**Explanation:** Robert Hooke formulated the law that states that within the elastic limit, the extension of an elastic material is directly proportional to its tension or compression.

**Explanation:** According to Hook’s law, the stress (σ) in a material is directly proportional to the strain (ε) within the elastic limit, where E is the Young’s modulus of elasticity.

**Explanation:** The non-linear elastic zone is the region between the elastic limit and the proportional limit where the relationship between stress and strain deviates from being linear.

**Explanation:** The factor of safety, according to the elastic theory of design, is the ratio of the yield stress (the stress at which the material begins to deform plastically) to the working stress (the maximum stress the material can safely withstand).

**Explanation:** Poisson’s ratio is defined as the ratio of the lateral strain to the longitudinal strain in a material subjected to uniaxial loading. It helps determine the material’s deformation behavior under stress.

**Explanation:** Poisson’s ratio is always less than one for common materials. It indicates the degree of lateral contraction that a material undergoes when stretched longitudinally.

**Explanation:** The typical values of Poisson’s ratio are 0.3 for steel and 0.15 for concrete. It may vary for different materials and is an important parameter in understanding their deformation behavior.

**Explanation:** The relationship between Poisson’s ratio (ν), Modulus of Rigidity (G), and Young’s Modulus (E) is given by ν = (E/2G) – 1/2. Given ν = 0.25, G/E = 0.4.

**Explanation:** The actual breaking stress of a ductile material from a tension test is typically greater than the ultimate strength due to necking that occurs during the test.

**Explanation:** The product EI, where E is the Young’s modulus and I is the second moment of area, is known as the flexural rigidity and represents a beam’s resistance to bending.

**Explanation:** Fatigue is the phenomenon of reduced material strength caused by repeated cyclic loading and unloading, leading to cracks and ultimately failure under a lower stress level than the material’s ultimate strength.

**Explanation:** Elasticity is the property of a material that allows it to return to its original shape and size after the removal of a deforming force, as long as the force is within the material’s elastic limit.

**Explanation:** A perfectly elastic body is one that fully regains its original shape and size after the removal of the deforming force, without any permanent deformation or energy loss.

**Explanation:** Stiffness is the load required to produce a unit deflection in a material or structure. It indicates how resistant a material is to deformation under an applied load.

**Explanation:** Ductility is the property of a material that allows it to undergo significant plastic deformation under tensile stress without rupture. It is associated with the ability to be drawn into wires.

**Explanation:** Mild steel is relatively ductile compared to cast iron, wrought iron, and bronze, as it can undergo significant deformation before fracturing.

**Explanation:** Toughness is the ability of a material to absorb energy and deform plastically before fracturing. It represents the area under the material’s stress-strain curve.

**Explanation:** Impact tests are performed to determine the toughness of a material by measuring the energy absorbed during the fracture of a standard notched specimen under an impact load.

**Explanation:** Malleability is the property of a material that allows it to be deformed into thin sheets or plates under compressive forces without rupturing. It is essential for processes such as rolling and forging.

**Explanation:** Fatigue of the metal refers to the phenomenon where a material fails at a stress lower than its ultimate stress, typically occurring after repeated applications of reversible tensile or compressive stress.

**Explanation:** The endurance limit is the maximum stress level a material can withstand indefinitely without failing under cyclic loading. It represents the safe threshold below which the material will not fail when subjected to a reversal of stress.

**Explanation:** Coaxing is the method of improving the fatigue resistance of a metal by subjecting it to progressively higher stress levels through repeated loading. This process can increase the metal’s endurance limit and prolong its fatigue life.

**Explanation:** Creep is the phenomenon where materials deform slowly over time under a constant load, particularly under high temperatures. It is a significant factor in the long-term behavior of materials subjected to constant stress.

**Explanation:** Permanent set refers to the irreversible deformation or strain that remains in a material or structure after the removal of the applied load. It represents the residual deformation even when the load is no longer present.

**Explanation:** A Young’s Modulus of zero would imply that the material is perfectly incompressible, meaning that it cannot be compressed or deformed under an applied load.

**Explanation:** The limit of proportionality, a point on the stress-strain curve, is dependent on the material’s properties and represents the limit beyond which Hooke’s law is no longer applicable.

^{2}

^{2}

^{2}

**Explanation:** The SI unit of the modulus of elasticity is the pascal (Pa), which is equivalent to one newton per square meter (N/m^{2}). It represents the ratio of stress to strain in a material under an applied load.

**Explanation:** Strain is a dimensionless quantity that represents the ratio of the change in size or shape of a material to its original size or shape. It is a measure of deformation and has no units.

**Explanation:** The yielding point is the stress level at which a material undergoes permanent deformation or elongation without any increase in the applied load. It marks the transition from elastic to plastic behavior.

**Explanation:** Tenacity is the ultimate strength of a material under tension, representing the maximum stress it can withstand before fracturing. It is an important mechanical property in understanding material behavior under tensile forces.

**Explanation:** Modulus of Elasticity (E) is determined by the ratio of the linear stress to the linear strain within the elastic limit of a material. It represents the material’s stiffness or rigidity.

**Explanation:** Young’s Modulus of elasticity is the ratio of the stress to the strain within the elastic limit of a material. It characterizes the material’s ability to deform elastically in response to an applied force.

**Explanation:** Modulus of Rigidity (G) is determined by the ratio of the shear stress to the shear strain in the elastic range of a material. It characterizes a material’s resistance to shearing forces.

**Explanation:** Bulk Modulus (K) is determined by the ratio of the normal stress applied equally on all six faces of a solid cube to the resulting volumetric strain. It characterizes a material’s response to uniform changes in pressure.

**Explanation:** The relationship among the modulus of elasticity (E), modulus of rigidity (N), and bulk modulus (K) is given by E = 9KN / 3K + N.

**Explanation:** Normal strain refers to the change in length per unit length of an object in the direction of the applied force. It is the ratio of the change in length to the original length of the material.

**Explanation:** Shear strain refers to the deformation that occurs in a material when subjected to parallel forces acting in opposite directions. It represents the change in the angle between the planes originally perpendicular to each other.

_{1}and E

_{2}are the modulus of elasticity of respective material.)

_{1}/E

_{2}

_{1}/E

_{2})

^{2}

_{1}/E

_{2})

^{3}

**Explanation:** The modular ratio of two materials is the ratio of their respective moduli of elasticity (E). It helps in understanding the relative stiffness of the materials when they are combined in a composite structure.

**Explanation:** Young’s Modulus generally decreases with an increase in temperature for most materials. This decrease is due to the increased thermal vibration of the material’s atoms, leading to a reduction in stiffness.

**Explanation:** Mild steel typically has the highest Young’s Modulus among the given materials. It is known for its high stiffness and ability to withstand considerable stress without significant deformation.

**Explanation:** Strain energy is the energy stored within a body as a result of deformation or strain. It represents the energy absorbed or stored due to the work done on the material during the process of straining.

**Explanation:** Strain energy of a member represents the work done on the member to deform it, resist elongation, and resist shortening. It is a measure of the potential energy stored in a material due to the applied forces and resulting deformations.

**Explanation:** Resilience is the strain energy stored in a member when it is strained within the elastic limit. It represents the capacity of a material to absorb energy and deform elastically without permanent damage.

**Explanation:** Proof resilience represents the maximum strain energy stored in a material at its elastic limit. It is a measure of the energy absorbed per unit volume up to the point where the material begins to deform plastically.

**Explanation:** Stress in a member refers to the resistance offered by the material per unit area to an applied force. It is the force acting on a unit area of the member and is a fundamental parameter in understanding the material’s behavior under loading.

**Explanation:** The stress due to temperature change in a member is influenced by the supporting end conditions. Thermal stress arises due to non-uniform temperature changes within a structure, leading to differential expansion or contraction.

**Explanation:** The stress required to initiate yielding in a material is significantly greater than the stress needed to continue the yielding process. Once yielding begins, the material undergoes plastic deformation at a lower stress level.

**Explanation:** The ratio of the intensity of stress in a suddenly loaded case to that of gradually applied load is two. This implies that the stress developed in a structure due to sudden loading is twice that of the stress resulting from a gradual or slowly applied load.

**Explanation:** The yielding point is the stress level at which a material undergoes permanent deformation more rapidly compared to the increase in the applied load. It marks the transition from elastic to plastic deformation.

**Explanation:** Tensile stress is the stress that develops within a body when equal and opposite forces act on it, tending to elongate or stretch it. It represents the internal force per unit area in the direction of the applied force.

**Explanation:** The bending moment acting on the plane of an element causes normal stress on the plane. This stress is perpendicular to the plane and is responsible for the normal forces induced within the material.

**Explanation:** As the elastic limit is reached, tensile strain increases more rapidly in proportion to the applied stress. This indicates that the material undergoes greater deformation for each incremental increase in stress.

**Explanation:** The ratio of elongations of a conical bar due to its own weight to that of a prismatic bar of the same length is 1:3. This ratio indicates the relative difference in elongation between the two types of bars under the influence of their own weight.

**Explanation:** Dead load of a member refers to the weight that is constant and permanent, primarily due to the self-weight of the structural elements and any fixed attachments. It is a crucial consideration in structural engineering.

**Explanation:** Stress in a beam due to simple bending is directly proportional to the distance from the neutral axis. This stress distribution is a fundamental characteristic of the internal forces in a beam subjected to bending.

**Explanation:** Compression members tend to buckle in the direction of the least radius of gyration. This is a critical consideration in the design and analysis of structural elements to prevent buckling failures.

**Explanation:** The maximum shear stress in a cross-section can occur at any fiber, depending on the configuration of the structure. It is important to consider the specific geometry and loading conditions to determine the location of the maximum shear stress.

**Explanation:** In an H section, the maximum shear stress typically occurs at the junction of the web and flanges. This location experiences the highest shear forces and is a critical point in the analysis of the H section under shear loading.

**Explanation:** If the stress produced by a prismatic bar is equal to the working stress, the area of the cross-section of the prismatic bar theoretically becomes infinite. This signifies that the cross-sectional area needs to be infinitely large to accommodate the given working stress.

**Explanation:** If all dimensions of a bar are increased in the proportion n:1, the maximum stress produced in the prismatic bar by its own weight will increase in the ratio of n:1. This emphasizes the relationship between dimensional changes and stress variations in a structural member.

**Explanation:** A static load is a type of load where the magnitude and direction of the force do not change with respect to time. It remains constant and does not induce dynamic effects on the structure.

**Explanation:** A hinge on rollers support has one reaction component. It can resist forces in only one specific direction, typically either vertical or horizontal, depending on the specific configuration and loading conditions.

**Explanation:** A hinged end of a general loading can have two reaction components. These components include both a horizontal and a vertical reaction that counteract the external loading applied to the structure.

**Explanation:** A cantilever beam is supported at one end, typically fixed, while the other end remains free. This configuration allows the beam to transmit load to the support where it is fixed, while the free end can experience deflection under loading.

**Explanation:** A free end permits displacement in any direction and also rotation, enabling the structure to move and rotate freely without any restraint. This end condition allows for greater flexibility in response to external loading.

**Explanation:** A beam supported over three rollers lying in the same plane is stable for loading with no component in the direction of the beam. This support configuration allows the beam to experience forces perpendicular to the beam but not in the direction of the beam itself.

**Explanation:** A material with zero elasticity is considered rigid. Such materials do not undergo deformation under normal loading conditions and exhibit no flexibility or resilience when subjected to external forces.

**Explanation:** An orthotropic material exhibits different properties in three perpendicular directions. These materials possess distinct material properties in mutually perpendicular planes, enabling varied responses to external forces.

**Explanation:** A material with identical properties in all directions is called isotropic. Such materials exhibit uniform behavior and physical properties regardless of the direction in which forces are applied.

**Explanation:** An isotropic material does not possess any of the mentioned properties. It refers to a material with uniform physical properties in all directions and exhibits consistent behavior under loading.

**Explanation:** A viscoelastic material demonstrates a time-dependent stress-strain relationship, indicating that its mechanical properties vary with time under the application of stress. It exhibits both viscous and elastic characteristics.

**Explanation:** A brittle material exhibits very little or almost no plastic zone before failure. It is prone to sudden and catastrophic failure without significant deformation or warning.

**Explanation:** The compression test is commonly used for testing the strength and behavior of brittle materials. It helps determine how a material responds to compressive forces and establishes its compressive strength and stress-strain characteristics.

**Explanation:** A brittle material is characterized by sudden failure without significant deformation or warning. It fails without extensive plastic deformation and often without any noticeable signs of impending failure.

**Explanation:** Brittle materials have low toughness because they exhibit small plastic deformation or no plastic deformation before failure. Their lack of ductility leads to limited energy absorption capacity before fracture occurs.

**Explanation:** A body with similar properties throughout, without any variation or differentiation in its composition or structure, is referred to as homogeneous. It exhibits uniform characteristics and behavior across its entirety.

**Explanation:** The moment of inertia of an area will be least with respect to the central axis. This axis represents the axis passing through the centroid of the area and is associated with the minimum moment of inertia.

**Explanation:** The square root of the ratio of the moment of inertia and the cross-sectional area of a member is known as the radius of gyration. It is a crucial parameter used to describe the structural behavior of a member under bending loads.

**Explanation:** The radius of gyration of a rectangular section is not directly proportional to any of the mentioned parameters. It is a critical geometric characteristic used to evaluate the resistance of a structural member to buckling under compression.

**Explanation:** The beam strongest in flexure will have the maximum section modulus. The section modulus is a critical parameter that measures a beam’s resistance to bending stress and is directly related to its strength and stiffness.

^{3}/12

^{3}/6

^{3}/12

^{3}/6

**Explanation:** The moment of inertia of a rectangular beam bxd is given by the formula bd^{3}/12, where ‘b’ is the breadth and ‘d’ is the depth of the beam.

^{4}/12

^{3}/12

^{4}

^{4}/3

**Explanation:** The moment of inertia of a square section is calculated using the formula b^{4}/12, where ‘b’ represents the length of one side of the square.

^{3}/12

^{3}/12

^{3}/3

^{3}/3

**Explanation:** The moment of inertia of a rectangular section (Bx D) about its base is determined using the formula BD^{3}/3, where ‘B’ is the breadth and ‘D’ is the depth of the section.

^{3}/12

^{3}/18

^{3}/36

**Explanation:** The moment of inertia of a triangular section b x h about the base is calculated using the formula bh^{3}/12, where ‘b’ is the base and ‘h’ is the height of the triangle.

^{3}/ 12

^{3}/ 18

^{3}/36

**Explanation:** The moment of inertia of a triangular section b x h about the center of gravity (c-g) is given by the formula bh^{3}/36, where ‘b’ is the base and ‘h’ is the height of the triangle.

**Explanation:** The ratio of the moment of inertia of a square section to that of a circular section for a given depth is typically greater than 1, suggesting that the square section has a higher moment of inertia compared to the circular section.

**Explanation:** The center of gravity of a semicircle is positioned 4r/3π above the base AB (diameter). This calculation helps determine the precise location of the center of gravity for a semicircular section.

**Explanation:** The center of gravity (c.g.) of a semi-circular arc is located at a distance of 2r/π from the base of the arc. This characteristic helps understand the distribution of weight in a semi-circular configuration.

^{2}/16

^{3}/32

^{3}/64

^{2}/64

**Explanation:** The section modulus of a circular section about an axis through its center of gravity (C.G.) is represented by the formula πd^{3}/32, where ‘d’ is the diameter of the circular section.

**Explanation:** Centrifugal force acts away from the center of a curve, leading to an outward force that tends to move objects in a curved path away from the center of the curve.

^{2}/R

^{2}/R

**Explanation:** Centrifugal force is given by the expression mv^{2}/R, where ‘m’ represents the mass of the object, ‘v’ denotes its velocity, and ‘R’ signifies the radius of the curve.

**Explanation:** Centrifugal force acts away from the center of the path, while centripetal force acts towards the center, serving as the inward force required to keep an object moving along a curved path.

**Explanation:** The shear force in a concrete beam is assumed to act perpendicular to the longitudinal axis, exerting a lateral force that tends to deform or cause shear deformation in the beam.

**Explanation:** The shear force on a beam is directly proportional to the sum of the transverse forces applied to the beam. It represents the cumulative effect of the transverse forces that tend to cause the beam to shear along its length.

**Explanation:** The rate of change of bending moment in a beam is equivalent to the shear force acting on the beam. It represents the variation in the internal bending moment along the length of the beam.

**Explanation:** The rate of change of shear force in a beam is referred to as the intensity of the load. It indicates the variation in the shear force along the length of the beam due to the applied loading conditions.

**Explanation:** The amount of shear force at the maximum bending moment is minimal. At the point of maximum bending moment, the shear force experiences a minimum value, indicating the specific conditions where the beam is most susceptible to bending.

**Explanation:** In the case of a simply supported beam subjected to a uniform distributed load (UDL), the maximum shear force occurs at the support locations. This characteristic helps identify the critical points of shear force distribution in such beams.

**Explanation:** The shear force diagram for a cantilever carrying a uniform distributed load (UDL) over its entire length takes the shape of a triangle. The distribution of the shear force follows a triangular pattern in such scenarios.

**Explanation:** The difference in the ordinate of the shear force between any two sections is equivalent to the area under the load curve between these two sections, along with the contribution from any concentrated load applied between the sections. This relation helps in understanding the distribution of loads and shear forces along the beam.

**Explanation:** In an I section, the web primarily takes almost all the shear force. This is due to the web’s orientation, which helps it resist the shear stress acting on the beam.

**Explanation:** When a prismatic bar is subjected to pure bending, it assumes the shape of an arc of a circle due to the bending moments acting on it.

**Explanation:** If a constant section is subjected to a uniform or pure bending moment throughout, its length bends to form a circular arc.

**Explanation:** A cable subjected to a uniformly distributed load (U.D.L.) over its entire span assumes a shape of a parabola due to the distribution of the load and the cable’s characteristics.

**Explanation:** The shear flow in a section can be defined as the total shear stress at a point. It is a crucial parameter used in understanding the distribution of shear stress in structural elements.

**Explanation:** The algebraic sum of the shear flow of a section in any direction must be equal to the shear force in that direction. This principle is essential in analyzing the equilibrium of shear forces in structural elements.

**Explanation:** The shear center is defined as the point about which the moment of shear flow is zero. It is a crucial concept in understanding the behavior of structural members under shear loads.

**Explanation:** The shear center in the case of a T-beam section is located at the center of gravity (C.G.) of the section. This characteristic influences the distribution of shear forces in T-beam structures.

**Explanation:** The shear force and bending moment are related by the equation V = dM/dx. This relationship helps in understanding the change in shear force with respect to the bending moment along the length of a beam.

**Explanation:** A shear force diagram of a simply supported beam showing constant shear force throughout the span is subjected to a couple at mid-span. This feature helps identify the nature of loading and support conditions in the beam.

^{2}y/dx

^{2})

^{3}y/dx

^{2})

^{3}y/dx

^{3})

**Explanation:** The shear force on a beam and the displacement are related by the equation V = EI(d^{3}y/dx^{3}). This relationship is crucial in understanding the deflection and shear force characteristics of beams under various loading conditions.

**Explanation:** The maximum number of transverse shear forces possible at one end of an element of a plane frame is one. Understanding this limit is crucial in analyzing the shear force distribution and equilibrium in plane frames.

**Explanation:** The maximum number of transverse shear forces possible at one end of an element of a plane truss is zero. This characteristic simplifies the analysis of shear forces in plane truss structures.

**Explanation:** The maximum bending moment induced in a simply supported beam subjected to a point load of 4 KN at the center of the beam and a span of 4 m is 4 KN-m. This calculation helps determine the critical points of bending in the beam.

**Explanation:** In a simply supported beam subjected to a point load at the center, the maximum bending moment occurs at the center. This characteristic is crucial in determining the critical points of bending in the beam under such loading conditions.

**Explanation:** The maximum bending moment in a simply supported beam loaded with a uniformly distributed load (UDL) of 2 t/m and having a span of 4m is 4 t-m. This calculation helps understand the critical bending moments induced by the distributed load.

**Explanation:** The maximum bending moment occurs at the center of a simply supported beam subjected to a point load at the center, a uniformly distributed load throughout the span, or a triangular load with the maximum intensity at the center. Understanding these loading conditions is essential in identifying critical bending points in beams.

**Explanation:** The maximum shear force induced in a simply supported beam subjected to a point load of 4 KN at the center of the beam and a span of 4 m is 2 KN. This calculation helps determine the critical points of shear force distribution in the beam.

**Explanation:** If the deflection of a beam is y, all the following statements are correct: θ = dy/dx, dθ/dx = d²y/dx², and M = EI/R. These relationships are fundamental in understanding the behavior of beams under various loading conditions.

^{3}y/dx²

**Explanation:** If y is the deflection of the beam, then the shear force is represented by d^{3}y/dx². This relationship helps in understanding the connection between the beam’s deflection and the induced shear force.

**Explanation:** The relation between deflection (y) and bending moment (M) is given by the equation M =-EI(d²y/dx²). This equation describes the relationship between the bending moment and the curvature of the beam.

**Explanation:** The relation between the radius of curvature (R), bending moment (M), and flexural rigidity (EI) is described by the equation M = EI/R. This equation helps in understanding the interplay between these parameters in bending situations.

**Explanation:** In simple bending theory, the assumption that a plane section before bending remains plane after bending implies that stress is proportional to strain at all sections. This assumption simplifies the analysis of bending in beams.

**Explanation:** Along the neutral axis of a simply supported beam, the fibers do not undergo any strain. This characteristic is essential in understanding the distribution of stresses and strains within the beam’s cross-section.

**Explanation:** The simple bending equation is given by the expression M/I = σ/y = E/R. This equation helps in calculating the bending stress, the curvature of the beam, and the Young’s modulus of the material.

**Explanation:** Maximum bending moment occurs where the shear force changes sign. Understanding this characteristic is crucial in identifying critical points of bending in beams under various loading conditions.

**Explanation:** In a beam where the shear force is maximum, the bending moment will be zero. This relationship between shear force and bending moment is a fundamental characteristic in beam analysis.

**Explanation:** The shape of the bending moment diagram for a simply supported beam having a point load at the center is triangular. Understanding the shape of the bending moment diagram helps in visualizing the distribution of moments along the beam.

**Explanation:** The bending moment diagram of a simply supported beam having a uniformly distributed load is parabolic. Understanding the shape of the bending moment diagram helps in analyzing the distribution of moments along the beam.

**Explanation:** The variation of the bending moment in the portion of the beam carrying a linearly varying load is cubic. Understanding this variation helps in calculating the critical bending moments induced by such loading conditions.

**Explanation:** The variation of the bending moment in the segment of a beam where the load is uniformly distributed is parabolic. Understanding this variation helps in analyzing the distribution of moments along the beam.

**Explanation:** The bending moment diagram for a cantilever beam subjected to a moment at the end of the beam would be rectangular. Understanding the shape of the bending moment diagram helps in visualizing the distribution of moments along the beam.

**Explanation:** In a beam simply supported at ends and subjected to a load, the maximum bending moment is located where the shear force is zero. Understanding this characteristic helps in identifying critical bending points in the beam.

**Explanation:** Point of contraflexure is a point where the bending moment changes sign. Identifying the point of contraflexure is crucial in understanding the variation of bending moments along the beam.

**Explanation:** In a continuous beam, the point where the bending moment changes sign is called the point of inflection. Understanding this point is important in analyzing the structural behavior of the beam.

**Explanation:** The point of contraflexure occurs in an overhanging beam. Understanding this characteristic is essential in analyzing the structural behavior and critical points of bending in such beams.

**Explanation:** In a fixed beam, the points of contraflexure for a UDL load, a concentrated load, or a moment applied load are two. Understanding the points of contraflexure is crucial in analyzing the bending behavior of fixed beams.

**Explanation:** In the case of a fixed beam loaded at a point at its center, the number of points at which the bending moment is zero is two. Understanding this characteristic is crucial in analyzing the behavior of fixed beams under various loading conditions.

**Explanation:** The maximum bending moment caused by a moving load on a simply supported beam is under the load. Understanding this characteristic helps in identifying critical points of bending induced by moving loads.

**Explanation:** The maximum bending moment caused by a moving load on a fixed-end beam occurs at the support. Understanding this characteristic helps in analyzing the critical points of bending induced by moving loads.

**Explanation:** When a cantilever beam carries a uniformly distributed load over its entire length, the shape of the shear force diagram is triangular, while the shape of the bending moment diagram is a quadratic parabola.

**Explanation:** In the segment of a beam where no external load is present, the variation of the bending moment is linear. This characteristic helps in understanding the behavior of beams under different loading conditions.

**Explanation:** The critical bending moment caused in a fixed end beam loaded with a uniformly distributed load throughout the span is given by the expression M = WL/12. Understanding this critical bending moment is essential in analyzing the structural behavior of fixed end beams.

**Explanation:** The maximum bending moment caused by a large number of equally spaced identical loads on a simply supported beam is given by the expression WL/8. Understanding this maximum bending moment is crucial in designing beams to withstand specific loads.

**Explanation:** The maximum bending moment caused by a moment M applied at a distance ‘a’ from one end on a simply supported beam is simply equal to the applied moment M. Understanding this characteristic helps in analyzing the effects of applied moments on beams.

^{2}

^{3}

**Explanation:** For a beam of uniform strength with a constant depth, the width will vary in proportion to the bending moment. Understanding this relationship is essential in designing beams with uniform strength.

^{2}/12

**Explanation:** In a simply supported beam with a triangular load, the maximum bending moment is given by the expression WL^{2}/12. Understanding this maximum bending moment helps in determining the critical points of stress and deformation in the beam.

^{3}/ 8EI

^{3}/ 48EI

^{3}/ 48EI

**Explanation:** The maximum deflection of a simply supported beam subjected to a concentrated load at the mid-point is given by the expression wL^{3} / 48EI. Understanding this maximum deflection is crucial in designing beams to ensure structural integrity.

**Explanation:** In a simply supported beam with a point load at the center, the maximum bending moment induced in the beam is given by the expression WL/4. Understanding this maximum bending moment is essential in determining the critical points of stress in the beam.

**Explanation:** In a simply supported beam carrying a load varying uniformly from zero at the left end to the maximum at the right end, the maximum bending moment occurs at a distance of 1/√3 from the left end. Understanding this characteristic helps in analyzing the critical points of stress and deformation in the beam.

**Explanation:** The load carrying capacity of a fixed beam is greater than that of a simply supported beam and a cantilever beam. Understanding this characteristic is crucial in designing beams for specific load requirements.

**Explanation:** A determinate beam can be analyzed with the help of three equations of statics. Understanding this analysis method is crucial in determining the internal forces and deformations in determinate beams.

**Explanation:** A beam fixed at both ends with a central load W in the middle will have zero bending moment at two places. Understanding this characteristic is essential in analyzing the internal forces and deformations in fixed beams.

**Explanation:** The maximum bending moment caused on a simply supported beam subjected to two equal concentrated loads spaced at an equal distance over the span is given by the expression WL/6. Understanding this maximum bending moment is crucial in designing beams to withstand specific loading conditions.

**Explanation:** A beam is said to be of uniform strength if the bending stress is the same throughout the beam. Understanding this characteristic is essential in designing beams for uniform loading conditions.

**Explanation:** A section of a beam is said to be in pure bending if it is subjected to a constant bending moment and zero shear force. Understanding this characteristic is crucial in analyzing the structural behavior of beams under different loading conditions.

**Explanation:** The maximum deflection of a beam occurs at the location where the slope is zero. Understanding this characteristic is essential in analyzing the critical points of deformation in beams.

**Explanation:** The slope of an elastic curve at the point of contraflexture need not be equal to zero. Understanding this characteristic is crucial in analyzing the deformations and critical points in beams.

**Explanation:** If the length of a simply supported beam carrying a concentrated load at the center is doubled, the deflection at the center will become eight times. Understanding this relationship is crucial in analyzing the effects of beam length on deflection.

^{3}/ 8EI

^{2}/ 5EI

^{3}/ 3EI

^{3}/ 2EI

**Explanation:** The maximum deflection in a cantilever beam carrying a concentrated load ‘w’ at the free end is given by the expression WL^{3} / 3EI. Understanding this maximum deflection is crucial in designing and analyzing cantilever beams under specific loading conditions.

^{3}/ 8EI

^{3}/ 5EI

^{3}/ 3EI

^{3}/ 2EI

**Explanation:** The maximum deflection in a cantilever beam carrying a uniformly distributed load over spans is given by the expression WL^{3} / 8EI. Understanding this maximum deflection is crucial in designing and analyzing cantilever beams under specific loading conditions.

^{3}/ 8EI

^{3}/ 48EI

^{3}/ 48EI

**Explanation:** The maximum deflection of a simply supported beam subjected to a concentrated load at the midpoint is given by the expression WL^{3} / 48EI. Understanding this maximum deflection is crucial in designing beams to ensure structural integrity.

^{3}/ 8EI

^{3}/ 48EI

^{3}/ 48EI

^{3}/ 384EI

**Explanation:** The maximum deflection of a simply supported beam subjected to a uniformly distributed load over the span is given by the expression 5WL^{3} / 384EI. Understanding this maximum deflection is crucial in designing beams to withstand specific loading conditions.

**Explanation:** The diagram showing the variation of bending moment along the span of the beam is called the Bending Moment Diagram (BMD). Understanding this diagram is essential in analyzing the critical points of stress and deformation in beams.

**Explanation:** A diagram that shows the variation of axial force along the span of the beam is called the thrust diagram. Understanding this diagram is crucial in analyzing the critical points of axial force in beams.

**Explanation:** A beam of uniform strength will have the same bending stress at every cross-section. Understanding this characteristic is crucial in designing beams for uniform loading conditions.

**Explanation:** If a beam is loaded transversely, the maximum compressive stress develops on the top fiber. Understanding this characteristic is crucial in analyzing the critical points of stress in beams.

**Explanation:** In a beam, the neutral plane does not change during deformation. Understanding this characteristic is crucial in analyzing the behavior of beams under different loading conditions.

**Explanation:** Longitudinal cracks observed in timber beams are due to shear failure between the layers. Understanding this characteristic is crucial in analyzing the failure modes of timber beams.

^{4}y/dx

^{4}) at any section for a beam is equal to

**Explanation:** The expression EI(d^{4}y/dx^{4}) at any section for a beam is equal to the load intensity at the section. Understanding this expression is crucial in analyzing the internal forces and deformations in beams.

**Explanation:** The slope of the curve of the Bending Moment (B.M.) diagram at any section will be equal to the ordinate of the shear force diagram at that section. Understanding this relationship is crucial in analyzing the critical points of stress and deformation in beams.

**Explanation:** The slope of the curve of the Shear Force (S.F.) diagram at any section will be equal to the ordinate of the loading diagram at that section. Understanding this relationship is crucial in analyzing the internal forces in beams.

**Explanation:** The difference between bending moment (BM) values at any two sections will be equal to the area of the Shear Force (SF) diagram between those two sections. Understanding this relationship is crucial in analyzing the internal forces and deformations in beams.

**Explanation:** The difference between Shear Force (SF) values at any two sections will be equal to the area of the loading diagram between those two sections. Understanding this relationship is crucial in analyzing the internal forces in beams.

**Explanation:** The bending moment in a cable carrying a system of loads will be zero at all points. Understanding this characteristic is crucial in analyzing the behavior of cables under different loading conditions.

^{2}is subjected to a force of P N. It is L mm long and of Young’s Modulus, E N/mm

^{2}. The strain will be

^{2})

**Explanation:** A member with a cross section of a mm^{2} is subjected to a force of P N. It is L mm long and of Young’s Modulus, E N/mm^{2}. The strain will be P/AE (mm/mm). Understanding this relationship is crucial in analyzing the deformation of materials under different loading conditions.

**Explanation:** The elongation of a bar can be found using the formula PI/AE. Understanding this relationship is crucial in analyzing the deformation of bars under different loading conditions.

**Explanation:** If α is the coefficient of linear expansion and T is the rise in temperature, then the thermal stress is given by ETα. Understanding this relationship is crucial in analyzing the effects of temperature on material stress.

**Explanation:** Thrust is induced in the case of inclined load. Understanding this characteristic is crucial in analyzing the forces acting on different structural elements.

**Explanation:** The diagram showing the variation of axial load along the span of the beam is called the thrust diagram. Understanding this diagram is crucial in analyzing the critical points of axial force in beams.

**Explanation:** In a simply supported beam carrying a uniformly distributed load (UDL), there are no points of contraflexure. Understanding the absence of points of contraflexure is crucial in analyzing the bending behavior of the beam under UDL.

**Explanation:** The bending moment in a cantilever beam can be calculated using the formula BM = (wL^{2})/2, where w is the load per unit length and L is the span of the beam. Plugging in the given values, we get BM = (4*1.8^{2})/2 = 6.48 kg-m.

**Explanation:** At a point where the shear force (SF) is zero, the bending moment (BM) can be either maximum or minimum, depending on the loading conditions and the type of beam. Understanding this relationship is crucial in analyzing the critical points of stress and deformation in beams.

**Explanation:** The rate of change of shear force along the span of a beam is called the intensity of the load. Understanding this concept is crucial in analyzing the internal forces and deformations in beams.

**Explanation:** The I-section is the most efficient in carrying bending moments due to its high moment of inertia, which helps in distributing the stresses effectively. Understanding the efficiency of different sections is crucial in designing beams for specific loading conditions.

**Explanation:** The value of the thrust can be calculated using the formula P*sin(θ), where P is the force magnitude and θ is the angle of inclination with the vertical. Plugging in the given values, we get Thrust = 5*sin(30°) = 2.5 kN.

**Explanation:** At the point of application of a concentrated load on a beam, there is a sudden change in the slope of the bending moment (BM) diagram. Understanding this characteristic is crucial in analyzing the critical points of stress and deformation in beams.

**Explanation:** The section modulus of a rectangular section is directly proportional to the area of the section. Understanding this relationship is crucial in analyzing the strength and stiffness of different beam sections.

**Explanation:** The maximum bending moment induced in a cantilever beam can be calculated using the formula M = P*(L-a), where P is the load, L is the length of the beam, and a is the distance of the load from the fixed end. Plugging in the given values, we get M = 10*(10-3) = 70 kN-m.

**Explanation:** The maximum shear force induced in a cantilever beam can be calculated using the formula SF = P, where P is the load. Plugging in the given value, we get SF = 10 kN.

**Explanation:** The reaction at end A of the beam shown is zero since there is no external load applied at that point. Understanding the distribution of reactions is crucial in analyzing the equilibrium of beams under different loading conditions.

**Explanation:** The bending moment at the center of the beam can be calculated using the formula M = (wL^{2})/8, where w is the load per unit length and L is the span of the beam. Plugging in the given values, we get M = (10*4^{2})/8 = 10 kN-m. The maximum bending moment occurs at the supports and can be calculated using the formula M = (wL^{2})/12, which gives M = (10*4^{2})/12 = 12 kN-m.

**Explanation:** The bending moment at the fixed end of the cantilever beam can be calculated using the formula M = P*a, where P is the load and a is the distance of the load from the fixed end. Plugging in the given values, we get M = 10*3 = 30 kN-m. The bending moment at the free end is zero since there is no external load applied at that point.

**Explanation:** The maximum bending moment in a simply supported beam occurs when the UDL is applied at the midspan. Understanding this characteristic is crucial in analyzing the critical points of stress and deformation in simply supported beams.

**Explanation:** The maximum bending moment produced in a simply supported beam subjected to a UDL can be calculated using the formula M = (wL^{2})/8, where w is the load per unit length and L is the span of the beam. Plugging in the given values, we get M = (10*4^{2})/8 = 20 kN-m.

**Explanation:** A long vertical member subjected to an axial compressive load is called a column. Columns are crucial structural elements used to support and transfer loads vertically, and their behavior is essential in structural design and analysis.

**Explanation:** A column that fails primarily due to direct stress is called a short column. Understanding the failure behavior of different types of columns is crucial in structural engineering and design.

**Explanation:** A column that fails primarily due to buckling is known as a long column. Understanding the failure behavior of different types of columns is crucial in structural engineering and design.

**Explanation:** The buckling load for a given column depends on both the length of the column and its least lateral dimension. Understanding this relationship is crucial in determining the stability and load-carrying capacity of columns.

**Explanation:** The effective length of a column with both ends hinged is simply the length of the column itself (L). Understanding the effective length of columns is crucial in analyzing their behavior and stability under different loading conditions.

**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.

**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.

**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.

**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.

^{2}

^{2}EI/4L

^{2}

^{2}EI/L

^{2}

^{2}EI/L

^{2}

**Explanation:** The crippling load for a column with both ends hinged is given by π^{2}EI/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.

^{2}EI/l

^{2}

^{2}EI/4l

^{2}

^{2}EI/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^{2}EI/l^{2}. This formula is used to calculate the critical load that causes buckling in the column under compressive forces.

^{2}EI/4l

^{2}

^{2}EI/l

^{2}

^{2}EI/l

^{2}

^{2}EI/l

**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^{2}EI/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.

**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.

**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.

**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.

**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.

**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.

**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.

^{2}& effective length =3.0m

**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.

**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.

**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.

**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.

**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.

**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.

**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.

^{2}/2

^{2}/4

^{2}/8

^{2}/16

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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).

**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.

^{3}/12

^{2}/24

^{2}d

^{2}/12

^{3}/24

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.