With Application to Physics 2
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Now as the components Of stress are linear functions of those of strain, we obtain the elementary result which we know to hold for the expansion of a bar according to Hooke's Law, viz. that the work is one half the product of the whole extention and the final tension of the bar.
2. Find the work done in the distortion of a body (without com- pression or dilatation at any point).
^ns, /x/(a* + 6" + c* + 2«i« + 2«2« + 20^^- For example, take the case of the torsion of a circular cylinder (Art. 37...1). Then 2«i = ^> 2«j = — ^; so that the work where r ia the distance of the element dil from the axis of the cylinder. This work is v72*a' where R = radius of cylinder.
If the torsion is produced by opposite couples applied at the ends, or by holding one end fixed and applying a couple of moment O to the other, this work is i ««•> ■^alC (r, as will presently be shown.
3. Two uniform bars, CB, BA (Fig. 184, p, 224, vol. I) are freely jointed to each other at By and have their ends C and A fixed by smooth pins ; if a weight, TT, so great that, in comparison, the weights of the bars may be neglected, is suspended from the joint B^ find the vertical distance through which B will descend.
What to read after A Treatise On Statics: With Application to Physics 2?
You can find similar books in the "Read Also" column, or choose other free books by George Minchin Minchin to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Now as the components Of stress are linear functions of those of strain, we obtain the elementary result which we know to hold for the expansion of a bar according to Hooke's Law, viz. that the work is one half the product of the whole extention and the final tension of the bar.
2. Find the work done in the distortion of a body (without com- pression or dilatation at any point).
^ns, /x/(a* + 6" + c* + 2«i« + 2«2« + 20^^- For example, take the case of the torsion of a circular cylinder (Art. 37...1). Then 2«i = ^> 2«j = — ^; so that the work where r ia the distance of the element dil from the axis of the cylinder. This work is v72*a' where R = radius of cylinder.
If the torsion is produced by opposite couples applied at the ends, or by holding one end fixed and applying a couple of moment O to the other, this work is i ««•> ■^alC (r, as will presently be shown.
3. Two uniform bars, CB, BA (Fig. 184, p, 224, vol. I) are freely jointed to each other at By and have their ends C and A fixed by smooth pins ; if a weight, TT, so great that, in comparison, the weights of the bars may be neglected, is suspended from the joint B^ find the vertical distance through which B will descend.
What to read after A Treatise On Statics: With Application to Physics 2?
You can find similar books in the "Read Also" column, or choose other free books by George Minchin Minchin to read onlineMoreLess
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