By A. E. H. LOVE

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**Extra resources for A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY**

**Example text**

II. is (16). given by 6 (a + 6)^ ^'a +o BENDING OF RODS IN ONE PLANE. 34 and that in BQ is given by a This can be thrown into the form The is deflexion [220 y given by at P +b : when the weight is at Q and P in is ^Q W (17). (18). We P when the weight is when the weight is at P. Q see that the deflexion at same as the deflexion at at Q is the Isolated load^ built-in ends. 220. Fig. 25. When beam is built in the bending moment at A and the horizontally at both ends let Then we have in ilfi at B.

Suggested A Prof. Voigf*, wh-en worked out, led to little better agreement, by and it appears that the attempt to trace the phenomena of impact Much more successful was the to vibrations must be abandoned. theory of Prof. Hertz ^ He suggested that the phenomena may depend on a local statical effect gradually produced and gradually The problem becomes a particular case of that solved by M. Boussinesq and Signor Cerruti which we have discussed in I. ch. IX. Prof Hertz made an independent investigation of the subsiding.

A and proportional to the bending moments at the are whose ordinates B, and draw through A, B the curve is isolated when this span bending moments at the points of AA' and BB' lines AB and simply supported at A and B and is under the given distribution of load. Let the verticals through the centroids of the triangles AA'B and BA'F meet AB in g and g', they are the vertical trisectors of the line AB, and let the vertical through the centroid of the curve of the bending moment when A and B are simply supported meet AB in G.

### A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY by A. E. H. LOVE

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