Strength of Materials MCQ Quiz - Objective Question with Answer for Strength of Materials - Download Free PDF

Explanation:

Strain Measuring Techniques for High-Temperature Environments

When selecting a strain measuring technique for high-temperature environments, it is critical to consider the durability and accuracy of the sensors under extreme conditions. Here, we analyze the given options:

1. Electrical resistance strain gauge (Option 1)

   • While widely used for various applications, electrical resistance strain gauges have limitations in high-temperature environments due to potential drift in resistance and insulation degradation.

2. Photoelastic coating (Option 2)

   • Photoelastic coatings are useful for visualizing strain distribution but are not ideal for high temperatures due to thermal sensitivity and potential for delamination.

3. Optical fiber strain sensors (Option 3)

   • Optical fiber strain sensors are highly suited for high-temperature environments due to their ability to withstand extreme temperatures and provide accurate measurements over a wide temperature range.

4. Brittle lacquer (Option 4)

   • Brittle lacquer is used for detecting strain by cracking patterns but is limited in high-temperature applications as it can degrade or perform inconsistently under thermal stress.

Conclusion

Analyzing the options, it is clear that optical fiber strain sensors (Option 3) are the most suitable for high-temperature environments due to their robustness and accuracy in such conditions, thus making them the best choice.

Explanation:

Brittle Coating Method

The brittle coating method is used to detect strain in materials by applying a brittle lacquer that cracks under stress. However, this method comes with certain disadvantages, primarily:

• Fragility and surface preparation are major concerns.

• It requires extensive surface preparation to ensure proper adhesion of the coating.

• The brittle nature of the coating means it can easily crack or damage during handling and application.

• Additionally, the method cannot be reused once the coating has cracked, requiring a new application for each test.

Analyzing the Given Options

1. "No visual output." (Incorrect)

   • The brittle coating method provides visual output in the form of cracks, which indicate areas of stress.

2. "Reusability." (Incorrect)

   • The method is not reusable; once the coating cracks, it needs to be reapplied for another test.

3. "Fragility and surface preparation." (Correct)

   • The coating is fragile and requires significant surface preparation.

   • Proper adhesion of the coating is crucial, which involves extensive surface preparation.

   • The fragility and the need for surface preparation make this a significant disadvantage.

4. "Cost." (Incorrect)

   • While cost can be a factor, it is not the primary disadvantage compared to fragility and surface preparation.

Explanation:

Gauge Factor of a Strain Gauge

The gauge factor of a strain gauge is a crucial parameter that indicates the sensitivity of the strain gauge. It is defined as the ratio of the relative change in electrical resistance to the mechanical strain. When a strain gauge is subjected to strain, its resistance changes, and the gauge factor quantifies this relationship. Mathematically, it is given by the formula:

• Gauge Factor (GF) = (ΔR / R) / ε

Analyzing the Given Options

1. Option 1: "Ratio of strain to voltage" (Incorrect)

   • The gauge factor is not defined in terms of voltage. While voltage may be involved in the measurement process, it is not part of the gauge factor definition.

2. Option 2: "Ratio of change in resistance to strain" (Correct)

   • This option correctly describes the gauge factor as the ratio of the change in electrical resistance (ΔR) to the mechanical strain (ε).

3. Option 3: "Ratio of resistance to current" (Incorrect)

   • This option refers to Ohm's law (V = IR), which is unrelated to the definition of the gauge factor.

4. Option 4: "Change in temperature per unit strain" (Incorrect)

   • The gauge factor does not involve temperature change. It is specifically related to the change in electrical resistance due to mechanical strain.

Explanation:

Two-Dimensional Photoelastic Analysis

In two-dimensional photoelastic analysis, the main objective is to visualize the stress distribution within a material subjected to external forces. This is done by observing patterns of light (fringes) through a polarized light setup. The key measurable parameter in this technique is the stress difference at any point, which can be related to the maximum shear stress.

• Stress-optic law: The stress difference (and hence maximum shear stress) is proportional to the fringe order observed.

• Fringe patterns indicate the loci of points with the same maximum shear stress.

Analyzing the Given Options

1. "Principal stress direction." (Not directly measured)

   • While the principal stress direction can be inferred from the orientation of fringes, it is not the parameter directly measured.

2. "Strain energy." (Not measured)

   • Strain energy is not directly measurable through photoelastic analysis. It is a derived quantity based on stress and strain.

3. "Maximum shear stress." (Correct answer)

   • The maximum shear stress is directly related to the fringe order observed in the photoelastic analysis.

   • The higher the fringe order, the higher the maximum shear stress at that point.

4. "Stress concentration factor." (Not directly measured)

   • The stress concentration factor is a derived quantity that indicates how much stress is amplified around discontinuities. It is not directly measured in photoelastic analysis.

Explanation:

Full-field Stress Visualization Methods

Full-field stress visualization is a technique used to observe and analyze the distribution of stress across a material or structure. This method is crucial in understanding how different areas of the material respond to applied loads and can help in identifying potential points of failure. The given options are various methods used in stress analysis, but only one provides full-field visualization.

1. Strain Gauge

   Strain gauges are devices used to measure the strain (deformation) in a specific area of an object. They do not provide full-field visualization as they only measure strain at discrete points where they are attached.

2. Brittle Coating

   Brittle coating is a method where a brittle lacquer is applied to the surface of a structure. When stress is applied, the coating cracks, indicating stress concentration areas. However, it does not provide a continuous full-field visualization, only indicating regions of high stress.

3. Photoelasticity

   Photoelasticity is an experimental technique for measuring the full-field distribution of stress. It utilizes polarized light passed through a transparent material under stress, creating a pattern of fringes that represent the stress distribution. This method provides a complete visual representation of the stress field, making it the correct answer.

4. Load Cell

   Load cells are transducers that convert force into an electrical signal. They are used to measure load or force applied to an object. Similar to strain gauges, load cells do not provide full-field visualization as they measure force at specific points.

Based on the explanations above, the method that gives full-field stress visualization is option 3: Photoelasticity.

Explanation:

Ductile material fails along the principal shear plane as they are weak in shear and brittle material fails along with principal normal stress.

In Brittle materials under tension test undergoes brittle fracture i.e their failure plane is 90° to the axis of load and there is no elongation in the rod that’s why the diameter remains same before and after the load. Example: Cast Iron, concrete etc.

But in case of ductile materials, material first elongates and then fail, their failure plane is 45° to the axis of the load. After failure cup-cone failure is seen. Example Mild steel, high tensile steel etc.

Explanation:

Perfectly Plastic Material:

For this type of material, there will be only initial stress required and then the material will flow under constant stress.

The chart shows the relation between stress-strain in different materials. 

Stress-Strain Curve	Type of Material or Body	Examples
	Rigidly Perfectly Plastic Material	No material is perfectly plastic
	Ideally plastic material.	Visco-elastic (elasto-plastic) material.
	Perfectly Rigid body	No material or body is perfectly rigid.
	Nearly Rigid body	Diamond, glass, ball bearing made of hardened steel, etc
	Incompressible material	Non-dilatant material, (water) ideal fluid, etc.
	Non-linear elastic material	Natural rubbers, elastomers, and biological gels, etc

Explanation:

• Change in the temperature causes the body to expand or contract.
• Thermal stress is created when a change in size or volume is constrained due to a change in temperature.
• So an increase in temperature creates compressive stress and a decrease in temperature creates tensile stress.

Explanation:

ϵv = ϵx + ϵy + ϵz

\( {ϵ_x} = \frac{1}{E}\left[ {{σ _x} - ν \left( {{σ _y} + {σ _z}} \right)} \right] \)

\({ϵ_{\rm{y}}} = \frac{1}{{\rm{E}}}\left[ {{σ _y} - ν \left( {{σ _x} + {σ _z}} \right)} \right] \)

\({ϵ_{\rm{z}}} = \frac{1}{{\rm{E}}}\left[ {{σ _z} - ν \left( {{σ _x} + {σ _y}} \right)} \right]\)

Total strain or volumetric strain is given by 

\( {ϵ_v} = \frac{1}{E} [ {σ_x} + {σ_y} + {σ_z} ](1-2ν) \)

There will be no change in volume if volumetric strain is zero.

ϵ_v = 0 ⇒  ν = 0.5

Explanation:

Since all the faces are free to expand the stresses due to temperature rise is equal to 0.

If the cube is constrained on all six faces, the stress produced in all three directions will be the same.

∴ thermal strain in x-direction = -α(ΔT) = \(\frac{{{\sigma _x}}}{E} - \nu \frac{{{\sigma _y}}}{E} - \nu \frac{{{\sigma _z}}}{E}\)

σ_x = σ_y = σ_z = σ

\(\sigma = - \frac{{\alpha \left( {{\rm{\Delta }}T} \right)E}}{{\left( {1 - 2\nu } \right)}}\)

Concept:

Let RA and RB be the reaction at support A and B respectively.

Free body diagram of the system is:

\(R_A=\frac{Pb}{L}\;\&\;R_B=\frac{Pa}{L}\)

Calculation:

Given:

As per figure P = 10 kN, a = 1 m and b = 2 m.

\(R_A=\frac{Pb}{L}\)

\(R_A=\frac{10\times2}{3}=\frac{20}{3}\;kN\)

\(R_B=\frac{10\times1}{3}=\frac{10}{3}\;kN\)

Explanation:-

Resilience

• The total strain energy stored in a body is commonly known as resilience. Whenever the straining force is removed from the strained body, the body is capable of doing work. Hence resilience is also defined as the capacity of a strained body for doing work on the removal of the straining force.
• It is the property of materials to absorb energy and to resist shock and impact loads.
• It is measured by the amount of energy absorbed per unit volume within elastic limit this property is essential for spring materials.
• The resilience of material should be considered when it is subjected to shock loading.

Proof resilience

• The maximum strain energy, stored in a body, is known as proof of resilience. The strain energy stored in the body will be maximum when the body is stressed upto the elastic limit. Hence the proof resilience is the quantity of strain energy stored in a body when strained up to the elastic limit.
• It is defined as the maximum strain energy stored in a body.
• So, it is the quantity of strain energy stored in a body when strained up to the elastic limit (ability to store or absorb energy without permanent deformation).

Modulus of resilience

• It is defined as proof resilience per unit volume.
• It is the area under the stress-strain curve up to the elastic limit.

Toughness:

• Toughness is defined as the ability of the material to absorb energy before fracture takes place.
• This property is essential for machine components that are required to withstand impact loads.
• Tough materials have the ability to bend, twist or stretch before failure takes place.
• Toughness is measured by a quantity called modulus of toughness. Modulus of toughness is the total area under the stress-strain curve in a tension test.
• Toughness is measured by Izod and Charpy impact testing machines.
• When a material is heated it becomes ductile or simply soft and thus less stress is required to deform the material and the stress-strain curve will shift down and the area under the curve decreases thus toughness decreases.
• Toughness decreases as temperature increases.

Hardness:

• Hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. 
• Hardness Testing measures a material’s strength by determining resistance to penetration.
• There are various hardness test methods, including Rockwell, Brinell, Vickers, Knoop and Shore Durometer testing.

When a material is subjected to repeated stresses, it fails at stresses below the yield point stresses. Such type of failure of a material is known as fatigue.

The slow and continuous elongation of a material with time at constant stress and high temperature below the elastic limit is called creep.

Explanation:

Elastic recovery/strain: The strain recovered after the removal of the load is known as elastic strain.

Plastic strain: The permanent changes in dimension after the removal of load is known as plastic strain.

The load is removed when the stress was 200 MPa and the corresponding strain was 0.03

After the removal of load, the body recovered and the final strain found was 0.01.

∴ Elastic strain = 0.03 - 0.01 ⇒ 0.02 and Plastic strain = 0.01 respectively.

Explanation:

Strain energy:

When a body is subjected to gradual, sudden, or impact load, the body deforms and work is done upon it. If the elastic limit is not exceeded, this work is stored in the body. This work-done or energy stored in the body is called strain energy.

Strain energy = Work done.

Case-I:

When a rigid body is slowly dropped on another body, it is a case of gradual loading:

Work-done on the bar = Area of load-deformation diagram \(⇒\frac{1}{2}\;×\;P\;×\;δ l\)

Work stored in the bar = Area of resistance deformation diagram

\(⇒\frac{1}{2}\;×\;R\;×\;δ l\)

\(⇒\frac{1}{2}\;×\;(\sigma\;×\;A)\;×\;δ l\;\;\;[\because R=\sigma A]\)

We can write;

\(⇒\frac{1}{2}\;×\;P\;×\;δ l=\frac{1}{2}\;×\;(\sigma\;×\;A)\;×\;δ l\)

\(\sigma_{gradual}=\frac{P}{A}\)

Case-II:

Work-done on the bar = Area of load-deformation diagram ⇒ P × δl

Work stored on the bar = Area of resistance deformation diagram

\(⇒\frac{1}{2}\;×\;R\;×\;δ l\)

\(⇒\frac{1}{2}\;×\;(\sigma\;×\;A)\;×\;δ l\;\;\;[\because R=\sigma A]\)

We can write;

\(P\times\delta l=\frac{1}{2}\;×\;(\sigma\;×\;A)\;×\;δ l\)

\(\sigma_{sudden}=\frac{2P}{A}\)

\(\therefore \frac{\sigma_{sudden}}{\sigma_{gradual}}=2\)

∴ maximum stress intensity due to suddenly applied load is twice the stress intensity produced by the load of the same magnitude applied gradually.

Impact Loading:

When a load is dropped from a height before it commences to load the body, such loading is known as Impact loading.

The ratio of the stress or deflection produced due to impact loading to the stress or deflection produced due to static or gradual loading is known as the Impact factor.

\(IF=\frac{\sigma_{impact}}{\sigma_{gradual}}=\frac{\Delta_{impact}}{\Delta_{gradual}}\)

\(IF=\frac{\sigma_{sudden}}{\sigma_{gradual}}=\frac{\Delta_{sudden}}{\Delta_{gradual}}=2\)

∴ deflection due to sudden loading is twice that of gradual loading.

Concept:

Stress at any section of the bar is given by,

\(stress, \sigma =\frac{{Load ~(P)}}{{Cross-sectional ~area~(A)}}\)

Calculation:

Given:

Load in section BC, P = 30 kN (compressive), 

cross-sectional area, A = 15 m² = 15 × 10⁶ mm²

\(stress~ in ~section ~BC, \sigma =\frac{{30~\times~10^3}}{{15~\times ~10^6}}=0.002~N/mm^2\)