Materials and sections

Structural steel in N–mm units: E = 200e3 N/mm², G = 77e3 N/mm², ρ = 8e-5 kg/mm³ (legacy value), ν = 0.3.

Structural steel in kN–m units: E = 200e6 kN/m², G = 77e6 kN/m², ρ = 80 kg/m³ (legacy value), ν = 0.3.

Material{T<:Real}

A linear-elastic structural material.

A Material carries the four scalar properties that linear member analysis can ever consume: stiffness in normal action (E), stiffness in shear (G), mass density (ρ), and the ratio that couples them (ν). It is immutable — to analyze a design change, construct a new Material.

Asap is units-agnostic: choose any consistent unit system (e.g. kN–m, N–mm, kip–in) and use it everywhere. Dimensions below are written in bracket notation.

Fields

• E::T: Young's (elastic) modulus — normal stress per unit normal strain [force/length²]
• G::T: shear modulus — shear stress per unit shear strain [force/length²]
• ρ::T: mass density — used for self-weight and (future) dynamic analysis [mass/length³]
• ν::T: Poisson's ratio — transverse contraction per unit axial extension [unitless]. For isotropic materials G = E / (2(1 + ν)).

Constructors

Material(E, G, ρ, ν)     # all four properties explicit
Material(E, ρ, ν)        # isotropic: G derived as E / (2(1 + ν))

Arguments are promoted to a common scalar type, so Material(200e6, 80, 0.3) and Material(200e6, 80.0, 0.3) are equivalent.

Examples

julia> steel = Material(200e6, 77e6, 8.0, 0.3)      # kN, m: E in kN/m²
julia> concrete = Material(30e6, 2.4, 0.2)           # G derived isotropically

See also Section, RigiditySection.

AbstractSection{T<:Real}

Supertype of all cross-sections.

A section's entire contract with the analysis layer is the rigidity accessor interface — five functions returning the only quantities a linear member stiffness matrix (or self-weight computation) ever consumes:

Kernels never read struct fields — they call these accessors. Any type implementing all five is a valid section, which is what lets a classical geometric Section and an effective-stiffness RigiditySection (cracked concrete, homogenized members) be used interchangeably anywhere.

RigiditySection{T} <: AbstractSection{T}

A cross-section defined directly by its rigidities — the products the stiffness matrix actually consumes — rather than by geometry and material.

This is the natural abstraction wherever an "equivalent stiffness" is the meaningful quantity:

• Cracked/effective concrete sections: build from ACI 318-19 stiffness modifiers (e.g. EI_eff = 0.35·Ec·Ig for beams, 0.70·Ec·Ig for columns), a Branson/Bischoff effective moment of inertia, or a full transformed-section analysis. For linear analysis this is exactly as expressive as any equivalent-E or transformed-I formulation, because only the products enter the equations.
• Homogenized/composite members, where no single (E, I) pair exists.
• Optimization parameterizations where rigidities are the design variables.

Because rigidities are stored, there is no meaningful area or material to derive mass from — so mass per unit length ρA is stored explicitly (do not back it out of the rigidities).

Fields

• EA::T: axial rigidity — force per unit axial strain [force]
• EIx::T: flexural rigidity about the strong axis [force·length²]
• EIy::T: flexural rigidity about the weak axis [force·length²]
• GJ::T: torsional rigidity [force·length²]
• ρA::T: mass per unit length, for self-weight and dynamics [mass/length]

Examples

julia> Ec, Ig, A, ρc = 30e6, 8e-4, 0.12, 2.4e3;

julia> cracked_beam = RigiditySection(Ec * A, 0.35 * Ec * Ig, 0.35 * Ec * Ig,
                                      0.1 * Ec * Ig, ρc * A)

See also Section, AbstractSection.

Section{T} <: AbstractSection{T}

A cross-section defined by its geometry and its Material — the standard modeling workflow when section dimensions and material are known separately.

Rigidities are derived on demand: EA(sec) = sec.material.E * sec.A, etc. If you instead know effective rigidities directly (cracked concrete, transformed sections, optimization parameterizations), use RigiditySection.

Fields

• material::Material{T}: the section's material (provides E, G, ρ)
• A::T: cross-sectional area [length²]
• Ix::T: second moment of area about the strong bending axis (local x-axis convention of the legacy library, paired with bending in the local x–y plane) [length⁴]
• Iy::T: second moment of area about the weak bending axis [length⁴]
• J::T: St. Venant torsional constant [length⁴]

Constructors

Section(material, A, Ix, Iy, J)   # full frame section
Section(material, A)              # axial-only (truss) section: Ix = Iy = J = 0

The axial-only form replaces the legacy TrussSection: a truss element only ever queries EA/ρA, so zero flexural/torsional properties are simply never read.

Examples

julia> steel = Material(200e6, 77e6, 8.0, 0.3);

julia> w = Section(steel, 1e-2, 8e-5, 3e-5, 5e-7)   # a wide-flange, kN–m

julia> bar = Section(steel, 5e-3)                    # truss bar, axial only

EA(section) -> T

Axial rigidity of the section: the force required to produce unit axial strain [force]. Section derives it as E·A; RigiditySection stores it.

EIx(section) -> T

Flexural rigidity about the section's strong axis [force·length²]. Governs bending in the element's local x–y plane. Section derives it as E·Ix; RigiditySection stores it.

EIy(section) -> T

Flexural rigidity about the section's weak axis [force·length²]. Governs bending in the element's local x–z plane. Section derives it as E·Iy; RigiditySection stores it.

GJ(section) -> T

St. Venant torsional rigidity [force·length²]: torque per unit rate of twist. Section derives it as G·J; RigiditySection stores it.

ρA(section) -> T

Mass per unit length of the member [mass/length]. Multiply by gravitational acceleration for self-weight per unit length. Section derives it as ρ·A; RigiditySection stores it explicitly.