CIE 110 - Materials: Probability Density Functions
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Questions and Answers

Which of the following stress-strain plots best represents a plastic material?

  • Inelastic, or plastic (correct)
  • Elastic
  • Elastic-inelastic
  • Elastic-plastic

    • Which unit is not a valid unit of stress?

  • ft lbs (correct)
  • Pascal
  • lbs/ft2
  • psi

    • If identical specimens of carbon fiber and steel fiber are subjected to the same stress, which will deform more?

  • The carbon fiber
  • The steel fiber (correct)
  • The two will deform the same amount
  • Cannot evaluate from information given

    • Is it possible for material B, which is weaker than material A, to be tougher than material A?

    <p>Yes</p> Signup and view all the answers

    What is the ultimate stress represented in the given data?

    <p>200,000 ps</p> Signup and view all the answers

    Which value represents the closest strain at yield?

    <p>0.004</p> Signup and view all the answers

    The ultimate stress indicates what load in pounds?

    <p>180,000 lbs.</p> Signup and view all the answers

    Which of these strains at yield is the highest?

    <p>0.20</p> Signup and view all the answers

    Which value does not represent a plausible ultimate stress?

    <p>15,000 ps</p> Signup and view all the answers

    What is the lowest possible strain at yield present in the options?

    <p>0.002</p> Signup and view all the answers

    Which of the following ultimate stresses is the lowest?

    <p>20,000 ps</p> Signup and view all the answers

    The highest ultimate stress figure in pounds is represented as:

    <p>180,000 lbs.</p> Signup and view all the answers

    What fraction of a normally distributed sample falls within +/- one standard deviation of the mean?

    <p>0.68</p> Signup and view all the answers

    What is the correct unit of standard deviation for the reported data?

    <p>psi</p> Signup and view all the answers

    Which option correctly identifies the yield stress based on the provided diagram?

    <p>8,000 psi</p> Signup and view all the answers

    Which option represents the strain at rupture in the tension test?

    <p>0.01</p> Signup and view all the answers

    What is the modulus of elasticity for the metallic alloy tested?

    <p>140,000 psi</p> Signup and view all the answers

    Which option is closest to the modulus of toughness indicated in the test results?

    <p>none of the above</p> Signup and view all the answers

    In the context of the tension test, what does the term 'elastic-plastic behavior' refer to?

    <p>Material deforms permanently upon reaching yield stress.</p> Signup and view all the answers

    The strain at which the material exhibits permanent deformation is known as what?

    <p>Plastic strain</p> Signup and view all the answers

    What is the closest yield stress of alloy 'B'?

    <p>50,000 psi</p> Signup and view all the answers

    The ultimate stress of alloy 'A' is closest to which value?

    <p>80,000 psi</p> Signup and view all the answers

    What is the strain at yield for alloy 'B' closest to?

    <p>0.2%</p> Signup and view all the answers

    Which alloy has a higher modulus of toughness?

    <p>Cannot be determined from the information given</p> Signup and view all the answers

    What does Hooke’s law refer to?

    <p>A linear relationship between stress and strain</p> Signup and view all the answers

    Which stress-strain plot best represents an elastic-plastic material?

    <p>Plot C</p> Signup and view all the answers

    If identically sized fibers of titanium and steel are subjected to the same stress, which will deform more?

    <p>The titanium fiber</p> Signup and view all the answers

    Which alloy likely has a higher yield point based on their properties?

    <p>Alloy 'B'</p> Signup and view all the answers

    What is the length of the test specimen used in the tension test?

    <p>4 inches</p> Signup and view all the answers

    What is the cross-sectional area of the specimen in the tension test?

    <p>0.10 in²</p> Signup and view all the answers

    Which of the following could represent a probability density function?

    <p>A curve that is completely above the x-axis and integrates to 1</p> Signup and view all the answers

    At what measured deformation did plastic deformation begin?

    <p>0.005 inches</p> Signup and view all the answers

    How far apart were the points where deformation was measured?

    <p>0.5 inches</p> Signup and view all the answers

    Can a probability density function and a cumulative distribution function represent the same distribution?

    <p>No, they represent different types of data.</p> Signup and view all the answers

    Which type of deformation occurred before the measured deformation of 0.005 inches?

    <p>Elastic deformation</p> Signup and view all the answers

    What is the likelihood that a specific wire will break at a force of 1000 lbs or less?

    <p>Dependent on the cumulative distribution function</p> Signup and view all the answers

    What is the probability that a particular wire will break at a force greater than 1200 lbs?

    <p>It is equal to the cumulative probability up to 1200 lbs.</p> Signup and view all the answers

    If the test specimen's cross-sectional area were to double, what would be its new area?

    <p>0.20 in²</p> Signup and view all the answers

    What is the total deformation measured when plastic deformation starts?

    <p>0.005 inches</p> Signup and view all the answers

    What breaking force is associated with a 10% probability of breaking?

    <p>The force at the 10th percentile</p> Signup and view all the answers

    If the specimen length were to increase to 8 inches while keeping the area the same, what would not change?

    <p>Cross-sectional area</p> Signup and view all the answers

    What is a likely outcome of repeating the tests using a standard on the standard deviation?

    <p>It will decrease due to less variability in testing conditions.</p> Signup and view all the answers

    When represents a 100-year storm event occurring this year?

    <p>It has a 1% probability of occurring.</p> Signup and view all the answers

    Which of the following describes the function of a histogram in this context?

    <p>It displays the frequency of wire failures at different bending cycles.</p> Signup and view all the answers

    Study Notes

    Quiz 1: CIE 110 - Materials

    • Probability Density Function Identification: Curve B is the probability density function from the provided graphs
    • Probability Density Function/Cumulative Distribution Function Relationship: A probability density function and a cumulative distribution function can represent the same distribution
    • Cumulative Distribution Plot: Used to show the breaking force of a metallic wire. The graph shows the cumulative probability against the breaking force (in lbs).

    Additional Questions

    • Probability of Wire Breaking at 1000 lbs or Less: Find the cumulative probability value on the graph corresponding to a breaking force of 1000 lbs
    • Probability of Wire Breaking Above 1200 lbs: Find the cumulative probability value corresponding to 1200 lbs then subtract that from 1
    • Breaking Force for 10% Probability: Locate 0.1 (10%) on the vertical axis of the cumulative probability graph. Read horizontally to the corresponding breaking force on the horizontal axis.
    • Mean Breaking Force: Determined by interpreting the cumulative probability graph; Requires additional analysis of the graph
    • 100-Year Storm Probability: Not calculable from given data
    • Effect of No Test Standard: Standard deviation would likely increase if no test standards are used.
    • Normally Distributed Data: If data is normally distributed, approximately 68% of the data will fall within +/- one standard deviation of the mean
    • Correct Standard Deviation Unit: The unit of standard deviation depends on the data. The units for cycles to failure are determined in the histogram

    Quiz 2: CIE 110 - Materials

    • Yield Stress: 28,000 psi or 7,000 lbs
    • Strain at Rupture: 0.005 inches
    • Modulus of Elasticity: 3,200,000 psi
    • Modulus of Toughness: Approximately 280 psi
    • Deflection Gauge Reading After Unloading: 0.014 in.
    • Plastic Material Stress-Strain Plot: Graph (c) of the provided plots is the one that best represents a plastic material
    • Invalid Stress Unit: ft lbs (foot-pounds) is not a valid unit of stress

    Quiz 2: 21 September 2022 - CIE 110 - Materials

    • Ultimate Stress: The maximum stress a material can withstand before fracture. (Using graph on page 5) The exact value requires further detailed analysis of the graph data.
    • Strain at Yield: Calculated from the load-deformation graph; the value should be given in a decimal format, not a percentage.
    • Modulus of Elasticity: Interpreted from the load-deformation graph
    • Load at .005 Inches Deformation: Based on visual analysis of the provided graph.
    • Elastic-Plastic Material Plot: Stress-Strain graph (c) best represents an elastic-plastic material

    Quiz 2: September 25, 2024 - CIE 110 - Materials

    • Yield Stress of Alloy B: The value depends on interpreting the graph of the load-deformation plot

    • Ultimate Stress of Alloy A: Read from the graph for Alloy A, and it should be in a form of psi.

    • Strain at Yield for Alloy B: Obtained from the values depicted on the load-deformation graph (Alloy B)

    • Modulus of Toughness: Cannot be determined from the given graph

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    Related Documents

    CIE 110 Materials Past Papers Quiz 1 & 2 - PDF

    Description

    This quiz focuses on understanding probability density functions and cumulative distribution functions in the context of materials. Participants will assess graphs and calculate probabilities related to the breaking force of metallic wires. It’s an essential evaluation for students in materials science.

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