Term
Actual structures and machines, are always absolutely rigid and never deform under the loads to which they are subjected.
T or F |
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Definition
False
Never absolutely rigid and deform |
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Term
| Forces acting on a rigid body can be represented by... |
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Definition
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Term
| Two important concepts associated with the effect of a force on a rigid body are... |
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Definition
| the moment of a force about a point and an axis |
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Term
| The combination of two forces which have the same magnitude, parallel lines of action, and opposite sense... |
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Definition
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Term
| Any system of forces acting on a rigid body can be replaced by an equivalent system consisting of one force acting at a given point and one couple called a.... |
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Definition
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Term
| In the case of concurrent, coplanar, or parallel forces, the equivalent FCS can be reduced to a single force called the ... of the system or to a single couple called the .... |
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Definition
resultant
resultant couple |
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Term
| Forces acting on rigid bodies can be separated into two groups: |
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Definition
| external and internal forces |
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Term
| The ________ represent the action of other bodies on the rigid body under consideration. They will either cause it to move or ensure that it remains at rest. |
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Definition
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Term
| The _________ are the forces which hold together the particles forming the rigid body. Forces holding the component parts together. |
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Definition
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Term
| Two forces are said to be ________ (have the same effect on a rigid body) if they have the same magnitude, direction and same LOA. |
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Definition
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Term
| The principle of transmissibility should be avoided or used with care, in determining.... |
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Definition
| internal forces and deformations |
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Term
| The _______ property does not apply to vector products. |
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Definition
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Term
| The _________ property holds with vector products. |
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Definition
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Term
The magnitude of MO measures the tendency of the force F to make the rigid body rotate about a fixed axis directed along MO.
T or F |
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Definition
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Term
| Although the moment MO of a force about a point depends upon the magnitude, the LOA, and the sense of the force, it _____ depend upon the actual position of the POA of the force along its LOA. |
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Definition
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Term
| The moment MO of a force F of given magnitude and direction ____________ of F. |
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Definition
| completely defines the line of action of |
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Term
Two forces F and F' are equivalent if, and only if, they are equal (have same magnitude and direction) and have equal moments about a given point O.
T or F |
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Definition
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Term
| The distributive property of vector products can be used to determine the moment of the resultant of several.... |
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Definition
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Term
The moment about a given point O of the resultant of several concurrent forces is not equal to the sum of the moments of the various forces about the same point O
T or F |
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Definition
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Term
| The ________ of two vectors P and Q is defined as the product of the magnitudes of P and Q and of the cosine of the angle Θ formed by P and Q. |
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Definition
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Term
| The dot product of two vectors is.... |
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Definition
commutative and distributive
P • Q = Q • P |
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Term
| The moment M of a couple is a ___________ which can be applied at any point. |
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Definition
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Term
| Two couples of F1 and -F1 and F2 and -F2 will have equal moments if... |
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Definition
| F1d1 = F2d2 , if the two couples lie in parallel planes (same plane) and have the same sense. |
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Term
| Two systems of forces are equivalent if we can transform one of them into the other by means of... |
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Definition
1. Resultant of two forces on a particle
2. Resolving a force into two components
3. Canceling two equal and opposite forces acting on the same particle
4. Attaching to the same particle two equal and opposite forces
5. Moving a force along its line of action |
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Term
| The vector representing a couple is called a... |
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Definition
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Term
Any force F acting on a rigid body can be moved to an arbitrary point O provided that a couple is added whose moment is equal to the moment of F about O.
T or F |
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Definition
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Term
| Any force-couple system consisting of a force F and a couple vector MO which are ___________ can be replaced by a single equivalent force. |
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Definition
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Term
| Any system of forces, however complex, can thus be reduced to an ______________ acting at a given point O. |
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Definition
| equivalent force-couple system |
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Term
| The __________ of the system, is obtained by adding the moments about O of all the forces of the system. |
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Definition
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Term
Two systems of forces are ________ if they can be reduced to the same force-couple system at a given point O.
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Definition
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Term
| Two systems of forces, F1, F2, F3,....., and F'1, F'2, F'3,....., which act on the same rigid body are ________ if, and only if the sums of the moments about a given point O of the forces of the two systems are, respectively, equal. |
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Definition
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Term
| To prove that two systems of forces are equivalent, the second of the relations must be established with respect to.... |
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Definition
only one point O
(and will hold to any point if the two systems are equivalent.) |
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Term
| When two systems of vectors resultants and moment resultants about an arbitrary point O are respectively equal, the two systems are said to be... |
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Definition
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Term
| If two systems of forces acting on a rigid body are equipollent, they are also equivalent. However this does not apply to _______ of vectors. |
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Definition
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Term
If two different system of forces acting on independent particles that do not form a rigid body are equipollent.
Since different forces will now act on the various particles, their effects on these particles will be different; the two systems of forces, while.... |
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Definition
| equipollent, are not equivalent |
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Term
| The systems of forces which can be reduced to a single force, or resultant, are therefore the systems for which the force R and the couple vector MoR are mutually perpendicular if these three cases... |
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Definition
1. Concurrent forces
2. Coplanar forces
3. Parallel forces |
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Term
| ....are applied at the same point and can therefore be added directly to obtain their resultant R. Always reduce to a single force. |
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Definition
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Term
| .... act in the same plane, which may be assumed to be the plane of the figure. |
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Definition
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Term
| ....have parallel lines of action and may or not have the same sense. |
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Definition
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Term
| This particular force-couple system is called a _______ b/c the resulting combination of push and twist. |
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Definition
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Term
A wrench consists of two _______ vectors, a force R and a couple vector.
M1 = pR |
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Definition
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Term
| Whe the force and the couple are both equal to zero the external forces form a system equivalent to zero, and the rigid body is said to be in..... |
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Definition
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Term
| The necessary and sufficient conditions for the equilibrium of a rigid body can be obtained by setting ___ and ___ equal to zero. |
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Definition
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Term
| The conditions for equilibrium of a rigid body can be expressed in which six scalar equations... |
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Definition
ΣFx = 0 ΣFy = 0 ΣFz = 0
ΣMx = 0 ΣMy = 0 ΣMz = 0 |
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Term
| When the free body diagram is made of several parts, the forces the various parts exert on each other ________ be included among the external forces. |
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Definition
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Term
| In solving a problem concerning the equilibrium of a rigid body, all _________ should be indicated on the free-body diagram. |
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Definition
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Term
| The magnitudes and directions of the ___________ should be clearly marked on the free-body diagram. |
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Definition
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Term
| Known external forces generally include the ______ of the free body and __________ for a given purpose. |
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Definition
| weight and forces applied |
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Term
| External forces represent the actions exerted ___ the free body ___ the ground and ___ the bodies which have been detached; they should be applied at the various points where the free body was supported by the ground or was connected to the other bodies. |
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Definition
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Term
| The _______ of the free body should also be included among the external forces, since it represents the attraction exerted by the earth on the various particles forming the free body. |
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Definition
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Term
| _____________ usually consists of the reactions, through which the ground and other bodies oppose a possible motin of the free body. |
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Definition
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Term
| The reactions constrain the free body to remain in the same position, and, for that reason, are sometimes called... |
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Definition
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Term
| Reactions are exerted at the points where the free body is _________ or _________ other bodies and should be clearly indicated. |
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Definition
supported by
connected to |
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Term
| The reactions exerted on a 2-D structure can be divided into three groups corresponding to three types of supports or connections: |
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Definition
| Reactions Equivalent to a Force with Known line of Action, of Unknown Direction and Magnitude, and a Couple. |
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Term
Supports and connections causing reactions of this type include rollers, rockers, frictionless surfaces, short link and cables, collars on frictionless rods, and frictionless pins in slots.
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Definition
| Reactions Equivalent to a Force with Known Line of Action |
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Term
| Reactions Equivalent to a Force with Known Line of Action involve ___ unknown, namely, the.... |
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Definition
1
magnitude of the reaction |
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Term
| Supports and connections causing reactions of this type include frictionless pins in fitted holes, hinges, and rough surfaces. |
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Definition
| Reactions Equivalent to a Force of Unknown Direction and Magnitude |
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Term
| Can prevent translation of the free body in all directions, but cannot prevent the body from rotating about the connection. |
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Definition
| Reactions Equivalent to a Force of Unknown Direction and Magnitude |
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Term
| Reactions Equivalent to a Force of Unknown Direction and Magnitude involve two unknowns and are usually represented by their... |
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Definition
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Term
| These reactions are caused by fixed supports, which oppose any motion of the free body and thus contrain it completely. |
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Definition
| Reactions Equivalent to a Force and a Couple |
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Term
| Reactions Equivalent to a Force and a Couple involve three unknowns, consisting usually of the two components of the _______ and the...... |
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Definition
| force and the moment of the couple |
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Term
| While the three equations of equilibrium of a rigid body in 2-D cannot be .... by additional equations, any of them can be ... by another equation. |
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Definition
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Term
| The types of supports that make it so the rigid body can not possibly move make the rigid body... |
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Definition
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Term
| While vertical motion is prevented the structure is free to move horizontally. The structure is said to be.... |
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Definition
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Term
| A rigid body is __________ whenever the supports, even though they may provide a sufficient number of reactions, are arranged in such a way that the reactions must be either concurrent or parallel. |
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Definition
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Term
| Supports involving statically indeterminate reactions should be used with care in the _______ of structures and only with a full knowledge of the problems they may cause. |
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Definition
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Term
| The _______ of structures possessing statically indeterminate reactions often can be partially carried out by the methods of statics. |
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Definition
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Term
| Structures which are designed to move ________ be only partially constrained. |
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Definition
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Term
| A particular case of equilibrium which is of considerable interest is that of a rigid body subjected to two forces often called a... |
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Definition
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Term
| It will be shown that if a two-force body is in equilibrium, the two forces must have the same _______, the same ______, and _______ |
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Definition
magnitude
LOA
opposite sense |
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Term
| A two-force body can be more generally defined as a rigid body subjected to forces acting at only.... |
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Definition
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Term
| a rigid body subjected to forces acting at only three points is called a... |
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Definition
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Term
| Consider a rigid body subjected to s system of forces which can be reduced to three forces acting at three points. If the body is in equilibrium, the LOA of the three forces must be either ______ or _______ |
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Definition
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Term
| If a rigid body is in equilibrium, the sum of the moments of F1, F2 and F3 about any axis must be... |
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Definition
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Term
| Express in vector form the conditions for the equilibrium of the rigid body considered. |
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Definition
| ΣF = 0 ΣMO = Σ(r × F) = 0 |
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Term
| In problems involving the equilibrium of a 3-D structure, there can be between _________ unknowns associated with the reaction at each support or connection. |
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Definition
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Term
| With equilibrium of a 3-D body if the reactions involve more than six unknowns, some of the reactions are ________ |
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Definition
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Term
| With equilibrium of a 3-D body if they involve fewer than six unknowns, the rigid body is only.... |
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Definition
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Term
| With equilibrium of a 3-D body with six or more unknowns, the rigid body will be ___________ is the reactions associated with the given supports either are parallel or intersect the same line. |
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Definition
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