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KB7044: Safety Factor Approach - Engineering Management Data Analysis Assessment Answer
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Subject Code: KB7044
Internal Code: 1AFGBF
You then feel that the vague classification of uncertainty into three arbitrary categories, although this serves the first task adequately well, does not fit very well with a rigorous risk-based modeling framework. The feasibility of this framework is to be illustrated with a “design case”. This proposed design case involves a given load, and the structure is to be
designed using a given material.
The next logical task is to set up an analytical framework to model the process using a risk-based approach which aims to estimate the load and the capability of the structure in an attempt to obtain a rational and defensible solution. The concept of balancing load versus the capability of the structure is illustrated in Figure 1.
Task 3
On the basis of this analytical framework, set up a spreadsheet to calculate the numerical values of the probability that the excess capacity <= 0 (i.e. risk of structure yielding) over a range of excess capacity (recommended range: 10 kN –
100 kN). A sample spreadsheet is shown in Table 3. You may also want to plot the sensitivity of the problem (over a variation of one or more parameters), the sensitivity of the decision problem over a range of yield stress’s standard deviation is shown in Figure 2.
Task 4
The risk-based model can then be used to determine an acceptable level of failure probability, and hence the optimum excess capacity (or margin) as a contrast to the safety factor approach. The main consideration is the trade-off between
additional material cost to provide a given level of excess capacity and the penalty cost incurred by failed components. For this exercise, the following data applies: Annual production rate, N = 100,000 pieces
Material cost
Cm = £9,000 per m2
Penalty cost = £200 per failed component,
CP, plus replacement material cost
ka = 20,000 where ka is a coefficient used to compute the additional material cost.
Task 6
Your first task is to solve the problem deterministically, employing equations (11) – (13), using Excel spreadsheets or MathCAD. The members of staff of the company are familiar with the deterministic solution procedure and this should be used as a starting point for the worked example before introducing the probabilistic solution procedure of simulation.
You may use the following data:
e = 85 mm
l = 350 mm
w = 250 mm
c = 175 mm
I=w^3/12
P = 1000 kN
What is the safety factor/margin against tensile failure?
TASK 7:
Task 9
Your last task is to explore the effect of eccentricity has on the tensile failure, and hence determine an optimum quality (as measured in terms of variability) eccentricity on the basis of cost. A batch size of 10,000 is to
be assumed for the cost calculations. The low safety margin against tensile failure is a reason for concern as the
concrete struts had already been fabricated. However, by using different setup processes the characteristics of eccentricity, e, can be varied. Essentially e can be modeled by Beta distributions between 60 and 90 mm but with different(Alpha) and (Beta) values (i.e. different skewness). The additional set up costs to achieve different characteristics of
eccentricity is shown in Table 4.
Engineering Management Data Analysis Assessment Answer
Task: Task 1 Organise/sort the data to see if patterns can be observed. Perform correlation and regression analysis on this set of data. Explain and interpret the results as clearly as possible. Task 2 Your second task is to look into variability in the yield stress of the material used. According to the supplier of the material, the yield stress of the material is 130 MPa. A sample consisting of 10 specimens have been prepared and tested. The results are shown in Table 2. Analyse the data by plotting histogram and/or x-y plot. Question: Is there sufficient evidence to accept the manufacturer’s claim that the mean yield stress of the material is 130 MPa? What would you recommend?
You then feel that the vague classification of uncertainty into three arbitrary categories, although this serves the first task adequately well, does not fit very well with a rigorous risk-based modeling framework. The feasibility of this framework is to be illustrated with a “design case”. This proposed design case involves a given load, and the structure is to be
designed using a given material.
The next logical task is to set up an analytical framework to model the process using a risk-based approach which aims to estimate the load and the capability of the structure in an attempt to obtain a rational and defensible solution. The concept of balancing load versus the capability of the structure is illustrated in Figure 1.
Task 3
On the basis of this analytical framework, set up a spreadsheet to calculate the numerical values of the probability that the excess capacity <= 0 (i.e. risk of structure yielding) over a range of excess capacity (recommended range: 10 kN –
100 kN). A sample spreadsheet is shown in Table 3. You may also want to plot the sensitivity of the problem (over a variation of one or more parameters), the sensitivity of the decision problem over a range of yield stress’s standard deviation is shown in Figure 2.
Task 4
The risk-based model can then be used to determine an acceptable level of failure probability, and hence the optimum excess capacity (or margin) as a contrast to the safety factor approach. The main consideration is the trade-off between
additional material cost to provide a given level of excess capacity and the penalty cost incurred by failed components. For this exercise, the following data applies: Annual production rate, N = 100,000 pieces
Material cost
Cm = £9,000 per m2
Penalty cost = £200 per failed component,
CP, plus replacement material cost
ka = 20,000 where ka is a coefficient used to compute the additional material cost.
Task 6
Your first task is to solve the problem deterministically, employing equations (11) – (13), using Excel spreadsheets or MathCAD. The members of staff of the company are familiar with the deterministic solution procedure and this should be used as a starting point for the worked example before introducing the probabilistic solution procedure of simulation.
You may use the following data:
e = 85 mm
l = 350 mm
w = 250 mm
c = 175 mm
I=w^3/12
P = 1000 kN
What is the safety factor/margin against tensile failure?
TASK 7:
- Length of the section, l, can be modeled by a normal distribution having a mean of 350 mm and a standard deviation of 20 mm.
- The width of the section, w, can be modeled by a normal distribution having a mean of 250 mm and a standard deviation of 12 mm.
- The load, P, can be modeled by a triangle distribution having a mode value, M, of 1000 kN, a low value, L, of 700 kN, and a high value, H, of 1200 kN, as shown in Figure 4. The triangle distribution is used when one is unable to model the parameter confidently with a precise distribution. In this case, the designer can only give a low, high and mode values of the parameters.
- The value of c can be taken as L/2.
Task 9
Your last task is to explore the effect of eccentricity has on the tensile failure, and hence determine an optimum quality (as measured in terms of variability) eccentricity on the basis of cost. A batch size of 10,000 is to
be assumed for the cost calculations. The low safety margin against tensile failure is a reason for concern as the
concrete struts had already been fabricated. However, by using different setup processes the characteristics of eccentricity, e, can be varied. Essentially e can be modeled by Beta distributions between 60 and 90 mm but with different(Alpha) and (Beta) values (i.e. different skewness). The additional set up costs to achieve different characteristics of
eccentricity is shown in Table 4.
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