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Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?
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Determine slope and deflection at D for the beam and loading shown in ...
Given:
- The beam has a length of L
- The beam has a rectangular cross-section with width b and height d
- The beam is simply supported at points A and C
- The beam is subjected to a uniformly distributed load w over its entire length
To find:
- The slope at point D
- The deflection at point D
Assumptions:
- The beam is made of a homogeneous and isotropic material
- The beam is in the linear elastic range
- The beam is loaded within its elastic limit
- The beam has a constant flexural rigidity (EI) along its length
Procedure:
1. Determine the reaction forces at points A and C:
- Since the beam is simply supported at points A and C, the vertical reaction forces at these points will be equal to half of the total load acting on the beam.
- The total load acting on the beam is equal to the product of the uniformly distributed load w and the length of the beam L.
- Therefore, the reaction forces at points A and C can be calculated as:
- RA = RC = (w * L) / 2
2. Calculate the bending moment at point D:
- The bending moment at point D can be determined by considering the equilibrium of moments about point D.
- Since the beam is symmetrically loaded and supported, the bending moment at point D will be zero.
3. Determine the slope at point D:
- The slope at point D can be calculated by considering the equation for the slope of a beam subjected to a bending moment.
- The slope at any point along the beam can be given by the equation: θ = M(x) / (EI)
- Since the bending moment at point D is zero, the slope at point D will also be zero.
4. Calculate the deflection at point D:
- The deflection at point D can be determined by integrating the equation for the slope of the beam.
- The equation for the deflection of the beam can be given by: δ = ∫(θ(x)) dx
- Since the slope at point D is zero, the deflection at point D will also be zero.
Conclusion:
- The slope at point D is zero.
- The deflection at point D is zero.
- This means that point D remains undeformed under the given loading condition.
- The flexural rigidity of the beam (EI) does not affect the slope or deflection at point D in this case.
- The beam has a length of L
- The beam has a rectangular cross-section with width b and height d
- The beam is simply supported at points A and C
- The beam is subjected to a uniformly distributed load w over its entire length
To find:
- The slope at point D
- The deflection at point D
Assumptions:
- The beam is made of a homogeneous and isotropic material
- The beam is in the linear elastic range
- The beam is loaded within its elastic limit
- The beam has a constant flexural rigidity (EI) along its length
Procedure:
1. Determine the reaction forces at points A and C:
- Since the beam is simply supported at points A and C, the vertical reaction forces at these points will be equal to half of the total load acting on the beam.
- The total load acting on the beam is equal to the product of the uniformly distributed load w and the length of the beam L.
- Therefore, the reaction forces at points A and C can be calculated as:
- RA = RC = (w * L) / 2
2. Calculate the bending moment at point D:
- The bending moment at point D can be determined by considering the equilibrium of moments about point D.
- Since the beam is symmetrically loaded and supported, the bending moment at point D will be zero.
3. Determine the slope at point D:
- The slope at point D can be calculated by considering the equation for the slope of a beam subjected to a bending moment.
- The slope at any point along the beam can be given by the equation: θ = M(x) / (EI)
- Since the bending moment at point D is zero, the slope at point D will also be zero.
4. Calculate the deflection at point D:
- The deflection at point D can be determined by integrating the equation for the slope of the beam.
- The equation for the deflection of the beam can be given by: δ = ∫(θ(x)) dx
- Since the slope at point D is zero, the deflection at point D will also be zero.
Conclusion:
- The slope at point D is zero.
- The deflection at point D is zero.
- This means that point D remains undeformed under the given loading condition.
- The flexural rigidity of the beam (EI) does not affect the slope or deflection at point D in this case.
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Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?
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Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? 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 Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?.
Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? 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 Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine slope and deflection at D for the beam and loading shown in fig.1 and take the flexural rigidity of the beam as?.
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