VOUSSOIR ARCHES 404. Definition. A voussoir arch is an arch composed of separate stones, called vaussoirs, which are so shaped and designed that the line of pressures between the stones is approximately per pendicular to the joints between the stones. So far as it affects the mechanics of the problem, it is assumed that the mortar in the joints between the voussoirs acts merely as a cushion, and that the mortar has no tensile strength whatever, even if the pressure at any joint should be such as to develop tensile action. It is this feature which constitutes the distinction between a voussoir arch and an elastic arch, which is assumed to be an arch of such material that tensile or trans verse stresses may be developed.
405. Distribution of the Pres= sure between Two Voussoirs. The unit-pressure on any joint is as sumed to vary in accordance with the location of the center of pres sure, as is illustrated in Fig. 219.
In the first case, where the center of pressure is over the center of the face of the joint and is per pendicular to it, the pressure will be uniformly distributed, and may be represented, as in Fig.219o, by a series of arrows which are all made equal, thus representing equal unit-pressures. As the center of pressure varies from the center of the joint, the unit-pressure on one side increases and the unit-pressure On the other side decreases, as shown in Fig. 210 b. The trapezoid in this diagram has the same area as the rectangle of the first diagram (a), and the center of pressure passes through the center of gravity of the trapezoid. As the center of pressure continues to move away from the center of the joint, the unit-pressure on one side becomes greater, and on the other side less, until the center of pressure is at a point c of the width of the joint away from the center. In this case (c),the center of pressure is at the extreme edge of the middle third of the joint. The group of pressures illustrated in diagram 'c becomes a triangle, which means that the pressure at one side of the joint has become just equal to zero, and that the maximum pressure at the other side of the joint is twice the average pressure. If the line of pressure varies still further from the center of the joint, the diagram of pressures will always be a triangle whose base is always three times the distance of the center of pressure from the nearest edge of the joint.
If the total pressure on that joint remains constant, then the intensity of pressure on one side of the joint becomes extreme, and may be sufficient to crush the stone. Also, since the elasticity of the stone (or of the mortar between the stones) will cause the stone (or mortar) to yield, the yielding being proportional to the pressure, the joint will open at the other side, where there is no pressure. In accord ance with this principle of the distribution of pressure, it is always specified that a design for an arch cannot be considered safe unless it is possible to draw a line of pressure (an equilibrium polygon) which shall at every joint pass through the middle third of that joint. If the line of pressure at any joint does not pass through the middle third, it means that such a joint will inevitably open, and make a had appearance, even though the unit-pressure on the other end of that joint is not so great that the masonry is actually crushed.
Since the actual crushing strength of stone is a rather uncertain and variable quantity, a larger factor of safety is usually employed with stone than with other materials of construction. This factor is usually made ten; and therefore, whenever the line of pressures passes through the edge of the middle third, the average unit-pressure on the joint should not be greater than of the crushing strength of the stone.
A table of these ultimate values has been given in Table I, Part I (page 10). They vary from about 3,000 pounds per square inch, for a sandstone found in Colorado, up to 28,000 pounds per square inch for a granite found in Minnesota. The weaker stone would hard ly be selected for any important work. Usually a stone whose ulti mate strength is 10,000 pounds per square inch or more, would be selected for a stone arch. Such a stone could be used with a working pressure of 500 pounds per square inch at any joint, assuming that the line of pressure does not pass outside of the middle third at any joint.