Permissible Stress

It is also necessary to check that the stress in the snap fit does not exceed the yield strength for the material (30 MN/m ). Allowing for a safety factor of 2, the maximum permissible stress will be 15 MN/m. ... 

In addition, the permissible stress for carbon steel at temperatures above 750° F is (for example in the German code) substantially lower than that allowed by ASME Section VIII, and the temperature breakpoint at which it becomes more... 

With a given size of a crack-like surface flaw (a) and a known geometrical function Y, the values of Kic and Kiscc can be used to calculate the permissible stress by Equation (7.11), for applications in air and the actual corrosive environment, respectively. For corrosive conditions one must take into account the deepest local corrosion defect that may develop during the plarmed lifetime. 

Design with sufficient corrosion allowance. Pipes, tanks, containers and other equipment are often made with a wall thickness twice the corrosion depth expected during the desired lifetime. However, this must of course depend on load and maximum permissible stresses too. 

These loads arise from interaction between the bridge and track by the shear resistance of the ballast against longitudinal displacement. Since there are upper limits of permissible stresses and relative displacements of the rails, the horizontal stiffness of piers, which prevents these limits being exceeded, had to be precalculated. 

Theoretically permissible stress levels, for example, can be derived from such creep line diagrams for each material (assuming an elongation of 1 % as is frequently done for calculations). The actual stress levels that can be used for... 

Table 13 below presents a summary of safety coefficients recommended for the different stress loads. The permissible stress load is calculated - taking stress concentration data into account - as follows ... 

As we saw in the last chapter, the use of permissible stresses to regulate the safety of structures came about as a result of the increasing development of elastic theory in the 19th century. In modern practice this method has been typified in Britain by B.S. 449 The Use of Structural Steel in Building 1969 and C. P. 114, the code dealing with concrete construction. It has been used in the standards of many countries (Section 3.4) but is now gradually being replaced by limit state methods. 

In the permissible stress approach, the loads are specified exactly, the response analysis is carried out on the basis of elastic theory, and the structure is assessed safe, if the calculated stresses are less than the specified permissible stress. There is no separate consideration of system and parameter uncertainty or the nature of the structure, nor the consequences of failure. The loads are specified usually by other codes of practice which recommend, for example in Britain, a mixture of fair average estimates for dead loads in B. S. 648, extreme maximal estimates for imposed loads in C.P. 3 Chapter V Part 1, and statistical estimates for wind load in C.P.3 Chapter V Part 2. The uncertainty is catered for informally by the safe conservative assumptions of the designer s theoretical model and formally by an appropriate choice of loads and permissible stress values. 

Consider, for example, the assessment of a simple steel member in a lattice girder subject to uniform tension. It is first necessary to define a critical stress above which the tie would be considered to have failed. Using elastic theory this would be tlic yield stress of the steel, The permissible stress is then obtained by dividing the critical stress by a safety factor which is Judged to be appropriate. For oxiitnple in B.S. 449 Table 2, the permissible stress of tension members of steel to H.S. 4360 Grade 43 is 16.S and its yield stress is 247 The... 

In order to demonstrate clearly the differences in approach between (a) the permissible stress, (b) the load factor, and (c) the limit state methods, a numerical... 

Imagine that there is some specified relationship R between a permissible stress and a calculated working stress. Imagine further that we have calculated a stress value o, and wish to calculate a corresponding permissible stress p,. This is done by composing a, with R, and this operation is defined by... 

The normalising factor is L S(y) 0.02 + 0.15 + 0,315 +. .. + 0i)15 = 4.35 and the cumulative distribution function is obtained by dividing each of these figures by 4.35 and adding cumulatively. The resulting distribution is shown in Fig. 6.6. A measure of the safety of the column is the probability < 1 ] = 0.715. This means the probability that working stress is less than, or equal to the permissible stress is less than or equal to 0.715. The probability of failure in this defined limit state is 1 — 0.715 = 0.282. Of course, in a real example this figure would be much smaller. 

It is significant that both the methods considered in the previous sections are derived directly from tlie available methods of structural response analysis. The permissible stress method results from the use of elasticity, the load factor method from the use of ultimate load theory and plasticity. In both of them, the specification of the loads is not a direct part of the method, and the way in which the safety is assessed, results very simply from the structural response analysis. In comparision to the effect Involved in developing the theories of response analysis, the effort put in to the safety assessment is trivial. 

The following example of the use of fuzzy sets is purposely simple and straightforward for illustration. It uses the idea of elastic permissible stresses to estimate whether or not a given column size is satisfactory, not because it is considered that this is the best way to proceed, but because it is easy to follow and understand. 

---