Structural engineering in the context of Direct stiffness method

A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases (fluids), slurries, powders and masses of small solids. It can also be used for structural applications; a hollow pipe is far stiffer per unit weight than the solid members.

In common usage the words pipe and tube are usually interchangeable, but in industry and engineering, the terms are uniquely defined. Depending on the applicable standard to which it is manufactured, pipe is generally specified by a nominal diameter with a constant outside diameter (OD) and a schedule that defines the thickness. Tube is most often specified by the OD and wall thickness, but may be specified by any two of OD, inside diameter (ID), and wall thickness. Pipe is generally manufactured to one of several international and national industrial standards. While similar standards exist for specific industry application tubing, tube is often made to custom sizes and a broader range of diameters and tolerances. Many industrial and government standards exist for the production of pipe and tubing. The term "tube" is also commonly applied to non-cylindrical sections, i.e., square or rectangular tubing. In general, "pipe" is the more common term in most of the world, whereas "tube" is more widely used in the United States.

A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term column applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a post. Supports with a rectangular or other non-round section are usually called piers.

For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces. Other compression members are often termed "columns" because of the similar stress conditions. Columns are frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In architecture, "column" refers to such a structural element that also has certain proportional and decorative features. These beautiful columns are available in a broad selection of styles and designs in round tapered, round straight, or square shaft styles. A column might also be a decorative element not needed for structural purposes; many columns are engaged, that is to say form part of a wall. A long sequence of columns joined by an entablature is known as a colonnade.

The ArcelorMittal Orbit (often referred to as the Orbit Tower or its original name, Orbit) is a 114.5-metre (376-foot) sculpture and observation tower in Queen Elizabeth Olympic Park in Stratford, London. It is Britain's largest piece of public art, and is intended to be a permanent lasting legacy of London's hosting of the 2012 Summer Olympic and Paralympic Games, assisting in the post-Olympics regeneration of the Stratford area. Sited between London Stadium (formerly called the Olympic Stadium) and the Aquatics Centre, it allows visitors to view the whole Olympic Park from two observation platforms.

Orbit was designed by Turner Prize–winning artist Anish Kapoor and Cecil Balmond of Arup Group, an engineering firm. Announced on 31 March 2010, it was expected to be completed by December 2011. The project came about after Mayor of London Boris Johnson and Olympics Minister Tessa Jowell decided in 2008 that the Olympic Park needed "something extra". Designers were asked for ideas for an "Olympic tower" at least 100 metres (330 ft) high: Orbit was the unanimous choice from proposals considered by a nine-person advisory panel. Kapoor and Balmond believed that Orbit represented a radical advance in the architectural field of combining sculpture and structural engineering, and that it combined both stability and instability in a work that visitors can engage with and experience via an incorporated spiral walkway. It has been both praised and criticised for its bold design, and has especially received criticism as a vanity project of questionable lasting use or merit as a public art project.

The Delft University of Technology (TU Delft; Dutch: Technische Universiteit Delft) is the oldest and largest Dutch public technical university, located in Delft, Netherlands. It specializes in engineering, technology, computing, design, and natural sciences.

It is considered one of the leading technical universities in Europe and is consistently ranked as one of the best schools for architecture and engineering in the world. According to the QS World University Rankings it ranked 3rd worldwide for architecture and 13th for Engineering & Technology in 2024. It also ranked 3rd best worldwide for mechanical and aerospace engineering, 3rd for civil and structural engineering, 11th for chemical engineering, and 12th for design.

Brutalist architecture is an architectural style that emerged during the 1950s in the United Kingdom, among the reconstruction projects of the post-war era. Brutalist buildings are characterised by minimalist construction showcasing the bare building materials and structural elements over decorative design. The style commonly makes use of exposed, unpainted concrete or brick, angular geometric shapes and a predominantly monochrome colour palette; other materials, such as steel, timber, and glass, are also featured.

Descended from Modernism, brutalism is said to be a reaction against the nostalgia of architecture in the 1940s. Derived from the Swedish word nybrutalism, the term "new brutalism" was first used by British architects Alison and Peter Smithson for their pioneering approach to design. The style was further popularised in a 1955 essay by architectural critic Reyner Banham, who also associated the movement with the French phrases béton brut ("raw concrete") and art brut ("raw art"). The style, as developed by architects such as the Smithsons, Hungarian-born Ernő Goldfinger, and the British firm Chamberlin, Powell & Bon, was partly foreshadowed by the modernist work of other architects such as French-Swiss Le Corbusier, Estonian-American Louis Kahn, German-American Ludwig Mies van der Rohe, and Finnish Alvar Aalto.

In structural engineering, structural elements are used in structural analysis to split a complex structure into simple elements (each bearing a structural load). Within a structure, an element cannot be broken down (decomposed) into parts of different kinds (e.g., beam or column).

Structural building components are specialized structural building products designed, engineered and manufactured under controlled conditions for a specific application. They are incorporated into the overall building structural system by a building designer. Examples are wood or steel roof trusses, floor trusses, floor panels, I-joists, or engineered beams and headers. A structural building component manufacturer or truss manufacturer is an individual or company regularly engaged in the manufacturing of components.

In structural engineering, a tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with tensegrity, which is a structural form with both tension and compression elements. Tensile structures are the most common type of thin-shell structures.

Most tensile structures are supported by some form of compression or bending elements, such as masts (as in The O₂, formerly the Millennium Dome), compression rings or beams.

In engineering, a foundation is the element of a structure which connects it to the ground or more rarely, water (as with floating structures), transferring loads from the structure to the ground. Foundations are generally considered either shallow or deep. Foundation engineering is the application of soil mechanics and rock mechanics (geotechnical engineering) in the design of foundation elements of structures.

The term structural system or structural frame in structural engineering refers to the load-resisting sub-system of a building or object. The structural system transfers loads through interconnected elements or members.

Commonly used structures can be classified into five major categories, depending on the type of primary stress that may arise in the members of the structures under major design loads. However any two or more of the basic structural types described in the following may be combined in a single structure, such as a building or a bridge in order to meet the structure's functional requirements.

In structural engineering, the tube is a system where, to resist lateral loads (wind, seismic, impact), a building is designed to act like a hollow cylinder, cantilevered perpendicular to the ground. This system was introduced by Fazlur Rahman Khan while at the architectural firm Skidmore, Owings & Merrill (SOM), in their Chicago office. The first example of the tube's use is the 43-story Khan-designed DeWitt-Chestnut Apartment Building, since renamed Plaza on DeWitt, in Chicago, Illinois, finished in 1966.

The system can be built using steel, concrete, or composite construction (the discrete use of both steel and concrete). It can be used for office, apartment, and mixed-use buildings. Most buildings of over 40 stories built since the 1960s are of this structural type.

A structural load or structural action is a mechanical load (more generally a force) applied to structural elements. A load causes stress, deformation, displacement or acceleration in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such as aircraft, satellites, rockets, space stations, ships, and submarines—are subject to their own particular structural loads and actions. Engineers often evaluate structural loads based upon published regulations, contracts, or specifications. Accepted technical standards are used for acceptance testing and inspection.

In structural engineering, deflection is the degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load. It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement).A longitudinal deformation (in the direction of the axis) is called elongation.

The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.Otherwise methods such as virtual work, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method are used. The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory.

In mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (compression). It is opposed to tensile strength which withstands loads tending to elongate, resisting tension (being pulled apart). In the study of strength of materials, compressive strength, tensile strength, and shear strength can be analyzed independently.

Some materials fracture at their compressive strength limit; others deform irreversibly, so a given amount of deformation may be considered as the limit for compressive load. Compressive strength is a key value for design of structures.

In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior.

In structural engineering, a structural beam or column can become unstable when excessive compressive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This can take the form of buckling or crippling. The general field of study is called structural stability.

The history of robots has its origins in the ancient world. During the Industrial Revolution, humans developed the structural engineering capability to control electricity so that machines could be powered with small motors. In the early 20th century, the notion of a humanoid machine was developed.

The first uses of modern robots were in factories as industrial robots. These industrial robots were fixed machines capable of manufacturing tasks which allowed production with less human work. Digitally programmed industrial robots with artificial intelligence have been built since the 2000s.

The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an ${\displaystyle I}$ (for an axis that lies in the plane of the area) or with a ${\displaystyle J}$ (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension, when working with the International System of Units, is meters to the fourth power, m, or inches to the fourth power, in, when working in the Imperial System of Units or the US customary system.

In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam. In order to maximize the second moment of area, a large fraction of the cross-sectional area of an I-beam is located at the maximum possible distance from the centroid of the I-beam's cross-section. The planar second moment of area provides insight into a beam's resistance to bending due to an applied moment, force, or distributed load perpendicular to its neutral axis, as a function of its shape. The polar second moment of area provides insight into a beam's resistance to torsional deflection, due to an applied moment parallel to its cross-section, as a function of its shape.

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 physical structures and their components. In contrast to theory of elasticity, the models used in structural 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 lattice tower, or truss tower, is a freestanding vertical framework tower. This construction is widely used in transmission towers carrying high-voltage electric power lines, in radio masts and towers (both self-radiating towers and those that support aerials) and in observation towers. Its advantage is good shear strength at a much lower weight than a tower of solid construction would have as well as lower wind resistance.

In structural engineering, the term lattice tower is used for a freestanding structure, while a lattice mast is a guyed mast supported by guy lines. Lattices of triangular (three-sided) cross-section are most common, particularly in North America. Square (four-sided) lattices are also widely used and are most common in Eurasia. A lattice towers is often designed as either a space frame or a hyperboloid structure.