coplanner & non-concurrent forces

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ATMIYA INSTITUTE OF TECHNOLOGY & SCIENCE MECHANICAL DEPARTMENT 3 rd SEMESTER COPLANNER & NON-CONCURRENT FORCES (MECHANICS OF SOLIDS – 2130003) PREPARED BY: Akash Ambaliya (140030119003) Akshay Amipara (140030119004) GUIDED BY: Sagar I. Shah (Asst. Prof.) MECH. DEPT.

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Page 1: COPLANNER & NON-CONCURRENT FORCES

ATMIYA INSTITUTE OF TECHNOLOGY & SCIENCEMECHANICAL DEPARTMENT

3rd SEMESTER

COPLANNER & NON-CONCURRENT FORCES

(MECHANICS OF SOLIDS – 2130003)

PREPARED BY:Akash Ambaliya (140030119003)

Akshay Amipara (140030119004)

GUIDED BY:Sagar I. Shah(Asst. Prof.)

MECH. DEPT.

Page 2: COPLANNER & NON-CONCURRENT FORCES

Definition• All forces do not meet at

a point, but lie in a single plane.

• An example is a ladder resting against wall when a person stands on a rung, which is not at its centre of gravity.

• In this case, for equilibrium, both the conditions of ladder need to be checked.

Page 3: COPLANNER & NON-CONCURRENT FORCES

Definition• The principles of equilibrium are also used to

determine the resultant of non-parallel, non-concurrent systems of forces.

• Simply put, all of the lines of action of the forces in this system do not meet at one point.

• The parallel force system was a special case of this type.

• Since all of these forces are not entirely parallel, the position of the resultant can be established using the graphical or algebraic methods of resolving co-planar forces discussed earlier or the link polygon.

Page 4: COPLANNER & NON-CONCURRENT FORCES

Resultant of Non-concurrent Forces

• If we want to replace a set of forces with a single resultant force we must make sure it has not only the total Fx, Fy but also the same moment effect (about any chosen point).

• It turns out that when we add up the moment of several forces we get the same answer as taking the moment of the resultant.

Page 5: COPLANNER & NON-CONCURRENT FORCES

Resultant of Non-concurrent Forces

• To obtain the total moment of a system of forces, we can either...– Calculate the moment caused by the

resultant of the system of forces about that point (So long as the resultant is in the RIGHT PLACE to create the right rotation).

– Calculate each moment (from each force separately) and add them up, keeping in mind the CW and CCW sign convention.

Page 6: COPLANNER & NON-CONCURRENT FORCES

Resultant of Non-concurrent Forces

• By using the principles of resolution composition & moment it is possible to determine analytically the resultant for coplanar non-concurrent system of forces.

• The procedure is as follows:– Select a Suitable Cartesian System for the given problem.– Resolve the forces in the Cartesian System– Compute fxi and fyi

– Compute the moments of resolved components about any point taken as the moment

– centre O. Hence find M0

Page 7: COPLANNER & NON-CONCURRENT FORCES

Resultant of Non-concurrent Forces

Page 8: COPLANNER & NON-CONCURRENT FORCES

Transformation of force to a force couple system• It is well known that moment of a force

represents its rotatary effect about an axis or a point.

• This concept is used in determining the resultant for a system of coplanar non-concurrent forces.

• For ay given force it is possible to determine an equivalent force – couple system.

Page 9: COPLANNER & NON-CONCURRENT FORCES

Transformation of force to a force couple system

Page 10: COPLANNER & NON-CONCURRENT FORCES

Transformation of force to a force couple system• A force F applied to a rigid body at a distance d from

the centre of mass has the same effect as the same force applied directly to the centre of mass and a couple Cℓ = Fd.

• The couple produces an angular acceleration of the rigid body at right angles to the plane of the couple.

• The force at the centre of mass accelerates the body in the direction of the force without change in orientation.

Page 11: COPLANNER & NON-CONCURRENT FORCES

Transformation of force to a force couple system• The general theorems are:

– A single force acting at any point O′ of a rigid body can be replaced by an equal and parallel force F acting at any given point O and a couple with forces parallel to F whose moment is M = Fd, d being the separation of O and O′.

• Conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately located.

• Any couple can be replaced by another in the same plane of the same direction and moment, having any desired force or any desired arm.

Page 12: COPLANNER & NON-CONCURRENT FORCES

Transformation of force to a force a couple system

Page 13: COPLANNER & NON-CONCURRENT FORCES

Applications of Couple Forces

• Couples are very important in mechanical engineering and the physical sciences. A few examples are:– The forces exerted by one's hand on a screw-

driver– The forces exerted by the tip of a screw-driver on

the head of a screw– Drag forces acting on a spinning propeller– Forces on an electric dipole in a uniform electric

field.– The reaction control system on a spacecraft.

Page 14: COPLANNER & NON-CONCURRENT FORCES

Example• Compute the

resultant for the system of forces shown in Fig 2 and hence compute the Equilibriant.

Page 15: COPLANNER & NON-CONCURRENT FORCES

Example (Solution)

Page 16: COPLANNER & NON-CONCURRENT FORCES

Thank You…