A general approach to the stress strength problem is the factor-of-safety method. A method as old as engineering designs itself, and hence often called the classical method of design. A design factor of safety nd, or n, sometimes called simply design factor, is defined by the relation
nd =strength/stress (5.1)
In this equation, the “strength” can be anything the designer chooses it to be. We shall often use such strength used as minimum, mean, yield, tensile, fatigue, and shear, as well as others. Of cause, the stress used must correspond in type and units to the strength. If the strength is shear strength in pounds-force per square inch (psi), then the stress must be a shear stress in psi too .Also both the strength and the stress must apply to the same point or set of point on the member being designed.
The language of designers often includes the terms stress allowable, allowable stresses, or simply allowable. These terms refer to reduced values of strengths that are used in design to determine the geometrical dimensions of parts sized according to strength. Finding these reduced values constitutes the fist part of the AISC procedure. Let us designate allowable normal stress σall and allowable shear stress τall. Then the relationship between allowable stress and specified minimum strength using the AISC code is specified as：
TENSION 0.45Sy≦σall≦0.60Sy
BEBDING 0.60 Sy≦σall≦0.75 Sy
The next part of the AISC code deals with determining the loads or forces that are used to obtain the stress. The procedure can be presented succinctly by the equation
F=∑Wd+∑W1+∑KF1+Fw+∑Fmisc (5.3)
There F is the force to be used in the appropriate stress equation. The components of this force are defined as follows.
The term ∑Wd is the sum of the dead loads. There consist of the weight of the steelwork, the materials fastened to it, and the parts supported by it.
The term ∑W1 is the sum of all the stationary or static live loads. This includes the weight of equipment, occupants, fixtures and the snow load if specified by an applicable code.
The force or the resultant of forces due to equipment that may be cause impact or dynamic loading is also considered to be a live load and is represented by the term F1. This factor is to be multiplied by a service factor K obtained from Table 1 (be omitted).
The term Fw in Eq. (5.3) is the wind load on the structure. Appropriate guidelines for this may be specified by local or regional codes.
The term ∑Fmisc must be included in some localities to account for the effects of earthquakes, hurricanes, or other extraordinary regional conditions.
The final step in the AISC procedure is to select dimensions of the member to be sized such that the design stress computed from the force F does nit exceed the allowable stress as given by Eq. (5.2); in other words, to select dimensions or geometry such that
σ ≤ σall or τ ≤ τall (5.4)
Where σ and τ may be called design values of the normal and shear stresses, respectively.
Allowable is needed to account for any uncertainties regarding the actual strength of a member. But the design factor in Eq. (5.1) is used account for uncertainties-one involving strength and the other involving the loading.
Sometimes it is useful to express the allowances for these uncertainties separately. By selecting the symbol ns and nL for design factor used to account for uncertainties of strength and load, respectively, we have
Thus, if the service factors of Table 1 (be omitted) were to be used, then we would select nL equal to K at the very least. Circumstances might require an even large value for nL.
Eq. (5.1) applies only when stress is linearly proportional to load. Cases frequently arise in which this is not true. Then Eq. (5.1) mist be case in the form
nd=strength in force units/applied force or load （5.6）
In specifying the sizes of machine parts, it is nearly always true that stock sizes must be used. Thus, in a particular application, it may turn out that use of 40mm tubing is subject to a normal stress greater than the allowable stress whereas 50mm tubing yields a value of the normal stress that is less than the allowable stress. If there are no stock size available between 40mm and 50mm, then the 50mm size must be selected. For reasons similar to and including this one it is desirable to define realized factor of safety nr, or n, as the ratio of the strength to the actual or computed stress. Then the realized factor of safety is defined by either by either of the equations
Where now σ and τ are the stresses computed using the final size selection. Thus design factor of safety represents our intention at the beginning of design, while realized factor of safety tells us what has actually been obtained in the design.
One of the questions that sometimes arise among engineers when they study reliability design for the first time is, but what is the factor of safety? The answer is that the factor of safety is simply not pertinent to the reliability approach. An element or part may be analyzed to determine its reliability, or it may be designed to a reliability specification. The factor of safety does not enter into either of there approaches.
Recalling that the factor of safety is the ratio of the minimum strength to the maximum stress, there is a way to acquire some additional insight into the problem. For example, we can be pretty certain that the minimum strength is around 3 or 4 standard deviations less than the mean strength. In the same way, the maximum stress will probably not exceed the sum of the mean stress and 3 or 4 standard deviations. We assume that the possibility of catastrophic situations has been accounted for in the statistical parameters. If, now, we are not too fussy, we might select 3 standard deviations for both and express the factor of safety as
n =(μs-3σs)/（μσ+3σσ） （5.8）
Eq. (5.8) will not be used in this book: It is presented so as to give you some insight into the two methods of design. Nether method is perfect. Both have their advantages. Safety and economy in design are strange and often antagonistic bedfellows. A thorough knowledge of both approaches is the surest guarantee of design success.
Selected from “Mechanical Engineering Design”, Fifth Edition, Joseph Edward Shigley, Charles R. Mischke, McGgraw-Hill Book Company, 1989.
一种普遍的解决应力强度问题的方法是材料的安全系数。这是一种和工程学一样久远的方法，并且从那时起就被作为工程设计的标准方法。设计中的安全系数nd或n，有时被简单的称之为设计系数，它由下式确定：
在这个方程式里，强度可以是设计者选定的任意强度。通常，我们选用平均应力、拉力、疲劳极限、剪切力等的最小值作为强度。当然，我们要保证应力与强度的单位和类型是一致的。如果强度是剪切力，单位是：磅每平方英寸，那么，应力也与之一致。同理，强度和应力必须有与被设计事物一致的意义。
设计者通常要给出许用应力或合应力应满足的条件。这些条件为确定满足强度要求的设计最小几何尺寸提供参考。找到这些条件的具体内容就是《钢结构手册》第一步。我们首先选定许用压应力σall和许用剪切应力τall，这时根据《钢结构手册》许用压应力和具体的最小应力关系为：
弯曲应力: 0.60 Sy≦σall≦0.75 Sy
《钢结构手册》的下一个步骤是确定由应力所产生的载荷。其具体关系可由下面的公式来解决：
F=∑Wd+∑W1+∑KF1+Fw+∑Fmisc (5.3)
力∑Wd是设计结构所产生载荷的总和，由钢铁结构和上面的附属材料以及其支撑部分组成。
力∑W1是静态的可变载荷，它包括：设备，货物质量，固定装置和规则具体指明的载荷。
动载荷是设备所受冲击所产生的合力，用符号F1表示。这一部分力要乘以从表一中查得的工作情况系数K。
公式(5.3)中的力Fw是结构的弯曲载荷，它由局部手册具体确定。
力∑Fmisc是因为地区性差异产生的，决定它的因素有：地震，飓风等异常的地方性因素。
根据《钢结构手册》，设计的最后一步是根据力F确定设计的各部分尺寸使其设计应力不超过有公式(5.2)所确定的许用应力。即：
可行性设计要考虑任何不确定因素和实际应力。由公式(5.1)确定的设计系数被用来确定不确定因素——它不但涉及应力也涉及载荷。
有时候我们要分开考虑不确定因素的限额。通过选择ns and和nL的设计系数来确定nd
例如，如果表一被用来确定许用工作系数，那么，我们就选用和K相匹配的系数nL。实际情况中，我们可能需要一个很大的nL值。
公式(5.1)仅仅适用于应力和载荷呈线性比例的情况。在实际情况中往往不是如此。这时公式(5.1)被表达为下式：
确定机器零件具体尺寸时，我们一般考虑用现有的材料去制造它。因此，在具体的应用中，如果用40毫米的管材所能承受的应力小于许用应力而50毫米的管材所能承受的应力大于许用应力。而在40毫米与50毫米之间没有其它的可用常备尺寸的管材，这时我们就要选用50毫米的管材。同理，我们可以同样的方式确定实际应用的安全系数nr, o或 n，即强度和实际估算许用应力的比值。它由以下所列的一个公式确定：
在这里，σ和τ被用来估算最终设计尺寸。因此设计安全系数在我们设计伊始提出设计目的，而实际安全系数告诉我们通过设计我们最终得到的结果。
当工程师们首次学习可靠性设计时常常产生这样的疑问：安全系数到底是什么？其实，安全系数只是一种解决可靠性设计的恰当方式。一种原理或其部分原理可以用来分析设计的可靠性，或者被制成一份可以参考的表格。但是安全系数不被用来讨论以上两种过程。
值得一提的是安全系数是最小强度和最大应力的比值，有一种方法可以让我们更深刻的理解这个问题。例如，我们确定最小强度比平均强度小3到4个单位的力，而最大强度比平均强度大3到4个单位的力。若我们采用统计学中的可能破坏性环境因素参数，并且，我们并不是过于讲究，那么，我们可以选用3个标准的偏差数将安全系数表达为：
n =(μs-3σs)/（μσ+3σσ） （5.8）
公式（5.8）并没有在本书中被使用。它的提及只是为了开扩我们对两种设计方法的认识。每一种方法都不完美。他们都有自己的优势和劣势。安全性和经济性是设计过程中陌路甚至常常发生冲突的两件事。合理解决这两件事情就意味着设计的成功。 | 
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