**Correct Answer: web**

**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.

**Correct Answer: arc of a circle**

**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.

**Correct Answer: circular arc**

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

**Correct Answer: parabola**

**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.

**Correct Answer: total shear stress at a point**

**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.

**Correct Answer: the shear force in that direction**

**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.

**Correct Answer: the point about which the moment of shear flow is zero**

**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.

**Correct Answer: at the C.G. of the section**

**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.

**Correct Answer: V = dM/dx**

**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.

**Correct Answer: a couple at mid span**

**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.

**Correct Answer: V = EI(d^3y/dx^3)**

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

**Correct Answer: one**

**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.

**Correct Answer: zero**

**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.

**Correct Answer: 4 KN-m**

**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.

**Correct Answer: center**

**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.

**Correct Answer: 4 t-m**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: 2 KN**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: d^3y/dx²**

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

**Correct Answer: M =-EI(d²y/dx²**

**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.

**Correct Answer: M = EI/R**

**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.

**Correct Answer: stress is proportional to strain at all sections**

**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.

**Correct Answer: fibers do not undergo strain**

**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.

**Correct Answer: M/I = σ/y = E/R**

**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.

**Correct Answer: shear force changes sign**

**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.

**Correct Answer: zero**

**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.

**Correct Answer: triangular**

**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.

**Correct Answer: parabolic**

**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.

**Correct Answer: cubic**

**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.

**Correct Answer: parabolic**

**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.

**Correct Answer: rectangle**

**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.

**Correct Answer: shear force is zero**

**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.

**Correct Answer: changes sign**

**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.

**Correct Answer: point of inflection**

**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.

**Correct Answer: overhanging only**

**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.

**Correct Answer: all of the above**

**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.

**Correct Answer: 2**

**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.

**Correct Answer: under the load**

**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.

**Correct Answer: at the support**

**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.

**Correct Answer: triangle and quadratic parabola**

**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.

**Correct Answer: linear**

**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.

**Correct Answer: M = WL/12**

**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.

**Correct Answer: WL/8**

**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.

**Correct Answer: M**

**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.

**Correct Answer: bending moment**

**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.

**Correct Answer: WL^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.

**Correct Answer: wL^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.

**Correct Answer: WL/4**

**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.

**Correct Answer: 1/√3 from the left end**

**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.

**Correct Answer: greater than simply supported beam and cantilever 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.

**Correct Answer: three equations of statics**

**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.

**Correct Answer: at two places**

**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.

**Correct Answer: WL/6**

**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.

**Correct Answer: bending stress is the same throughout the beam**

**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.

**Correct Answer: constant bending moment and zero shear force**

**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.

**Correct Answer: zero slope location**

**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.

**Correct Answer: need not be equal to zero**

**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.

**Correct Answer: eight times**

**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.

**Correct Answer: WL^3 / 3EI**

**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.

**Correct Answer: WL^3 / 8EI**

**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.

**Correct Answer: WL^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.

**Correct Answer: 5WL^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.

**Correct Answer: BMD**

**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.

**Correct Answer: thrust diagram**

**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.

**Correct Answer: bending stress**

**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.

**Correct Answer: top fiber**

**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.

**Correct Answer: does not change during deformation**

**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.

**Correct Answer: shear failure between the layers**

**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.

**Correct Answer: load intensity at the section**

**Explanation:** The expression EI(d^4y/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.

**Correct Answer: the ordinate of shear force diagram at that section**

**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.

**Correct Answer: the ordinate of loading diagram at that section**

**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.

**Correct Answer: the area of SF diagram between those two sections**

**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.

**Correct Answer: the area of the loading diagram between those two sections**

**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.

**Correct Answer: zero at all points**

**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.

**Correct Answer: P/AE(mm/mm)**

**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.

**Correct Answer: PI/AE**

**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.

**Correct Answer: ETα**

**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.

**Correct Answer: inclined load**

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

**Correct Answer: thrust diagram**

**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.

**Correct Answer: 0**

**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.

**Correct Answer: 6.48 kg-m**

**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.

**Correct Answer: either maximum or minimum**

**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.

**Correct Answer: intensity of load**

**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.

**Correct Answer: I-section**

**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.

**Correct Answer: 2.5 kN**

**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.

**Correct Answer: sudden change in the slope of BM**

**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.

**Correct Answer: area of the section**

**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.

**Correct Answer: 70 kN-m**

**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.

**Correct Answer: 10 kN**

**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.

**Correct Answer: zero**

**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.

**Correct Answer: 10 kN-m, 12 kN-m**

**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.

**Correct Answer: 30 kN-m, 0**

**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.

**Correct Answer: mid**

**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.

**Correct Answer: 20 kN-m**

**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.

**Correct Answer: column**

**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.

**Correct Answer: short column**

**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.

**Correct Answer: long column**

**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.

**Correct Answer: both length and least lateral dimension**

**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.

**Correct Answer: L**

**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.

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

### ▸ What topics are covered in Mechanics of Materials & Structures MCQs for Civil Engineers?

Topics include stress and strain, bending moments, shear force, torsion, deflection, and material properties. For detailed MCQs, visit gkaim.com.

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### ▸ What is the significance of studying Mechanics of Materials in civil engineering?

Studying Mechanics of Materials is crucial for understanding the behavior of different materials under various loads and designing safe structures. Detailed MCQs on this topic can be found at gkaim.com.

### ▸ How can I improve my understanding of structural analysis through MCQs?

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### ▸ Are there mock tests available for Mechanics of Materials & Structures?

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

Common questions include those on stress and strain calculations, bending moment diagrams, shear force diagrams, and deflection of beams. Find detailed MCQs at gkaim.com.

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### ▸ How important is the study of deflection in Mechanics of Materials?

The study of deflection is crucial for ensuring the stability and safety of structures. Detailed MCQs on deflection and other key topics are available at gkaim.com.