# Category: Structural analysis

Structural dynamics
Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves
Statically indeterminate
In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the inte
Free body diagram
A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it.In physics and engineering, a
Finite element limit analysis
A finite element limit analysis (FELA) uses optimisation techniques to directly compute the upper or lower bound plastic collapse load (or limit load) for a mechanical system rather than time stepping
Marcus' method
Marcus' method (also referred to as Marcus's method and Method of Marcus) is a structural analysis method which was designed to design concrete slabs with rectangular, orthogonal shapes. It represents
Theorem of three moments
In civil engineering and structural analysis Clapeyron's theorem of three moments is a relationship among the bending moments at three consecutive supports of a horizontal beam. Let A,B,C-D be the thr
Second moment of area
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 distr
Solution procedure for Indeterminate Structures
Solving a structure means determining the unknown internal forces, reactions and displacements of the structure. When a structure can be solved by using the equations of static equilibrium alone, it i
Buckling
In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under
Von Mises yield criterion
The maximum distortion criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress reaches a critical value. It is a par
Direct integration of a beam
Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam. For a beam with an applied weight , taking downward to be positive
Reinforced solid
In solid mechanics, a reinforced solid is a brittle material that is reinforced by ductile bars or fibres. A common application is reinforced concrete. When the concrete cracks the tensile force in a
Mechanical load is the physical stress on a mechanical system or component. Loads can be static or dynamic. Some loads are specified as part of the design criteria of a mechanical system. Depending on
Wood method
The Wood method, also known as the Merchant–Rankine–Wood method, is a structural analysis method which was developed to determine estimates for the effective buckling length of a compressed member inc
Structural analysis
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
Unified framework
Unified framework is a general formulation which yields nth - order expressions giving mode shapes and natural frequencies for damaged elastic structures such as rods, beams, plates, and shells. The f
Castigliano's method
Castigliano's method, named after Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for hi
Unit dummy force method
The Unit dummy force method provides a convenient means for computing displacements in structural systems. It is applicable for both linear and non-linear material behaviours as well as for systems su
Young's modulus
Young's modulus , the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a s
Geometrically and materially nonlinear analysis with imperfections included
Geometrically and materially nonlinear analysis with imperfections included (GMNIA), is a structural analysis method designed to verify the strength capacity of a structure, which accounts for both pl
Infinite element method
The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The method divides the domain concerned i
Hooke's law
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, w
Cantilever method
The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically
ATILA
ATILA is a finite element analysis software package developed for the analysis of two and three dimensional mechanical structures that contain active piezoelectric & magnetostrictive materials. It is
A cascade chart is tool that can be used in damage tolerance analysis to determine the proper inspection interval, based on reliability analysis, considering all the context uncertainties. The chart i
Guyan reduction
In computational mechanics, Guyan reduction, also known as static condensation, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial terms of th
Influence line
In engineering, an influence line graphs the variation of a function (such as the shear, moment etc. felt in a structural member) at a specific point on a beam or truss caused by a unit load placed at
Müller-Breslau's principle
The Müller-Breslau principle is a method to determine influence lines. The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displaceme
Incremental dynamic analysis
Incremental dynamic analysis (IDA) is a computational analysis method of earthquake engineering for performing a comprehensive assessment of the behavior of structures under seismic loads. It has been
Hu–Washizu principle
In continuum mechanics, and in particular in finite element analysis, the Hu–Washizu principle is a variational principle which says that the action is stationary, where is the elastic stiffness tenso
STAAD or (STAAD.Pro) is a structural analysis and design software application originally developed by Research Engineers International in 1997. In late 2005, Research Engineers International was bough
Stress–strain curve
In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring th
Applied element method
The applied element method (AEM) is a numerical analysis used in predicting the continuum and discrete behavior of structures. The modeling method in AEM adopts the concept of discrete cracking allowi
Betti's theorem
Betti's theorem, also known as Maxwell–Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {Pi} i=1,...,n and {Q
Moment distribution method
The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. The method only acco
Ply (layer)
A ply is a layer of material which has been combined with other layers in order to provide strength. The number of layers is indicated by prefixing a number, for example 4-ply, indicating material com
Prokon
PROKON Structural Analysis and Design is a suite of commercial software for structural analysis and design. PROKON software is produced by South African company Prokon Software Consultant (Pty) Ltd. T
HyperSizer
HyperSizer is computer-aided engineering (CAE) software used for stress analysis and of metallic and composite structures. Originally developed at the US National Aeronautics and Space Administration
Slope deflection method
The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney. The slope deflection method was widely used for more than a decade until the mom
Structural element
Structural elements are used in structural analysis to split a complex structure into simple elements. Within a structure, an element cannot be broken down (decomposed) into parts of different kinds (
Yield (engineering)
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a
Dynamic design analysis method
The dynamic design analysis method (DDAM) is a US Navy-developed analytical procedure for evaluating the design of equipment subject to dynamic loading caused by underwater explosions (UNDEX). The ana
Duhamel's integral
In theory of vibrations, Duhamel's integral is a way of calculating the response of linear systems and structures to arbitrary time-varying external perturbation.
Finite element method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the tradi
ROHR2
ROHR2 is a pipe stress analysis CAE system from SIGMA Ingenieurgesellschaft mbH, based in Unna, Germany. The software performs both static and dynamic analysis of complex piping and skeletal structure
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff i
Yield surface
A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the str
Crumpling
In geometry and topology, crumpling is the process whereby a sheet of paper or other two-dimensional manifold undergoes disordered deformation to yield a three-dimensional structure comprising a rando
Euler's critical load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: where * , Euler's critical load (longitudinal compression load on col
Moment-area theorem
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 18
Johnson's parabolic formula
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B.
Flexibility method
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its
Plastic bending
Plastic bending is a nonlinear behavior particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analys
Hogging and sagging
In solid mechanics, structural engineering, and shipbuilding, hogging and sagging describe the shape that a beam or similar long object will deform into when loading is applied. Hogging describes a be
Dynamic substructuring
Dynamic Substructuring (DS) is an engineering tool used to model and analyse the dynamics of mechanical systems by means of its components or substructures. Using the dynamic substructuring approach o
Bigoni–Piccolroaz yield criterion
The Bigoni–Piccolroaz yield criterion is a yielding model, based on a phenomenological approach, capable of describing the mechanical behavior of a broad class of pressure-sensitive granular materials
Energy principles in structural mechanics
Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work do
Deflection (engineering)
In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection dista
Euler–Bernoulli beam theory
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carryi
Fatigue (material)
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typi
Fracture mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack
Limit analysis
Limit analysis is a structural analysis field which is dedicated to the development of efficient methods to directly determine estimates of the collapse load of a given structural model without resort
Self-buckling
A column can buckle due to its own weight with no other direct forces acting on it, in a failure mode called self-buckling. In conventional column buckling problems, the self-weight is often neglected
Section modulus
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius
Soil-structure interaction
Ground–structure interaction (SSI) consists of the interaction between soil (ground) and a structure built upon it. It is primarily an exchange of mutual stress, whereby the movement of the ground-str
Factor of safety
In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety fac
Yoshimura buckling
In mechanical engineering, Yoshimura buckling is a triangular mesh buckling pattern found in thin-walled cylinders under compression along the axis of the cylinder, producing a corrugated shape resemb
Huber's equation
Huber's equation, first derived by a Polish engineer Tytus Maksymilian Huber, is a basic formula in elastic material tension calculations, an equivalent of the equation of state, but applying to solid
Shear and moment diagram
Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear force and bending moment at a gi
Direct stiffness method
As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures inclu
Matrix method
The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. The method is carried out, using either a stiffness matrix or a flexibility
A structural load or structural action is a force, deformation, or acceleration applied to structural elements. A load causes stress, deformation, and displacement in a structure. Structural analysis,
Fixed end moment
The fixed end moments are reaction moments developed in a beam member under certain load conditions with both ends fixed. A beam with both ends fixed is statically indeterminate to the 3rd degree, and
SESAM (FEM)
Sesam is a software suite for structural and hydrodynamic analysis of ships and offshore structures. It is based on the displacement formulation of the Finite Element Method. The first version of Sesa
Crack growth equation
A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of fatigue cracks can result in catastrophic failure, particularly in the case of airc
Williot diagram
The Williot diagram is a graphical method to obtain an approximate value for displacement of a structure which submitted to a certain load. The method consists of, from a graph representation of a str
Smoothed finite element method
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the fini
Timoshenko–Ehrenfest beam theory
The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest early in the 20th century. The model takes into account shear deformation and rotational bending effects, ma
Seismic analysis
Seismic analysis is a subset of structural analysis and is the calculation of the response of a building (or nonbuilding) structure to earthquakes. It is part of the process of structural design, eart
Bending stiffness
The bending stiffness is the resistance of a member against bending deformation. It is a function of the Young's modulus , the second moment of area of the beam cross-section about the axis of interes
Discontinuity layout optimization
Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse. U
Zero force member
In the field of engineering mechanics, a zero force member is a member (a single truss segment) in a truss which, given a specific load, is at rest: neither in tension, nor in compression. In a truss
Strain energy
In physics, the elastic potential energy gained by a wire during elongation with a tensile (stretching) force is called strain energy. For linearly elastic materials, strain energy is: where σ is stre
Loubignac iteration
In applied mathematics, Loubignac iteration is an iterative method in finite element methods. It gives continuous stress field. It is named after Gilles Loubignac, who published the method in 1977.
Torsion constant
The torsion constant is a geometrical property of a bar's cross-section which is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous lin
Transmissibility (structural dynamics)
Transmissibility, in the context of Structural Dynamics, can be defined as the ratio of the maximum force on the floor as a result of the vibration of a machine to the maximum machine force: Where is
Wood–Armer method
The Wood–Armer method is a structural analysis method based on finite element analysis used to design the reinforcement for concrete slabs. This method provides simple equations to design a concrete s
Clapeyron's theorem (elasticity)
In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the exte
AFGROW
AFGROW (Air Force Grow) is a Damage Tolerance Analysis (DTA) computer program that calculates crack initiation, fatigue crack growth, and fracture to predict the life of metallic structures. Originall
Michell structures
Michell structures are structures that are optimal based on the criteria defined by A.G.M. Michell in his frequently referenced 1904 paper. Michell states that “a frame (today called truss) (is optima
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 or
Virtual work
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 a
Membrane analogy
The elastic membrane analogy, also known as the soap-film analogy, was first published by pioneering aerodynamicist Ludwig Prandtl in 1903.It describes the stress distribution on a long bar in torsion
Stress–strain analysis
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mech
Stress functions
In linear elasticity, the equations describing the deformation of an elastic body subject only to surface forces (or body forces that could be expressed as potentials) on the boundary are (using index
Smart intelligent aircraft structure
The term "smart structures" is commonly used for structures which have the ability to adapt to environmental conditions according to the design requirements. As a rule, the adjustments are designed an
Macaulay's method
Macaulay’s method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay’s technique is very convenient for ca
Elastic instability
Elastic instability is a form of instability occurring in elastic systems, such as buckling of beams and plates subject to large compressive loads. There are a lot of ways to study this kind of instab
Proper orthogonal decomposition
The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics and structural analysis (lik
Cauchy stress tensor
In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine compon