Term
Actual structures and machines, are always absolutely rigid and never deform under the loads to which they are subjected.
T or F 

Definition
False
Never absolutely rigid and deform 


Term
Forces acting on a rigid body can be represented by... 

Definition


Term
Two important concepts associated with the effect of a force on a rigid body are... 

Definition
the moment of a force about a point and an axis 


Term
The combination of two forces which have the same magnitude, parallel lines of action, and opposite sense... 

Definition


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.... 

Definition


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 .... 

Definition
resultant
resultant couple 


Term
Forces acting on rigid bodies can be separated into two groups: 

Definition
external and internal forces 


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. 

Definition


Term
The _________ are the forces which hold together the particles forming the rigid body. Forces holding the component parts together. 

Definition


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. 

Definition


Term
The principle of transmissibility should be avoided or used with care, in determining.... 

Definition
internal forces and deformations 


Term
The _______ property does not apply to vector products. 

Definition


Term
The _________ property holds with vector products. 

Definition


Term
The magnitude of M_{O} measures the tendency of the force F to make the rigid body rotate about a fixed axis directed along M_{O}.
T or F 

Definition


Term
Although the moment M_{O} 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. 

Definition


Term
The moment M_{O} of a force F of given magnitude and direction ____________ of F. 

Definition
completely defines the line of action of 


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 

Definition


Term
The distributive property of vector products can be used to determine the moment of the resultant of several.... 

Definition


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 

Definition


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. 

Definition


Term
The dot product of two vectors is.... 

Definition
commutative and distributive
P • Q = Q • P 


Term
The moment M of a couple is a ___________ which can be applied at any point. 

Definition


Term
Two couples of F_{1} and F_{1} and F_{2} and F_{2} will have equal moments if... 

Definition
F_{1}d_{1} = F_{2}d_{2} , if the two couples lie in parallel planes (same plane) and have the same sense. 


Term
Two systems of forces are equivalent if we can transform one of them into the other by means of... 

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 


Term
The vector representing a couple is called a... 

Definition


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 

Definition


Term
Any forcecouple system consisting of a force F and a couple vector M_{O} which are ___________ can be replaced by a single equivalent force. 

Definition


Term
Any system of forces, however complex, can thus be reduced to an ______________ acting at a given point O. 

Definition
equivalent forcecouple system 


Term
The __________ of the system, is obtained by adding the moments about O of all the forces of the system. 

Definition


Term
Two systems of forces are ________ if they can be reduced to the same forcecouple system at a given point O.


Definition


Term
Two systems of forces, F_{1}, F_{2}, F_{3},....., 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. 

Definition


Term
To prove that two systems of forces are equivalent, the second of the relations must be established with respect to.... 

Definition
only one point O
(and will hold to any point if the two systems are equivalent.) 


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... 

Definition


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. 

Definition


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.... 

Definition
equipollent, are not equivalent 


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 Mo^{R} are mutually perpendicular if these three cases... 

Definition
1. Concurrent forces
2. Coplanar forces
3. Parallel forces 


Term
....are applied at the same point and can therefore be added directly to obtain their resultant R. Always reduce to a single force. 

Definition


Term
.... act in the same plane, which may be assumed to be the plane of the figure. 

Definition


Term
....have parallel lines of action and may or not have the same sense. 

Definition


Term
This particular forcecouple system is called a _______ b/c the resulting combination of push and twist. 

Definition


Term
A wrench consists of two _______ vectors, a force R and a couple vector.
M_{1} = pR 

Definition


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..... 

Definition


Term
The necessary and sufficient conditions for the equilibrium of a rigid body can be obtained by setting ___ and ___ equal to zero. 

Definition


Term
The conditions for equilibrium of a rigid body can be expressed in which six scalar equations... 

Definition
ΣF_{x }= 0 ΣF_{y }= 0 ΣF_{z} = 0
ΣM_{x} = 0 ΣM_{y} = 0 ΣM_{z} = 0 


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. 

Definition


Term
In solving a problem concerning the equilibrium of a rigid body, all _________ should be indicated on the freebody diagram. 

Definition


Term
The magnitudes and directions of the ___________ should be clearly marked on the freebody diagram. 

Definition


Term
Known external forces generally include the ______ of the free body and __________ for a given purpose. 

Definition
weight and forces applied 


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. 

Definition


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. 

Definition


Term
_____________ usually consists of the reactions, through which the ground and other bodies oppose a possible motin of the free body. 

Definition


Term
The reactions constrain the free body to remain in the same position, and, for that reason, are sometimes called... 

Definition


Term
Reactions are exerted at the points where the free body is _________ or _________ other bodies and should be clearly indicated. 

Definition
supported by
connected to 


Term
The reactions exerted on a 2D structure can be divided into three groups corresponding to three types of supports or connections: 

Definition
Reactions Equivalent to a Force with Known line of Action, of Unknown Direction and Magnitude, and a Couple. 


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.


Definition
Reactions Equivalent to a Force with Known Line of Action 


Term
Reactions Equivalent to a Force with Known Line of Action involve ___ unknown, namely, the.... 

Definition
1
magnitude of the reaction 


Term
Supports and connections causing reactions of this type include frictionless pins in fitted holes, hinges, and rough surfaces. 

Definition
Reactions Equivalent to a Force of Unknown Direction and Magnitude 


Term
Can prevent translation of the free body in all directions, but cannot prevent the body from rotating about the connection. 

Definition
Reactions Equivalent to a Force of Unknown Direction and Magnitude 


Term
Reactions Equivalent to a Force of Unknown Direction and Magnitude involve two unknowns and are usually represented by their... 

Definition


Term
These reactions are caused by fixed supports, which oppose any motion of the free body and thus contrain it completely. 

Definition
Reactions Equivalent to a Force and a Couple 


Term
Reactions Equivalent to a Force and a Couple involve three unknowns, consisting usually of the two components of the _______ and the...... 

Definition
force and the moment of the couple 


Term
While the three equations of equilibrium of a rigid body in 2D cannot be .... by additional equations, any of them can be ... by another equation. 

Definition


Term
The types of supports that make it so the rigid body can not possibly move make the rigid body... 

Definition


Term
While vertical motion is prevented the structure is free to move horizontally. The structure is said to be.... 

Definition


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. 

Definition


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. 

Definition


Term
The _______ of structures possessing statically indeterminate reactions often can be partially carried out by the methods of statics. 

Definition


Term
Structures which are designed to move ________ be only partially constrained. 

Definition


Term
A particular case of equilibrium which is of considerable interest is that of a rigid body subjected to two forces often called a... 

Definition


Term
It will be shown that if a twoforce body is in equilibrium, the two forces must have the same _______, the same ______, and _______ 

Definition
magnitude
LOA
opposite sense 


Term
A twoforce body can be more generally defined as a rigid body subjected to forces acting at only.... 

Definition


Term
a rigid body subjected to forces acting at only three points is called a... 

Definition


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 _______ 

Definition


Term
If a rigid body is in equilibrium, the sum of the moments of F_{1}, F_{2} and F_{3} about any axis must be... 

Definition


Term
Express in vector form the conditions for the equilibrium of the rigid body considered. 

Definition
ΣF = 0 ΣM_{O} = Σ(r × F) = 0 


Term
In problems involving the equilibrium of a 3D structure, there can be between _________ unknowns associated with the reaction at each support or connection. 

Definition


Term
With equilibrium of a 3D body if the reactions involve more than six unknowns, some of the reactions are ________ 

Definition


Term
With equilibrium of a 3D body if they involve fewer than six unknowns, the rigid body is only.... 

Definition


Term
With equilibrium of a 3D 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. 

Definition

