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A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1?
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A rigid beam ABCD is hinged at D and supported by two springs at A and...
Solution:
To find the ratio of forces of spring at A and B, we need to analyze the equilibrium conditions of the beam.
Equilibrium of the beam:
Since the beam is rigid, it will remain in equilibrium when the sum of all the forces acting on it is zero and the sum of all the moments about any point is zero.
Forces acting on the beam:
1. Vertical load at C (downward)
2. Force exerted by the spring at A (upward)
3. Force exerted by the spring at B (upward)
Moments about point D:
Since the beam is hinged at D, it will not experience any moment about this point.
Equilibrium equations:
1. Sum of vertical forces = 0
2. Sum of moments about point D = 0
Analysis:
Let's assume the force exerted by the spring at A is F_A and the force exerted by the spring at B is F_B.
1. Sum of vertical forces:
F_A + F_B - Load at C = 0
F_A + F_B = Load at C
2. Sum of moments about point D:
(F_A)(AB) - (F_B)(BC) = 0
F_A * 2 - F_B = 0
F_A = F_B/2
Substituting the value of F_A in the first equation:
F_B/2 + F_B = Load at C
3F_B/2 = Load at C
F_B = 2/3 * Load at C
Ratio of forces:
Now, we can find the ratio of forces of spring at A and B by dividing F_A by F_B.
F_A/F_B = (F_B/2) / F_B = 1/2
Therefore, the ratio of forces of spring at A to that of spring at B is 1/2 or 0.5.
Hence, the correct option is (d) 1.
To find the ratio of forces of spring at A and B, we need to analyze the equilibrium conditions of the beam.
Equilibrium of the beam:
Since the beam is rigid, it will remain in equilibrium when the sum of all the forces acting on it is zero and the sum of all the moments about any point is zero.
Forces acting on the beam:
1. Vertical load at C (downward)
2. Force exerted by the spring at A (upward)
3. Force exerted by the spring at B (upward)
Moments about point D:
Since the beam is hinged at D, it will not experience any moment about this point.
Equilibrium equations:
1. Sum of vertical forces = 0
2. Sum of moments about point D = 0
Analysis:
Let's assume the force exerted by the spring at A is F_A and the force exerted by the spring at B is F_B.
1. Sum of vertical forces:
F_A + F_B - Load at C = 0
F_A + F_B = Load at C
2. Sum of moments about point D:
(F_A)(AB) - (F_B)(BC) = 0
F_A * 2 - F_B = 0
F_A = F_B/2
Substituting the value of F_A in the first equation:
F_B/2 + F_B = Load at C
3F_B/2 = Load at C
F_B = 2/3 * Load at C
Ratio of forces:
Now, we can find the ratio of forces of spring at A and B by dividing F_A by F_B.
F_A/F_B = (F_B/2) / F_B = 1/2
Therefore, the ratio of forces of spring at A to that of spring at B is 1/2 or 0.5.
Hence, the correct option is (d) 1.
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A rigid beam ABCD is hinged at D and supported by two springs at A and...
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A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1?
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A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1? 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 A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1?.
A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1? 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 A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in figure. The beam carries a vertical load at C, stiffness of spring at A is 2K and that of B is K. what will be the ratio of forces of spring at A and that of spring at B. Options (a) 4, (b) 3, (c) 2, (d) 1?.
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