Statics
Statics is a basic engineering mechanics course that deals with force, moment, balance, support reactions, balance of rigid bodies, truss systems, frame and machine elements, distributed loads, modeling of fluid-induced loads, internal forces, N–T–M diagrams and area moment of inertia.
Course Content
ChaptersThe place of statics in engineering, the concept of equilibrium, rigid-body idealization and the effect of forces on mechanical systems are discussed. Newton's laws are interpreted in the context of static problems. The concepts of free body diagram, external force, internal force, support, connection and load idealization are introduced. In this section, the physical and mathematical importance of establishing correct models in statics problems is emphasized.
Vector representation of forces, separation into Cartesian components, two- and three-dimensional force systems are examined. Unit vectors, position vector, direction cosines and application of force along a line are studied through worked examples and problem solving. This chapter focuses on the reduction of multiple forces to resultant forces and the physical interpretation of force systems.
The moment of a force about a point or axis is considered using the vector product. The concepts of force couple, equivalent force-couple system and transfer of force to different points are examined. Moment calculation in two- and three-dimensional systems, direction of moment, sign convention and engineering interpretations are studied through worked examples and problem solving.
Equilibrium equations for particle and rigid body equilibrium are established systematically. Force and moment equations are used in two-dimensional and three-dimensional equilibrium problems. Correct drawing of the free-body diagram, identification of unknown reactions, and selection of the appropriate set of equations are improved by worked examples and problem solving.
Basic support and connection types such as roller, joint, built-in, cable, rod, pin and sliding connections are examined. It is explained in which directions each support type can carry force or moment. Calculation and physical meaning of support reactions in beam, frame and simple machine systems are studied through worked examples and problem solving.
Cage systems are modeled through two-force members and pin connections. Rod forces are calculated using the method of joints and the method of sections. Determination of tensile and compression elements, zero force elements, selection of appropriate cross-sections and structural behavior of truss systems are examined through worked examples and problem solving.
In frame and machine systems, multi-force elements, pin connections and interaction forces between elements are discussed. The system is divided into sub-parts, a free-body diagram is drawn for each element, and the equilibrium equations are solved together. In this section, force transfer in machine elements, connected mechanisms and carrier frames is examined with an engineering interpretation.
The concepts of center of gravity, center of mass and centroid are discussed through area and volume distributions. The equivalent resultant force and application point of linear, surface and volumetric distributed loads are calculated. Static equivalent worked examples and problem solving of triangular, trapezoidal and general variable distributed loads is studied.
Pressure distributions acting on surfaces, external loads caused by wind or flow, and how fluid-induced loads are transferred to static systems are examined at a basic level. Emphasis is placed on modeling such loads as equivalent distributed load, resultant force and moment. Establishing equilibrium equations for load-bearing elements, plates, poles and surfaces subject to pressure is studied through worked examples and problem solving.
The cross-method of sections is used to determine the internal forces in beam and frame elements. The concepts of normal force, shear force and bending moment are introduced. How the internal forces in any cross-section of an element are obtained by equilibrium equations, sign conventions and load-internal force relations are studied through worked examples and problem solving.
Normal force, shear force and bending moment diagrams are drawn for beams and simple frame elements. The effects of point load, distributed load, moment load and support reactions on the diagrams are examined. Physical and mathematical interpretation of N–T–M diagrams is made using the differential relationships between load, shear force and bending moment.
The concept of area moment of inertia is discussed through the effect of section geometry on bending behavior. Area moment of inertia calculations are made for rectangular, circular, triangular and compound areas. Parallel axis theorem, polar area moment of inertia, principal axes and moment of inertia calculation in compound sections are studied with worked examples and problem solving. In this section, the importance of area moment of inertia in terms of strength and structural design is interpreted.
Targeted Learning Outcomes
- Physically interpret the basic principles of statics, rigid-body idealization and the concept of equilibrium.
- Separate forces into vector components and calculate resultant force and moment
- Establish equilibrium equations by drawing a free body diagram suitable for particle and rigid body equilibrium.
- Accurately transfer support reactions, connection forces and external loads to the model
- Calculate element forces in truss, frame and machine systems with systematic methods
- Represent distributed loads and fluid-induced loads as equivalent resultant forces and moments
- Draw N–T–M diagrams by determining internal forces in beam and frame elements.
- Relate centroid and area moment of inertia calculations in compound areas to engineering applications.