Theory of Structures and Strength of Materials

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 Excerpt: ... in the material in the plane MN at a distance y from the neutral axis is 2(Pcosa) 2(Pcosa) y, _. fy= J2(PP Sin -) = // the signs depending upon the kind of stress. It will be observed that this formula is composed of two intensities, the one due to a direct pull or thrust, the other due to a bending action. The latter is proportional to the distance of the unit area under consideration from the neutral axis. It is sometimes assumed that the same law of variation of stress holds true over the real or imaginary joints of masonry and brickwork structures, e.g., in piers, chimney-stacks, walls, arches, etc. In such cases the loci of the centres of pressure correspond to the neutral axis of a beam, and the maximum and minimum values of the intensity occur at the edges of the joint. Example I. A horizontal beam of length /, depth d, and sectional area A is supported at the ends, and carries a weight Fat its middle point. It is also subjected to the action of a force H acting in the direction of its length. First. Let the line of action of H coincide with the axis of the beam. The intensity of the stress in the skin at the centre But c oc d, and / = At? oc Ad n being a coefficient depending upon the form of the section. If the section is a circle, - = 8; if a rectangle, n=6. Hence, the skin stress = i4---J, since M =. 4 Wl If the load W is uniformly distributed, M =-5-. Thus, a very small load on the beam may considerably in crease the intensity of stress, and this intensity will be still further increased by the deflection of the beam under its load, so that, in order to prevent excessive straining, it is often necessary to introduce more supports than are actually required to make the beam sufficiently ...