This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Constraints and Statical Determinacy”.
1. To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports.
a) True
b) False
View Answer
Explanation: To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports. The more the stable are the supports the more the stable is the equilibrium, that is the more easily is the equilibrium is achived.
2. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support P.
a) -217N
b) 80N
c) 700N
d) -250N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
3. What is redundant support?
a) The supports consisting of hinge and a roller
b) The supports consisting of hinge only
c) The supports consisting of roller only
d) The supports more than necessary to hold the structure
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Explanation: The supports if are more than the supports required to hold the structure are termed as the reductant supports. It becomes statically indeterminate. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium.
4. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the horizontal reaction at the support P.
a) 0N
b) 80N
c) 200N
d) 100N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
5. Statically indeterminacy means?
a) There will be less equations available for equilibrium than the unknown loadings
b) There will be more equations available for equilibrium than the unknown loadings
c) There will be equal equations available for equilibrium as the unknown loadings
d) The support reactions are opposite to each other
View Answer
Explanation: Statically indeterminacy is the condition when less equations are available for equilibrium than the unknown loadings. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium. Thus this is the stuff which one needs to prevent from happening.
6. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the horizontal reaction at the support R.
a) 0N
b) 30N
c) 20N
d) 10N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
7. The additional equations invented in the statically indeterminacy condition is solved by __________
a) Deformation conditions at the point of supports
b) Rotational equations
c) Translation equations
d) Linear rotation equations
View Answer
Explanation: The additional equations invented in the statically indeterminacy condition is solved by deformation conditions at the point of supports. This are the conditions which are based on the physical and the chemical properties of the body. A different study for this is done in mechanics of material.
8. The generation of equal equations available for equilibrium as the unknown loadings always guarantees the stability of the body.
a) True
b) False
View Answer
Explanation: The generation of equal equations available for equilibrium as the unknown loadings doesn’t always guarantees the stability of the body. It is defined on the basis of the supports that are their supporting the body. Or it also depends on the types of the forces that are acting, i.e. the three or two force system.
9. In 3D the body will be improperly constrained if the axis is intersected by the reaction forces.
a) The statement is right
b) The statement is wrong
c) The statement is right if there is ‘2D’
d) The statement is right if there is ‘support reaction’
View Answer
Explanation: In 3D the body will be improperly constrained if the axis is intersected by the reaction forces. This is because there will be small moments which will occur in the real situations. But they will not be matched in the calculations done for determining the equilibrium. Thus the statement is right.
10. The improper constraining leading to instability occurs when ___________________
a) The reactive forces are parallel
b) The reactive forces are perpendicular
c) The reactive forces are equal
d) The reactive forces are rotational
View Answer
Explanation: If the forces are parallel (the reactive forces) then this creates an instability. That is this is also a type of improper constraining which is resulting in instability of the structure. Thus reactive forces are parallel are resulting in the instability of the body.
11. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the sum of all the vertical forces at the supports.
a) 1280N
b) 80N
c) 200N
d) 100N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
12. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support Q.
a) 707N
b) 80N
c) 200N
d) 100N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
13. What is partially constrained?
a) There will be less equations available for equilibrium than the reactive forces
b) There will be more equations available for equilibrium than the reactive forces
c) There will be equal equations available for equilibrium as the reactive forces
d) The support reactions are opposite to each other
View Answer
Explanation: The situation may arise when there will be more equations available for equilibrium than the reactive forces. This condition is known as partially constrained. This is also one of the factor which is giving instability to the structure.
14. If all the reactive forces are intersecting at the common point or pass through a common axis when _____________
a) The body is in equilibrium
b) The body is said to be achieve stability but no equilibrium
c) The body is said to be improperly constrained
d) The body is in deformation
View Answer
Explanation: If all the reactive forces are intersecting at the common point or pass through a common axis then the body is said to be improperly constrained. Whether it may be the reactive forces being parallel. Or be it the forces meeting at a common point. The body is said to be improperly constrained.
15. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support R.
a) 790N
b) 80N
c) 200N
d) 100N
View Answer
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.
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