Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/359

Rh FRAMES.] BRIDGES 315 pier cannot counterbalance must be compounded with the reaction due to the linear arch calculated for the permanent load of the unloaded span. With the reaction thus com puted the linear arch resulting in the unloaded span must be constructed, and the stresses examined on the top and bottom flanges of the rib. The theory now given for a stiff rib used as an arch is equally applicable to a stiff rib hung as a suspension bridge. -18. Wooden Arches. Arches have occasionally been built of wood with ribs elaborately constructed of bent timber, scarfed and bolted together ; the strength of such a rib could be calculated in the way indicated for metal ribs, but the mode of construction is not to be recom mended. When wood is employed it should be used in simple straight balks built into a framed arch. 49. Practical Details of Metal Arches. The common form of metal arch is a cast-iron rib of IE section and of small depth. This rib is intended to be sufficient, unaided, to bear the whole weight of the superstructure. The spandrils, made of some kind of lattice work (or occasion ally a mere arcade), bear the roadway, and to some extent stiffen the rib beneath. The rib may with advantage be made much deeper than has been the practice, and may consist of tubes framed as in the St Louis Bridge, fig. 5, Plate XVIII., so as to form a single stiff rib. Where, to gain head way, a rib of small depth at the crown is desirable, the rib might with advantage be deepened at the haunches. Wrought iron is a very suitable material for small arches, where the permanent load is insufficient to prevent tension from occurring in some parts of the rib. Cast-iron and cast-steel are better materials for large spans ; for moderate spans a good form of metal arch will be shown under the head of &quot;Frames&quot; (fig. 77), being that in which a lower member is braced to the upper member carrying the road way so as to form a true frame ; for very large spans a single deep rib, or a frame with parallel members arranged as an arch, may be adopted. This design has the advan tage over that shown in fig. 77 of avoiding very long bracing at the abutments. V. FRAMES. 50. Preliminary. A frame is a rigid structure composed of straight struts and ties. The struts and ties are called the members or pieces of the frame. The frame as a whole may be subject to a bending moment, but each bar, pillar, rod, or cord in the structure is thereby simply extended or compressed so that the total stress on a given member is the same at all its cross sections, while the intensity of stress is uniform for all the parts of any one cross section. This result must follow in any frame, the members of which are so connected that the joints offer little or no resistance to change in the relative angular position of the members. Thus if the members are pinned together, the joint consisting of a single circular pin, the centre of which lies in the axis of the piece, it is clear that the direction of the only stress which can be transmitted from pin to pin will coincide with this axis. The axis becomes, therefore, a line of resistance, and in reasoning of the stresses on frames we may treat the frame as consisting of simple straight lines from joint to joint. When the members .of a frame consist of iron rods as ties, combined with struts formed by angle iron or T iron of the usual sizes, or by pieces of timber of the ordinary dimensions, it is found by experiment that the stresses on the several members do not differ sen sibly whether these members are pinned together with a single pin or rigidly jointed by several bolts or rivets. Frames are much used as girders, and they also give useful designs for suspension and arched bridges. A frame used to support a weight is often called a truss ; the stresses on the various members of a truss can be computed for any given load with greater accuracy than the intensity of stress on the various parts of a continuous structure such as a tubular girder, or the rib of an arch. Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame, except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load. Both assumptions are consistent with the facts in the case of any bridge truss. 51. Classes of Frames used as Trusses. Frames used as bridge trusses should never be designed so that the elongation or compression of one member can elongate or compress any other member. An example will serve to make the meaning of this limitation clearer. Let a frame consist of the five members AB, BD, DC, CA, CB (fig. 63), jointed at the points A, B, C, and ^ ^ D, and all capable of resisting tension and compression. This frame will be rigid, i.e., it cannot be distorted without causing an alteration in the length of one or more of the members ; but if from ~ _ Uj} a change of temperature or any other cause one or all of the mem- Fig. 63. bers change their length, this will not produce a stress on any member, but will merely cause a change in the form of the frame. Such a frame as this cannot be self -strained. A workman, for instance, cannot produce a stress on one member by making some other member of a wrong length. Any error of this kind will merely affect the form of the frame ; if, however, another member be introduced between A and D, then if BC be shortened AD will be strained so as to extend it, and the four other members will be compressed ; if CB is lengthened AD will thereby be com pressed, and the four other members extended ; if the workman does not make CB and AD of exactly the right length they and all the members will be permanently strained. These stresses will be unknown quantities, which the designer cannot take into account, and such a combina tion ought therefore never to be adopted. A frame of this second type is said to have one redundant member. If the members AD and CB were flexible cords there would be no redundant members ; for the tightening of one diagonal would throw no sensible stress on the other diagonal, since it is supposed incapable of resisting a thrust. Both diagonals, if flexible, are required to prevent the quadrilateral from getting out of shape. Members capable of bearing only one kind of strain might receive the name of semi-members. 52. External Forces on Frame. Frames used as bridge trusses are in equilibrium under the external forces applied to them. These forces are (1) the loads, (2) the reactions at the points of support. The loads are to be referred to the joints as follows : (1) find the resultant of the load carried by any two joints ; (2) resolve that load into two vertical components acting through the two joints; (3) com pound the several components acting at each joint into one resultant. This process gives a frame with external forces equivalent to the actual loads, but acting only at the joints. The frames are always supported at a joint, and the reactions of the supports are therefore also forces acting at joints. The load between any two joints is directly supported by the member of the frame joining them; the stresses due to the direct action of this partial load must, where great accuracy is wanted, be added to the stresses computed on the assumption that the loads have been applied directly to the joints. Generally the stresses due to the direct action of the load between two joints may