Transcript
Institute of Technology of Cambodia Subject: Mechanics
Chapter 02: Statics (Systems of force)
Subject: Mechanics
Lectured by: Mr. Sok Piseth
Group: GIM (I3)
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Projection of the force on an axis
Institute of Technology of Cambodia Subject: Mechanics
Addition of two concurrent forces
Institute of Technology of Cambodia Subject: Mechanics
The force in Cartesian system of reference
Institute of Technology of Cambodia Subject: Mechanics
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)
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Moment of a force about a given point
Institute of Technology of Cambodia Subject: Mechanics
Moment of a force about the origin of the system of reference
Institute of Technology of Cambodia Subject: Mechanics
Moment of a force about the origin of the system of reference
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Moment of a force about a given axis
Institute of Technology of Cambodia Subject: Mechanics
Moment of a force about a given axis
Institute of Technology of Cambodia Subject: Mechanics
Torsor statics
τ = R
M
R = 𝑅𝑥
𝑅𝑦
𝑅𝑧
M = 𝑀𝑥
𝑀𝑦
𝑀𝑧
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Couple
-By definition couple is the system made from two parallel forces with the same magnitudes and opposite senses.
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Reduction of a force in a given point
Institute of Technology of Cambodia Subject: Mechanics
Reduction of a system of forces in a given point
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Invariants of the system of forces. Minimum moment, central axis
Institute of Technology of Cambodia Subject: Mechanics
Invariants of the system of forces. Minimum moment, central axis
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Systems of coplanar forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of coplanar forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of coplanar forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of coplanar forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of coplanar forces
Institute of Technology of Cambodia Subject: Mechanics
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.
Institute of Technology of Cambodia Subject: Mechanics
Systems of parallel forces. Center of parallel forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of parallel forces. Center of parallel forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of parallel forces. Center of parallel forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of parallel forces. Center of parallel forces
Institute of Technology of Cambodia Subject: Mechanics
Systems of parallel forces. Center of parallel forces
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