Structural engineering

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Structural engineering is a field of engineering that deals with the design of structural systems with the purpose of supporting and resisting various loads. Though other disciplines touch on this field, a physical object or system is truly considered a part of structural engineering, regardless of its central scientific or industrial application, if its main function is designed to resist loads and dissipate energy. Structural engineering is usually considered a specialty discipline within civil engineering, but it can also be studied in its own right.^[1]

A structural engineer is most commonly involved in the design of buildings and nonbuilding structures^[2]but also plays an essential role in designing machinery where structural integrity of the design item impacts safety and reliability. Large man-made objects, from furniture to medical equipment to a variety of vehicles, require significant design input from a structural engineer.

Structural engineers ensure that their designs satisfy a given "design intent", predicated on safety criteria (e.g. structures do not collapse without due warning under any circumstances), or serviceability or performance criteria (e.g. floor vibration and building sway do not result in discomfort for the occupants). Structural engineers are responsible for making creative and efficient use of funds and materials to achieve these goals. ^[2]

Contents 1 Etymology 2 The structural engineer 3 History of structural engineering 3.1 Pre-twentieth century structural engineering developments 3.2 Modern developments in structural engineering 3.3 Significant structural failures 4 Specialisations 4.1 Building structures 4.2 Civil engineering structures 4.3 Mechanical structures 5 Structural elements 5.1 Columns 5.2 Beams 5.2.1 Trusses 5.3 Plates 5.4 Shells 5.5 Arches 5.6 Catenaries 6 Structural engineering theory 6.1 Loads 6.2 Strength 6.3 Stiffness 6.4 Safety factors 6.4.1 Load cases 6.5 Newton's Laws of Motion 6.6 Statical determinacy 6.7 Elasticity 6.8 Plasticity 6.9 The Euler-Bernoulli beam equation 6.10 Buckling 7 Materials 7.1 Iron 7.1.1 Wrought iron 7.1.2 Cast iron 7.1.3 Steel 7.1.4 Stainless steel 7.2 Concrete 7.3 Aluminium 7.4 Composites 7.5 Masonry 7.6 Timber 7.7 Other structural materials 8 See also 9 References 10 Notes 11 External links

[edit] Etymology

The term structural derives from the Latin word structus, which is "to pile, build assemble". The first use of the term structure was c.1440.^[3] The term engineer derives from the old French term engin, meaning "skill, cleverness" and also 'war machine'. This term in turn derives from the Latin word ingenium, which means "inborn qualities, talent", and is constructed of in- "in" + gen-, the root of gignere, meaning "to beget, produce." The term engineer is related to ingenious.^[4]

The term structural engineer is generally applied only to those who have completed a degree in structural engineering. The term engineer in isolation varies widely in its use and application, and can, depending on the geographical location of its use, refer to many different technical and creative professions in its common usage.

[edit] The structural engineer

Main article: Structural engineer

Structural engineers are responsible for producing engineering design or analysis. Entry-level structural engineers may design the individual structural elements of a structure, for example the beams, columns, and floors of a building. More experienced engineers would be responsible for the structural design and integrity of an entire system, such as how a building in its entirety resists vertical and lateral forces on it without collapsing or failing to function.

Structural engineers often specialise in particular fields, such as bridge engineering, building engineering, pipeline engineering, industrial structures or special structures such as vehicles or aircraft.

Structural engineering has existed since humans first started to construct their own structures. It became a more defined and formalised profession with the emergence of the architecture profession as distinct from the engineering profession during the industrial revolution in the late 19th Century. Until then, the architect and the structural engineer were often one and the same - the master builder. Only with the understanding of structural theories that emerged during the 19th and 20th century did the professional structural engineer as it is known now begin to exist.

The role of a structural engineer today involves a significant understanding of both static and dynamic loading, and the structures that are available to resist them. The complexity of modern structures often requires great creativity in order to support and resist the loads they are subjected to. A structural engineer will typically have a three, four or five year undergraduate degree, followed by a minimum of three years of professional practice before being able to be considered fully qualified.^[5]

Structural engineers are licensed or accredited by different learned societies and regulatory bodies around the world (for example, the Institution of Structural Engineers in the UK)^[5]. Depending on the degree course they have studied, they may be accredited (or licensed) as just structural engineers, or as civil and as structural engineers.

[edit] History of structural engineering

Structural engineering dates back to at least 2700 BC when the step pyramid for Pharoah Djoser was built by Imhotep, the first engineer in history known by name. Pyramids were the most common major structures built by ancient civilisations because it is a structural form which is inherently stable and can be almost infinitely scaled (as opposed to most other structural forms, which cannot be linearly increased in size in proportion to increased loads).^[6]

Throughout ancient and medieval history most architectural design and construction was carried out by artisans, such as stone masons and carpenters, rising to the role of master builder. No theory of structures existed and understanding of how structures stood up was extremely limited, and based almost entirely on empirical evidence of 'what had worked before'. Knowledge was retained in guilds and seldom supplanted by advances. Structures were repetitive, and increases in scale were incremental.^[6]

No record exists of the first calculations of the strength of structural members or the behaviour of structural material, but the profession of structural engineer only really took shape with the industrial revolution and the re-invention of concrete (see History of concrete). The physical sciences underlying structural engineering began to be understood in the Renaissance and have been developing ever since.

[edit] Pre-twentieth century structural engineering developments

• In the 27th century BC, Imhotep was the first structural engineer known by name and constructed the first step pyramid in ancient Egypt.

• In the 26th century BC, the Great Pyramid of Giza was constructed in Egypt. It remained the largest man-made structure for millennia and was considered an unsurpassed feat in architecture until the 19th century AD.^[7]

• In the 3rd Century BC Archimedes published his work On the Equilibrium of Planes in two volumes, in which he sets out the Law of the Lever, stating:

“

Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.

”

Archimedes used the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, paraboloids, and hemispheres. ^[8] Archimedes work on this and his work on calculus and geometry, together with Euclidian geometry, underpin much of the mathematics and understanding of structures in modern structural engineering.

• Roman engineers pioneered large structures in masonry and concrete, many of which are still standing today. They include aqueducts, thermae, columns, lighthouses, defensive walls and harbours. Their methods are recorded by Vitruvius in his De Architectura written in 25 BC, a manual of civil and structural engineering with extensive sections on materials and machines used in construction. One reason for their success is their accurate surveying techniques based on the dioptra, groma and chorobates.

• In the 11th and 12th centuries AD, al-Biruni and al-Khazini were the first to apply experimental scientific methods to statics and dynamics, particularly for determining specific weights, such as those based on the theory of balances and weighing. They unified statics and dynamics into the science of mechanics, and they combined the fields of hydrostatics with dynamics to give birth to hydrodynamics. They applied the mathematical theories of ratios and infinitesimal techniques, and introduced algebraic and fine calculation techniques into the field of statics. They were also the first to generalize the theory of the centre of gravity and the first to apply it to three-dimensional bodies. They also founded the theory of the ponderable lever and created the "science of gravity" which was later further developed in medieval Europe.^[9]

• In the 15th and 16th centuries, Leonardo da Vinci, despite lacking beam theory and calculus produced many engineering designs based on scientific observations and rigour, including a design for a bridge to span the Bosporus. Though dismissed at the time, the design has since been judged to be both feasible and structurally valid^[10]

• In 1638 Galileo published Dialogues Relating to Two New Sciences^[11], outlining the sciences of the strength of materials and the motion of objects (essentially defining gravity as a force giving rise to a constant acceleration). It was the first establishment of a scientific approach to structural engineering, including the first attempts to develop a theory for beams. This is also regarded as the beginning of structural analysis, the mathematical representation and design of building structures.

• In 1676 Robert Hooke first stated Hooke's Law, providing a scientific understanding of elasticity of materials and their behaviour under load.^[12]

• In 1687 Sir Isaac Newton published Philosophiae Naturalis Principia Mathematica, setting out his Laws of Motion, providing for the first time an understanding of the fundamental laws governing structures.^[13]

• In the 17th century Sir Isaac Newton and Gottfried Leibniz independently developed the Fundamental theorem of calculus, providing one of the most important mathematical tools in engineering.^[14]

• In the 18th century Leonhard Euler pioneered much of the mathematics and many of the methods which allow structural engineers to model and analyse structures. Specifically, he developed the Euler-Bernoulli beam equation with Daniel Bernoulli circa 1750 - the fundamental theory underlying most structural engineering design.^[15][16]

• In the 18th century Johann (Jean) Bernoulli (1667-1748) and Daniel Bernoulli (1700-1782) are credited with formulating the theory of virtual work, providing a tool using equilibrium of forces and compatibility of geometry to solve structural problems. In 1717 Jean Bernoulli wrote to Pierre Varignon explaining the principle of virtual work, while in 1726 Daniel Bernoulli wrote of the "composition of forces".^[17]

• In 1757 Leonhard Euler derived the Euler buckling formula, greatly advancing the ability of engineers to design compression elements.^[16]

• In 1821 Claude-Louis Navier formulated the general theory of elasticity in a mathematically usable form. In his lecons of 1826 he explored a great range of different structural theory, and was the first to highlight that the role of a structural engineer is not to understand the final, failed state of a structure, but to prevent that failure in the first place.^[15] In 1826 he also established the elastic modulus as a property of materials independent of the second moment of area, allowing engineers for the first time to both understand structural behaviour and structural materials.^[18]

• In 1873 Carlo Alberto Castigliano presented his dissertation "Intorno ai sistemi elastici", which contains his theorem for computing displacement as partial derivative of the strain energy.^[19]

[edit] Modern developments in structural engineering

Throughout the late 19th and early 20th centuries, materials science and structural analysis underwent development at a tremendous pace.

• In 1824, Portland cement was patented by the engineer Joseph Aspdin as "a superior cement resembling Portland Stone", British Patent no. 5022. Although different forms of cement already existed (Pozzolanic cement was used by the Romans as early as 100 B.C. and even earlier by the ancient Greek and Chinese civilizations) and were in common usage in Europe from the 1750s, the discovery made by Aspdin used commonly available, cheap materials, making concrete construction an economical possibility.^[20]

• In 1848 Joseph-Louis Lambot built a rowing boat of ferrocement - the forerunner of modern reinforced concrete. He patented his system of mesh reinforcement and concrete in 1855, one year after W.B. Wilkinson also patented a similar system.^[21]

• In the 1850s Henry Bessemer developed the Bessemer process to produce steel. He gained patents for the process in 1855 and 1856 and successfully completed the conversion of cast iron into cast steel in 1858.^[22] Eventually mild steel would replace both wrought iron and cast iron as the preferred metal for construction.

• In 1867, a reinforced concrete planting tub was patented by Joseph Monier in Paris, using steel mesh reinforcement similar to that used by Lambot and Wilkinson. Monier took the idea forward, filing several patents for tubs, slabs and beams, leading eventually to the Monier system of reinforced structures, the first use of steel reinforcement bars located in areas of tension in the structure. ^[23]

• During the late 19th century, great advancements were made in the use of cast iron, gradually replacing wrought iron as a material of choice. Ditherington Flax Mill in Shrewsbury, designed by Charles Bage, was the first building in the world with an interior iron frame. It was built in 1797. In 1792 William Strutt had attempted to build a fireproof mill at Belper in Derby (Belper West Mill), using cast iron columns and timber beams within the depths of brick arches that formed the floors. The exposed beam soffits were protected against fire by plaster. This mill at Belper was the world's first attempt to construct fireproof buildings, and is the first example of fire engineering. This was later improved upon with the construction of Belper North Mill, a collaboration between Strutt and Bage, which by using a full cast iron frame represented the world's first "fire proofed" building.^[24][25]

• The Forth Bridge was built by Benjamin Baker, Sir John Fowler and William Arrol in 1889, using steel, one of the first major uses of the material, and a landmark construction in bridge design.

• In 1889, the wrought-iron Eiffel Tower was built by Gustave Eiffel and Maurice Koechlin, demonstrating the potential of construction using iron, despite the fact that steel construction was already being used elsewhere.

• During the late 19th century, Russian structural engineer Vladimir Shukhov developed analysis methods for tensile structures, thin-shell structures and new structural geometries such as hyperboloid structures. Pipeline transport was pioneered by Vladimir Shukhov and the Branobel company in the late 19th century.

• From 1892 onwards François Hennebique's firm used his patented reinforced concrete system to build thousands of structures throughout Europe. Thaddeus Hyatt in the US and Wayss & Freitag in Germany also patented systems. The firm AG für Monierbauten constructed 200 reinforced concrete bridges in Germany between 1890 and 1897 ^[26]

• During the first third of the 20th century, Robert Maillart and others pioneered the use of reinforced concrete, and greatly furthered the understanding of its behaviour. Maillart noticed that many concrete bridge structures were significantly cracked, and as a result left the cracked areas out of his next bridge design - correctly believing that if the concrete was cracked, it was not contributing to the strength. Wilhelm Ritter formulated the truss theory for the shear design of reinforced concrete beams in 1899, and Emil Mörsch improved this in 1902. He went on to demonstrate that treating concrete in compression as a linear-elastic material was a conservative approximation of its behaviour^[27]. Concrete design and analysis has been progressing ever since, with the development of analysis methods such as yield line theory, based on plastic analysis of concrete (as opposed to linear-elastic), and many different variations on the model for stress distributions in concrete in compression^{[28] [29]}

• Prestressed concrete, pioneered by Eugène Freyssinet with a patent in 1928, gave a novel approach in overcoming the weakness of concrete structures in tension. Freyssinet constructed an experimental prestressed arch in 1908 and later used the technology in a limited form in the Plougastel Bridge in France in 1930. He went on to build six prestressed concrete bridges across the Marne River, firmly establishing the technology.^[30]

• In 1930 Professor Hardy Cross's developed his Moment Distribution Method, allowing the real stresses of many complex structures to be approximated quickly and accurately.^[31]

• In the mid 20th century John Fleetwood Baker developed the plasticity theory of structures, providing a powerful tool for the safe design of steel structures.^[31]

• In the second half of the 20th century, Fazlur Khan, designed structural systems that remain fundamental to all high-rise skyscrapers and which he employed in his structural designs for the John Hancock Center in 1969 and Sears Tower in 1973.^[32] Khan's central innovation in skyscraper design and construction was the idea of the "tube" and "bundled tube" structural systems for tall buildings.^[33][34] Another innovation that Khan developed was the concept of X-bracing, which reduced the lateral load on the building by transferring the load into the exterior columns. This allowed for a reduced need for interior columns thus creating more floor space, and can be seen in the John Hancock Center.

• In 1987 Jörg Schlaich and Kurt Schafer published the culmination of almost ten years of work on the strut and tie method for concrete analysis - a tool to design structures with discontinuities such as corners and joints.^[35]

• In the late 20th and early 21st centuries the development of powerful computers has allowed finite element analysis to become a significant tool for structural analysis and design. The development of finite element programs has led to the ability to accurately predict the stresses in complex structures, and allowed significant advances in structural engineering design and architecture. In the 1960s and 70s computational analysis was used in a significant way for the first time on the design of the Sydney Opera House roof. Many modern structures could not be understood and designed without the use of computational analysis.^[36]

Developments in the understanding of materials and structural behaviour in the latter part of the 20th century have been significant, with detailed understanding being developed of topics such as fracture mechanics, earthquake engineering, composite materials, temperature effects on materials, dynamics and vibration control, fatigue, creep and others. The depth and breadth of knowledge now available in structural engineering, and the increasing range of different structures and the increasing complexity of those structures has led to increasing specialisation of structural engineers.

[edit] Significant structural failures

Main article: Structural failure

Mechanical failure modes
Buckling
Corrosion
Creep
Fatigue
Fracture
Impact
Melting
Mechanical overload
Thermal shock
Wear
Yielding
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Structural engineering has advanced significantly because of the greater understanding of structures achieved from studying structural failures. The history of structural engineering contains many collapses and failures. Amongst the most significant in developing structural engineering knowledge are:

• On 24 May 1847 the Dee Bridge collapsed as a train passed over it, with the loss of 5 lives. It was designed by Robert Stephenson, using cast iron girders reinforced with wrought iron struts. The bridge collapse was subject to one of the first formal inquiries into a structural failure. The result of the enquiry was that the design of the structure was fundamentally flawed, as the wrought iron did not reinforce the cast iron at all, and due to repeated flexing it suffered a brittle failure due to fatigue.^[37]

• The Dee bridge disaster was followed by a number of cast iron bridge collapse, including the collapse of the first Tay Rail Bridge on 28 December 1879, also when a train passed over it. 75 people lost their lives. The bridge failed because of poorly made cast iron, and the failure of the designer Thomas Bouch to consider wind loading on the bridge. The collapse resulted in cast iron largely being replaced by steel construction, and a complete redesign of the Forth Railway Bridge of 1890. The Forth Bridge was as a result the first entirely steel bridge in the world.^[38]

• In 1940 the first Tacoma Narrows Bridge collapsed spectacularly due to wind induced resonant vibration with positive feedback (causing continually increasing amplitude). This collapse, and the research that followed, led to increased understanding of wind/structure interactions, including the phenomenon of flutter, a torsional mode of vibration. Several bridges were altered following the collapse to prevent a similar event occurring again. The only fatality was 'Tubby' the dog.^[38]

• During 1954 two de Havilland Comet C1 jet airliners, the world's first commercial airliner, crashed with the loss of all on board. After lengthy investigations, and the grounding of all Comet airliners, the cause was discovered to be metal fatigue at the corners of the windows. The square corners had led to stress concentrations which after continual stress cycles from pressurisation and de-pressurisation, failed catastropically in flight. The research into the failures led to significant improvements in understanding of fatigue loading of airframes, and the redesign of the Comet and all subsequent airliners to incorporate rounded corners to doors and windows.

• On 16 May 1968 the 22 storey residential tower Ronan Point in the London borough of Newham collapsed when a relatively small gas explosion on the 18th floor caused a structural wall panel to be blown away from the building. The tower was constructed of precast concrete, and the failure of the single panel caused one entire corner of the building to collapse. The panel was able to be blown out because there was insufficient reinforcement steel passing between the panels. This also meant that the loads carried by the panel could not be redistributed to other adjacent panels, because there was no route for the forces to follow. As a result of the collapse, building regulations were overhauled to prevent disproportionate collapse, and the understanding of precast concrete detailing was greatly advanced. Many similar buildings were altered or demolished as a result of the collapse.^[39]

• On 17 July 1981, two suspended walkways through the lobby of the Hyatt Regency in Kansas City, Missouri, collapsed, killing 114 people at a tea dance. The collapse was due to a late change in design, altering the method in which the rods supporting the walkways were connected to them, and inadvertently doubling the forces on the connection. The failure highlighted the need for good communication between design engineers and contractors, and rigorous checks on designs and especially on contractor proposed design changes. The failure is a standard case study on engineering courses around the world, and is used to teach the importance of ethics in engineering.^[40][41]

• On 19 April 1995, the nine storey concrete framed Alfred P. Murrah Federal Building in Oklahoma was struck by a huge car bomb causing partial collapse, resulting in the deaths of 168 people. The bomb, though large, caused a significantly disproportionate collapse of the structure. The bomb blew all the glass off the front of the building and completely shattered a ground floor reinforced concrete column (see brisance). At second storey level a wider column spacing existed, and loads from upper storey columns were transferred into fewer columns below by girders at second floor level. The removal of one of the lower storey columns caused neighbouring columns to fail due to the extra load, eventually leading to the complete collapse of the central portion of the building. The bombing was one of the first to highlight the extreme forces that blast loading from terrorism can exert on buildings, and led to increased consideration of terrorism in structural design of buildings.^[42]

• On 11 September 2001, the two towers of the World Trade Center in New York were struck by airplanes. Though the towers initially withstood the impact, the jet fuel on board caused fires which ultimately caused the buildings to collapse due to buckling failures in the perimeter gravity frame. Both towers collapsed in their entirety because as each floor collapsed, it fell on the floor below and caused it too to collapse. This mode of collapse is known as progressive collapse. The significant investigations into the collapse led to changes in the way tall buildings are designed to withstand both fire and terrorism, and the methods in which people escape in emergencies.

[edit] Specialisations

[edit] Building structures

See also: Building engineering

Structural building engineering includes all structural engineering related to the design of buildings. It is the branch of structural engineering that is close to architecture.

Structural building engineering is primarily driven by the creative manipulation of materials and forms and the underlying mathematical and scientific principles to achieve an end which fulfils its functional requirements and is structurally safe when subjected to all the loads it could reasonably be expected to experience, while being economical and practical to construct. This is subtly different to architectural design, which is driven by the creative manipulation of materials and forms, mass, space, volume, texture and light to achieve an end which is aesthetic, functional and often artistic.

The architect is usually the lead designer on buildings, with a structural engineer employed as a sub-consultant. The degree to which each discipline actually leads the design depends heavily on the type of structure. Many structures are structurally simple and led by architecture, such as multi-storey office buildings and housing, while other structures, such as tensile structures, shells and gridshells are heavily dependent on their form for their strength, and the engineer may have a more significant influence on the form, and hence much of the aesthetic, than the architect. Between these two extremes, structures such as stadia, museums and skyscrapers are complex both architecturally and structurally, and a successful design is a collaboration of equals.

The structural design for a building must ensure that the building is able to stand up safely, able to function without excessive deflections or movements which may cause fatigue of structural elements, cracking or failure of fixtures, fittings or partitions, or discomfort for occupants. It must account for movements and forces due to temperature, creep, cracking and imposed loads. It must also ensure that the design is practically buildable within acceptable manufacturing tolerances of the materials. It must allow the architecture to work, and the building services to fit within the building and function (air conditioning, ventilation, smoke extract, electrics, lighting etc). The structural design of a modern building can be extremely complex, and requires a large team to complete.

Structural engineering specialties for buildings include:

• Earthquake engineering
• Façade engineering
• Fire engineering
• Roof engineering
• Tower engineering
• Wind engineering

[edit] Civil engineering structures

Civil structural engineering includes all structural engineering related to the built environment, excluding occupiable buildings. It includes:

Bridges Dams Earthworks Foundations Offshore structures Pipelines

Power stations Railways Retaining structures and walls Roads Tunnels Waterways

The structural engineer is the lead designer on these structures, and often the sole designer. In the design of structures such as these, structural safety is of paramount importance (in the UK, designs for dams, nuclear power stations and bridges must be signed off by a chartered engineer).

Civil engineering structures are often subjected to very extreme forces, such as large variations in temperature, dynamic loads such as waves or traffic, or high pressures from water or compressed gases. They are also often constructed in corrosive environments, such as at sea, in industrial facilities or below ground.

[edit] Mechanical structures

The design of static structures assumes they always have the same geometry (in fact, so-called static structures can move significantly, and structural engineering design must take this into account where necessary), but the design of moveable or moving structures must account for fatigue, variation in the method in which load is resisted and significant deflections of structures.

The forces which parts of a machine are subjected to can vary significantly, and can do so at a great rate. The forces which a boat or aircraft are subjected to vary enormously and will do so thousands of times over the structure's lifetime. The structural design must ensure that such structures are able to endure such loading for their entire design life without failing.

These works can require mechanical structural engineering:

• Airframes and fuselages
• Boilers and pressure vessels
• Coachworks and carriages
• Cranes
• Elevators
• Escalators
• Marine vessels and hulls

[edit] Structural elements

Any structure is essentially made up of only a small number of different types of elements:

• Columns
• Beams
• Plates
• Arches
• Shells
• Catenaries

[edit] Columns

Main article: Column

Columns are elements that carry only axial force - either tension or compression - or both axial force and bending. The design of a column must check the axial capacity of the element, and the buckling capacity.

The buckling capacity is the capacity of the element to withstand the propensity to buckle because of inaccuracies in straightness or position of the column. Its capacity depends upon its geometry, material and the effective length of the column, which depends upon the restraint conditions at the top and bottom of the column. This is shown in the table on the right, where the effective length is K * l where l is the real length of the column.

The capacity of a column to carry axial load depends on the degree of bending it is subjected to, and vice versa. This is represented on an interaction chart and is a complex non-linear relationship.

[edit] Beams

Main article: Beam

A beam may be:

• cantilevered (supported at one end only with a fixed connection)
• simply supported (supported vertically but able to rotate at the supports)
• continuous (supported vertically and unable to rotate at the supports)

Beams are elements which carry pure bending only. Bending causes one section of a beam (divided along its length) to go into compression and the other section into tension. The compression section must be designed to resist buckling and crushing, while the tension section must be able to adequately resist the tension.

[edit] Trusses

Main article: Truss

A truss is a lightweight version of a beam, which allows the required strength and stiffness to be achieved with a smaller amount of material than a solid beam. A truss consists of top and bottom members which carry tension or compression, with linking 'lacers' which transfer the forces to these members and restrain them, ensuring the truss acts as a single structural element. In a pin-jointed truss (where all joints are essentially hinges), the individual elements of a truss carry only axial load. From experiments it can be shown that even trusses with rigid joints will behave as though the joints are pinned. 

Trusses are usually utilised to span large distances, where it would be uneconomical and unattractive to use solid beams.

[edit] Plates

Plates carry bending in two directions. A concrete flat slab is an example of a plate. Plates are understood by using continuum mechanics, but due to the complexity involved they are most often designed using a codified empirical approach, or computer analysis.

They can also be designed with yield line theory, where an assumed collapse mechanism is analysed to give an upper bound on the collapse load (see Plasticity). This is rarely used in practice.

[edit] Shells

Main article: Thin-shell structure

See also: Gridshell

Shells derive their strength from their form, and carry forces in compression in two directions. A dome is an example of a shell. They can be designed by making a hanging-chain model, which will act as a catenary in pure tension, and inverting the form to achieve pure compression.

[edit] Arches

Main article: Arch

Arches carry forces in compression in one direction only, which is why it is appropriate to build arches out of masonry. They are designed by ensuring that the line of thrust of the force remains within the depth of the arch.

[edit] Catenaries

Main article: Tensile structure

Catenaries derive their strength from their form, and carry transverse forces in pure tension by deflecting (just as a tightrope will sag when someone walks on it). They are almost always cable or fabric structures. A fabric structure acts as a catenary in two directions.

[edit] Structural engineering theory

Structural engineering depends upon a detailed knowledge of loads, physics and materials to understand and predict how structures support and resist self-weight and imposed loads. To apply the knowledge successfully a structural engineer will need a detailed knowledge of mathematics and of relevant empirical and theoretical design codes.

The criteria which govern the design of a structure are either serviceability (criteria which define whether the structure is able to adequately fulfil its function) or strength (criteria which define whether a structure is able to safely support and resist its design loads). A structural engineer designs a structure to have sufficient strength and stiffness to meet these criteria.

Loads imposed on structures are supported by means of forces transmitted through structural elements. These forces can manifest themselves as:

• tension (axial force)
• compression (axial force)
• shear
• bending, or flexure (a bending moment is a force multiplied by a distance, or lever arm, hence producing a turning effect or torque)

[edit] Loads

Structural loads on structures are generally classified as live (imposed) loads and dead loads.

Live loads are transitory or temporary loads, and are relatively unpredictable in magnitude. They may include the weight of a building's occupants and furniture, the forces/weights of wind and water, temperature, vibration, seismic activity, blast loading, fire loading and temporary loads the structure is subjected to during construction.

Dead loads are permanent, and may include the weight of the structure itself and all major permanent components. Dead load may also include the weight of the structure itself supported in a way it wouldn't normally be supported, for example during construction.

[edit] Strength

Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress or shear stress. The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa).

A structure fails the strength criterion when the stress (force divided by area of material) induced by the loading is greater than the capacity of the structural material to resist the load without breaking, or when the strain (percentage extension) is so great that the element no longer fulfils its function (yield).

See also:

See also: Tensile strength, Compressive strength, and Shear strength

[edit] Stiffness

Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.

The deflection of a structure under loading is dependent on its stiffness. The dynamic response of a structure to dynamic loads (the natural frequency of a structure) is also dependent on its stiffness.

In a structure made up of multiple structural elements, the elements will carry loads in proportion to their relative stiffness - the stiffer an element, the more load it will attract.

A structure is considered to fail the chosen serviceability criteria if it is insufficiently stiff to have acceptably small deflection or dynamic response under loading.

The inverse of stiffness is the flexibility.

See also: Flexibility method and Matrix stiffness method

[edit] Safety factors

The safe design of structures requires a design approach which takes account of the statistical likelihood of the failure of the structure. Structural design codes are based upon the assumption that both the loads and the material strengths vary with a normal distribution.

The job of the structural engineer is to ensure that the chance of overlap between the distribution of loads on a structure and the distribution of material strength of a structure is acceptably small (it is impossible to reduce that chance to zero).

It is normal to apply a partial safety factor to the loads and to the material strengths, to design using 95th percentiles (two standard deviations from the mean). The safety factor applied to the load will typically ensure that in 95% of times the actual load will be smaller than the design load, while the factor applied to the strength ensures that 95% of times the actual strength will be higher than the design strength.

The safety factors for material strength vary depending on the material and the use it is being put to and on the design codes applicable in the country or region.

[edit] Load cases

A load case is a combination of different types loads with safety factors applied to them. A structure is checked for strength and serviceability against all the load cases it is likely to experience during its lifetime.

Typical load cases for design for strength (ultimate load cases; ULS) are:

1.4 x Dead Load + 1.6 x Live Load

1.2 x Dead Load + 1.2 x Live Load + 1.2 x Wind Load

A typical load case for design for serviceability (characteristic load cases; SLS) is:

1.0 x Dead Load + 1.0 x Live Load

Different load cases would be used for different loading conditions. For example, in the case of design for fire a load case of 1.0 x Dead Load + 0.8 x Live Load may be used, as it is reasonable to assume everyone has left the building if there is a fire.

In multi-storey buildings it is normal to reduce the total live load depending on the number of storeys being supported, as the probability of maximum load being applied to all floors simultaneously is negligibly small.

It is not uncommon for large buildings to require hundreds of different load cases to be considered in the design.

[edit] Newton's Laws of Motion

Main article: Newton's Laws of Motion

The most important natural laws for structural engineering are Newton's Laws of Motion

Newton's First Law states that every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

Newton's Second Law states that the rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction. Mathematically, F=ma (force = mass x acceleration).

Newton's Third Law states that all forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.

With these laws it is possible to understand the forces on a structure and how that structure will resist them. The Third Law requires that for a structure to be stable all the internal and external forces must be in equilibrium. This means that the sum of all internal and external forces on a free-body diagram must be zero:

• : the vectorial sum of the forces acting on the body equals zero. This translates to

Σ H = 0: the sum of the horizontal components of the forces equals zero;

Σ V = 0: the sum of the vertical components of forces equals zero;

• : the sum of the moments (about an arbitrary point) of all forces equals zero.

[edit] Statical determinacy

Main article: Statically indeterminate

A structural engineer must understand the internal and external forces of a structural system consisting of structural elements and nodes at their intersections.

A statically determinate structure can be fully analysed using only consideration of equilibrium, from Newton's Laws of Motion.

A statically indeterminate structure has more unknowns than equilibrium considerations can supply equations for (see simultaneous equations). Such a system can be solved using consideration of equations of compatibility between geometry and deflections in addition to equilibrium equations, or by using virtual work.

If a system is made up of b bars, j pin joints and r support reactions, then it cannot be statically determinate if the following relationship does not hold:

r + b = 2j

It should be noted that even if this relationship does hold, a structure can be arranged in such a way as to be statically indeterminate.^[43]

[edit] Elasticity

Main article: Elasticity

See also: Hooke's Law

Much engineering design is based on the assumption that materials behave elastically. For most materials this assumption is incorrect, but empirical evidence has shown that design using this assumption can be safe. Materials that are elastic obey Hooke's Law, and plasticity does not occur.

For systems that obey Hooke's Law, the extension produced is directly proportional to the load:

where

x is the distance that the spring has been stretched or compressed away from the equilibrium position, which is the position where the spring would naturally come to rest [usually in meters],

F is the restoring force exerted by the material [usually in newtons], and

k is the force constant (or spring constant). This is the stiffness of the spring. The constant has units of force per unit length (usually in newtons per metre)

[edit] Plasticity

Main article: Plasticity

Some design is based on the assumption that materials will behave plastically.^[31] It applies to ductile materials. It can be used for reinforced concrete structures assuming they are underreinforced and the steel reinforcement fails before the concrete.

Plasticity theory states that the point at which a structure collapses (reaches yield) lies between an upper and a lower bound on the load, defined as follows:

• If, for a given external load, it is possible to find a distribution of moments that satisfies equilibrium requirements, with the moment not exceeding the yield moment at any location, and if the boundary conditions are satisfied, then the given load is a lower bound on the collapse load.

• If, for a small increment of displacement, the internal work done by the structure, assuming that the moment at every plastic hinge is equal to the yield moment and that the boundary conditions are satisfied, is equal to the external work done by the given load for that same small increment of displacement, then that load is an upper bound on the collapse load.

If the correct collapse load is found, the two methods will give the same result for the collapse load.^[44]

Plasticity theory depends upon a correct understanding of when yield will occur. A number of different models for stress distibution and approximations to the yield surface of plastic materials exist:^[15]

• Mohr's circle
• Von Mises yield criterion
• Henri Tresca

[edit] The Euler-Bernoulli beam equation

Main article: Euler-Bernoulli beam equation

The Euler-Bernoulli beam equation defines the behaviour of a beam element (see below). It is based on five assumptions:

(1) continuum mechanics is valid for a bending beam
(2) the stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section.
(3) the bending moment at a particular cross section varies linearly with the second derivative of the deflected shape at that location.
(4) the beam is composed of an isotropic material
(5) the applied load is orthogonal to the beam's neutral axis and acts in a unique plane.

A simplified version of Euler-Bernoulli beam equation is:

Here u is the deflection and w(x) is a load per unit length. E is the elastic modulus and I is the second moment of area, the product of these giving the stiffness of the beam.

This equation is very common in engineering practice: it describes the deflection of a uniform, static beam.

Successive derivatives of u have important meaning:

• is the deflection.

• is the slope of the beam.

• is the bending moment in the beam.

• is the shear force in the beam.

A bending moment manifests itself as a tension and a compression force, acting as a couple in a beam. The stresses caused by these forces can be represented by:

where σ is the stress, M is the bending moment, y is the distance from the neutral axis of the beam to the point under consideration and I is the second moment of area. This equation allows a structural engineer to assess the stress in a structural element when subjected to a bending moment.

[edit] Buckling

When subjected to compressive forces it is possible for structural elements to deform significantly due to the destabilising effect of that load. The effect can be initiated or exacerbated by possible inaccuracies in manufacture or construction.

The Euler buckling formula defines the axial compression force which will cause a strut (or column) to fail in buckling.

where

F = maximum or critical force (vertical load on column),

E = modulus of elasticity,

I = area moment of inertia, or second moment of area

l = unsupported length of column,

K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.

For both ends pinned (hinged, free to rotate), K = 1.0.

For both ends fixed, K = 0.50.

For one end fixed and the other end pinned, K = 0.70.

For one end fixed and the other end free to move laterally, K = 2.0.

This value is sometimes expressed for design purposes as a critical buckling stress.

where

σ = maximum or critical stress

r = the least radius of gyration of the cross section

Other forms of buckling include lateral torsional buckling, where the compression flange of a beam in bending will buckle, and buckling of plate elements in plate girders due to compression in the plane of the plate.

[edit] Materials

Structural engineering depends on the knowledge of materials and their properties, in order to understand how different materials support and resist loads.

Common structural materials are:

[edit] Iron

[edit] Wrought iron

Main article: Wrought iron

Wrought iron is the simplest form of iron, and is almost pure iron (typically less than 0.15% carbon). It usually contains some slag. Its uses are almost entirely obsolete, and it is no longer commercially produced.

Wrought iron is very poor in fires. It is ductile, malleable and tough. It does not corrode as easily as steel.

[edit] Cast iron

Main article: Cast iron

Cast iron is a brittle form of iron which is weaker in tension than in compression. It has a relatively low melting point, good fluidity, castability, excellent machinability and wear resistance. Though almost entirely replaced by steel in building structures, cast irons have become an engineering material with a wide range of applications, including pipes, machine and car parts.

Cast iron retains high strength in fires, despite its low melting point. It is usually around 95% iron, with between 2.1-4% carbon and between 1-3% silicon. It does not corrode as easily as steel.

[edit] Steel

Main articles: Steel and Structural steel

See also: Steel frame

Steel is a iron alloy with between 0.2 and 1.7% carbon.

Steel is used extremely widely in all types of structures, due to its relatively low cost, high strength to weight ratio and speed of construction.

Steel is a ductile material, which will behave elastically until it reaches yield (point 2 on the stress-strain curve), when it becomes plastic and will fail in a ductile manner (large strains, or extensions, before failure at point 3 on the curve). Steel is equally strong in tension and compression.

Steel is very weak in fires, and must be protected in most buildings. Because of its high strength to weight ratio, steel buildings typically have low thermal mass, and require more energy to heat (or cool) than similar concrete buildings.

The elastic modulus of steel is approximately 205 GPa

Steel is very prone to corrosion (rust).

[edit] Stainless steel

Main article: Stainless steel

Stainless steel is an iron-carbon alloy with a minimum of 10.5% chromium content. There are different types of stainless steel, containing different proportions of iron, carbon, molybdenum, nickel. It has similar structural properties to steel, although its strength varies significantly.

It is rarely used for primary structure, and more for architectural finishes and building cladding.

It is highly resistant to corrosion and staining.

[edit] Concrete

Main articles: Concrete and Reinforced concrete

Concrete is used extremely widely in building and civil engineering structures, due to its low cost, flexibility, durability and high strength. It also has high resistance to fire.

Concrete is brittle material, which is very strong in compression and very weak in tension. It behaves non-linearly at all times. Because it has essentially zero strength in tension, it is almost always used as reinforced concrete, a composite material. It is a mixture of sand, aggregate, cement and water. It is placed in a mould, or form, as a liquid, and then it sets (goes off), due to a chemical reaction between the water and cement. The reaction produces a significant amount of heat.

Concrete increases in strength continually from the day it is cast. It shrinks over time as it dries out, and deforms over time due to a phenomenon called creep. Its strength depends highly on how it is mixed, poured, cast, compacted and cured (kept wet while setting). It can be cast into any shape that a form can be made for. Its colour, quality and finish depend upon the complexity of the structure, the material used for the form and the skill of the pourer.

Concrete is a non-linear, non-elastic material, and will fail suddenly, with a brittle failure, unless adequate reinforced with steel. An "under-reinforced" concrete element will fail with a ductile manner, as the steel will fail before the concrete. An "over-reinforced" element will fail suddenly, as the concrete will fail first. Reinforced concrete elements should be designed to be under-reinforced so users of the structure will receive warning of impending collapse.

The elastic modulus of concrete can vary widely and depends on the concrete mix, age and quality, as well as the on the type and duration of loading applied to it. It is usually taken as approximately 25 GPa for long-term loads once it has attained its full strength (usually considered to be at 28 days after casting). It is taken as approximately 38 GPa for very short-term loading, such as footfalls.

Concrete has very favourable properties in fire - it is not adversely affected by fire until it reaches very high temperatures. It also has very high mass, so it is good for providing sound insulation and heat retention (leading to lower energy requirements for the heating of concrete buildings). This is offset by the fact that producing and transporting concrete is very energy intensive.

[edit] Aluminium

Main articles: Aluminium and Aluminum alloy

Aluminium is a soft, lightweight, malleable metal. The yield strength of pure aluminium is 7–11 MPa, while aluminium alloys have yield strengths ranging from 200 MPa to 600 MPa. Aluminium has about one-third the density and stiffness of steel. It is ductile, and easily machined, cast, and extruded.

Corrosion resistance is excellent due to a thin surface layer of aluminium oxide that forms when the metal is exposed to air, effectively preventing further oxidation. The strongest aluminium alloys are less corrosion resistant due to galvanic reactions with alloyed copper.

Aluminium is used in some building structures (mainly in facades) and very widely in aircraft engineering because of its good strength to weight ratio. It is a relatively expensive material.

In aircraft it is gradually being replaced by carbon composite materials.

[edit] Composites

Main article: Composites

Composite materials are used increasingly in vehicles and aircraft structures, and to some extent in other structures. They are increasingly used in bridges, especially for conservation of old structures such as Coalport cast iron bridge built in 1818. Composites are often anisotropic (they have different material properties in different directions) as they can be laminar materials. They most often behave non-linearly and will fail in a brittle manner when overloaded.

They provide extremely good strength to weight ratios, but are also very expensive. The manufacturing processes, which are often extrusion, do not currently provide the economical flexibility that concrete or steel provide. The most commonly used in structural applications are glass-reinforced plastics.

[edit] Masonry

Main article: Masonry

Masonry has been used in structures for hundreds of years, and can take the form of stone, brick or blockwork. Masonry is very strong in compression but cannot carry tension (because the mortar between bricks or blocks is unable to carry tension). Because it cannot carry tension, it also cannot carry bending, so masonry walls become unstable at relatively small heights. High masonry structures require stabilisation against lateral loads from buttresses (as with the flying buttresses seen in many European medieval churches) or from windposts.

Historically masonry was constructed with no mortar or with lime mortar. In modern times cement based mortars are used.

Since the widespread use of concrete, stone is rarely used as a primary structural material, often only appearing as a cladding, because of its cost and the high skills needed to produce it. Brick and concrete blockwork have taken its place.

Masonry, like concrete, has good sound insulation properties and high thermal mass, but is generally less energy intensive to produce. It is just as energy intensive as concrete to transport.

[edit] Timber

Main article: Timber

Timber is the oldest of structural materials, and though mainly supplanted by steel, masonry and concrete, it is still used in a significant number of buildings. The properties of timber are non-linear and very variable, depending on the quality, treatment of wood and type of wood supplied. The design of wooden structures is based almost entirely on empirical evidence.

Wood is strong in tension and compression, but can be weak in bending due to its fibrous structure. Wood is relatively good in fire as it chars, which provides the wood in the centre of the element with some protection and allows the structure to retain some strength for a reasonable length of time.

[edit] Other structural materials

• Adobe
• Bamboo
• Mud bricks
• Roofing materials

[edit] See also

• Structural engineer
• List of structural engineers
• Architects
• Architectural engineering
• Civil engineering
• Mechanical engineering

[edit] References

• Blank, Alan; McEvoy, Michael; Plank, Roger (1993). Architecture and Construction in Steel. Taylor & Francis. ISBN 0419176608.
• Bradley, Robert E.; Sandifer, Charles Edward (2007). Leonhard Euler: Life, Work and Legacy. Elsevier. ISBN 0444527281.
• Castigliano, Carlo Alberto (translator: Andrews, Ewart S.) (1966). The Theory of Equilibrium of Elastic Systems and Its Applications. Dover Publications.
• Chapman, Allan. (2005). England's Leornardo: Robert Hooke and the Seventeenth Century's Scientific Revolution. CRC Press. ISBN 0750309873.
• Dym, Clive L. (1997). Structural Modeling and Analysis. Cambridge University Press. ISBN 0521495369.
• Dugas, René (1988). A History of Mechanics. Courier Dover Publications. ISBN 0486656322.
• Feld, Jacob; Carper, Kenneth L. (1997). Construction Failure. John Wiley & Sons. ISBN 0471574775.
• Galilei, Galileo. (translators: Crew, Henry; de Salvio, Alfonso) (1954). Dialogues Concerning Two New Sciences. Courier Dover Publications. ISBN 0486600998
• Hewson, Nigel R. (2003). Prestressed Concrete Bridges: Design and Construction. Thomas Telford. ISBN 0727727745.
• Heyman, Jacques (1998). Structural Analysis: A Historical Approach. Cambridge University Press. ISBN 0521622492.
• Heyman, Jacques (1999). The Science of Structural Engineering. Imperial College Press. ISBN 1860941893.
• Hognestad, E. A Study of Combined Bending and Axial Load in Reinforced Concrete Members. University of Illinois, Engineering Experiment Station, Bulletin Series N. 399.
• Hosford, William F. (2005). Mechanical Behavior of Materials. Cambridge University Press. ISBN 0521846706.
• Hoogenboom, P.C.J. . Historical Overview of Concrete Modelling.
• Kirby, Richard Shelton (1990). Engineering in History. Courier Dover Publications. ISBN 0486264122.
• Labrum, E.A. (1994). Civil Engineering Heritage. Thomas Telford. ISBN 072771970X.
• Leonhardt, A. (1964). Vom Caementum zum Spannbeton, Band III (From Cement to Prestressed Concrete). Bauverlag GmbH.
• MacNeal, Richard H. (1994). Finite Elements: Their Design and Performance. Marcel Dekker. ISBN 0824791622.
• Mir, Ali (2001). Art of the Skyscraper: the Genius of Fazlur Khan. Rizzoli International Publications. ISBN 0847823709.
• Mörsch, E. (Stuttgart, 1908). Der Eisenbetonbau, seine Theorie und Anwendun, (Reinforced Concrete Construction, its Theory and Application). Konrad Wittwer, 3th edition.
• Nedwell,P.J.; Swamy,R.N.(ed) (1994). Ferrocement:Proceedings of the Fifth International Symposium. Taylor & Francis. ISBN 0419197001.
• Newton, Isaac; Leseur, Thomas; Jacquier, François (1822). Philosophiæ Naturalis Principia Mathematica. Oxford University.
• Nilson, Arthur H.; Darwin, David; Dolan, Charles W. (2004). Design of Concrete Structures. McGraw-Hill Professional. ISBN 0072483059.
• Petroski, Henry (1994). Design Paradigms: Case Histories of Error and Judgment in Engineering. Cambridge University Press. ISBN 0521466490.
• Prentice, John E. (1990). Geology of Construction Materials. Springer. ISBN 041229740X.
• Rozhanskaya, Mariam; Levinova, I. S. (1996). "Statics" in Morelon, Régis & Rashed, Roshdi (1996). Encyclopedia of the History of Arabic Science, vol. 2-3, Routledge. ISBN 0415020638
• Schlaich, J., K. Schäfer, M. Jennewein (1987). "Toward a Consistent Design of Structural Concrete". PCI Journal, Special Report, Vol. 32, No. 3.
• Scott, Richard (2001). In the Wake of Tacoma: Suspension Bridges and the Quest for Aerodynamic Stabilitya. ASCE Publications. ISBN 0784405425.
• Swank, James Moore (1965). History of the Manufacture of Iron in All Ages. Ayer Publishing. ISBN 0833734636.
• Turner, J.; Clough, R.W.; Martin, H.C.; Topp, L.J. (1956). "Stiffness and Deflection of Complex Structures". Journal of Aeronautical Science Issue 23.
• Virdi, K.S. (2000). Abnormal Loading on Structures: Experimental and Numerical Modelling. Taylor & Francis. ISBN 0419259600.
• Whitbeck, Caroline (1998). Ethics in Engineering Practice and Research. Cambridge University Press. ISBN 0521479444.

[edit] Notes

See above for references to publications and academic papers.

[edit] External links

• Institution of Structural Engineers (IStructE)
• Structural Engineering Association - International
• National Council of Structural Engineers Associations
• Structural Engineering Institute

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