Systems of Forces and Moments Flashcards
What is statics the study of?
Statics is the study of rigid bodies that are stationary.
What does a rigid body require to be stationary?
To be stationary, a rigid body must be in static equilibrium. In other words, has no unbalanced forces acting on it.
What actions are forces categorized in?
Forces are categorized as a push or a pull that one body exerts on another.
Force is a vector quantity because…
It has a magnitude, direction, and point of application.
What are external forces?
Actions of other bodies on a rigid body.
What do unbalanced external forces cause?
Unbalanced external forces will cause motion of the body.
What are internal forces?
The forces that hold together parts of the rigid body.
What do unbalanced internal forces cause?
Unbalanced internal forces will cause deformation of a body. Motion is never caused by internal forces.
How are forces frequently represented?
Forces are frequently represented in terms of unit vectors and force components.
What is a unit vector?
A unit vector is a vector of unit length directed along a coordinate axis.
How are unit vectors used in vector equations?
Unit vectors are used in vector equations to indicate direction without affecting magnitude.
What are the three unit vectors in the rectangular coordinate system?
The three unit vectors in the rectangular coordinate system are i for the x direction, j for the y direction and k for the z direction.
What is the resultant force equal to in two dimensions when the component forces are know?
The resultant force is equal to the square root of the addition of the sum of the forces in the x direction squared, and the sum of the forces in the y direction squared.
What is the angle of the resultant with respect to the x axis?
The angle made with respect to the x axis is equal to arctangent of the sum of the forces in the y direction divided by the sum of the forces in the x direction.
How are the components found of a force?
The components of a two or three dimensional force can be found from its direction cosines.
What are the direction cosines?
Are the cosines of the true angles made by the force vector with x, y and z axes.
What are the force components equal to using the direction of cosines?
The force components are equal to the product of the resultant force and the direction cosines.
What are the direction of cosines equal to using the force components?
The direction cosine of the axis in question, is equal to the force component divided by the resultant force.
What is the resultant force of a three dimensional force when the force components are known?
The resultant force is equal to the square root of the addition of the sum of the forces in the x direction squared, the sum of the forces in the y direction squared and the sum of the forces in the z direction squared.
How are the forces or dimensions found using ratios?
The ratio of a force component to resultant force is equal to the ratio of the dimension correlating to that force component to the dimension correlating to the resultant force.
What is a moment?
The name given to the tendency of a force to rotate, turn, or twist a rigid body about an actual or assumed pivot point.
What does a moment do to an unrestrained body?
It causes the unrestrained body to rotate.
What does a moment do to a restrained body?
There is no rotation due to an equal an opposite moment being applied by the restrained body.
When does a rigid body experience a moment?
A rigid body will always experience a moment when a force is applied to it.
When does a rigid body not experience a moment?
When the line of action of the force passes through the center of rotation will the moment be zero.
Are moments vectors?
Yes moments are vectors because they have a magnitude, direction and point of application.
What is the moment equal to?
The moment is equal to the cross product of the position vector and the force vector.
What is the position vector?
The position vector is the length or distance from the origin to the point where the force is being applied.
How is the moment vector about the origin projected onto an axis?
The dot product of the Moment vector and unit vector of the axis of projection is used.
How are the components of a moment calculated using rectangular coordinates and component forces?
They are found by summing the moments caused by each component force about the axis in question.
How are the components of a moment calculated using angles?
They are found by the product of the resultant moment and the direction of cosines of a force.
What is the resultant equal to?
The resultant force is equal to the square root of the addition of the sum of the moments in the x direction squared, the sum of the moments in the y direction squared and the sum of the moments in the z direction squared.
What is required for the components of the moments to found using the angles and rectangular coordinates?
The force vector applied at a point must be referenced to an origin at (0,0,0).
What is a couple?
Any pair of equal, opposite and parallel forces.
What are couples equivalent to?
A couple is equivalent to a single moment vector.
What cancels out in a couple?
Since the two forces are opposite in sign, the x, y, and z components of the forces cancel out.
What is a body induced to by the couple?
A body is induced to rotate without translation.
How can a couple be counteracted?
A couple can be counteracted only by another couple.
Can a couple be moved to any location without affecting the equilibrium requirements?
Yes
What is a force couple system?
The combination of the moved force and the couple.
What defines the moved force in the force couple system?
If a force, is moved a distance, from the original point of application.
What defines the moment in the force couple system?
The couple added to counteract the induced couple.
How can a force couple system be replaced?
It can be replaced by a single force located a distance equal to the moment divided by the force away.
What are a system of forces and moments in three dimensional space, statically equivalent to?
A single resultant force vector plus a single resultant moment vector.
Can the resultant system of forces and moments in three dimensional space, be equal to zero?
Either or both of these resultants can be equal to zero.
What are the x, y , and z components of the resultant force equal to?
Are the sums of the x, y , and z components of the individual forces.
What are the x, y , and z components of the resultant moment equal to?
It includes the moments of all system forces around the reference axes plus the components of all system moments.
When is an object static?
When it is stationary.
What does a object require to be stationary?
To be stationary, all of the forces and moments on the object must be in static equilibrium.
What is static equilibrium?
For an object to be in static equilibrium, the resultant force and moment vectors must both be zero.
What are concurrent force systems?
A concurrent force system is a category of force systems where all of the forces act at the same point.
What is needed to reach static equilibrium, if all of the forces are concurrent forces?
If the forces on a body are all concurrent forces, then only force equilibrium is necessary to ensure static equilibrium.
What are two or three force members?
Members limited to loading by two or three forces in the same plane.
How can a two force member be in equilibrium?
A two force member can be in equilibrium, only if the two forces have the same line of action (are collinear) and are equal but opposite.
How can a three force member be in equilibrium?
A three force member can be in equilibrium only if the three forces are concurrent or parallel.
When is a rigid body force system said to be statically determinant?
When the equations of equilibrium are independent.
Can a statically determinant body be solved for all unknowns?
Yes
When is a rigid body force system said to be statically indeterminate?
When the body has more supports than are necessary for equilibrium.
Can a statically indeterminant body be solved for all unknowns?
Yes but in a statically indeterminant system. The redundant supports or redundant members need to removed to make the system determinant.
What are redundant supports and redundant members?
Those supports or members that can be removed or reduced in restraint without affecting the equilibrium position.
What is the degree of indeterminacy?
The number of redundant members.
What is a free body diagram?
It’s a representation of a body in equilibrium, showing all applied forces, moments, and reactions.
What do free body diagram not consider?
The internal structure or construction of the body.
What are the resultant of all the forces and moments equal to on the free body diagram?
Since the body is in equilibrium, they are equal to zero.
Any portions of the body that are conceptually removed, need to be replaced by what to maintain equilibrium in the free body diagram?
Must be replaced by the forces and moments those parts impart to the body.
What does a roller support?
It only supports vertical forces.
What does a pin support?
It supports vertical and horizontal forces.
What does a fixed connection support?
It supports vertical and horizontal forces, and a moment.
What is the procedure for finding the determinant reactions in two dimensional problems?
Establish a convenient set of coordinate axes. draw the free body diagram. Resolve the reaction at the pinned support. Establish a positive direction of rotation. Write the equilibrium equation for the moments about the pinned connection. Write the equilibrium equation for the forces in the vertical direction. Substitute the known vertical reaction from step 5 into the equilibrium equation from step 6. Write the equilibrium equation for the forces in the horizontal direction. If necessary, combine the horizontal and vertical force components at the pinned connection into a resultant reaction.
