Mechanical Properties of Materials
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Questions and Answers

What is the 0.1% proof stress defined as?

  • The stress required to produce a permanent strain of 0.1 on removal of the stress
  • The stress required to produce a permanent strain of 0.001 on removal of the stress (correct)
  • The stress required to produce a permanent strain of 0.01 on removal of the stress
  • The stress required to produce a permanent strain of 0.01% on removal of the stress

    • What is ductility measured by?

  • Only percentage reduction in area
  • Neither percentage elongation nor percentage reduction in area
  • Only percentage elongation
  • Both percentage elongation and percentage reduction in area (correct)

    • What is the formula to calculate percentage elongation?

  • (Lf + Lo) / Lo x 100%
  • Lo / Lf x 100%
  • (Lf - Lo) / Lo x 100% (correct)
  • Lf / Lo x 100%

    • What is the classification of a material with a percentage elongation of 3 in a gauge length of 50 mm?

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

    Why is a factor of safety important in designing a structure?

    <p>To keep the working stresses within safe limits</p> Signup and view all the answers

    What is the formula to calculate percentage reduction in area?

    <p>(Ao - Af) / Ao x 100%</p> Signup and view all the answers

    What is the main reason for using a factor of safety in designing a structure?

    <p>Because of possible errors arising from various sources</p> Signup and view all the answers

    What is the definition of 0.2% proof stress?

    <p>The stress required to produce a permanent strain of 0.002 on removal of the stress</p> Signup and view all the answers

    What is the primary consideration when dealing with flanged joints?

    <p>Elasticity of the packing</p> Signup and view all the answers

    What is the modulus of elasticity of the high strength steel rod?

    <p>200 GPa</p> Signup and view all the answers

    What is the length of each segment of the prismatic bar AD?

    <p>500 mm</p> Signup and view all the answers

    What is the cross-sectional area of the prismatic bar AD?

    <p>900 mm2</p> Signup and view all the answers

    What is the modulus of elasticity of the copper bar?

    <p>120 GPa</p> Signup and view all the answers

    Why can the cylinder head be treated as rigid?

    <p>Due to the low deformation of the nuts</p> Signup and view all the answers

    What is the load P1 acting at point B?

    <p>13 kN</p> Signup and view all the answers

    What is the load P3 acting at point D?

    <p>50 kN</p> Signup and view all the answers

    What is the type of shear shown in Figure 3.7 (a)?

    <p>Single shear</p> Signup and view all the answers

    What is the diameter of the rivet used in Example 3.4?

    <p>16 mm</p> Signup and view all the answers

    What is the purpose of the punch in Example 3.3?

    <p>To create a hole in a steel plate</p> Signup and view all the answers

    What is the type of shear shown in Figure 3.7 (b)?

    <p>Double shear</p> Signup and view all the answers

    What is the force required to punch a hole in the steel plate in Example 3.3?

    <p>116 kN</p> Signup and view all the answers

    What is the load transmitted through the rivet in Example 3.4?

    <p>5 kN</p> Signup and view all the answers

    What is the purpose of the diagram shown in Figure 3.8?

    <p>To analyze the equilibrium of an elementary block in a state of shear</p> Signup and view all the answers

    What is the diameter of the punch used in Example 3.3?

    <p>19 mm</p> Signup and view all the answers

    What is the direction of a positive shear stress acting on a positive face of an element?

    <p>In the direction of one of the coordinate axes</p> Signup and view all the answers

    What is the sign of shear strain when the angle between two positive faces is increased?

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

    What is the direction of a positive face of an element?

    <p>Outward normal directed in the positive direction of a coordinate axis</p> Signup and view all the answers

    What is the relationship between shear stress and shear strain within the linear elastic region?

    <p>Shear stress is directly proportional to shear strain</p> Signup and view all the answers

    What is the sign of shear stress acting on a negative face of an element if it acts in the negative direction of an axis?

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

    What is the equation that relates shear stress and shear strain within the linear elastic region?

    <p>τ = Gγ</p> Signup and view all the answers

    What is the physical meaning of the shearing modulus of elasticity (Modulus of Rigidity)?

    <p>Ratio of shear stress to shear strain</p> Signup and view all the answers

    What is the shape of the τ versus γ diagram for many materials?

    <p>Similar to the σ versus ε diagram</p> Signup and view all the answers

    Under what condition do the coordinates x and ȳ become negative?

    <p>When the centroid is to the left of the y-axis</p> Signup and view all the answers

    What is the shape shown in Example 4.1?

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

    What is special about the centroids of the shapes shown in the figures?

    <p>They coincide with the geometric centres</p> Signup and view all the answers

    What is a common location for the centroid of a shape?

    <p>At the geometric centre</p> Signup and view all the answers

    What is a table of centroids commonly found in?

    <p>Both A and B</p> Signup and view all the answers

    In the context of centroids, what is 'h' likely to represent?

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

    Study Notes

    Proof Stress

    • 0.1% proof stress is the stress required to produce a permanent strain of 0.001 on removal of the stress.
    • 0.2% proof stress is used to determine the proof stress of a material.

    Ductility and Brittleness

    • Ductility is the capacity of a material to be drawn out plastically before breaking.
    • Ductility is measured by percentage elongation and percentage reduction in area.
    • Percentage elongation is defined as (Lf - Lo) / Lo × 100%, where Lf is the distance between gauge marks at fracture and Lo is the original gauge length.
    • Percentage reduction in area is defined as (Ao - Af) / Ao × 100%, where Af is the final area of the fracture section and Ao is the original cross-sectional area.
    • A material is generally classified as brittle if the percentage elongation is less than 5 in a gauge length of 50 mm.

    Factor of Safety

    • A safety factor is necessary in designing a structure to ensure working stresses remain within safe limits.
    • The safety factor takes into account possible errors in knowledge of the magnitude and position of application of the load, dimensions of the member, and properties of the material.

    Problem 2.1

    • A high-strength steel rod with diameter d = 25 mm and modulus of elasticity E = 200 GPa must transmit a tensile load P = 134 kN.
    • If the length L of the rod is 1 m, the final length is 1.00136 m.
    • The ratio of the length of the rod to the increase in length is 735.
    • If the increase in length is limited to 3.8 mm, the maximum load Pmax that can be permitted is 373.4 kN.

    Problem 2.2

    • A prismatic bar AD is subjected to loads P1, P2, and P3 acting at points B, C, and D, respectively.
    • The displacement δD at the free end of the bar is 0.755 mm.
    • To reduce the displacement at end D to half of its original value, the load P3 should be 22.8 kN.

    Rivets in Single and Double Shear

    • A rivet is said to be in single shear when the shearing takes place at one cross-section of the rivet.
    • A rivet is said to be in double shear when the shearing takes place over two cross-sections of the rivet.

    Complementary Shear Stress

    • The sign convention for shear stress and shear strain is related to that of coordinate axes.
    • Positive shear stress acts in the direction of one of the coordinate axes, and negative shear stress acts in the negative direction of the axis.
    • Positive shear strain occurs when the angle between two positive or two negative faces is reduced, and negative shear strain occurs when the angle between two positive or two negative faces is increased.

    Relationship between Shear Stress and Shear Strain

    • The τ versus γ diagram is similar in shape to the σ versus ε diagram.
    • Within the linear elastic region, the shear stress and shear strain are directly proportional, given by τ = Gγ, where G is the shearing modulus of elasticity (Modulus of Rigidity).

    Centroid

    • The centroid of a shape is the point where the shape would balance if it were placed on a fulcrum.
    • The coordinates of the centroid can be positive or negative depending on the position of the centroid with respect to the reference axes.
    • Tables of centroids for various shapes are available in text books and handbooks.

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    Description

    Learn about the mechanical properties of materials, including proof stress, ductility, and brittleness, and how they are measured.

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