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The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If the
length of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of the
beam will become:
(A) 8mm (B) 16mm fo) 4mm (D) 32mm?
length of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of the
beam will become:
(A) 8mm (B) 16mm fo) 4mm (D) 32mm?
Most Upvoted Answer
The maximum deflection of a simply supported beam carrying a point loa...
**Solution:**
To solve this problem, we can use the concept of beam deflection and the relationship between deflection and the length of the beam.
Let's assume that the original length of the beam is L, and the maximum deflection at the center of the beam is d.
According to the given information, the maximum deflection of the beam carrying a point load W at the center is 2mm.
Now, let's consider the deflection equation for a simply supported beam carrying a point load at the center:
δ = (W * L^3) / (48 * E * I)
Where:
- δ is the maximum deflection at the center of the beam
- W is the point load acting at the center of the beam
- L is the length of the beam
- E is the modulus of elasticity of the material of the beam
- I is the moment of inertia of the beam
Since we are keeping the same load W at the center of the beam and doubling the length of the beam, the new length of the beam will be 2L.
Now, let's calculate the new maximum deflection of the beam:
δ' = (W * (2L)^3) / (48 * E * I)
= (W * 8 * L^3) / (48 * E * I)
= (2 * W * L^3) / (48 * E * I) * 4
= 4 * δ
Therefore, the new maximum deflection of the beam will be 4 times the original maximum deflection.
Since the original maximum deflection is 2mm, the new maximum deflection will be:
4 * 2mm = 8mm
Hence, the correct option is (A) 8mm.
To solve this problem, we can use the concept of beam deflection and the relationship between deflection and the length of the beam.
Let's assume that the original length of the beam is L, and the maximum deflection at the center of the beam is d.
According to the given information, the maximum deflection of the beam carrying a point load W at the center is 2mm.
Now, let's consider the deflection equation for a simply supported beam carrying a point load at the center:
δ = (W * L^3) / (48 * E * I)
Where:
- δ is the maximum deflection at the center of the beam
- W is the point load acting at the center of the beam
- L is the length of the beam
- E is the modulus of elasticity of the material of the beam
- I is the moment of inertia of the beam
Since we are keeping the same load W at the center of the beam and doubling the length of the beam, the new length of the beam will be 2L.
Now, let's calculate the new maximum deflection of the beam:
δ' = (W * (2L)^3) / (48 * E * I)
= (W * 8 * L^3) / (48 * E * I)
= (2 * W * L^3) / (48 * E * I) * 4
= 4 * δ
Therefore, the new maximum deflection of the beam will be 4 times the original maximum deflection.
Since the original maximum deflection is 2mm, the new maximum deflection will be:
4 * 2mm = 8mm
Hence, the correct option is (A) 8mm.
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The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm?
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The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm? 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 The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm?.
The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm? 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 The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum deflection of a simply supported beam carrying a point load W at center is 2mm. If thelength of this beam is doubled keeping the same load W at the center of the beam, maximum deflection of thebeam will become: (A) 8mm (B) 16mm fo) 4mm (D) 32mm?.
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