Structural Engineering Glossary

A measure of a material's stiffness, defined as the ratio of stress to strain in the linear elastic region. Denoted as E, it represents how much a material will deform under a given load.

A geometric property that describes how a cross-section's area is distributed about an axis. It determines a beam's resistance to bending and is denoted as I.

The displacement of a structural element from its original position under load. Maximum deflection is often limited by building codes to prevent serviceability issues.

The internal moment that causes a beam to bend when subjected to external loads. It represents the sum of moments about a point in the cross-section.

The normal stress induced in a beam due to bending. Calculated as σ = M·c/I, where M is bending moment, c is distance from neutral axis, and I is moment of inertia.

The ratio of effective column length to radius of gyration (λ = KL/r). It characterizes how prone a column is to buckling. Higher values indicate more slender columns that are more susceptible to elastic buckling.

The equivalent length of a column with pinned ends that would buckle at the same load. Calculated as Le = K×L, where K is the effective length factor depending on end conditions and L is the actual length.

A geometric property that relates moment of inertia to cross-sectional area: r = √(I/A). It represents the distance from the centroid at which the entire area could be concentrated to produce the same moment of inertia.

The maximum and minimum normal stresses that occur on planes where shear stress is zero. These are eigenvalues of the stress tensor and represent the extreme values of normal stress at a point.

The mathematical process of converting stress components from one coordinate system to another rotated system. On Mohr's Circle, rotation in physical space by angle θ corresponds to 2θ rotation on the circle.

The largest shear stress that occurs at a point, equal to half the difference between maximum and minimum principal stresses: τ_max = (σ₁ - σ₂)/2. On Mohr's Circle, it equals the circle radius.

The force applied to a material divided by its original cross-sectional area: σ = F/A₀. Also called nominal stress, it does not account for the change in area during deformation.

The change in length divided by the original length: ε = ΔL/L₀. Also called nominal strain, it is dimensionless but often expressed as a percentage or in microstrain (με).

The force divided by the instantaneous (current) cross-sectional area: σₜ = F/A. Related to engineering stress by σₜ = σₑ(1 + εₑ) for uniform deformation. More accurate for large strains.

The natural logarithm of the ratio of current to original length: εₜ = ln(L/L₀) = ln(1 + εₑ). Also called logarithmic or natural strain. Additive for sequential deformations.

The geometric center of a cross-section, where the first moment of area equals zero. For symmetric shapes, the centroid lies on the axis of symmetry. Moments of inertia are typically calculated about axes through the centroid.

The axis within a beam cross-section where bending stress is zero. Fibers above the neutral axis are in tension or compression (depending on bending direction), while those below are in the opposite state.

A formula relating moment of inertia about any axis to the centroidal moment of inertia: I = I_c + Ad², where I_c is centroidal moment of inertia, A is area, and d is distance between parallel axes.

A geometric property relating bending moment to bending stress: S = I/c, where I is moment of inertia and c is distance from neutral axis to extreme fiber. Used in the bending stress formula: σ = M/S.