Strength Of Materials In Me — Part 1 MCQs with Explanations

A lap joint can experience both single and double shear. In a single shear lap joint , the forces act in a single plane, and the joint is subjected to shear along one plane only. In a double shear lap joint , the forces are distributed over two planes, effectively reducing the shear stress in each plane. Therefore, the correct answer is Option C: Both A and B .

The correct answer is Option B: Less than Here's why: In mechanical engineering, specifically in the study of pressure vessels, we categorize them as either "thin shells" or "thick shells" based on the ratio of their wall thickness (t) to their inner diameter (D). A pressure vessel is considered a thin shell when the wall thickness is relatively small compared to its diameter. This allows us to make certain simplifying assumptions in our calculations of stress and strain. The generally accepted criterion is: If t/D < 1/10 , then the vessel is considered a thin shell. This means the wall thickness (t) must be less than one-tenth of the diameter (D). If the wall thickness is too large compared to the diameter (t/D >= 1/10), it's considered a thick shell, and different, more complex formulas are needed.

$$\frac{{{\text{w}}l}}{6}$$ is the correct answer to “A simply supported beam with a gradually varying load from zero at ‘B’ and ‘w’ per unit length at ‘A’ is shown in the below figure. The shear force at ‘B’ is equal to”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

* Slenderness Ratio: This is a way to measure how likely a column is to buckle (bend sideways) under a load. It's calculated by dividing the column's effective length by its least radius of gyration. * Short Columns: These are columns that are relatively stocky. They tend to fail due to crushing (the material being squeezed) rather than buckling. * Long Columns: These are columns that are relatively slender. They are more likely to buckle under load. * Medium Columns: These columns behaviour lies between short and long columns. * General Rule: A common rule of thumb is that columns with a slenderness ratio less than 80 are generally classified as short columns . They primarily fail due to compressive stresses exceeding the material's yield strength. * Weak Columns: This term isn't directly related to slenderness ratio in the same defining way as short or long columns. A weak column could be weak due to material properties or manufacturing defects, regardless of its slenderness ratio. Therefore, a slenderness ratio less than 80 indicates a short column that's prone to crushing rather than buckling.

Neither in tension nor in compression is the correct answer to “The layer at the center of gravity of the beam as shown in the below figure, will be”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

In tension is the correct answer to “The lower layer of the beam as shown in the below figure, will be”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Poisson's ratio: It is the ratio of lateral strain to longitudinal strain when a material is subjected to axial loading. Value for cast iron: For cast iron, Poisson's ratio typically ranges between 0.23 and 0.27 , depending on its composition and grade. Reason: Cast iron exhibits brittle behavior and has a lower Poisson's ratio compared to ductile materials, which tend to have higher values. The lower range of Poisson's ratio reflects the limited lateral expansion in cast iron under axial compression or tension. Significance: Understanding the Poisson's ratio of cast iron is crucial for analyzing its deformation characteristics and ensuring its appropriate use in engineering applications, such as engine blocks and machine parts.

$$\frac{l}{{\sqrt 3 }}$$ is the correct answer to “The maximum bending moment for the beam shown in the below figure, lies at a distance of ________ from the end B.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Hooke's law is a fundamental principle in mechanics that states that the strain in a material is directly proportional to the applied stress, provided the material's elastic limit is not exceeded. Limit of Proportionality: This is the point up to which Hooke's law is valid. Beyond this limit, the material will not follow the linear relationship between stress and strain, as it starts to experience non-linear deformation. Yield Point: This is the point where the material begins to deform plastically. While Hooke's law is valid up to this point, it is specifically associated with the limit of proportionality, which is slightly before the yield point. Breaking Point: This is the point at which the material fails and breaks. Hooke's law does not apply here as the material has surpassed its elastic limit. Elastic Limit: This is the maximum extent to which a material can be stretched or compressed and still return to its original shape. Hooke's law is valid up to the elastic limit, but the term "limit of proportionality" is more precise for this specific context.

Hooke's Law: Hooke's Law states that the stress in a material is directly proportional to the strain, as long as the material remains within its elastic behavior. Elastic Limit: The elastic limit is the maximum stress a material can withstand without experiencing permanent deformation. Beyond this point, the material will not return to its original shape when the load is removed. Plastic Limit: Incorrect, as this is the point where the material starts to exhibit plastic deformation, far beyond the elastic behavior. Yield Point: Incorrect, as this is the point where noticeable plastic deformation begins, which is beyond the elastic limit. Limit of Proportionality: Incorrect, as this is the point where the stress-strain curve begins to deviate from linearity, but the material may still obey Hooke's Law up to the elastic limit. Conclusion: A material obeys Hooke's Law up to its Elastic Limit , making Option B the correct answer.

50 MPa is the correct answer to “The state of stress at a point in a loaded member is shown in the below figure. The magnitude of maximum shear stress is”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Ultimate stress is the correct answer to “In the below figure, the stress corresponding to point ‘D’ is”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

In a cantilever beam , the maximum bending moment occurs at the support where the beam is fixed. When the load at the end is increased, the stress at the support increases significantly. As a result, the failure is most likely to occur at the support , where the bending stress is the highest.

$$\frac{{{\text{w}}l}}{3}$$ is the correct answer to “For the beam shown in the below figure, the shear force at A is equal to”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Young's modulus is defined as the ratio of longitudinal stress to longitudinal strain . Longitudinal stress: This is the force per unit area applied in the direction of the length of a material. Longitudinal strain: This is the deformation or change in length divided by the original length of the material. Young's modulus provides a measure of the stiffness of a material and is a fundamental property in the field of strength of materials.

The Factor of Safety (FoS) is a measure used in engineering to ensure that structures or components will perform safely under expected loads. It is defined as the ratio of the ultimate stress (the maximum stress a material can withstand before failure) to the working stress (the stress that the material is expected to endure during normal use). Factor of Safety Formula: The formula for Factor of Safety is: FoS = Ultimate Stress / Working Stress This ensures that the component or structure has enough strength to handle unexpected loads or conditions safely. Option B: Working stress to ultimate stress This option is incorrect as it represents the reciprocal of the Factor of Safety. Option C: Breaking stress to ultimate stress Breaking stress is essentially synonymous with ultimate stress, so this option does not correctly describe the Factor of Safety. Option D: Ultimate stress to breaking stress Since breaking stress and ultimate stress are the same, this option also does not describe the Factor of Safety correctly. Therefore, the correct answer is Option A: Ultimate stress to working stress .

Stress is nothing but the resisting force since due to temperature rise body will expand and if this expansion due to temperature change is restricted then only resisting stress (thermal stress) will come into play since expansion is not restricted that's why no stress is occurring.

$$\frac{{{\text{W}}{{\text{a}}^2}{{\text{b}}^2}}}{{3{\text{E}}Il}}$$ is the correct answer to “For a beam, as shown in the below figure, the deflection at C is (where E = Young's modulus for the beam material and $$I$$ = Moment of inertia of the beam section.)”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Radius is the correct answer to “The maximum shear stress, in the given figure, is equal to __________ of the Mohr's circle.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

$$\sqrt {\frac{{{l^2} - {{\text{a}}^2}}}{3}} $$ from B is the correct answer to “For a beam, as shown in the below figure, the maximum deflection lies at”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Curve C is the correct answer to “In the below figure, __________ represents glass.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Mild steel is the correct answer to “In the below figure, curve D represents_________.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

When a composite bar made up of different materials, such as steel and copper, is heated, it experiences thermal expansion. Since steel has a higher coefficient of thermal expansion compared to copper, the following stress distribution occurs: Steel (outer material) expands more and tends to elongate, resulting in tensile stress. Copper (inner material) expands less and tends to contract, resulting in compressive stress. So, in a composite bar made up of steel and copper bars of equal lengths heated through 100°C, the stresses developed shall be tensile in steel and compressive in copper . This is represented by Option B .

Between points B and C is the correct answer to “A simply supported beam of length 'l' carries a point load 'W' at a point C as shown in the below figure. The maximum deflection lies at”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Half the difference of two principal stresses is the correct answer to “The radius of the Mohr’s circle in the given figure is equal to”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

The maximum stress is the correct answer to “In the below figure, the point E represents.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

1.6 radian is the correct answer to “A circular shaft fixed at, A has diameter D for half of its length and diameter D/2 over the other half, as shown in the below figure. If the rotation of B relative to A is 0.1 radian, the rotation of C relative to B will be”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Length increases, width and thickness decreases is the correct answer to “When a bar of length l, width b and thickness t is subjected to a pull of P, its”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Length decreases, width and thickness increases is the correct answer to “When a bar of length l, width b and thickness t is subjected to a push of P, its”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Pitch is the correct answer to “The center to center distance, between two consecutive rivets in a row, is called”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

d = 6t is the correct answer to “According to Unwin's formula, the relation between diameter of rivet hole (d) and thickness of plate (t) is given by (where d and t are in mm)”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Stretch is the correct answer to “When it is indicated that a member is elastic, it means that when force is applied, it will”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Size of the drilled or reamed hole is the correct answer to “In riveted boiler joints, all stresses, shearing, bearing and tensile are based on the”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Tensile strength is the correct answer to “Transverse fillet welds are designed for”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

$$\frac{{{\pi ^2}{\text{E}}I}}{{{l^2}}}$$ is the correct answer to “According to Euler's column theory, the crippling load for a column length $$l$$ hinged at both ends, is”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Zero is the correct answer to “The shear force of a cantilever beam of length $$l$$ carrying a uniformly distributed load of w per unit length is _________ at the free end.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Zero is the correct answer to “The bending moment of a cantilever beam of length $$l$$ and carrying a uniformly distributed load of w per unit length is __________ at the free end.”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

The material A is more ductile than material B is the correct answer to “If percentage reduction in area of a certain specimen made of material 'A' under tensile test is 60% and the percentage reduction in area of a specimen with same dimensions made of material 'B' is 40%, then”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

$$\frac{I}{{\text{y}}}$$ is the correct answer to “The section modulus (Z) of a beam is given by”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.

Proof resilience is the correct answer to “The maximum strain energy that can be stored in a body is known as”. This question is standard in competitive examination syllabi for Strength Of Materials In Me.