【正文】 o place the c. g. s. much below the kern without producing tension in the top fibers at transfer. The end section, however, presents an entirely different set of requirements. Since there is no external moment at the end, it is best to arrange the tendons so that the c. g. s. will coincide with the c. g. c. at the end section, so as to obtain a uniform stress distribution. In any case, it is necessary to place the c. g. s. within the kern if tensile stresses are not permitted at the ends, and not too far outside the kern to avoid tension stress in excess of allowable values.It is not possible to meet the conflicting requirements of both the midspan and the end sections by a layout such as ( a ). For example, if the c. g. s. is located all along the lower kern point, which is the lowest point permitted by the end section, a satisfactory lever arm is not yet attained for the internal resisting moment at midspan. If the c. g. s. is located below the kern, a bigger lever arm is obtained for resisting the moment at midspan, but stress distribution will be more unfavorable at the ends. Besides, too much camber may result from such a layout, since the entire length of the beam is subjected to negative bending due to prestress. In spite of these objections, this simple arrangement is often used, especially for short spans.Fig 87. Layouts for pretensioned beams.For a uniform concrete section and a straight cable, it is possible to get a more desirable layout than ( a ) by simple varying the soffit of the beam, as in Fig. 87( b ) and ( c )。 ( b ) has a bent soffit, while ( c ) has a curved one. For both layouts, the c. g. s. at midspan can be depressed as low as desired, while that at the ends can be kept near the c. g. c. If the soffit can be varied at will, it is possible to obtain a curvature that will best fit the given loading condition。 for example, a parabolic soffit will suit a uniform loading. While these two layouts are efficient in resisting moment and favorable in stress distribution, they possess three disadvantages. First, the formwork is more plicated than in ( a ). Second, the curved or bent soffit is often impractical in a structure, for architectural or functional reasons. Third, they cannot be easily produced on a longline pretensioning bed.When it is possible to vary the extrados of concrete, a layout like Fig. 87( d ) or ( e ) can be advantageously employed. These will give a favorable height at midspan, where it is most needed, and yet yield a concentric or nearly concentric prestress at end section. Since the depth is reduced for the end sections, they must be checked for share resistance. For ( d ), it should also be noted that the critical section may not be at midspan but rather at some point away from it where the depth has decreasd appreciably while the external moment is still near the maximum. Beam ( d ), however, is simple in formwork than ( e ), which has a curved extrados.Most pretensioning plants in the United States have buried anchors along the stressing beds so that the tendons for a pretensioned beam can be bent, Fig. 87( f ) and ( g ). It may be economical to do so ,if the beam has to be of straight and uniform section, and if the MG is heavy enough to warrant such additional expense of bending. Means must be provided to reduce the frictional loss of prestress produced by the bending of the tendons. For example, the tendons may be tensioned first from the ends and then bent at the harping points.It is evident from the above discussion that many different layouts are possible. Only some basic forms are described here, the variations and binations being left to the discretion of the designer. The correct layout for each structure will depend upon the local conditions and the practical requirements as well as upon theoretical considerations.Most of the layouts for pretensioned beams can be used for posttensioned ones as well. But, for posttensioned beams, Fig. 88, it is not necessary to keep the tendons straight, since slightly bent or curved tendons can be as easily tensioned as straight ones. Thus, for a beam of straight and uniform section, the tendons are very often curved as in Fig. 88( a ). Curving the tendons will permit favorable positions of c. g. s. to be obtained at both the end and midspan sections, and other points as well. Fig 88. Layouts for posttensioned beams.A bination of curved or bent tendons with curved or bent soffits is frequently used, Fig. 88( b ), when straight soffits are not required. This will permit a smaller curvature in the tendons, thus reducing the friction. Curved or bent cables are also bined with beams of variable depth, as in ( c ). Combinations of straight and curved tendons are sometimes found convenient, as in ( d ).Variable steel area along the length of a beam is occasionally preferred. This calls for special design of the beam and involves details which may offset its economy in weight of steel. In Fig. 88( e ), some cables are bent upward and anchored at top flanges. In ( f ), some cables are stopped part way in the bottom flange. These arrangements will save some steel but may not be justified unless the saving is considerable as for very long spans carrying heavy loads.83 Cable ProfilesWe stated in the previous section that the layout of simple beams is controlled by the maximum moment and end sections so that, after these two sections are designed, other sections can often be determined by inspection. It sometimes happens, however, that intermediate points along the beam may also be critical, and in many instances it would be desirable to determine the permissible and desirable profile for the tendons. To do this, a limiting zone for the location of c. g. s. is first obtained, then the tendons are arranged so that their centroid will lie within the zone.The method described here is intended for simple beams, but it also serves as an introduction to the soluti