Structural Formulas calculators

Beams & Frames

• Straight Beam — Shear, Moment, Slope & Deflection Alpha · 2026-09-23 — Single-span elastic beam — 6 load types x 6 end restraints, including thermal and imposed-displacement loading
• Elastic Frame — Reactions & Deformation Alpha · 2026-08-27 — Planar U-frame (two columns + top beam), pinned at both ends — three load types on the top beam
• Beam on Elastic Foundation Alpha · 2026-09-02 — Winkler foundation — shear, moment, slope and deflection for a uniform beam resting on a continuously reacting elastic medium; finite-length and…
• Beam-Column — Axial Load with Transverse Loading Alpha · 2026-09-23 — Shear, moment, slope and deflection of a beam that also carries an axial load — compression magnifies bending, tension reduces it; ends held against…

Curved Beams & Rings

• Circular Ring — Bending Moment, Hoop & Shear Force Alpha · 2026-06-25 — Thin circular ring under in-plane radial point loads — two opposing forces or n equally spaced forces

Torsion

• Torsion of Non-circular & Hollow Sections Alpha · 2026-06-25 — 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 Alpha · 2026-08-27 — Uniform pressure or central point load on a solid circular plate — simply supported or fixed edge
• Rectangular Plate Bending Alpha · 2026-09-02 — Maximum stress, deflection and edge reaction of a uniform-thickness rectangular plate

Shells & Pressure Vessels

• Thin-Walled Pressure Vessel — Membrane Stresses & Deformations Alpha · 2026-06-25 — 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 Alpha · 2026-06-25 — 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 Alpha · 2026-06-25 — 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 Alpha · 2026-08-27 — Critical loads for circular ring, circular arch and narrow rectangular beam — 5 classic buckling cases

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