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Which of the following statement is(are) correct?
- a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.
- b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.
- c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.
- d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axis
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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Which of the following statement is(are) correct?a)Under bending the c...
Under bending the curvature of a beam is the reciprocal of its radius of curvature. The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram. A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple. At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axis
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Which of the following statement is(are) correct?a)Under bending the c...
Statement a: Under bending, the curvature of a beam is the reciprocal of its radius of curvature.
Explanation:
When a beam is subjected to bending, it undergoes deflection and develops a curvature. The curvature is a measure of how much the beam deviates from being straight. The radius of curvature is defined as the radius of the circular arc that approximates the shape of the beam at a particular point.
The statement is correct because the curvature of a beam is indeed the reciprocal of its radius of curvature. This means that as the radius of curvature decreases (i.e., the beam becomes more curved), the curvature increases. Similarly, as the radius of curvature increases (i.e., the beam becomes less curved), the curvature decreases.
Statement b: The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.
Explanation:
When a beam is subjected to bending, the bending moment varies along its length. The bending moment diagram represents the variation of bending moment along the beam, while the shear diagram represents the variation of shear force along the beam.
The slope of a graph represents the rate of change of the variable with respect to the horizontal axis. In this case, the slope of the bending moment diagram represents the rate of change of bending moment along the beam.
The statement is correct because the slope at any point on the bending moment diagram is indeed given by the shear at the corresponding point on the shear diagram. This can be mathematically expressed as:
Slope of bending moment diagram = Shear at corresponding point on shear diagram
Statement c: A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.
Explanation:
A couple is a system of forces with equal magnitudes, parallel lines of action, and opposite sense. When a concentrated couple is applied to a beam, it creates a moment that tends to rotate the beam.
The statement is correct because a concentrated couple applied to a beam at any section will indeed cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple. This abrupt change in bending moment is due to the introduction of a new moment that is added to or subtracted from the existing bending moment at that section.
Statement d: At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axis.
Explanation:
When a beam is subjected to bending, the internal stresses develop in the beam. These stresses are known as flexural stresses or normal stresses and they vary across the beam's cross-section.
The statement is correct because at any section of the beam, the flexural stress or normal stress will indeed be maximum at the surface farthest from the neutral axis. This is because the fibers located farther from the neutral axis experience a greater distance from the centroid of the cross-section, resulting in a greater moment arm and therefore higher stress. The stress decreases as we move closer to the neutral axis.
In conclusion, all the given statements (a, b, c, and d) are correct.
Explanation:
When a beam is subjected to bending, it undergoes deflection and develops a curvature. The curvature is a measure of how much the beam deviates from being straight. The radius of curvature is defined as the radius of the circular arc that approximates the shape of the beam at a particular point.
The statement is correct because the curvature of a beam is indeed the reciprocal of its radius of curvature. This means that as the radius of curvature decreases (i.e., the beam becomes more curved), the curvature increases. Similarly, as the radius of curvature increases (i.e., the beam becomes less curved), the curvature decreases.
Statement b: The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.
Explanation:
When a beam is subjected to bending, the bending moment varies along its length. The bending moment diagram represents the variation of bending moment along the beam, while the shear diagram represents the variation of shear force along the beam.
The slope of a graph represents the rate of change of the variable with respect to the horizontal axis. In this case, the slope of the bending moment diagram represents the rate of change of bending moment along the beam.
The statement is correct because the slope at any point on the bending moment diagram is indeed given by the shear at the corresponding point on the shear diagram. This can be mathematically expressed as:
Slope of bending moment diagram = Shear at corresponding point on shear diagram
Statement c: A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.
Explanation:
A couple is a system of forces with equal magnitudes, parallel lines of action, and opposite sense. When a concentrated couple is applied to a beam, it creates a moment that tends to rotate the beam.
The statement is correct because a concentrated couple applied to a beam at any section will indeed cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple. This abrupt change in bending moment is due to the introduction of a new moment that is added to or subtracted from the existing bending moment at that section.
Statement d: At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axis.
Explanation:
When a beam is subjected to bending, the internal stresses develop in the beam. These stresses are known as flexural stresses or normal stresses and they vary across the beam's cross-section.
The statement is correct because at any section of the beam, the flexural stress or normal stress will indeed be maximum at the surface farthest from the neutral axis. This is because the fibers located farther from the neutral axis experience a greater distance from the centroid of the cross-section, resulting in a greater moment arm and therefore higher stress. The stress decreases as we move closer to the neutral axis.
In conclusion, all the given statements (a, b, c, and d) are correct.
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Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice Which of the following statement is(are) correct?a)Under bending the curvature of a beam is the reciprocal of its radius of curvature.b)The slope at any point on the bending moment diagram is given by the shear at the corresponding point on the shear diagram.c)A concentrated couple applied to a beam at any section will cause the bending moment at the section to change abruptly by an amount equal to the moment of the couple.d)At any section of the beam, the flexural stress, or normal stress, will be maximum (have the greatest magnitude) at the surface farthest from the neutral axisCorrect answer is option 'A,B,C,D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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