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1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be?
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1. Beam A - B - C is supported by a hinge at A and a vertical spring o...
Solution:
Given data:
- Stiffness of the vertical spring at B, k = 25 N/m*m
- Distance AB = 2 m
- Distance BC = 3 m
- Vertical load at C = 100 N
To find: Vertical deflection at point C
Analysis:
- As the beam is supported by a hinge at A, the reaction at A will be vertical.
- Let the reaction at A be RA.
- Let the deflection at point B be δB and the deflection at point C be δC.
- As the vertical spring is present at point B, the force in the spring will be k * δB.
- As the beam is in equilibrium, the sum of vertical forces at any point of the beam will be zero.
∑Fy = 0
RA - 100 N - k * δB = 0
- The moment about point A will be zero as there are no external moments acting on the beam.
∑Ma = 0
RA * 2 m - 100 N * 3 m - k * δB * 1 m = 0
RA = 25 N
- The deflection at point C can be found by considering the force balance at point B.
∑Fy = 0
k * δB - 100 N - k * δC = 0
δC = (k * δB - 100 N) / k
δC = (25 N/m*m * δB - 100 N) / 25 N/m*m
δC = δB - 4 mm
- Hence, the vertical deflection at point C is δC = δB - 4 mm.
Conclusion:
- The vertical deflection at point C is δC = δB - 4 mm.
- The deflection at point B can be found by considering the force balance at point A.
- The reaction at A is found to be RA = 25 N.
Given data:
- Stiffness of the vertical spring at B, k = 25 N/m*m
- Distance AB = 2 m
- Distance BC = 3 m
- Vertical load at C = 100 N
To find: Vertical deflection at point C
Analysis:
- As the beam is supported by a hinge at A, the reaction at A will be vertical.
- Let the reaction at A be RA.
- Let the deflection at point B be δB and the deflection at point C be δC.
- As the vertical spring is present at point B, the force in the spring will be k * δB.
- As the beam is in equilibrium, the sum of vertical forces at any point of the beam will be zero.
∑Fy = 0
RA - 100 N - k * δB = 0
- The moment about point A will be zero as there are no external moments acting on the beam.
∑Ma = 0
RA * 2 m - 100 N * 3 m - k * δB * 1 m = 0
RA = 25 N
- The deflection at point C can be found by considering the force balance at point B.
∑Fy = 0
k * δB - 100 N - k * δC = 0
δC = (k * δB - 100 N) / k
δC = (25 N/m*m * δB - 100 N) / 25 N/m*m
δC = δB - 4 mm
- Hence, the vertical deflection at point C is δC = δB - 4 mm.
Conclusion:
- The vertical deflection at point C is δC = δB - 4 mm.
- The deflection at point B can be found by considering the force balance at point A.
- The reaction at A is found to be RA = 25 N.
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1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be?
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1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be? 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 1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be?.
1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be? 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 1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. Beam A - B - C is supported by a hinge at A and a vertical spring of stiffness 25N / m * m at B. AB = 2 m and BC = 3m . If a vertical load of 100 N is applied at C, vertical deflection at C will be?.
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