Question

A simply supported beam of length ? = 5.0 m subjected to a concentrated load applied at mid-span. Assume that the load P is normally distributed with ?_P = 100 kN and coefficient of variation ?_P = 0.25 . (a) If the maximum moment that the beam can resist is equal to m_R = 150.0 kN - m , what is the probability of failure of the beam? (b) If the maximum probability of failure allowed by the design code is 2%, what is the minimum flexural resistance m_R that the beam must have?

          A simply supported beam of length ? = 5.0 m subjected to a concentrated load applied at mid-span. Assume that the load P is normally distributed with ?_P = 100 kN and coefficient of variation ?_P = 0.25 .

(a) If the maximum moment that the beam can resist is equal to m_R = 150.0 kN - m , what is the probability of failure of the beam?

(b) If the maximum probability of failure allowed by the design code is 2%, what is the minimum flexural resistance m_R that the beam must have?

A simply supported beam of length ? = 5.0 m subjected to a concentrated load applied at mid-span. Assume that the load P is normally distributed with ?P = 100 kN and coefficient of variation ?P = 0.25 .

(a) If the maximum moment that the beam can resist is equal to mR = 150.0 kN - m , what is the probability of failure of the beam?

(b) If the maximum probability of failure allowed by the design code is 2%, what is the minimum flexural resistance mR that the beam must have?

Added by Vickie E.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Chai Santi

11/18/2022

Step 1

In this case, P is a random variable with mean pp = 100 kN and standard deviation 6p = 0.25*pp = 25 kN. The maximum moment that the beam can resist is mR = 150 kN-m. The moment caused by the load is a random variable with mean μM = pp*L/4 = 100*5/4 = 125 kN-m and Show more…

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simply supported beam of length l = 5.0 m subjected to a concentrated load applied at mid-span. Assume that the load P is normally distributed with μ_P = 100 kN and coefficient of variation δ_P = 0.25. (a) If the maximum moment that the beam can resist is equal to m_R = 150.0 kN - m, what is the probability of failure of the beam? (b) If the maximum probability of failure allowed by the design code is 2%, what is the minimum flexural resistance m_R that the beam must have?