16 Questions
What is the minimum cross sectional area required for a steel rod of 1 m length to transmit a force of 15 kN without stretching more than 1 mm? (E of steel is 200 GPa)
75 mm2
What is the unit of strain?
No unit
What is the proper sequence of the following limits in terms of stress and strain: Proportional limit, elastic limit, yielding, failure?
Proportional limit, elastic limit, yielding, failure
What is the volumetric strain for a bar subjected to normal stress on all its surfaces?
$E(1-2v)(\sigma_x + \sigma_y + \sigma_z)$
What is the strain produced in a bar of length L meters that extends by l mm under a tensile force of P?
$0.001 l/L$
If a tensile load of 500 N is applied to a circular rod of diameter 5 mm, the normal stress is approximately:
25 MPa
What is the ratio of direct stress to the corresponding volumetric strain when a body is subjected to three mutually perpendicular stresses of equal intensity?
Poisson’s ratio
What is the equation that represents the increase in length of a circular rod of uniform cross-section A, length L, and material Young’s modulus E, when subjected to a tensile force of P?
$P L / AE$
If a steel bar of 40 mm × 40 mm square cross-section is subjected to an axial compressive load of 200 kN, with a length of 2 m and Young's modulus E = 200 GPa, what is the change in length of the bar?
2.70 mm
Up to which point in the stress-strain curve of a material is Hooke's Law valid?
Elastic limit
Which statement is true about stress and pressure?
Intensity of pressure at a point is same in all directions whereas stress depends on load and direction.
Which material among the following is the most elastic?
Rubber
For which material is Poisson's ratio nearly zero?
$ ext{Rubber}$
If Poisson's ratio for a material is 0.5, what is the relationship between its elastic modulus and shear modulus?
Four times its shear modulus
What is 1000 kN/mm2 equal to?
$1 × 10^3$ Mpa
What does stress due to unit strain signify?
Modulus of elasticity
Study Notes
Mechanics of Materials
- The minimum cross-sectional area required for a steel rod of 1 m length to transmit a force of 15 kN without stretching more than 1 mm is dependent on the Young's modulus of steel (200 GPa).
- The unit of strain is dimensionless.
Stress and Strain Limits
- The correct sequence of limits in terms of stress and strain is: Proportional limit, elastic limit, yielding, failure.
Volumetric Strain
- The volumetric strain for a bar subjected to normal stress on all its surfaces is three times the linear strain.
Strain Calculation
- Strain produced in a bar of length L meters that extends by l mm under a tensile force of P is given by the formula: strain = (l mm / L m).
Normal Stress
- Normal stress on a circular rod of diameter 5 mm under a tensile load of 500 N is approximately 25.46 MPa.
Volumetric Strain and Stress
- The ratio of direct stress to the corresponding volumetric strain when a body is subjected to three mutually perpendicular stresses of equal intensity is 3.
Hooke's Law
- The equation representing the increase in length of a circular rod of uniform cross-section A, length L, and material Young's modulus E, when subjected to a tensile force of P is: ΔL = (PL)/(AE).
Compressive Load
- The change in length of a 40 mm × 40 mm square cross-section steel bar subjected to an axial compressive load of 200 kN, with a length of 2 m and Young's modulus E = 200 GPa is 0.5 mm.
Hooke's Law Validity
- Hooke's Law is valid up to the proportional limit in the stress-strain curve of a material.
Stress and Pressure
- Stress and pressure are both measured in units of force per unit area, but they are different in terms of their direction and application.
Material Elasticity
- The material among the following that is the most elastic is not specified in the given text, but generally, rubber is considered to be one of the most elastic materials.
Poisson's Ratio
- The material for which Poisson's ratio is nearly zero is cork.
- If Poisson's ratio for a material is 0.5, the relationship between its elastic modulus and shear modulus is: E = 3G.
Unit Conversion
- 1000 kN/mm2 is equal to 1 GPa.
Stress and Strain
- Stress due to unit strain signifies the modulus of elasticity of a material.
Test your knowledge of simple stress and strain in the context of strength of materials with this quiz. Includes questions on units of strain, proper sequence of material behavior, and determining the minimum cross-sectional area required to transmit a specific force.
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