THE BASIC FUNDAMENTALS OF STATICS The physical laws used in this study that govern the action and reaction of forces on a body include Sir Isaac Newton’s first and third Laws; First Law – A body at rest will remain at rest and any body in motion will move uniformly in a straight line unless acted upon by a force – which is a condition in structures called EQUILIBRIUM. Third Law – For every force of action, there is a reaction that is equal in magnitude, opposite in direction, and has the same line of action – which is the basic concept of FORCE.

Forces acting on a body generally cause two effects, and not necessarily simultaneously: a) It will cause the body to move if it is at rest or change the motion of the body if it is already in motion. b) It will cause a deformation of the body if the body is restrained. a horizontal beam will bend a member in compression will shorten a member in tension will stretch a member in shear will distort

A force is a QUANTITY, caused by an object that has mass, or weight – or a force is caused due to a RESISTANCE to a mass or weight. Forces in mathematics are represented by an illustration called a VECTOR, which is simply a representation that has MAGNITUDE, or value, and a DIRECTION. Use of vectors is a simple way to mathematically represent forces in order to determine the solution to a structural situation. Vectors can also be used to represent distance, mass, or area, but their elementary use in structures is to represent forces.

CHARACTERIZATION of a vector is evidenced by: 1 MAGNITUDE – the quantity of a force, a numerical measure of its intensity, usually in units of pounds or Newtons. 2 DIRECTION – the line of action of a force, such as gravity pulling downward due to weight, or resistance of a restraint pushing that weight upward to negate actual movement and remain static. 3 POINT OF APPLICATION – a location that generally describes the origin of a force.

 A weight supported from a ceiling by a string is represented by a vector, the line with the arrowhead that defines direction  A weight represented by a vector, supported by a post, using a vector to indicate resistance, the direction of each defined by the arrowheads.

 The magnitude of the force shown as 100 pounds, and the resistance shown as 100 pounds, both directions defined by the arrowheads. Point of application is the small circle.

In analysis of structural elements, it is necessary to add the effects of two or more forces to determine the net effect as though ONLY ONE FORCE produced the same result. This one force is called the RESULTANT of a series of forces. Parallelogram Law: If two forces act concurrently at a point, the resultant force can be represented by the diagonal of the parallelogram formed by the sides, parallel and proportional to the two forces.

 Illustration: If an object is under the influence of two forces as shown that tend to drag it along, and the magnitude of the two forces are illustrated by the length of their lines, then; A Which direction will the object be moved? B What is the magnitude of a single force that will move the object.

 Consider two forces 1 & 2, each represented by a straight line vector that indicates their magnitudes by the lengths, and directions by the arrowheads.  The two forces, acting together would have an influence on the object.  By the graphic parallelogram method, the RESULTANT, of the two forces can be constructed as shown, its value indicated by the graphic length.  The RESULTANT has the same effect on the object as do forces 1 & 2.

Obviously, if the numerical value of the vectors is known, and the directions defined by angles with some reference, the magnitude of the Resultant can be found using trigonometry. It can also be found graphically if the diagram is drawn accurately to scale. For instance this illustration was done by a cadd drawing, and the system is accurate enough that the lengths of the lines can simply be measured. Doing this on the drawing, F-1 measures units at an angle of 48 degrees, and F-2 measures 8.57 units at an angle of 115 degrees. The Resultant measures units at an angle of 78 degrees. The units can be in inches, feet, pounds, Newtons, or any other system of units, and the relationship between the forces and the resultant will remain the same. If the units are in pounds, realize that the single pound force has the same influence on the object as do the two forces of and 8.57 pound forces.

 On a cadd system, the angles are measured from the right side X axis of the Cartesian Coordinates, in a counter – clockwise direction.

 In the study of statics, the relationship of forces will be significant in determining structural qualities required to resist forces that occur in the built environment.  The X and Y axes of the Cartesian Coordinates system will become the reference for forces that have directions upward, downward, or at any angle.  Forces that are not parallel to the X and Y axes are the RESULTANT of component forces that are parallel and perpendicular to those axes.