很明显，梁的受压区能够承担一个有限数量的扭矩，水平钢筋一也可以通过销栓作用提供一定的抗扭强度。
现己发现〔例如由马托克(Mattock)〕，如果有一定数量的弯矩存在，则巳开裂截面的抗扭强度就大约是未开裂截面极限抗扭强度的一半。因此，也就是说构件在裂缝形成之后还可以承受开裂扭矩的一半。这时承受的扭矩已经到可该把它对弯曲作用的影响忽略不计的程度。而ACl 318一71是把这一有限的扭矩所对应的名义扭转剪应力偏子保守地假定为开裂剪应力6fe'psi(0.5fe'N/mm2)的40%。
'?v?0.4(6f te) （8.12）
x2y因而开裂后仅由混凝土截面承受的扭矩便可由公式8.8展示为： Te?v1e
3同理，对于复合截面，由公式8.8a可得:
x2yvte （8.13） Te??3其中应按图8.4所示对悬出部分进行限制。
当Tm/Mm>0.5时(即扭转作用较为显著时)，观察到的是脆性破坏.而当弯矩较为显著时(即Tm/Mm<0.5时)，就可望产生较为具有延性的破坏。梁的抗扭强度只有在增加腹筋的情况下才能提高。抗弯钢筋的数量看来对混凝土截面的抗扭能力没有影响。 在T形和L形梁中，翼缘的挑出部分对抗扭强度是起作用的。这已通过独立梁得到证实。当翼缘是楼板的一部分时，它的有效宽度是难以确定的。当由千于版中负弯矩的作用面有可能如图8.9所示沿边梁形成一条屈服线时，翼缘的一大部分看来就不大可能再提供什么抗扭强度了。在这种情况下只依靠矩形截面就比较合理。 8.4无腹筋梁中伯扭转与剪切
显然就叠加的意义来说由扭矩和剪应力所引起的剪应力在矩形梁截面的一边是相加，而在对面一边则是相减。这样接着产生的临界斜拉应力又会受到混凝土中弯曲拉应力的进一步影响，因为不可能只作用剪力而同时却没有弯矩产生。现在还没有听说已经研究出了一个在考虑弯曲作用的情况下对剪切与扭转的相互作用进行分析的十分合理的理论.由子这个原因就必须依靠由试验得到的经验数据。在设置的抗弯钢筋多于需要的条件下，就有可通过实验来研究剪扭联合作用时的破坏判别条件.通常在这类试验中都要在荷载增大直至破坏的过程中使扭矩与剪力的比值维持不变，然而实际上却可能是一种作用首先发生，并在另一种作用显著增大之前就使构件产生了与其作用相应的裂分布图形。因此在分析试验结果方而权且偏于保守是合理的。
图8.10绘出了在典型的扭一剪共同作用试脸中获得的试验点子的散布倩况，它还表明只要选用了足够低的剪切.斜向开裂和扭转斜向开裂应力值，一条圆弧形的相互作用曲线(对这一组特定试验进行了公称化处理)是可以用于设计的。对于这些不设腹筋的梁来说，由公式7.5和公式8.8计算出来的、对途中所绘出的那些试验点子形成了近似下限的剪应力和扭转剪应力值分别为
ve2.68fe'psi(0.22fe'N/mm2) vte?4.80fe'psi(0.41fe'N/mm2)
这个圆弧形相互作用关系曲线是现行ACI规范条文的基础。为了方便起见，可以把已开裂截面在极限荷载时所承受的相互作用的剪力值和扭矩值用名义应力表示为：
(vte2.4fe')2?(ve2fe')2?1 （8.14）
式中:vtm—在极限情况下引起的由混凝土承受的名义扭转应力，由公式8.8给出；Vm-在极限情况下引起的由棍凝土承受的剪应力，由公式7.5给出。
图8.10 扭转与剪力的相互作用
原文:
Strength and Deformationof Members with Torsion
Dr. A. Meher Prasad
8.1 INTRODUCTION
Torsion in reinforced concrete structures often arises from continuity between members. For this reason torsion received; relatively scant attention during the first half of this century, and the omission from design considerations apparently had no serious consequences. During ;the last 10 to 15 years, a great increase in research activity has advanced the understanding of the problem significantly. Numerous aspects of torsion in concrete have been,and currently are being, examined in various parts of the world. The first significant organized pooling of knowledge and research effort in this field was a symposium sponsored by the American Concrete Institute. The symposium volume also reviews much of the valuable pioneering work.
Most code references to torsion to date have relied on ideas borrowed from the behavior of homogeneous isotropic elastic materials. The current ACI code8.2 incorporates for the first time detailed design recommendations for torsion. These recommendations are based on a considerable volume of experimental evidence, but they are likely to be further modified as additional information from current research efforts is consolidated.
Torsion may arise as a result of primary or secondary actions. The case of primary torsion occurs when the external load has no alternative to being resisted but by torsion. In such situations the torsion, required to maintain static equilibrium, can be uniquely determined. This case may also be refer-red to as equilibrium torsion. It is primarily a strength problem because the structure, or its component, will collapse if the torsional resistance cannot be supplied. A simple beam, receiving eccentric line loadings along its span,cantilevers and eccentrically loaded box girders, as illustrated in Figs. 8.1and 8.8, are examples of primary or equilibrium torsion.
In statically indeterminate structures, torsion cart also arise as a secondary action from the requirements of continuity. Disregard for such continuity in the design may lead to excessive crack widths but need not have more serious consequences. Often designers intuitively neglect such secondary torsional effects. The edge beams of frames, supporting slabs or secondary-beams, are typical of this situation (see Fig. 8.2). In a rigid jointed space structure it is hardly possible to avoid torsion arising from the compatibility of deformations. Certain structures, such as shells elastically restrained by edge beams,\
of torsion than are other.
The present state of knowledge allows a realistic assessment. of the torsion that may arise in statically indeterminate reinforced concrete structures at various stages of the loading.
Torsion in concrete structures rarely occurs. without other actions.
Usually flexure, shear, and axial forces are also present. A great many of the more recent studies have attempted to establish the laws of interactions that may exist between torsion and other structural actions. Because of the large number of parameters involved, some effort is still required to assess reliably all aspects of this complex behavior.
8.2PLAIN CONCRETE SUBJECT TO TORSION
The behavior of reinforced concrete in torsion, before the onset of cracking,can be based ors the study of plain concrete because the contribution of rein-force ment at this stage is negligible.
8.2.1 Elastic Behavior
For the assessment of torsional effects in plain concrete, we can use the well-known approach presented inmost texts on structural mechanics. The classical solution of St.Venant can be applied to the common rectangular concrete section. Accordingly, the maximum torsional shearing stress vt is generated at the middle of the long side and can be obtained from