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When supported on three points, out of the 12 degrees of freedom the number of degrees of reedom arrested in a body is
[IES-1993]
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'D'. Can you explain this answer?
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When supported on three points, out of the 12 degrees of freedom the n...
When supported on three points, following six degrees of freedom are arrested.
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When supported on three points, out of the 12 degrees of freedom the n...
To understand the answer to this question, let's break it down step by step:
- When a body is supported on three points, it means that the body is resting on three separate contact points or surfaces. These contact points can be considered as constraints that restrict the movement of the body.
- In general, a rigid body in space has 6 degrees of freedom (DOF) associated with it. These 6 DOFs can be categorized as three translational DOFs and three rotational DOFs.
- The translational DOFs involve movement along the x, y, and z axes, while the rotational DOFs involve rotation around these three axes.
- When the body is supported on three points, it is effectively constrained in all translational DOFs. This means that the body cannot move along the x, y, and z axes.
- Additionally, when a body is supported on three points, it is also partially constrained in rotational DOFs. This is because the body can still rotate around the axis perpendicular to the contact points. However, it cannot rotate around the axes parallel to the contact points.
- Therefore, when a body is supported on three points, it has 3 DOFs arrested due to translational constraints and 3 DOFs partially arrested due to rotational constraints.
- The total number of DOFs arrested in the body is the sum of these two categories, which is 3 + 3 = 6.
Based on the above explanation, we can conclude that when a body is supported on three points, out of the 12 degrees of freedom, the number of degrees of freedom arrested in the body is 6. Therefore, the correct answer is option 'D'.
- When a body is supported on three points, it means that the body is resting on three separate contact points or surfaces. These contact points can be considered as constraints that restrict the movement of the body.
- In general, a rigid body in space has 6 degrees of freedom (DOF) associated with it. These 6 DOFs can be categorized as three translational DOFs and three rotational DOFs.
- The translational DOFs involve movement along the x, y, and z axes, while the rotational DOFs involve rotation around these three axes.
- When the body is supported on three points, it is effectively constrained in all translational DOFs. This means that the body cannot move along the x, y, and z axes.
- Additionally, when a body is supported on three points, it is also partially constrained in rotational DOFs. This is because the body can still rotate around the axis perpendicular to the contact points. However, it cannot rotate around the axes parallel to the contact points.
- Therefore, when a body is supported on three points, it has 3 DOFs arrested due to translational constraints and 3 DOFs partially arrested due to rotational constraints.
- The total number of DOFs arrested in the body is the sum of these two categories, which is 3 + 3 = 6.
Based on the above explanation, we can conclude that when a body is supported on three points, out of the 12 degrees of freedom, the number of degrees of freedom arrested in the body is 6. Therefore, the correct answer is option 'D'.
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When supported on three points, out of the 12 degrees of freedom the number of degrees of reedom arrested in a body is [IES-1993]a)3b)4c)5d)6Correct answer is option 'D'. Can you explain this answer?
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