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A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:
- a)2.25 δ
- b)0.67 δ
- c)1.5 δ
- d)0.44 δ
Correct answer is option 'A'. Can you explain this answer?
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A simply supported beam of rectangular section 4 cm by 6 cm carries a ...
To find the deflection of the beam, we can use the formula:
δ = (PL³)/(48EI)
Where δ is the deflection, P is the concentrated load, L is the span length, E is the modulus of elasticity, and I is the moment of inertia.
First, we need to determine the moment of inertia for the rectangular section of the beam. For a rectangular section, the moment of inertia is given by:
I = (bh³)/12
Where b is the width and h is the height of the section.
Substituting the values, we get:
I = (4 x 6³)/12 = 72 cm⁴
Next, we need to determine the modulus of elasticity for the material of the beam. Assuming it is made of steel, we can use a typical value of E = 200 GPa (or 200,000 N/mm²).
Now we can substitute all the values into the formula for deflection:
δ = (P x L³)/(48EI)
We are not given the value of P, but we can assume it is a significant load that causes a noticeable deflection. Let's say P = 10 kN (or 10,000 N).
The span length is not given either, but let's assume it is 4 meters (or 4000 mm).
Substituting all the values, we get:
δ = (10,000 x 4000³)/(48 x 200,000 x 72) = 8.33 mm
Therefore, the deflection of the beam under the mid-span concentrated load is approximately 8.33 mm.
δ = (PL³)/(48EI)
Where δ is the deflection, P is the concentrated load, L is the span length, E is the modulus of elasticity, and I is the moment of inertia.
First, we need to determine the moment of inertia for the rectangular section of the beam. For a rectangular section, the moment of inertia is given by:
I = (bh³)/12
Where b is the width and h is the height of the section.
Substituting the values, we get:
I = (4 x 6³)/12 = 72 cm⁴
Next, we need to determine the modulus of elasticity for the material of the beam. Assuming it is made of steel, we can use a typical value of E = 200 GPa (or 200,000 N/mm²).
Now we can substitute all the values into the formula for deflection:
δ = (P x L³)/(48EI)
We are not given the value of P, but we can assume it is a significant load that causes a noticeable deflection. Let's say P = 10 kN (or 10,000 N).
The span length is not given either, but let's assume it is 4 meters (or 4000 mm).
Substituting all the values, we get:
δ = (10,000 x 4000³)/(48 x 200,000 x 72) = 8.33 mm
Therefore, the deflection of the beam under the mid-span concentrated load is approximately 8.33 mm.
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A simply supported beam of rectangular section 4 cm by 6 cm carries a ...
The answer is d) 2.25 times delta. Delta having inverse proportion with Moment of Inertia. Therefore when the line of axis changes in perpendicular direction i.e. loading parallel to 4cm side. Moment of Inertia changes . Hence, the value of delta by comparing with 1st condition becomes 2.25 times delta in 1st condition.
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A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer?
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A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer? 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 simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer?.
A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer? 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 simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam of rectangular section 4 cm by 6 cm carries a mid -span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is δ. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be:a)2.25 δb)0.67 δc)1.5 δd)0.44 δCorrect answer is option 'A'. Can you explain this answer?.
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