Class StructuralAnalysis

java.lang.Object
org.episteme.natural.engineering.structural.StructuralAnalysis
public class StructuralAnalysis extends Object
Structural analysis calculations. Modernized to use high-precision Real and typed Quantities.
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • simpleBeamDeflectionUniform

      public static Real simpleBeamDeflectionUniform(Real w, Real L, Real E, Real I)
      Simply supported beam: maximum deflection at center. δ_max = (5 * w * L⁴) / (384 * E * I)

    • simpleBeamDeflectionPoint

      public static Real simpleBeamDeflectionPoint(Real P, Real L, Real E, Real I)
      Simply supported beam: deflection under point load at center. δ_max = (P * L³) / (48 * E * I)

    • cantileverDeflectionUniform

      public static Real cantileverDeflectionUniform(Real w, Real L, Real E, Real I)
      Cantilever beam: deflection at free end under uniform load. δ_max = (w * L⁴) / (8 * E * I)

    • cantileverDeflectionPoint

      public static Real cantileverDeflectionPoint(Real P, Real L, Real E, Real I)
      Cantilever beam: deflection at free end under point load. δ_max = (P * L³) / (3 * E * I)

    • simpleBeamMomentUniform

      public static Real simpleBeamMomentUniform(Real w, Real L)
      Maximum bending moment for simply supported beam with uniform load. M_max = w * L² / 8

    • cantileverMomentUniform

      public static Real cantileverMomentUniform(Real w, Real L)
      Maximum bending moment for cantilever with uniform load. M_max = w * L² / 2

    • bendingStress

      public static Real bendingStress(Real moment, Real distanceFromNA, Real momentOfInertia)
      Bending stress. σ = M * y / I

    • shearStress

      public static Real shearStress(Real shearForce, Real firstMoment, Real momentOfInertia, Real width)
      Shear stress in beam. Ï„ = V * Q / (I * b)

    • rectangleMomentOfInertia

      public static Real rectangleMomentOfInertia(Real width, Real height)
      Second moment of area for rectangle. I = b * h³ / 12

    • circleMomentOfInertia

      public static Real circleMomentOfInertia(Real radius)
      Second moment of area for circle. I = π * r⁴ / 4

    • sectionModulus

      public static Real sectionModulus(Real momentOfInertia, Real distanceToExtreme)
      Section modulus. S = I / y_max

    • eulerBucklingLoad

      public static Real eulerBucklingLoad(Real E, Real I, Real L, Real K)
      Column buckling (Euler formula). P_cr = π² * E * I / (K * L)²

    • slendernessRatio

      public static Real slendernessRatio(Real K, Real L, Real radiusOfGyration)
      Slenderness ratio. λ = K * L / r

    • radiusOfGyration

      public static Real radiusOfGyration(Real momentOfInertia, Real area)
      Radius of gyration. r = √(I / A)

    • trussMemberForce

      public static Real trussMemberForce(Real angleDegrees, Real jointForce)
      Truss member force (method of joints - simplified).

    • torsionalShearStress

      public static Real torsionalShearStress(Real torque, Real radius)
      Torsional shear stress in circular shaft. τ = T * r / J where J = πr⁴/2

    • angleOfTwist

      public static Real angleOfTwist(Real torque, Real length, Real shearModulus, Real radius)
      Angle of twist. θ = T * L / (G * J)

    • bendingStressQ

      public static Quantity<Pressure> bendingStressQ(Quantity<?> moment, Quantity<Length> distanceFromNA, Real momentOfInertia)
      Bending stress using Quantity types. Note: moment is represented as Quantityinvalid input: '<'?> (typically Energy/Torque units N*m).

    • eulerBucklingLoadQ

      public static Quantity<Force> eulerBucklingLoadQ(Quantity<Pressure> E, Real I, Quantity<Length> L, Real K)
      Euler buckling load using Quantity types.