Statics of
Rigid Bodies
Force System – collection of forces acting at specified location.
Types of Force System:
A. Concurrent Force System – a force system in which all forces are acting
on the same point.
B. Parallel Force System – a force system in which all forces are parallel to
each other.
C. Non-concurrent and Non-parallel – a force system in which the forces
are not acting on same point at the same time not parallel.
(A.)
(B.)
(C.)
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MOMENT OF FORCE – it is the rotational effect of force into a specific point
or in a body. It is the product of force and perpendicular line/distance.
VARIGNON’S THEOREM – states that the moment of a force about any point
is equal to the sum of the moments of the components of the force about
same point.
RESULTANT – simplest force combination which can replace the original
forces without altering the external effect on the rigid body to which the
forces are applied.
EQUILIBRANT – a single force when added, the system will be in
equilibrium.
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Vectors in Two-Dimensional Space
1. Vector Components – the projections of the vector
on the coordinate axis.
2. Sign Convention of Vector Components
Note:
Vector to the Right and Upward are positive.
Vector to the Left and Downward are negative.
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Resultant of Two or More Parallel Vector
Case 1 (Parallel Vectors)
For vectors parallel horizontally:
For vectors parallel vertically:
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Case 2 (Perpendicular Vectors)
By Pythagorean Theorem:
Case 3 (Vectors acting at an angle other than 90⁰)
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RESULTANT OF CONCURRENT FORCES
𝑅=
(𝑅𝑥 )2 +(𝑅𝑦 )2
Where;
𝑅𝑥 =
𝐹𝑥
𝑅𝑦 =
𝐹𝑦
𝑅𝑦
𝜃 = 𝑡𝑎𝑛−1 (𝑅𝑥 )
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