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 matrix. “The flexibility method is not conducive to computer programming” – Weaver, Gere.

Simply so, what is stiffness matrix method?

Direct stiffness method. It is a matrix method that makes use of the members’ stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method (FEM).

What are the properties of stiffness matrix?

The stiffness matrix is an inherent property of the structure. Element stiffness is obtained with respect to its axes and then transformed this stiffness to structure axes.The properties of stiffness matrix are as follows: Stiffness matrix issymmetric and square. In stiffness matrix, all diagonal elements are positive.

How is rigidity measured?

The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress, and so take the units of reciprocal stress, e.g. 1/Pa.

What is the 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.

What is the shape function?

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.

What is a stiff material?

Young’s modulus measures the resistance of a material to elastic (recoverable) deformation under load. A stiff material has a high Young’s modulus and changes its shape only slightly under elastic loads (e.g. diamond). A flexible material has a low Young’s modulus and changes its shape considerably (e.g. rubbers).

What is shear stiffness?

In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: where = shear stress is the force which acts is the area on which the force acts = shear strain.

What causes stiffness in joints?

Joint stiffness is the sensation of difficulty moving a joint or the apparent loss of range of motion of a joint. Joint stiffness often accompanies joint pain and/or swelling. Joint stiffness can be caused by injury or disease of the joint and is a common finding in the arthritis conditions.

What is meant by rotational stiffness?

Stiffness (k) is the relationship between an applied force and the displacement the force produces. This relationship can be defined for two common cases: In the rotational case, the applied torque (T) is proportional to the angular displacement (theta) of one side/end with respect to the other.

What is the stiffness of a beam?

Bending stiffness. From Wikipedia, the free encyclopedia. The bending stiffness ( ) is the resistance of a member against bending deformation. It is a function of elastic modulus , the area moment of inertia of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.

What is meant by stiffness factor?

Stiffness factor is the ratio of moment of inertia of cross section of beam or wire to it’s length. You can see Stiffness factor is the measure of ‘resistance to bending’

What is stiffness material?

Young’s modulus, also known as the elastic modulus, is a measure of the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material.

What is the meaning of flexural rigidity?

Flexural rigidity is defined as the force couple required to bend a non-rigid structure in one unit of curvature or it can be defined as the resistance offered by a structure while undergoing bending.

What is the unit of flexural rigidity?

Flexural rigidity of a plate has units of Pa. m3, i.e. one dimension of length less from the one for the rod, as it refers to the moment per unit length per unit of curvature, and not the total moment. I is termed as moment of inertia.J is denoted as 2nd moment of inertia/polar moment of inertia.

What is meant by pure bending?

Pure bending is a condition of stress where a bending moment is applied to a beam without the simultaneous presence of axial, shear, or torsional forces. Pure bending occurs only under a constant bending moment (M) since the shear force (V), which is equal to , has to be equal to zero.

What is neutral axis in RCC?

The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid.

What do you mean by pure shear?

In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly.

What is coaxial strain?

Strain paths are divided into two major types, those in which the principal axes of strain remain fixed with respect to the material (coaxial strain paths), and those in which they rotate (non-coaxial strain paths). The characteristics of the two types of strain path are explained.

What is shear strain geology?

Study of geological shear is related to the study of structural geology, rock microstructure or rock texture and fault mechanics. The process of shearing occurs within brittle, brittle-ductile, and ductile rocks. Within purely brittle rocks, compressive stress results in fracturing and simple faulting.

What is the stiffness of metal?

On the material side, stiffness depends on the modulus of elasticity, also known as Young’s Modulus and abbreviated as E. Young’s Modulus is the ratio of stress to strain at very small strains. Young’s Modulus for steel (29 million PSI) is three times that of aluminum (10 million PSI).

What is stiffness in muscles?

Muscle stiffness is when your muscles feel tight and you find it more difficult to move than usual, especially after rest. This is different from muscle rigidity and spasticity. With these two symptoms, your muscles stay stiff even when you’re not moving. Muscle stiffness usually goes away on its own.

What is the difference between strength and stiffness?

For purposes of the following discussion strength, stiffness and failure are defined as follows: Strength – The ability of the material to support a load without breaking (physical failure) Stiffness – The ability of the material to distribute a load and resist deformation or deflection (functional failure)

What is spring force measured in?

Units of measurement. In SI units, displacements are measured in meters (m), and forces in newtons (N or kg. m/s2). Therefore, the spring constant k, and each element of the tensor κ, is measured in newtons per meter (N/m), or kilograms per second squared (kg/s2).