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.) 2 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. 3 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. 4 Resultant of Two or More Parallel Vector Case 1 (Parallel Vectors) For vectors parallel horizontally: For vectors parallel vertically: 5 Case 2 (Perpendicular Vectors) By Pythagorean Theorem: Case 3 (Vectors acting at an angle other than 90⁰) 6 RESULTANT OF CONCURRENT FORCES 𝑅= (𝑅𝑥 )2 +(𝑅𝑦 )2 Where; 𝑅𝑥 = 𝐹𝑥 𝑅𝑦 = 𝐹𝑦 𝑅𝑦 𝜃 = 𝑡𝑎𝑛−1 (𝑅𝑥 ) 7