Applied force: see external force.
Brittle: A brittle structure or material exhibits low ductility, meaning that it exhibits very little inelastic deformation before complete failure.
Centroid: Similar to the concept of center of gravity, except that it applies to a two dimensional shape rather than an object. For a given shape, the centroid location corresponds to the center of gravity for a thin flat plate of that shape, made from a homogeneous material.
Component (of a vector): Any vector can be expressed as a collection of vectors whose sum is equal to the original vector. Each vector in this collection is a component of the original vector. It is common to express a vector in terms of components which are parallel to the x and y axes.
Concentrated force: A force considered to act along a single line in space. Concentrated forces are useful mathematical idealizations, but cannot be found in the real world, where all forces are either body forces acting over a volume or surface forces acting over an area.
Connection: Connection is similar to the concept of support, except that connection refers to a relationship between members in a structural model. A connection restrains degrees of freedom of one member with respect to another. For each restrained degree of freedom, there is a corresponding force transferred from one member to the other; forces associated with unrestrained degrees of freedom are zero. See fixed connection and pin connection.
Couple: A system of forces composed of two equal forces of opposite direction, offset by a distance. A couple is statically equivalent to a moment whose magnitude equals the magnitude of the force times the offset distance.
Degree of Freedom: A displacement quantity which defines the shape and location of an object. In the two dimensional plane, a rigid object has three degrees of freedom: two translations and one rotation. In three dimensional space, a rigid object has six degrees of freedom (three translations and three rotations).
Ductility: Ductility generally refers to the amount of inelastic deformation which a material or structure experiences before complete failure. Quantitatively, ductility can be defined as the ratio of the total displacement or strain at failure, divided by the displacement or strain at the elastic limit.
Elastic energy: The energy stored in deformed elastic material (e.g., a watch spring). Elastic energy equals where k is the stiffness, and is the associated deflection. Elastic energy is sometimes called elastic potential energy because it can be recovered when the object returns to its original shape; see potential energy.
E-Modulus: see modulus of elasticity.
Energy: A property of a body related to its ability to move a force through a distance opposite the force's direction; energy is the product of the magnitude of the force times the distance. Energy may take several forms: see kinetic energy, potential energy, and elastic energy.
Fixed support: In two dimensions, a fixed support restrains three degrees of freedom: two translations and one rotation.
Flexibility: Flexibility is the inverse of stiffness. When a force is applied to a structure, there is a displacement in the direction of the force; flexibility is the ratio of the displacement divided by the force. High flexibility means that a small load produces a large displacement.
Force: A directed interaction between two objects that tends to change the momentum of both.Since a force has both direction and magnitude, it can be expressed as a vector
Force System: see system of forces.
Inertial Force: A fictitious force used for convenience in visualizing the effects of forces on bodies in motion. For an accelerating body, the inertial force is considered as a body force whose resultant acts at the object's center of gravity in a direction opposite the acceleration. The magnitude of the force is the mass of the object times the magnitude of the acceleration.
Internal force: Forces which hold an object together when external forces or other loads are applied. Internal forces are sometimes called resisting forces since they resist the effects of external forces.
Internal hinge: see pin connection.
Linear Elastic: A force-displacement relationship which is both linear and elastic. For a structure, this means the deformation is proportional to the loading, and deformations disappear on unloading. For a material, the concept is the same except strain substitutes for deformation, and stress substitutes for load.
Load: An external force. The term load is sometimes used to describe more general actions such as temperature differentials or movements such as foundation settlements.
Magnitude: A scalar value having physical units.
Modulus of elasticity: The proportional constant between stress and strain for material with linear elastic behavior: calculated as stress divided by strain. Modulus of elasticity can be interpreted as the slope of the stress-strain graph. It is usually denoted as E, sometimes known as Young's Modulus Y, or E-Modulus.
Moment of inertia: Moment of inertia has two distinct but related meanings: 1) it is a property of a an object relating to the magnitude of the moment required to rotate the object and overcome its inertia. 2) A property of a two dimensional cross section shape with respect to an axis, usually an axis through the centroid of the shape.
Moment Release: see pin connection.
Moment resisting-connection: see fixed connection.
Normal stress: Stress acting perpendicular to an imaginary plane cutting through an object. Normal stress has two senses: compression and tension. Normal stress is often simply called stress.
Pin support: In two dimensions, a pin support restrains two translation degrees of freedom but does not restrain rotation. When considering reaction forces, a pin support is usually considered to have two force components: one each about the x and y axes respectively.
Plastic: see inelastic.
Potential Energy: The energy stored in a raised object (e.g. the weights in a grandfather clock). Potential energy equals mgh, where m is mass, g is the acceleration of gravity, and h is the vertical distance from a reference location. It is called potential energy because the energy can be regained when the object is lowered. This type of potential energy is sometimes called gravitational potential energy in order to distinguish it from elastic potential energy: see elastic energy.
Pressure: Pressure is a similar idea to stress, the force intensity at a point, except that pressure means something acting on the surface of an object rather than within the material of the object. When discussing the pressure within a fluid, the meaning is equivalent to stress.
Resisting force: see internal force.
Rigid: An idealized concept meaning something which does not deform under loading. In fact, all objects deform under loading, but in modelling it can be useful to idealize very stiff objects as rigid.
Rigid connection: see fixed connection.
Rotation: Motion of an object where the path of every point is a circle or circular arc. A rotation is defined by a point and vector which determine the axis of rotation. The direction of the vector is the direction of the axis and the magnitude of the vector is the angle of rotation.
Section Modulus: A property of a cross sectional shape, which depends on shape, and orientation. Section modulus is usually denoted S, and S = I/c, where I = moment of inertia about an axis through the centroid, and c is the distance from the centroid to the extreme edge of the section.
Shear strain: Strain measuring the intensity of racking in the material. Shear strain is measured as the change in angle of the corners of a small square of material.
Stability: Stability is best defined as the opposite of instability, which is the occurrence of large structural deformations which are not the result of material failure.
Statically determinate: A statically determinate structure is one where there is only one distribution of internal forces and reactions which satisfies equilibrium. In a statically determinate structure, internal forces and reactions can be determined by considering nothing more than equations of equilibrium.
Statically equivalent: Two force systems are statically equivalent when their resultants are equal. Physically, this means that the force systems tend to impart the same motion when applied to an object; note that the distribution of resulting internal forces in the object may be different.
Stiffness: This is a general term which may be applied to materials or structures. When a force is applied to a structure, there is a displacement in the direction of the force; stiffness is the ratio of the force divided by the displacement. High stiffness means that a large force produces a small displacement. When discussing the stiffness of a material, the concept is the same, except that stress substitutes for force, and strain substitutes for displacement; see modulus of elasticity.
Strength: A very general term that may be applied to a material or a structure. In a material, strength refers to a level of stress at which there is a significant change in the state of the material, e.g., yielding or rupture. In a structure, strength refers to a level of level of loading which produces a significant change in the state of the structure, e.g., inelastic deformations, buckling, or collapse.
Structural model: An idealization for analysis purposes of a real or conceived structure. A structural model includes boundaries limiting the scope of the analysis. Supports occur at these boundaries, representing things which hold the structure in place.
Support: A support contributes to keeping a structure in place by restraining one or more degrees of freedom. In a structural model, supports represent boundary entities which are not included in the model itself, e.g., foundations, abutments, or the earth itself. For each restrained translation degree of freedom at a support, there is a corresponding reaction force; for each restrained rotation degree of freedom, there is a reaction moment.
Surface force: A force applied to the surface of an object.
Transmissibility: The principle stating that a force has the same external effect on an object regardless of where it acts along its line of action.
Velocity: A vector quantity equal to the rate that position changes with time.