Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment.
Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures.
A truss is an assembly of members such as beams, connected by nodes, that creates a rigid structure.
The year 1725 in science and technology involved some significant events.
In physics and engineering, a free body diagram is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members, or be a compact body. A series of free bodies and other diagrams may be necessary to solve complex problems. Sometimes in order to calculate the resultant force graphically the applied forces are arranged as the edges of a polygon of forces or force polygon.
A beam is a structural element that primarily resists loads applied laterally across the beam's axis. Its mode of deflection is primarily by bending, as loads produce reaction forces at the beam's support points and internal bending moments, shear, stresses, strains, and deflections. Beams are characterized by their manner of support, profile, equilibrium conditions, length, and material.
Louis Poinsot was a French mathematician and physicist. Poinsot was the inventor of geometrical mechanics, showing how a system of forces acting on a rigid body could be resolved into a single force and a couple.
A truss bridge is a bridge whose load-bearing superstructure is composed of a truss, a structure of connected elements, usually forming triangular units. The connected elements, typically straight, may be stressed from tension, compression, or sometimes both in response to dynamic loads. There are several types of truss bridges, including some with simple designs that were among the first bridges designed in the 19th and early 20th centuries. A truss bridge is economical to construct primarily because it uses materials efficiently.
In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.
In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action.
The work of a force on a particle along a virtual displacement is known as the virtual work.
Antonio Luigi Gaudenzio Giuseppe Cremona was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and algebraic surfaces, particularly through his paper Introduzione ad una teoria geometrica delle curve piane, and was a founder of the Italian school of algebraic geometry.
In the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each pair of faces in G that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Thus, each edge e of G has a corresponding dual edge, whose endpoints are the dual vertices corresponding to the faces on either side of e. The definition of the dual depends on the choice of embedding of the graph G, so it is a property of plane graphs rather than planar graphs. For planar graphs generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph.
Robert Maillart was a Swiss civil engineer who revolutionized the use of structural reinforced concrete with such designs as the three-hinged arch and the deck-stiffened arch for bridges, and the beamless floor slab and mushroom ceiling for industrial buildings. His Salginatobel (1929–1930) and Schwandbach (1933) bridges changed the aesthetics and engineering of bridge construction dramatically and influenced decades of architects and engineers after him. In 1991 the Salginatobel Bridge was declared an International Historic Civil Engineering Landmark by the American Society of Civil Engineers.
In the field of engineering mechanics, a zero force member is a member in a truss which, given a specific load, is at rest: neither in tension, nor in compression.
In engineering, an influence line graphs the variation of a function at a specific point on a beam or truss caused by a unit load placed at any point along the structure. Common functions studied with influence lines include reactions, shear, moment, and deflection (Deformation). Influence lines are important in designing beams and trusses used in bridges, crane rails, conveyor belts, floor girders, and other structures where loads will move along their span. The influence lines show where a load will create the maximum effect for any of the functions studied.
Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using either the moment area method or the conjugate beam method.
The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam. A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.
A structural support is a part of a building or structure that provides the necessary stiffness and strength in order to resist the internal forces and guide them safely to the ground. External loads that act on buildings cause internal forces in building support structures. Supports can be either at the end or at any intermediate point along a structural member or a constituent part of a building and they are referred to as connections, joints or restraints.
In architecture, the funicular curve is an approach used to design the compression-only structural forms using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by Robert Hooke in 1675. If the hanging rope carries just its own weight, the resulting curve is a catenary.
In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that facilitated analysis based on linear algebra. The beginning of the 21st century was marked by a "renaissance" of the technique driven by its addition to the computer-aided design tools thus enabling the architects to instantly visualize form and forces.
