**Correct Answer: core**

**Explanation:** The core of a column refers to the central area of the cross-section where the compressive load can be applied without inducing tensile stresses. This region is crucial for maintaining the structural integrity of the column under compressive forces.

**Correct Answer: d/4**

**Explanation:** To ensure that the stress remains within the permissible limits, the load may be applied anywhere within a concentric circle of diameter d/4 for a circular column. This practice helps in preventing excessive stress concentrations in the column.

**Correct Answer: rhombus of diagonals b/3 and h/3**

**Explanation:** The core of a rectangular column is the region at the center of the cross-section, forming a rhombus defined by the diagonals b/3 and h/3. This area is critical in ensuring the load distribution and stability of the column under compressive forces.

**Correct Answer: 4P**

**Explanation:** In a column with both ends fixed, the crippling load is equal to 4 times the applied load P. This value is crucial in determining the maximum load that the column can withstand without buckling under compressive forces.

**Correct Answer: π^2EI/L^2**

**Explanation:** The crippling load for a column with both ends hinged is given by π^2EI/L^2, where E is the modulus of elasticity and I is the moment of inertia of the column’s cross-section. This value helps determine the critical load at which the column experiences buckling.

**Correct Answer: P= 2π^2EI/l^2**

**Explanation:** Euler’s formula for a column of length 1 with one end fixed and the other hinged is given by the equation P= 2π^2EI/l^2. This formula is used to calculate the critical load that causes buckling in the column under compressive forces.

**Correct Answer: P = π^2EI/4l^2**

**Explanation:** The crippling load for a column of length 1 with one end fixed and the other end free is given by the formula P = π^2EI/4l^2. This value is critical in understanding the load capacity of the column when one end is fixed and the other end is free.

**Correct Answer: less**

**Explanation:** The buckling load is typically less than the crushing load for a long column. Buckling refers to the sudden failure of a column under compressive forces, and the load at which this occurs is generally lower than the load at which the material would undergo crushing failure.

**Correct Answer: 2 l**

**Explanation:** The effective length of a column that is held in position and restrained in direction at one end will be 2 times the length of the column. This factor is crucial in understanding the behavior of the column under various loading conditions and restraints.

**Correct Answer: 1/√2**

**Explanation:** The effective length of a column that is fixed at one end and hinged at the other end is 1 divided by the square root of 2, denoted as 1/√2. This factor is important in calculating the critical load for buckling in columns with specific end conditions.

**Correct Answer: 2l**

**Explanation:** The equivalent length of a column fixed at one end and free at the other end is 2 times the length of the column. This concept is useful in understanding the effective behavior of the column under different loading and boundary conditions.

**Correct Answer: slenderness ratio**

**Explanation:** The slenderness ratio is the ratio of the effective length of a column to the minimum radius of gyration of its cross-sectional area. This ratio plays a crucial role in determining the stability of the column under compressive forces.

**Correct Answer: 242**

**Explanation:** The slenderness ratio of a column is calculated by dividing its effective length by the minimum radius of gyration of its cross-sectional area. In this case, the slenderness ratio is 242 for the given dimensions of the column.

**Correct Answer: 30**

**Explanation:** The slenderness ratio is obtained by dividing the effective length of the column by the minimum radius of gyration of its cross-sectional area. In this case, the slenderness ratio is 30 for the given values of moment of inertia, area, and effective length.

**Correct Answer: 173.2**

**Explanation:** The slenderness ratio is calculated as the ratio of the effective length of the column to the minimum radius of gyration of its cross-sectional area. For the given dimensions, the slenderness ratio is 173.2.

**Correct Answer: sal**

**Explanation:** In the context of short columns with equal sections, the term “sal” refers to the condition where the column takes the maximum load before failure. This term is used to describe the maximum load-bearing capacity of short columns under compressive forces.

**Correct Answer: none of the above**

**Explanation:** Rankine’s constant, which is used in the context of columns, does not depend on the length or diameter of the column. Instead, it is a material-dependent constant used in calculations related to the buckling and stability of columns.

**Correct Answer: the equilibrium is satisfied**

**Explanation:** In the analysis of a truss structure, the analysis is considered complete when the equilibrium conditions are satisfied. This involves ensuring that all external reactions are determined and the internal member forces meet the requirements of equilibrium.

**Correct Answer: compression member**

**Explanation:** A strut refers to a specific type of structural member that primarily undergoes compressive forces. Struts are often used in the construction of various architectural and engineering structures to withstand and support compressive loads.

**Correct Answer: is subjected axial tension only**

**Explanation:** A tie is a type of structural member that experiences axial tension forces. Ties are commonly used in various structures to withstand and transmit tensile loads, providing stability and support to the overall system.

**Correct Answer: wl^2/8**

**Explanation:** The maximum bending moment for a simply supported beam loaded with a uniformly distributed load (UDL) of w/m over a span l is wl^2/8. This formula is derived based on the mechanics of the beam’s response to the UDL and is a fundamental concept in structural engineering.

**Correct Answer: volumetric strain**

**Explanation:** Volumetric strain is the ratio of the change in volume to the original volume of a material. It is a measure of the material’s deformation under stress and is a significant parameter in the study of material properties and behavior under various loading conditions.

**Correct Answer: 4t**

**Explanation:** According to the principle of equilibrium, the reaction at point B for the given simply supported beam carrying a load of 10 t would be 4 t. This is derived from the fact that the sum of the upward and downward forces must balance each other to maintain equilibrium.

**Correct Answer: top layer**

**Explanation:** When a rectangular beam is loaded transversely, the maximum compressive stress is developed on the top layer of the beam. This stress distribution occurs due to the mechanics of the beam’s deformation under the transverse load, leading to the highest compression at the top layer.

**Correct Answer: WL/8**

**Explanation:** The maximum bending moment for a simply supported beam carrying a uniformly distributed load (UDL) W over a span L is WL/8. This principle is crucial in understanding the internal forces and stresses experienced by the beam under various loading conditions.

**Correct Answer: varying loads, well below ultimate static load**

**Explanation:** Fatigue refers to the failure of a material under repeated or fluctuating loads that are typically well below the material’s ultimate static load. This phenomenon is a significant concern in engineering design and material selection, particularly in structures subjected to cyclic loading.

**Correct Answer: axial loading**

**Explanation:** When a rod is pulled simultaneously at both ends, it experiences axial loading, where the forces are applied along the longitudinal axis of the rod. This type of loading results in tensile or compressive stresses within the rod, depending on the direction of the forces.

**Correct Answer: plastic**

**Explanation:** A member that does not return to its original shape after the load producing deformation is removed is said to be in a plastic state. Plastic deformation refers to the permanent change in the shape of a material, indicating that it has surpassed its elastic limit and undergone permanent deformation.

**Correct Answer: Hooke’s law**

**Explanation:** Hooke’s law states that within the elastic limits, the strain produced in a material is directly proportional to the stress producing it. This fundamental principle serves as a basis for understanding the linear relationship between stress and strain in elastic materials.

**Correct Answer: ultimate stress**

**Explanation:** The ratio of the largest load in a test to the original cross-sectional area of the piece is known as the ultimate stress. This value indicates the maximum stress that a material can withstand before failure occurs and is a critical parameter in material testing and design.

**Correct Answer: bending stress**

**Explanation:** The resistance offered by internal stresses to the bending of a beam is known as bending stress. This stress arises due to the internal forces that develop in response to the external bending moment, contributing to the beam’s stability and load-bearing capacity.

**Correct Answer: elongate the member**

**Explanation:** Tensile internal forces tend to elongate the member, causing it to stretch along the axis in the direction of the applied force. This phenomenon is commonly observed in materials subjected to tensile loading and is essential to consider in the design and analysis of structures.

**Correct Answer: P/2**

**Explanation:** The magnitude of a shear force at a distance of L/4 from either end of a simply supported beam with load P applied at midspan is equal to P/2. This principle is based on the distribution of shear forces along the length of the beam under specific loading conditions.

**Correct Answer: triangular**

**Explanation:** The bending moment diagram of a simply supported beam with a point load at the centre of the span takes the shape of a triangular curve. This diagram represents the variation of bending moments along the length of the beam and is a fundamental tool in understanding the internal forces within the beam.

**Correct Answer: area**

**Explanation:** Stress is defined as force per unit area and is a measure of the internal resistance of a material to external forces. It is typically expressed in units of force per unit area, such as Pascals (Pa) or Newtons per square meter (N/m²).

**Correct Answer: ultimate stress**

**Explanation:** The unit failure stress is commonly referred to as the ultimate stress. It represents the maximum stress that a material can withstand before failure occurs. This value is crucial in understanding a material’s strength and is an essential consideration in the design and analysis of structures.

**Correct Answer: bd^3/12**

**Explanation:** The moment of inertia of an object with a rectangular section, where ‘b’ is the width and ‘d’ is the depth, is given by the formula bd^3/12. This moment of inertia is a crucial parameter in analyzing the bending and torsional characteristics of structural elements.

**Correct Answer: Elastic limit**

**Explanation:** Hooke’s law is valid only within the elastic limit of a material, beyond which the material exhibits plastic deformation. The elastic limit is the threshold beyond which the material does not return to its original shape after the load producing deformation is removed.

**Correct Answer: A vector quantity**

**Explanation:** The velocity of a moving body is a vector quantity, as it possesses both magnitude and direction. This characteristic distinguishes it from a scalar quantity, which has only magnitude and no direction, such as speed.

**Correct Answer: non-coplanar concurrent forces**

**Explanation:** Non-coplanar concurrent forces are those forces that intersect at one point but are not confined to a single plane. These forces have different directions and lines of action, leading to complex force systems that require careful analysis and consideration in structural engineering and mechanics.

**Correct Answer: is less when the lift is moving downwards**

**Explanation:** The tension in a cable supporting a lift is less when the lift is moving downwards. This is due to the opposing forces acting on the lift, leading to a decrease in tension compared to when the lift is stationary or moving upwards.

**Correct Answer: medians of the triangle meet**

**Explanation:** The centre of gravity of a triangle is located at the point where the three medians of the triangle intersect. A median is a line segment that joins a vertex of a triangle to the midpoint of the opposite side. The intersection of these medians defines the triangle’s centroid.

**Correct Answer: period of impact**

**Explanation:** The total time of collision and restitution of two bodies is known as the period of impact. This term is used to describe the duration during which two bodies interact, experiencing a collision followed by the restitution of their original shapes or positions.

**Correct Answer: Fixed at one end and free at the other end**

**Explanation:** A cantilever beam is a structural element that is fixed at one end and free at the other end. It is commonly used in various engineering applications and is known for its ability to withstand different types of loading conditions while projecting horizontally from a support.

**Correct Answer: strut**

**Explanation:** The inclined member that carries a compressive load in the case of frames and trusses is called a strut. Struts are essential components in various structural systems, providing stability and support against compressive forces acting along their longitudinal axes.

**Correct Answer: Bending moment is constant**

**Explanation:** A beam is said to be loaded in pure bending when the bending moment along its length remains constant. This condition implies that the external loading on the beam is such that it creates a uniform bending moment throughout its span without the influence of shear forces.

**Correct Answer: Longitudinal stress/ longitudinal strain**

**Explanation:** Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material. It is a fundamental mechanical property that characterizes a material’s stiffness and elasticity in the direction of the applied force.

**Correct Answer: the deformation per unit length**

**Explanation:** Mathematically, strain is defined as the deformation per unit length of a material. It is a measure of the relative change in length or shape of a material under the influence of external forces. Strain is typically expressed as a dimensionless quantity.

**Correct Answer: maximum**

**Explanation:** If the shear force along a section of a beam is zero, the bending moment at the section is at its maximum. This principle is a key aspect of the relationship between shear force and bending moment in a beam, helping to understand the internal behavior and stresses within the structure.

**Correct Answer: 16 KN-m**

**Explanation:** The total moment at the center of the cantilever beam can be calculated by integrating the moment due to the uniformly distributed load and the point load. For this specific case, the total moment at the center is 16 KN-m.

## FAQs on Mechanics of Materials & Structures MCQs for Civil Engineers

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### ▸ What are common questions in Mechanics of Materials & Structures MCQs?

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