Mechanics Statics (system of force)

Institute of Technology of Cambodia Subject: Mechanics

Chapter 02: Statics (Systems of force)

Subject: Mechanics

Lectured by: Mr. Sok Piseth

Group: GIM (I3)


The force

The force is defined as the action of a body about another body and it is a vector quantity. The vector quantity, the force, has four characteristic: magnitude, direction, sense and point of application.


Projection of the force on an axis


Addition of two concurrent forces


The force in Cartesian system of reference


The resultant forces of a system of concurrent forces (Theorem of projections)

-Geometrical method (rule of polygonal line and parallelogram) -Analytical method (theorem of projection)


Sample problem01

Problem01. Is given a system of forces as in the figure below in which the magnitudes of the forces are: F1 = 10N; F2 = 20N; F3 = 17.3 N. Calculate and represent the resultant force of the system of forces.


Moment of a force about a given point


Moment of a force about the origin of the system of reference


Sample problem02 Problem02. Is given a system of force as in the figure below. Is asked to calculate the resultant moment of this system about the point O (the origin of the reference system) knowing the magnitudes of the forces: F 1 = 2F, F 2 = 4F, F 3 = F and F 4 = 3F.


Moment of a force about a given axis


Torsor statics

τ = R

M

R = 𝑅𝑥

𝑅𝑦

𝑅𝑧

M = 𝑀𝑥

𝑀𝑦

𝑀𝑧


Sample problem03 Problem03. For the system of forces from the figure below. that acts on the sides of a parallelipipedium by known sides calculate the resultant moment with respect to the origin of the reference system. Are known: F 1 = 2F, F 2 = F, F 3 = 3F, F 4 = 2F, F 5 = 4F.


Couple

-By definition couple is the system made from two parallel forces with the same magnitudes and opposite senses.


Varignon’s theorem

This theorem says: for a system of concurrent forces the resultant moment of the system, calculated about a point, is equal to the moment of the resultant force of the system about the same point.


Reduction of a force in a given point


Reduction of a system of forces in a given point


Sample problem04 Problem04. About the paralelipipedium from the figure. acts a system of forces as in the picture. Knowing the magnitudes of the forces: F1=3F, F2 =F, F3 = 5F, F4=3F, F5 = 4F, F6 = 2F, calculate and represent the force-couple system in point O and after in point A.


Invariants of the system of forces. Minimum moment, central axis


Sample problem05 Problem05. The system of forces from the figure. acts about the cube by the side l. Knowing the magnitudes of the forces: F1 = F2 = F, F3 = F4 = F√2, calculate and represent the minimum force-couple system.


Varignon’s theorem for an arbitrary system of forces

For an arbitrary system of forces that has as simplest equivalent system an unique resultant force, the resultant moment of the system about an any point is equal to the moment of the unique resultant force about the same point.


Systems of coplanar forces


Sample problem06 Problem06. Represent the simplest equivalent system for the given system of coplanar forces from the picture. The magnitudes of the forces are: F1 = 3F, F2=2F, F3= 2F√2, F4 = F√13.


Systems of parallel forces. Center of parallel forces

Mechanics Statics (system of force)

Engineering

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