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A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,
- a)4
- b)2
- c)6
- d)8
Correct answer is option 'B'. Can you explain this answer?
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A simply supported beam of span 4m is subjected to a point load of 10k...
Understanding Beam Deflection
In structural engineering, the deflection of beams under load is a crucial aspect of design. The maximum slope (theta) at mid-span can be determined using the relationships established in beam theory.
Key Principles
- Simply Supported Beam: A beam supported at both ends with no moment resistance.
- Point Load: A concentrated force applied at a specific point on the beam, in this case, at mid-span.
Deflection Calculations
The formula for the maximum slope (theta) at mid-span for a simply supported beam subjected to a point load can be expressed as:
Theta = (PL^2) / (2EI)
Where:
- P = Point load
- L = Span of the beam
- E = Modulus of elasticity (constant for the same beam)
- I = Moment of inertia (also constant for the same beam)
First Loading Condition (10 kN Load)
- Load (P1) = 10 kN
- Span (L) = 4 m
Maximum slope (theta1) for the first loading condition:
Theta1 = (10 kN * (4 m)^2) / (2 * E * I)
Second Loading Condition (5 kN Load)
- Load (P2) = 5 kN
- Span (L) = 4 m
Maximum slope (theta2) for the second loading condition:
Theta2 = (5 kN * (4 m)^2) / (2 * E * I)
Ratio of Maximum Slopes
To find the ratio of the maximum slopes:
Ratio = Theta1 / Theta2 = [(10 kN * (4 m)^2) / (2 * E * I)] / [(5 kN * (4 m)^2) / (2 * E * I)]
This simplifies to:
Ratio = 10 kN / 5 kN = 2
Conclusion
The ratio of the maximum slope in the two loading conditions is 2, which corresponds to option 'B'. This shows that as the load increases, the slope of the beam also increases proportionally.
In structural engineering, the deflection of beams under load is a crucial aspect of design. The maximum slope (theta) at mid-span can be determined using the relationships established in beam theory.
Key Principles
- Simply Supported Beam: A beam supported at both ends with no moment resistance.
- Point Load: A concentrated force applied at a specific point on the beam, in this case, at mid-span.
Deflection Calculations
The formula for the maximum slope (theta) at mid-span for a simply supported beam subjected to a point load can be expressed as:
Theta = (PL^2) / (2EI)
Where:
- P = Point load
- L = Span of the beam
- E = Modulus of elasticity (constant for the same beam)
- I = Moment of inertia (also constant for the same beam)
First Loading Condition (10 kN Load)
- Load (P1) = 10 kN
- Span (L) = 4 m
Maximum slope (theta1) for the first loading condition:
Theta1 = (10 kN * (4 m)^2) / (2 * E * I)
Second Loading Condition (5 kN Load)
- Load (P2) = 5 kN
- Span (L) = 4 m
Maximum slope (theta2) for the second loading condition:
Theta2 = (5 kN * (4 m)^2) / (2 * E * I)
Ratio of Maximum Slopes
To find the ratio of the maximum slopes:
Ratio = Theta1 / Theta2 = [(10 kN * (4 m)^2) / (2 * E * I)] / [(5 kN * (4 m)^2) / (2 * E * I)]
This simplifies to:
Ratio = 10 kN / 5 kN = 2
Conclusion
The ratio of the maximum slope in the two loading conditions is 2, which corresponds to option 'B'. This shows that as the load increases, the slope of the beam also increases proportionally.
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Community Answer
A simply supported beam of span 4m is subjected to a point load of 10k...
Slope of simply supported beam (ϴ1) = W1L2/16EI
Slope of simply supported beam (ϴ2) = W2L2/16EI
ϴ1/ ϴ2 = W1/W2 = 10/5 = 2
Slope of simply supported beam (ϴ2) = W2L2/16EI
ϴ1/ ϴ2 = W1/W2 = 10/5 = 2
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A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer?
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A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? 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 simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer?.
A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? 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 simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer?.
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A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A simply supported beam of span 4m is subjected to a point load of 10kN at mid span of the beam. In another loading condition the same beam is subjected to a load of 5 KN at mid span of beam. The ratio of the maximum slope in these two loading conditions will be,a)4b)2c)6d)8Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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