A Treatise On The Principles And Practice Of Dock Engineering

CONDITIONS OF STABILITY. 175 having a considerable backward slope, but from the very nature of their functions this ideal is unattainable in dock walls, and it follows that a certain portion of each bed joint is more highly stressed than the remainder. The intensity is greatest at the outside edge, and, assuming the joint to be a perfect one, it diminishes uniformly as it recedes from the face. If it reach a zéro value, it may do so either at the back of the wall or at some point within the wall. The latter alternative should be avoided, as it entails a tensile stress beyond the compressive limit—a stress which bed joints are ill adapted to resist, and which, accordingly, they should not be called upon to undergo. In fig. 95, A B is a horizontal bed joint and RO represents, in line of action and magnitude, the resultant pressure upon the joint. Resolve R into its two components, N R and N O respectively, parallel and perpendicular to A B. The former constitutes a shearing stress, which will be considered later; the latter is the total direct compression NC upon A B. At A set up the perpendicular AD=2 ^. Then, assum- ing compression to vanish at the point B, join D B and the triangle A D B will be the graphical representation of the amount and distribution of pres- sure over thejoint, AB. For the area of the triangle A DB ^-E) =N O. And, since the effect of any system of loading is equivalent to supposing the whole concentrated at its centre of gravity, the line NC necessarily passes through the centre of gravity of the triangle A D B in order to conform to the condition of zero stress at B. Clearly, then, this entails A C= AB In other words, the resultant thrust passes through the extremity of the middle third of the wall, but if tension in the joint is to be avoided, it may not exceed this limit. The resultant passes through the centre of section (E, fig. 96) when AD there is uniformity of stress throughout, and A K = —is the mean intensity. The stress diagram in this case is, accordingly, a rectangle AB AB having the same area. Between the two limits AE=—and A C=— (for we may disregard as inapplicable all values exceeding these) the diagram