This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The shear at any section is measured by the projection onto the normal to the arch rib, of the corresponding ray of the force diagram. It is seldom that the shear is a serious factor in the design of an arch. Whenever (as in the case just being worked out) the equilibrium polygon coincides approximately with the. arch rib, the shear is very small. When the amount of the thrust is definitely computed, as determined above, the amount of the shear at the same point may be readily determined at the same time.
For example, the shear at the abutment is the projection of the ray O3.r onto the line O3w, which is parallel to the normal to the curve at B. This line, sealed at the rate of 5,000 pounds per inch, indicates a shear of about 2,200 pounds. Dividing this by 225, the area of the section of the arch at that point, the unit-shear is less than 10 pounds per square inch, which of course may be neglected. The shear in any arch may be very easily tested by noting the portion of the special equilibrium polygon which makes the largest angle with the direction of the arch rib at any point; the larger the angle, the greater the shear. If the arch is tested at that point, and the shear is found to be insignificant, or well within the power even of plain concrete to carry, there is no need for further investigation.
On the other hand, there are minor stresses which occur in arches as well as other concrete structures, which must be provided for. These are caused by a possible excessive concentration of loading; possible structural weakness due to a poor quality of concrete in comparatively limited areas; the effect of slight settlement of the foundations, etc. On account of these various stresses, which are more or less non-computable, it is the usual practice to insert bars, which are not only useful in taking up shear, but also tend to bind the whole structure together, make it act more nearly as a unit, and permit the structural weakness in local spots to be made up by the strength of the sounder portions of concrete around it; and therefore shear bars are put in, such as are illustrated in Fig. 235. These bars are laced between the upper and lower sets of bars that run parallel with the axis of the arch. By this means, not only are the upper and lower sets of reinforcing bars tied together, but the bars have such a direction that they can take up any shearing force which may, by any chance, be developed.