Structural Formulas calculators

Beams & Frames

• Straight Beam — Shear, Moment, Slope & Deflection — Single-span elastic beam — 6 load types x 6 end restraints, including thermal and imposed-displacement loading
• Elastic Frame — Reactions & Deformation — Planar U-frame (two columns + top beam), pinned at both ends — three load types on the top beam

Curved Beams & Rings

• Circular Ring — Bending Moment, Hoop & Shear Force — Thin circular ring under in-plane radial point loads — two opposing forces or n equally spaced forces

Torsion

• Torsion of Non-circular & Hollow Sections — Saint-Venant uniform torsion — torsional stiffness K, angle of twist θ and maximum shear stress τ_max for 9 section types

Flat Plates

• Circular Plate — Deflection, Slope & Stress — Uniform pressure or central point load on a solid circular plate — simply supported or fixed edge

Shells & Pressure Vessels

• Thin-Walled Pressure Vessel — Membrane Stresses & Deformations — Cylindrical shell (axial load / radial pressure / capped pressure) and spherical shell (internal/external pressure) — classical membrane theory of shells
• Long Cylindrical Shell — Edge-Load Bending — Axisymmetric bending of semi-infinite thin cylindrical shell under radial edge shear or edge moment — exponential-trigonometric closed-form solution…
• Thick-Walled Pressure Vessel — Lamé Stresses — Exact Lamé solution for through-wall stress distribution in a thick-walled cylinder or sphere under internal or external pressure

Buckling & Elastic Stability

• Elastic Stability — Buckling of Rings, Arches & Beams — Critical loads for circular ring, circular arch and narrow rectangular beam — 5 classic buckling cases

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