Design of Partially Prestressed Concrete Members

There is a distinct trend in current design practice toward the use of partially prestressed beams, in which flexural tensile stress or even cracking is permitted in the concrete in the service load stage or for occasional overloads. Cracks, if they occur, are usually small and well distributed, and normally close completely when the load that produced them is removed.

在目前的设计实践中，明显地倾向于采用部分预应力梁。对于这种梁，在使用荷载阶段或者在偶尔的超载时，容许混凝土产生弯曲拉应力，甚至容许开裂。如果产生裂缝，它们通常都比较小，分布也比较均匀，而且当使裂缝产生的荷载卸去之后，裂缝通常可以完全闭合。

It is argued convincingly that cracking has long been an accepted feature of reinforced concrete members and that there is no reason to penalize prestressed concrete designs by requiring that cracks be eliminated completely, even though this is possible. Furthermore, the condition of no tension or limited tension in a prestressed structure rarely exists. If combined effects including shear and torsion are taken into account, the calculated principal stresses usually exceed the tensile strength of the concrete. In regions of concentrated loads, load transfer, or anchorage of tendons, tensile stresses cannot be avoided. Also, in most cases, a structure is prestressed in only one direction, so that in the transverse direction it acts as ordinary reinforced concrete. In view of these facts, it is hard to justify a requirement for no flexural cracking.

可以令人信服地证实，长期以来裂缝一直是钢筋混凝凝土构件所容许的特征，并且，即使有可能的话，也没有理由在预混凝土设计中完全消除裂缝。而且在预应力结构中，很少存在没有拉应力或者拉应力受到限制的情况。如果考虑到剪切和扭转的组合作用，则计算的主应力往往超过混凝土的抗拉强度。在集中荷载、荷载传递或预应力筋锚固等区域，拉应力是不可避免的。此外，在大多数情况下，结构仅在一个方向施加预应力，因此它在横向同普通混凝土一样工作。从这些事实来看，就难以证明没有裂缝的要求是合理的。

The advantages of partial prestressing are important. A smaller prestress force will be required, permitting reduction in the number of tendons and anchorages. The necessary flexural strength may be provided in such cases either by a combination of prestressed tendons and non-prestressed reinforcing bars, or by an adequate number of high-tensile tendons prestressed to a level lower than the permitted limit. In some cases a combination of stressed and unstressed tendons is used. Since the prestressing force is less, the size of the bottom flange, which is required mainly to resist the compression when a beam is in the unloaded stage, can be reduced or eliminated altogether. This leads in turn to significant simplification and cost reduction in the construction of forms, as well as resulting in structures that are more pleasing esthetically. Furthermore, by relaxing the requirement for low service load tension in the concrete, a significant improvement can be made in the deflection characteristics of a beam. Troublesome upward camber of the member in the unloaded stage can be avoided, and the prestress force selected primarily to produce the desired deflection for a particular loading condition. The behavior of partially prestressed beams, should they be overloaded to failure, is apt to be superior to that of fully prestressed beams, because the improved ductility provides ample warning of distress.

部分预应力有很大的优点，它需要较小的预张拉力，因此可以减少预应力筋和锚具的数量。在此种情况下，必要的抗弯强度或者由预应力钢筋和非预应钢筋共同提供，或者由预张拉至低于容许值的足够数量的高强钢筋来保证。在某些情况下，可以同时使用张拉的和非张拉的钢筋。因为预张拉力较小，主要为承受梁在未加荷载阶段所需的底面，翼缘尺寸就可以减小或完全取消。这样又使得模板结构得到显著的简化和减少模板费用，并且做成在美观上更令人满意的结构。此外，由于放松了对混凝土中在使用荷载下的拉应力要求，梁的挠度特性可以得到显著的改善。构件可以避免产生在未加荷载阶段过大的上拱度，而且对于特定的荷载情况，可以通过选择预张拉力来获得所要求的挠度。部分预应力梁如遇超载而破坏，其工作性能也往往优于全预应力梁，因为得到改善了的延性能够为事故提供充分的预兆。

The design of structural members based on strength requirements is appealing, because in all but unusual cases the most important single characteristic of a structure is its strength, which establishes the degree of safety incorporated into its design. For reinforced concrete members, strength requirements usually provide the starting point in proportioning cross sections and determining steel areas. Only later is the design checked for satisfactory serviceability, with specific reference to cracking and deflection at the service load level. Checking of service load stresses is often dispensed with.

以强度要求为依据的构件设计是受人欢迎的，因为，除了极罕见的情况以外，结构唯一最重要的性能就是结构的强度，它确定了设计中所体现的安全度。对于钢筋混凝土构件，强度要求通常可作为拟定截面尺寸和确定钢筋面积的出发点。其后才专门根据使用荷载下的裂缝和挠度，为满足使用要求而做设计校核。通常不用进行使用荷载应力的验算。

An analogous approach is proposed for prestressed concrete, although there are some complications. For reinforced concrete, consideration is usually limited to underreinforced beams, for which the steel is at the yield stress at failure. With the tensile force thus known, the compressive area of the cross section is easily calculated from the summation of horizontal forces. With the centroid of the compression area known, the internal resisting lever arm is known and an explicit equation can be written for the ultimate resisting moment. This equation can be rearranged to permit direct solution for the required concrete dimensions and tensile steel area. For prestressed concrete, on the other hand, the stress in the steel at flexural failure is at some value  usually less than the tensile strength . It may be more or less than the nominal yield stress . The compression concrete area, which is a function of steel stress at failure, is not easily established at the outset of the design process, so the internal lever arm between compressive and tensile resultants is not known.

对于预应力混凝土，虽然复杂一些，也建议采用类似的方法。对于钢筋混凝凝土，通常只限于考虑低筋梁，这种梁在破坏时，钢筋达到屈服应力。这样，当拉力为已知时，便可通过对水平力求和来计算截面的受压面积。当受压面积的形心为已知时，就可以知道抵拉内力偶臂，并可对极限抵抗弯矩写出清楚的计算公式。这一公式可以被重新整理，使其能直接求解需要的混凝土尺寸和受拉钢筋面积。另一方面，对于预应力混凝土，弯曲破坏时的钢筋应力通常处于比抗拉强度小的某个值 ，它可能大于或小于标称屈服应力。作为破坏时钢筋应力函数的混凝土受压面积，在设计过程开始时是不容易确定的，因而压应力与拉应力两合力之间的内力偶臂也无法求得。

However, in practical cases, a trial concrete section may be found by assuming that the tendon stress at failure is 0. 9 times the ultimate strength . Refinement will be found necessary only in cases when there is an unusually large percentage of steel. For flanged sections, the internal lever arm at failure is very nearly equal to the distance from the tensile steel centroid to the middepth of the flange.

然而，在实际场合下，假定破坏时预应力钢筋的应力为0.9倍的极限强度，即可求出混凝土的试算截面。只有在钢筋百分率相当大时，才需要进行精确计算。对于有翼缘的截面，破坏时的内力偶臂非常接近于受拉钢筋重心至翼缘厚度中心的距离。