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A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end?
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A cantilever beam of span L flexural rigidity E1 is subjected to a hog...
Slope and Deflection of a Cantilever Beam
Given:
- Span of the cantilever beam = L
- Flexural rigidity = E1
- Bending moment at the free end = M
Slope at the Free End:
- The slope at the free end of a cantilever beam subjected to a hogging bending moment can be calculated using the equation:
θ = -M*L^2 / (2*E1)
Deflection at the Free End:
- The deflection at the free end of a cantilever beam can be calculated using the equation:
δ = -M*L^3 / (3*E1)
Explanation:
- The negative sign in the slope and deflection equations indicates the direction of the deflection and slope.
- The deflection and slope are directly proportional to the bending moment and the cube of the span length.
- The flexural rigidity of the beam also plays a crucial role in determining the slope and deflection.
Conclusion:
- By applying the above equations, you can calculate the slope and deflection at the free end of a cantilever beam subjected to a hogging bending moment. Remember to consider the units of the values provided to ensure accurate results.
Given:
- Span of the cantilever beam = L
- Flexural rigidity = E1
- Bending moment at the free end = M
Slope at the Free End:
- The slope at the free end of a cantilever beam subjected to a hogging bending moment can be calculated using the equation:
θ = -M*L^2 / (2*E1)
Deflection at the Free End:
- The deflection at the free end of a cantilever beam can be calculated using the equation:
δ = -M*L^3 / (3*E1)
Explanation:
- The negative sign in the slope and deflection equations indicates the direction of the deflection and slope.
- The deflection and slope are directly proportional to the bending moment and the cube of the span length.
- The flexural rigidity of the beam also plays a crucial role in determining the slope and deflection.
Conclusion:
- By applying the above equations, you can calculate the slope and deflection at the free end of a cantilever beam subjected to a hogging bending moment. Remember to consider the units of the values provided to ensure accurate results.
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A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end?
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A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end?.
A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of span L flexural rigidity E1 is subjected to a hogging bending moment M at this free end. Calculate the slope and deflection at this free end?.
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