The people behind Mathalino. Skip to main content. Engineering Mechanics. Content so far Contents so far Subscribe to MATHalino. Please join our community. Login or Register or Login With Facebook. Like us on Facebook. Rectangular Components of a Force. Moment of a Force about a Point. Resultant of Concurrent Forces. It shows the forces acting on the body instead of the geometrical constraints through the supports.
Chapter 5. This procedure is still valid when a mechanical system becomes movable dynamic due to freeing. In this case, the system is regarded as being frozen when the reaction forces are determined. Section 5. An external force acts from the outside on a mechanical system. Active forces as well as reaction forces are external forces. Internal forces act between the parts of a system. They also can be visualized only by imaginary cutting or sectioning of the body.
If the body in Fig. Accordingly, the system initially consists of the complete body at rest. After the cut, the system consists of two parts that act on each other through area forces in such a way that each part is in equilibrium. This procedure, which enables calculation of the internal forces, is called the method of sections.
It is valid for systems in equilibrium as well as for systems in motion.
If the entire body in Fig. As stated in Section 1. Consequently, the principle of transmissibility can be used in the analysis of the external forces. However, this principle can generally not be applied to internal forces. In this case, the body is sectioned by imaginary cuts, therefore it matters whether an external force acts on one or the other part. The importance of internal forces in engineering sciences is derived from the fact that their magnitude is a measure of the stress in the material. This axiom states that a force always has a counteracting force of the same magnitude but of opposite direction.
Therefore, a force can never exist alone. If a hand is pressed against a wall, the hand exerts a force F on the wall Fig. An opposite force of the same magnitude acts from the wall on the hand. These forces can be made visible if the two bodies are separated at the area of contact. Note that the forces act upon 1.
Analogously, a body on earth has a certain weight G due to gravity. In short: The forces that two bodies exert upon each other are of the same magnitude but of opposite directions and they lie on the same line of action. Volume 3. It is valid for longrange forces as well as for short-range forces, and it is independent of whether the bodies are at rest or in motion.
They are characterized by a normal vector n that points outward from the interior of the beam. As in the case of plane problems, we cut the beam at an arbitrary position x compare Section 7. Statically indeterminate systems cannot be solved with the aid of the equilibrium conditions alone. It consists of a square and two triangles. If the two bodies are merely touching each other i.
Force is another important element that is considered; however, from a physical point of view, force is a derived quantity. All other mechanical quantities, such as velocity, momentum or energy can be expressed by these four quantities. The geometrical space where mechanical processes take place is threedimensional.
The magnitude of a physical quantity is completely expressed by a number and the unit. In numerical calculations units are treated in the same way as numbers. In physical equations, each side and each additive term must have the same dimension. This should always be kept in mind when equations are formulated or checked. Table 1.
Customary Unit SI Equivalent 1 ft 0. Customary system of units is still frequently used although the SI system is recommended. As division and multiples of length the inch in , yard yd and mile mi are used. In Table 1. In any case, it is important that engineers express themselves clearly and in a way that can be readily understood since they have to present the formulation as well as the solution of a problem to other engineers and to people with no engineering background.
This book contains the most important formulas and more than completely solved problems from Statics. It provides engineering students material to. Editorial Reviews. From the Back Cover. This book contains the most important formulas and more than completely solved problems from Statics. It provides .
Formulation of the engineering problem. Establishing a mechanical model that maps all of the essential characteristics of the real system.
Considerations regarding the quality of the mapping. Solution of the mechanical problem using the established model. This is usually done with the aid of a sketch of the mechanical system. Symbols must be assigned to the unknown quantities.
It should be ensured in advance that the number of equations is equal to the number of unknowns. Discussion and interpretation of the solution. In the examples given in this textbook, usually the mechanical model is provided and Step 3 is concentrated upon, namely the solution of mechanical problems on the basis of models. Nevertheless, it should be kept in mind that these models are mappings of real bodies or systems whose behavior can sometimes be judged from daily experience. Therefore, it is always useful to compare the results of a calculation with expectations based on experience.
Regarding the accuracy of the results, it is necessary to distinguish between the numerical accuracy of calculations and the accuracy of the model. A numerical result depends on the precision of the input data and on the precision of our calculation. Therefore, the results can never be more precise than the input data.
Consequently, results should never be expressed in a manner that suggests a non-existent accuracy e.
The accuracy of the result concerning the behavior of the real system depends on the quality of the model. For example, the trajectory of a stone that has been thrown can be determined by taking air resistance into account or by disregarding it. It is the task of the engineer to develop a model in such a way that it has the potential to deliver the accuracy required for the concrete problem. Examples of such idealizations: rigid body, concentrated force. Such forces are called concurrent forces. Note that forces always act on a body; there are no forces without action on a body.
If all the forces acting on a body act in a plane, they are called coplanar forces. Students will learn in this chapter how to determine the resultant of a system of concurrent forces and how to resolve force vectors into given directions. They will also learn how to correctly isolate the body under consideration and draw a free-body diagram, in order to be able to formulate the conditions of equilibrium. It is postulated that the two forces can be replaced by a statically equivalent force R. This postulate is an axiom; it is known as the parallelogram law of forces.
The force R is called the resultant of F 1 and F 2. It is the diagonal of the parallelogram for which F 1 and F 2 are adjacent sides. The construction of the parallelogram is the geometrical representation of the summation of the vectors see Appendix A. Such a system is called a coplanar system of concurrent forces. The resultant can be obtained through successive application of the parallelogram law of forces.
Therefore, they do not have to act at point A; only their lines of action have to intersect at this point. This procedure has the disadvantage that the lines of action cannot be seen to intersect at one point. This disadvantage, however, is more than compensated for by the fact that the construction can easily be extended to an arbitrary number of n forces, which are added head-to-tail as shown in Fig.
The resultant R is the vector that points from the initial point a to the endpoint b of the force polygon.