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Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?
- a)ML/EI
- b)ML/2EI
- c)M2L/EI
- d)M2L/2EI
Correct answer is option 'D'. Can you explain this answer?
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To calculate the strain energy stored in a beam under constant bending moment, we can use the formula:
Strain energy = (M^2 * L) / (2 * EI)
Where:
- M is the bending moment
- L is the length of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam's cross-section
Let's break down the formula and explain each term:
1. Bending Moment (M):
The bending moment is the internal moment that causes bending in the beam. It is a measure of the intensity of the bending load applied to the beam. In this case, the bending moment is assumed to be constant throughout the length of the beam.
2. Length of the Beam (L):
The length of the beam is simply the distance between the points where the bending moment is acting. It is an important parameter in calculating the strain energy stored in the beam.
3. Modulus of Elasticity (E):
The modulus of elasticity is a measure of the stiffness of the material. It describes how a material deforms under stress. It is a material property and is specific to each material.
4. Moment of Inertia (I):
The moment of inertia is a measure of the beam's resistance to bending. It depends on the shape and dimensions of the beam's cross-section. A beam with a higher moment of inertia will be stiffer and will store more strain energy.
5. Strain Energy:
Strain energy is the potential energy stored in a deformed material. In the case of a beam subjected to bending, the strain energy is stored in the form of internal stresses and deformations within the beam.
The formula for strain energy in a beam under constant bending moment (D) is derived from the principles of beam theory and can be derived using calculus and the concept of work done. The derivation is beyond the scope of this explanation.
In summary, the correct expression for strain energy stored in a beam of length L and uniform cross-section, subjected to constant bending moment M, is given by option D: (M^2 * L) / (2 * EI).
Strain energy = (M^2 * L) / (2 * EI)
Where:
- M is the bending moment
- L is the length of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam's cross-section
Let's break down the formula and explain each term:
1. Bending Moment (M):
The bending moment is the internal moment that causes bending in the beam. It is a measure of the intensity of the bending load applied to the beam. In this case, the bending moment is assumed to be constant throughout the length of the beam.
2. Length of the Beam (L):
The length of the beam is simply the distance between the points where the bending moment is acting. It is an important parameter in calculating the strain energy stored in the beam.
3. Modulus of Elasticity (E):
The modulus of elasticity is a measure of the stiffness of the material. It describes how a material deforms under stress. It is a material property and is specific to each material.
4. Moment of Inertia (I):
The moment of inertia is a measure of the beam's resistance to bending. It depends on the shape and dimensions of the beam's cross-section. A beam with a higher moment of inertia will be stiffer and will store more strain energy.
5. Strain Energy:
Strain energy is the potential energy stored in a deformed material. In the case of a beam subjected to bending, the strain energy is stored in the form of internal stresses and deformations within the beam.
The formula for strain energy in a beam under constant bending moment (D) is derived from the principles of beam theory and can be derived using calculus and the concept of work done. The derivation is beyond the scope of this explanation.
In summary, the correct expression for strain energy stored in a beam of length L and uniform cross-section, subjected to constant bending moment M, is given by option D: (M^2 * L) / (2 * EI).
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Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer?.
Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?a)ML/EIb)ML/2EIc)M2L/EId)M2L/2EICorrect answer is option 'D'. Can you explain this answer?.
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