Determine the reliability of a tension bar using @Risk

1
Reliability Example

• Determine the reliability of a tension bar using
  _at_Risk

Ft A
P
Limit State Ft A / P
2
Reliability Example

• Reliability using _at_Risk
• R 1 - P(u)
• where,
• P(u) NUP / N
• NUP Number of unsatisfactory performances
  at limit state lt 1.0
• N number of iterations

3
Reliability Example

• _at_Risk Random Variables
• Ultimate tensile strength, Ft
• mean, m 40 ksi standard deviation, s 4 ksi
• assume normal distribution
• Load, P
• mean, m 15 kips standard deviation, s 3
  kips,
• assume normal distribution
• Area, A
• constant (no degradation) circular cross section
• A 0.5 in2

4
Reliability Example

• Perform for 1000, 10000 and 100000 iterations to
  show convergence
• Reliability results at 100000 iterations
• P(u) R
• _at_Risk ? ?
• TSFD 0.14 0.86