In a structural reliability problem, the load effect S and resistance R are statistically independent and are modeled using the Gumbel and the Weibull probability distribution (see Table 2 at the end of the Reader), respectively, with the following statistics: µ₂ = 2,000 kips 8 = 0.30 and HR = CSF -μs §₂ = 0.20 where CSF denotes the central safety factor (CSF =). Evaluate numerically the probability of failure Hs Pr according to each of the two following formulas presented in class, for CSF =1.5, 3.0, 5.0. In each case (i.e., each value of CSF): . PF = [FR(S)fs (s) ds s\fs(s)d PF = [[1 - Fs (r)] fr (r) dr • plot the marginal PDFs of R and S on the same (r, s) axis; • plot the normalized (for a unit area) deaggregation of the probability of failure p as a function of s. On the same figure, plot the marginal PDF of S and this deaggregation function. • plot the normalized (for a unit area) deaggregation of the probability of failure pr as a function of r. On the same figure, plot the marginal PDF of R and this deaggregation function.

In a structural reliability problem, the load effect S and resistance R are statistically independent and are modeled using the Gumbel and the Weibull probability distribution (see Table 2 at the end of the Reader), respectively, with the following statistics: µ₂ = 2,000 kips 8 = 0.30 and HR = CSF -μs §₂ = 0.20 where CSF denotes the central safety factor (CSF =). Evaluate numerically the probability of failure Hs Pr according to each of the two following formulas presented in class, for CSF =1.5, 3.0, 5.0. In each case (i.e., each value of CSF): . PF = [FR(S)fs (s) ds s\fs(s)d PF = [[1 - Fs (r)] fr (r) dr • plot the marginal PDFs of R and S on the same (r, s) axis; • plot the normalized (for a unit area) deaggregation of the probability of failure p as a function of s. On the same figure, plot the marginal PDF of S and this deaggregation function. • plot the normalized (for a unit area) deaggregation of the probability of failure pr as a function of r. On the same figure, plot the marginal PDF of R and this deaggregation function.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter7: Length And Length-related Variables In Engineering

Section: Chapter Questions

Problem 43P: A 10 cm long rectangular bar (when subjected to a tensile load) deforms by 0.1 mm. Calculate the...

See similar textbooks

Similar questions

A 10 cm long rectangular bar (when subjected to a tensile load) deforms by 0.1 mm. Calculate the normal strain.
A structural member with a rectangular cross section as shown in the accompanying figure is used to support a load of 2500 N. What type of material do you recommend be used to carry the load safely? Base your calculations on the yield strength and a factor of safety of 2.0.
The results of a tensile test are shown in Table 1.5.2. The test was performed on a metal specimen with a circular cross section. The diameter was 3 8 inch and the gage length (The length over which the elongation is measured) was 2 inches. a. Use the data in Table 1.5.2 to produce a table of stress and strain values. b. Plot the stress-strain data and draw a best-fit curve. c. Compute the, modulus of elasticity from the initial slope of the curve. d. Estimate the yield stress.
Bourdon-type pressure gauges are used in thousands of applications. A deadweight tester is a device that is used to calibrate pressure gauges. Investigate the operation of a deadweight pressure tester. Write a brief report to discuss your findings.
Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43
The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular cross section of 0.2011in.2 in area and a gage length (the length over which the elongation is measured) of 2.000 inches. The specimen was not loaded to failure. a. Generate a table of stress and strain values. b. Plot these values and draw a best-fit line to obtain a stress-strain curve. c. Determine the modulus of elasticity from the slope of the linear portion of the curve. d. Estimate the value of the proportional limit. e. Use the 0.2 offset method to determine the yield stress.
In concrete work, Fuller and Thompson (1907) suggested that a dense packing of grains can be achieved if the percent finer (p) and grain size (D) are related by the following equation, where n is a constant varying in the range of 0.3-0.6. Dmax is the size of the largest grain within the soil. p=(DDmax)n100 This equation is sometimes used in roadwork for selecting the aggregates. a. For n = 0.5, show that the soil is well graded. b. If n = 0.5 and Dmax = 19.0 mm, find the percentages of gravel, sand, and fines within the soil. Use the Unified Soil Classification System.
For Problem 19.1, using Equations (19.1) and (19.6), calculate the mean and standard deviation of the class scores.
Two line loads q1 and q2 of infinite lengths are acting on top of an elastic medium, as shown in Figure P8.6. Find the vertical stress increase at A.