The roadway of timber-bridges is usually a flooring of boards laid upon the joists; for, in eases where sand and stones are employed, it is found that their weight, together with the humidity they engender, causes the timbers of such bridges speedily to decay. This, however, is flir from being a general rule; and many splendid erections of this descrip tion are rapidly being destroyed, owing to a want of attention to this important particular. Some have proposed to cover the surface of the roadway with lead, iron, copper, ke., but the increased expense will be a great obstacle to their fre quent introduction : we would recommend the wood pave ment to be laid as a covering for the roadway of all timber bridges. The parapet or handrail of these bridges is frequently of wood, or it may be of cast and wrought iron; now, how ever, that it has been shown how important an addition to the strength of a bridge the sides of a beam are, and that it acts usetblly in the direction of its depth, if it has only sufficient breadth to prevent its y ielding laterally, we would suggest that in future it should be made available to sustain the bridge, in addition to its present purposes of ornament and protection.
Draw Bridges of timber, made after the manner of a float, to draw up or let down, as occasions serve, the gate of a town or castle, may be made in several different ways, but the most common are made with 'dyers twice the length of the gate, and a foot in diameter. The inner space is traversed w lilt a cross, which serves for a counterpoise; and the chains which hang from the extremities of the plycrs to lift up or let down the bridge, are of iron or brass. Such bridges are to be seen at Stirling and Edinburgh castles, at the Tower of London, at the castle of Vincennes, and many other regularly-fortified places. In navigable rivers, it is sometimes necessary to form the middle arch of bridges with two movable platforms, to be raised occasionally, in order to let the masts and rigging of ships pass the bridge. There are two piers which support the drawbridge, one of the plat forms of which is raised, and the other let down, having a beam for its plyer. To this drawbridge are suspended two movable braces, which, resting on the supports, press against the bracket and thereby strengthen it.
It is one of the first principles of statics, that if two forces are represented, both in amount and direction, by the sides of a parallelogram. then their resultant will be represented by the diagonal of such parallelogram. likewi e in direction amid intensity. if we reduce The polygonal framing. of which many wooden bridges- arc formed, to their simplest form, that of two beams abutting against one another, and resting upon two solid supports at their lower ends, we find that, inasmuch as the forces will act in the beams, their weight or gravity tending to keep the ends of the beams against each other by preventing them from rising, will be represented by a vertical line passing through their paints of contact, which will be the diagonal of the parallelogram thrilled by the beams and lines drawn parallel to them at such a point in each as would limit the length of the line to what would fitly represent the force acting in the direction of the beam. and it is evident that the beams
being in equilibria their horizontal thrusts must be equal and contrary, and consequently will be neutralized by their joint action.
The fact is, in a polygonal framing of any kind, there are three forces exerted at every joint; one in the direction of each beam, and one, a vertical three, acting by gravity. which being the diagonal of the parallelogram constructed upon the beams, is the resultant of the other two, anti which, by acting as a counterpoise to the others, keeps the system it) equilibria.
To construct a polygon in any particular instance, we must know the direction and amount of each of the threes, and their points of application; when these are given, we may readily construct the successive sides of a polygonal bridge. It is a well-known fact that gravity always acts vertically; we 'nay, therelbre, take a line perpendicular to the horizon, and mark upon it a number of divisions, each one represent ing the etThet of gravity at every successive joint; having, then, found a point at such a distance from it as will repre sent the horizontal strains which, 101'11 Sy,te111 of forces in equilibria, are always equal, and connecting that point with the several divisions niarked• on the vertical line, we shall have a number of right lines which, both in direction and intensity, will respectively represent the three acting at each joint or angle of the framework. Then, by drawing lines parallel to these, placing them one after the other, we shall construct a polygonal frame which will be in equilibria, bear ing in mind that the compressions of any two sides of the polygon are reciprocally as the sines of the angles which they with the vertical lines, or directly as the secants of their inclination to the horizon.
In order to find the resultant of two forces acting in a given angle, e must add to the stun of the squares of the threes twice their products multiplied into the en-snil of the angle, and extract the square root. of the stun. and this will give the required resultant. Again; to ascertain the angle between the resultant and one Of the composants, we must divide the product of the sine of the given angle and the lesser force by the product of the co-sine of that angle, and the same force, to which the greater three must be a hied.