Questions and Answers
What is the 0.1% proof stress defined as?
What is ductility measured by?
What is the formula to calculate percentage elongation?
What is the classification of a material with a percentage elongation of 3 in a gauge length of 50 mm?
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Why is a factor of safety important in designing a structure?
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What is the formula to calculate percentage reduction in area?
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What is the main reason for using a factor of safety in designing a structure?
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What is the definition of 0.2% proof stress?
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What is the primary consideration when dealing with flanged joints?
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What is the modulus of elasticity of the high strength steel rod?
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What is the length of each segment of the prismatic bar AD?
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What is the cross-sectional area of the prismatic bar AD?
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What is the modulus of elasticity of the copper bar?
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Why can the cylinder head be treated as rigid?
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What is the load P1 acting at point B?
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What is the load P3 acting at point D?
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What is the type of shear shown in Figure 3.7 (a)?
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What is the diameter of the rivet used in Example 3.4?
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What is the purpose of the punch in Example 3.3?
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What is the type of shear shown in Figure 3.7 (b)?
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What is the force required to punch a hole in the steel plate in Example 3.3?
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What is the load transmitted through the rivet in Example 3.4?
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What is the purpose of the diagram shown in Figure 3.8?
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What is the diameter of the punch used in Example 3.3?
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What is the direction of a positive shear stress acting on a positive face of an element?
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What is the sign of shear strain when the angle between two positive faces is increased?
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What is the direction of a positive face of an element?
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What is the relationship between shear stress and shear strain within the linear elastic region?
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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?
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What is the equation that relates shear stress and shear strain within the linear elastic region?
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What is the physical meaning of the shearing modulus of elasticity (Modulus of Rigidity)?
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What is the shape of the τ versus γ diagram for many materials?
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Under what condition do the coordinates x and ȳ become negative?
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What is the shape shown in Example 4.1?
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What is special about the centroids of the shapes shown in the figures?
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What is a common location for the centroid of a shape?
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What is a table of centroids commonly found in?
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In the context of centroids, what is 'h' likely to represent?
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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.