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A beam simply supported at the ends carries a load W at the Centre, causing deflection y. If the depth of the section of the beam is doubled, the deflection at the Centre will be
- a)y
- b)1/2y
- c)1/4 y
- d)1/8y
Correct answer is option 'D'. Can you explain this answer?
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A beam simply supported at the ends carries a load W at the Centre, c...
Deflection at C:
y =
y2 = 1/8 × y
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A beam simply supported at the ends carries a load W at the Centre, c...
Question:
A beam simply supported at the ends carries a load W at the Centre, causing deflection y. If the depth of the section of the beam is doubled, the deflection at the Centre will be
a) y
b) 1/2y
c) 1/4y
d) 1/8y
Answer:
To solve this problem, let's analyze the relationship between the deflection and the depth of the beam section.
Key Point:
Deflection of a beam is inversely proportional to the cube of its depth.
Explanation:
When the depth of the beam section is doubled, the deflection at the center can be determined by comparing the new deflection (y') with the original deflection (y).
Key Point:
The relationship between the deflection and the depth of a beam section can be expressed as: Deflection ∝ 1/depth^3
When the depth of the beam section is doubled, the new depth becomes 2d, where d is the original depth.
Therefore, the new deflection (y') can be expressed as:
y' ∝ 1/(2d)^3
y' ∝ 1/8d^3
y' = k/(8d^3) --------(1)
Since the load and the boundary conditions remain the same, the constant k remains constant for both the original and the new deflection.
Now, let's compare the original deflection (y) with the new deflection (y').
y ∝ 1/d^3
y = k/d^3 --------(2)
To compare equations (1) and (2), we can write:
y' = y/8
This shows that the new deflection (y') is 1/8th of the original deflection (y).
Therefore, the correct answer is option d) 1/8y.
A beam simply supported at the ends carries a load W at the Centre, causing deflection y. If the depth of the section of the beam is doubled, the deflection at the Centre will be
a) y
b) 1/2y
c) 1/4y
d) 1/8y
Answer:
To solve this problem, let's analyze the relationship between the deflection and the depth of the beam section.
Key Point:
Deflection of a beam is inversely proportional to the cube of its depth.
Explanation:
When the depth of the beam section is doubled, the deflection at the center can be determined by comparing the new deflection (y') with the original deflection (y).
Key Point:
The relationship between the deflection and the depth of a beam section can be expressed as: Deflection ∝ 1/depth^3
When the depth of the beam section is doubled, the new depth becomes 2d, where d is the original depth.
Therefore, the new deflection (y') can be expressed as:
y' ∝ 1/(2d)^3
y' ∝ 1/8d^3
y' = k/(8d^3) --------(1)
Since the load and the boundary conditions remain the same, the constant k remains constant for both the original and the new deflection.
Now, let's compare the original deflection (y) with the new deflection (y').
y ∝ 1/d^3
y = k/d^3 --------(2)
To compare equations (1) and (2), we can write:
y' = y/8
This shows that the new deflection (y') is 1/8th of the original deflection (y).
Therefore, the correct answer is option d) 1/8y.
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A beam simply supported at the ends carries a load W at the Centre, causing deflection y. If the depth of the section of the beam is doubled, the deflection at the Centre will bea) yb) 1/2yc) 1/4 yd) 1/8yCorrect answer is option 'D'. Can you explain this answer?
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