Safety of Structures

The principal scope of specifications is to provide general principles and computational methods in order to verify safety of structures. The 'safety factor', which according to modern trends is independent of the nature and combination of the materials used, can usually be defined as the ratio between the conditions which yield failure of the construction and the worst predictable working conditions. This ratio is also proportional to the inverse of the probability (risk) of failure of the structure.

规范的主要目的是提供一般性的设计原理和计算方法，以便验算结构的安全性。就日前的趋势而言，安全系数是与所使用的材料性质及其组合情况无关，通常把它定义为结构发生破坏的条件与结构可预料的最不利的工作条件之比值。这个比值还与结构的破坏概率（危险率）成反比。

Failure has to be considered not only as overall collapse of the structure but also as unserviceability or, according to a more precise, common definition, as the reaching of a 'limit state' which causes the construction not to accomplish the task it was designed for. There are two categories of limit state:

(a) Ultimate limit state, which corresponds to the highest value of the load-bearing capacity. Examples include local buckling or global instability of the structure; failure of some sections and subsequent transformation of the structure into a mechanism; failure by fatigue; elastic or plastic deformation or creep that cause a substantial change of the geometry of the structure; and sensitivity of the structure to alternating loads, to fire and to explosions.

(b) Service limit states, which are functions of the use and durability of the structure. Examples include excessive deformations and displacements without instability; early or excessive cracks; large vibrations; and corrosion.

破坏不仅仅指结构的整体破坏，而且还指结构不能正常地使用，或者，用更为确切的话来说，把破坏看成是结构已经达到不能继续承担其设计荷载的“极限状态”。通常有两类极限状态，即：

(1)强度极限状态，它相当于结构能够达到的最大承载能力。其例子包括结构的局部屈曲和整体不稳定性；某些截面失效，随后结构转变为机构；疲劳破坏；引｜起结构几何形状显著变化的弹性变形或塑性变形或徐变；结构对交变荷载、火灾和爆炸的敏感性。

(2)使用极限状态，它对应着结构的使用功能和耐久性。其例子包括结构失稳之前的过大变形和位移；早期开裂或过大的裂缝；较大的振动和腐蚀。

Computational methods used to verify structures with respect to the different safety conditions can be separated into:

(a) Deterministic methods, in which the main parameters are considered as nonrandom parameters.

(b) Probabilistic methods, in which the main parameters are considered as random parameters.

根据不同的安全度条件，可以把结构验算所采用的计算方法分成：

(1)确定性的方法，在这种方法中，把主要参数看作非随机参数。

(2)概率方法，在这种方法中，主要参数被认为是随机参数。

Alternatively, with respect to the different use of factors of safety, computational methods can be separated into:

(a) Allowable stress method, in which the stresses computed under maximum loads are compared with the strength of the material reduced by given safety factors.

(b) Limit states method, in which the structure may be proportioned on the basis of its maximum strength. This strength, as determined by rational analysis, shall not be less than that required to support a factored load equal to the sum of the factored live load and dead load (ultimate state).

此外，根据安全系数的不同用途，可以把结构的计算方法分为：

(1)容许应力法，在这种方法中，把结构承受最大荷载时计算得到的应力与经过特定安全系数折减后的材料强度作比较。

(2)极限状态法，在这种方法中，结构的工作状态是以其最大强度为依据来衡量的。由理论分析确定的这一最大强度应不小于结构承受计算荷载所算的强度（极限状态）。计算荷载等于分别乘以荷载系数的活载与恒载之和。

The stresses corresponding to working (service) conditions with unfactored live and dead loads are compared with prescribed values (service limit state). From the four possible combinations of the first two and second two methods, we can obtain some useful computational methods. Generally, two combinations prevail:

(a) Deterministic methods, which make use of allowable stresses.

(b) Probabilistic methods, which make use of limit states.

把对应于不乘以荷载系数的活载和恒载的工作（使用）条件的应力与规定值（使用极限状态）相比较。根据前两种方法和后两种方法的四种可能组合，我们可以得到一些实用的计算方法。通常采用下面两种计算方法：

(1)确定性的方法，这种方法采用容许应力。

(2)概率方法，这种方法采用极限状态。

The main advantage of probabilistic approaches is that, at least in theory, it is possible to scientifically take into account all random factors of safety; which are then combined to define the safety factor. Probabilistic approaches depend upon:

(a) Random distribution of strength of materials with respect to the conditions of fabrication and erection (scatter of the values of mechanical properties throughout the structure);

(b)Uncertainty of the geometry of the cross-sections and of the structure (faults and imperfections due to fabrication and erection of the structure);

(c)Uncertainty of the predicted live loads and dead loads acting on the structure;

(d)Uncertainty related to the approximation of the computational method used (deviation of the actual stresses from computed stresses). 

至少在理论上，概率法的主要优点是可以科学地考虑所有随机安全系数，然后将这些随机安全系数组合成确定的安全系数。概率法取决于：

(1)制作和安装过程中材料强度的随机分布（整个结构的力学性能值的分散性）；

(2)截面和结构几何尺寸的不确定性（由结构制作和安装造成的误差和缺陷而引起的）；

(3)对作用在结构上的活载和恒载的预测的不确定性；

(4)与所采用的近似计算方法有关的不精确性（实际应力与计算应力的偏差）。

Furthermore, probabilistic theories mean that the allowable risk can be based on several factors, such as:

(a) Importance of the construction and gravity of the damage by its failure;

(b) Number of human lives which can be threatened by this failure;

(c) Possibility and/ or likelihood of repairing the structure;

(d) Predicted life of the structure.

此外，概率理论意味着允许的后险率可以以若干因素为依据，例如：

(1)建筑物的重要性和建筑物破坏造成的危害性；

(2)由于建筑物破坏使生活受到威胁的人数；

(3)修复建筑物的可能性；

(4)建筑物的预期寿命。

All these factors are related to economic and social considerations such as:

(a) Initial cost of the construction;

(b) Amortization funds for the duration of the construction;

(c) Cost of physical and material damage due to the failure of the construction;

(d) Adverse impact on society;

(e) Moral and psychological views.

所有这些因素均与经济和社会条件有关，例如：

(1)建筑物的初始建设费；

(2)建筑物使用期限内的折旧费；

(3）由于建筑物破坏而造成的物质和材料损失费，

(4)在社会上造成的不良影响啊；

(5)精神和心理上的考虑。

The definition of all these parameters, for a given safety factor, allows construction at the optimum cost. However, the difficulty of carrying out a complete probabilistic analysis has to be taken into account. For such an analysis the laws of the distribution of the live load and its induced stresses, of the scatter of mechanical properties of materials, and of the geometry of the cross-sections and the structure have to be known. Furthermore, it is difficult to interpret the interaction between the law of distribution of strength and that of stresses because both depend upon the nature of the material, on the cross-sections and upon the load acting on the structure.

These practical difficulties can be overcome in two ways. The first is to apply different safety factors to the material and to the loads, without necessarily adopting the probabilistic criterion. The second is an approximate probabilistic method which introduces some simplifying assumptions (semi-probabilistic methods).

就给定的安全系数而论，所有这些参数的确定都是以建筑物的最佳成本为依据的。但是，应该考虑到进行全概率分析的困难。对于这种分析来说，应该了解活载及其所引起的应力的分布规律、材料的力学性能的分散性和截面及结构几何尺寸的分散性。此外，由于强度的分布规律和应力的分布规律取决定于材料的性质、截面的形式、作用在结构上的荷载，因此，阐明这两种分布规律之间的相互关系是困难的。这些实际困难可以采用两种方法来克服。第一种方法对材料和荷载采用不同的安全系数，而不需要采用概率准则；第二种方法是引入一些简化假设的近似概率方法（半概率方法）。