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The deformation of a bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight will be:
- a)The same
- b)One-fourth
- c)Half
- d)Double
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The deformation of a bar under its own weight as compared to that when...
Elongation of bar due to its own weight=Pl/2AE
Elongation of bar due to axial load=Pl/AE
Now comparing both..we will take the ratio.. (Pl/2AE)÷(Pl/AE)=1/2...i.e half
Most Upvoted Answer
The deformation of a bar under its own weight as compared to that when...
Deformation of a Bar under its Own Weight Compared to Axial Load
When a bar is subjected to its own weight, it is called self-weight deformation. When it is subjected to an axial load equal to its own weight, it is called an external load deformation. The deformation of the bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight can be explained as follows:
Explanation:
- The deformation of the bar under its own weight is given by δ = (wL^3)/(3EI), where w is the weight per unit length of the bar, L is the length of the bar, E is the modulus of elasticity, and I is the area moment of inertia.
- The deformation of the bar under an axial load equal to its own weight is given by δ = (wL)/(2AE), where A is the cross-sectional area of the bar.
- Comparing the two equations, we see that the deformation under an axial load is half of the deformation under self-weight.
Therefore, the correct answer is option C, i.e., half.
When a bar is subjected to its own weight, it is called self-weight deformation. When it is subjected to an axial load equal to its own weight, it is called an external load deformation. The deformation of the bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight can be explained as follows:
Explanation:
- The deformation of the bar under its own weight is given by δ = (wL^3)/(3EI), where w is the weight per unit length of the bar, L is the length of the bar, E is the modulus of elasticity, and I is the area moment of inertia.
- The deformation of the bar under an axial load equal to its own weight is given by δ = (wL)/(2AE), where A is the cross-sectional area of the bar.
- Comparing the two equations, we see that the deformation under an axial load is half of the deformation under self-weight.
Therefore, the correct answer is option C, i.e., half.
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The deformation of a bar under its own weight as compared to that when...
Deformation of a Bar
Deformation refers to the change in the shape or size of an object under the influence of an external force. When a bar is subjected to an external force, it undergoes deformation. The amount of deformation depends on the magnitude of the external force and the properties of the material.
Deformation of a Bar under its Own Weight
When a bar is placed in a horizontal position, it experiences a force due to its own weight. This force is known as the self-weight of the bar. The self-weight of the bar causes it to deform. The amount of deformation depends on the material properties of the bar and the length of the bar.
Deformation of a Bar under Direct Axial Load
When a bar is subjected to a direct axial load, it experiences a force that is applied along its longitudinal axis. This force causes the bar to deform. The amount of deformation depends on the magnitude of the force and the material properties of the bar.
Comparison of Deformation under Self-Weight and Direct Axial Load
When a bar is subjected to a direct axial load equal to its own weight, the deformation of the bar will be different from the deformation that occurs when the bar is under its own weight. The deformation of the bar under its own weight will be less than the deformation that occurs under the direct axial load. This is because the self-weight force is distributed over the entire length of the bar while the direct axial load is applied at a single point.
Therefore, the deformation of a bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight will be half.
Deformation refers to the change in the shape or size of an object under the influence of an external force. When a bar is subjected to an external force, it undergoes deformation. The amount of deformation depends on the magnitude of the external force and the properties of the material.
Deformation of a Bar under its Own Weight
When a bar is placed in a horizontal position, it experiences a force due to its own weight. This force is known as the self-weight of the bar. The self-weight of the bar causes it to deform. The amount of deformation depends on the material properties of the bar and the length of the bar.
Deformation of a Bar under Direct Axial Load
When a bar is subjected to a direct axial load, it experiences a force that is applied along its longitudinal axis. This force causes the bar to deform. The amount of deformation depends on the magnitude of the force and the material properties of the bar.
Comparison of Deformation under Self-Weight and Direct Axial Load
When a bar is subjected to a direct axial load equal to its own weight, the deformation of the bar will be different from the deformation that occurs when the bar is under its own weight. The deformation of the bar under its own weight will be less than the deformation that occurs under the direct axial load. This is because the self-weight force is distributed over the entire length of the bar while the direct axial load is applied at a single point.
Therefore, the deformation of a bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight will be half.
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