在复合应力作用下的(混凝土)强度.docx

在复合应力作用下的(混凝土)强度
在许多结构中,混凝土同时受到不同方向各种应力的作用.例如在梁中大部分混凝土同时承受压力和剪力,再楼板和基础中,混凝土同时承受两个相互垂直方向的压力外加剪力的作用.根据材料力学学习中已知的方法,无论怎样复杂的复合应力状态,都可化为三个相互垂直的主应力,它们作用在材料适当定向的单元立方体上.三个主应力中的任意一个或者全部既可是拉应力,也可是压应力.如果其中一个主应力为零,则为双轴应力状态。如果有两个主应力为零，则为单轴应力状态，或为简单压缩或为简单拉伸。在多数情况下，根据简单的试验，如圆柱体强度f'c和抗拉强度f't，只能够确定材料在单轴应力作用下的性能。为了预测混凝土在双轴应力或三轴应力作用下的结构强度，在通过试验仅仅知道f'c 或f'c与f't的情况下，需要通过计算确定混凝土在上述复合应力状态下的强度。
尽管人们连续不断地进行了大量的研究，但仍然没有得出有关混凝土在复合应力作用下的强度的通用理论。经过修正的各种强度理论，如最大拉应力理论、莫尔-库仑理论和八面体应力理论 (以上理论都在材料力学课本中讨论过)应用于混凝土，取得了不同程度的进展。现在的试验结果表明，极限拉应变 (它是平均正应力的函数)可能是一个通用的混凝土破坏标准。目前这些理论中没有一个被普遍接受，其中许多还有明显的自相矛盾的地方。建立一个通用的强度理论的主要困难在于混凝土的高度非均质特性和混凝土在高应力下和断裂时，其性能受微小裂缝和其他不连续现象的影响程度较大。
然而，至少对双轴应力的各种试验确定了混凝土的强度。各种试验结果可用图1这样的相互作用图的形式表现出来。该图把朝方向1的强度表示为作用在方向2的应力的函数。所有的应力都根据单轴抗压强度f'c而无量纲化了。在表示双轴压力的象限中可以看出，其强度可达到比单轴抗压强度大20%左右，强度增加的量取决于f2和f1的比值。在双轴受拉情况下，方向1的强度与方向2的拉应力无关。当方向2的拉应力与方向1的压应力同时作用时，抗压强度几乎呈线性下降。例如，大约是单轴抗拉强度的一半的横向拉应力，将使抗压强度减小到单轴抗压强度的一半。这一点在预测深梁或剪力墙内裂缝的出
现方面具有非常重要的意义。
混凝土三轴强度的实验研究很少，主要是因为在三个方向同时加荷实际上难以避免由加荷设备产生的很大约束。根据现有资料，关于混凝土三轴强度可得出以下初步结论:(1)在三轴压应力相等状态下，混凝土的强度可能比单轴抗压强度高一个数量级，(2)对于双轴压应力相等并在第三个方向上有一较小的压应力的状态，其强度可指望增加20%以上，(3)在压应力与至少另外一个方向的拉应力同时作用的应力状态下，中间主应力是无足轻重的，抗压强度可以根据图1可靠地预计出来。
莫尔-库仑理论可用来近似地描述三轴应力对强度的影响。它代表莫尔理论的特殊形式，规定材料破坏的包络线，使任何一个与包络线相切的莫尔应力圆都代表引起材料破坏的复合应力。对于此处的莫尔应力圆，水平直径的两个端点由三个主应力中的最大和最小主应力所决定，因此应力圆的大小和位置不受中间主应力的影响。图2中的应力圆1表示应力为f't时简单拉伸引起的破坏，而应力圆2表示应力为f'c时的压力破坏。破坏的包络线可以近似地用两条直线表示，如图。试验研究表明，在受压一侧与应力圆2相切的直线具有37。的倾角。在受拉一侧，直线是一截线，与应力圆1相切。

英文原文
Strength under Combined Stress
In many structural situations concrete is subjected simultaneously to various stresses acting in various directions. For instance,in beams much of the concrete is subject simultaneously to compression and shear stresses and in slabs and footings to compression in two perpendicular directions plus shear.By methods well knowcan be reduced to three principal stresses acting n in the study of strength of materials, any state of combined stress, no matter how complex, at right angles to each other on an appropriately oriented elementary cube in the material. Any or all of the principal stresses can be either tension or compression. If one of them is zero, a state of biaxial stress is said to exist; if two of them are zero, the state of stress is uniaxial, either simple compression or simple tension. In most cases only the uniaxial strength properties of a material are known from simple tests, such as the cylinder strength f'c and the tensile strength f't. For predicting the strengths of structures in which concrete is subject to biaxial or triaxial stress, it would be desirable to be able to calculate the strength of concrete in such states of stress, knowing from tests only either f'c or f'c and f't.
In spite of extensive and continuing research, no general theory of the strength of concrete under combined stress has yet emerged. Modifications of various strength theories , such as the maximum-tension stress, the Mohr-Coulomb, and the octahedral-stress theories, all of which are discussed in strength-of-materials texts, have been adapted with varying partial success to concrete. Current experimental evidence indicates that limiting tensile strain, which is a function of mean normal stress, may be a failure criterion which is generally applicable. At present none of these theories has been generally accepted, and many have obvious internal contradictions. The main difficulty in developing an adequate general strength theory lies in the highly nonhomogeneous nature of concrete and in the degree to which its behavior at high stresses and at fracture is influenced by microcracking and other discontinuity phenomena.
However, the strength of concrete has been well established by tests at least for the biaxial state. Results may be presented in the form of an interaction diagram such as Fig.1 which shows the strength in direction 1 as a function of the stress applied in direction 2. All stresses are nondimensionalized in terms of the uniaxial compressive strength f'c. It is seen that in the quadrant representing biaxial compression a strength increase as great as about 20 percent over the uniaxial compressive strength is attained, the amount of increase depending upon the ratio of f2 to f1.In the biaxial tension-stress state, the strength in direction 1 is independent of tension in direction 2. When tension in direction 2 is combined with compression in direction 1, the compressive strength is reduced almost linearly. For example, lateral tension of about half the uniaxial tensile strength will reduce the compressive strength by half compared with the uniaxial compressive strength. This fact is of the greatest importance in predicting cracking in deep beams or shear walls, for example.
Experimental investigations into the triaxial strength of concrete have been few, due mainly to the practical difficulty of applying load in three directions simultaneously without introducing significant restraint from the loading equipment. From information now available the following tentative conclusions can be drawn relative to the triaxial .strength of concrete:(1) in a state of equal triaxial compression, concrete strength may be an order of magnitude larger than the uniaxial compressive strength; (2) for equal biaxial compression combined with a smaller value of compression in the third direction, a strength increase greater than 20 percent can be expected; and (3) for stress states including compression combined with tension in at least one other direction,the intermediate principal stress is of little consequence,and the compressive strength can be predicted safely based on Fig. 1.
The Mohr-Coulomb theory can be used to describe in an approximate way the influence of triaxiality on strength.It represents a special form of the Mohr theory and defines a failure envelope such that any Mohr stress circle which is tangent to the envelope represents a combination of stresses that will cause failure of the material. For Mohr's stress circle as used here, the two endpoints of the horizontal diameter are defined by the largest and smallest of the three principal stresses, so that the size and location of the crcle is not influenced by the intermediate principal stress. In Fig. 2 Circle 1 represents failure in simple tension at a stress f't and Circle 2 failure in compression at a stress f'c. The failure envelope can be approximated by two straight lines as shown. From experimental studies the slope of the line tangent to Circle 2 on the compression side has an inclination of 37。. On the tension side, the line is laid from the intercept, tangent to Circle 1.