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But there are many points in our theory which are justified only on the assumption that displacements are small compared with the dimensions of the body. Then our present small compared with 2c We shall return bending of thin ; that solution will only hold provided is, to this point in is must be small compared with Re Chapter 14 when we deal with the b'^ plates. ( CHAPTER IV. THE EMPIRICAL BASIS OF ELASTICITY. Hooke's law. have already assumed some of the empiricaj properties of materials in Chapter II.

En whose stress depends very much on what may be regarded as the unknown accidents of manufacture, to make test pieces at the same time and under the same conditions as the actual material that is to be used in a structure. This gives some guarantee that the ultimate stress assumed in calculating the factor of safety is very nearly correct for the piece to which the calculation applies. similar piece of material dealing with material 45. Viscosity in solid bodies. elastic body may be set vibrating in different sorts of ways^ Any and these vibrations always die out after a short time.

X x dy dx dx having its centre at x, y, 2, and take the means stresses on the faces to be the stresses at the middle of the face concerned. The middle points of the two faces perpendicular to the axis of x have coordinatey shall deal APPLIED ELASTICITY 22 3'' {^'dli^-^'' ±^Sy, Y. z) ^^^^ ^^^ '^)' and {x, n, middle points of the other faces are at {x, y %±\dz). Let the body force per unit mass at {x, y, z) have components X, Z, and let q be the density of the body. The mass of the block being Qdxdydz, the body force on the block has components qXdx dydz, qY dxdydz, qZdxdydz.

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