2DFrameCalc: Online 2D Plane Frame Analysis

Analysis method

Linear-elastic, small-displacement, first-order Euler–Bernoulli plane-frame analysis. Each node has two translations and one rotation. Member stiffness includes axial deformation and in-plane bending; member-end pin releases are handled by static condensation (removing the released end moment from the assembled member stiffness).

One-way members and supports use an iterative active-state solution. Their load combinations are solved from the factored loads, rather than assuming that the active elements remain the same in every case.

Units and sign conventions

Global +X is right and +Y is up; positive nodal moment and rotation about Z are anticlockwise. Local X runs from the start node to the end node; positive local transverse load is perpendicular to it, towards local +Y. Positive axial diagram values denote compression; negative values denote tension.

The bending diagram starts at −Mi and ends at −Mj: member-table end moments and bending-diagram ordinates use opposite signs. The shear diagram starts at Vy and ends at Vj. For a horizontal simply supported beam under downward load, positive bending-diagram values indicate sagging.

The unit selector converts supported grid inputs and on-screen results to US customary units. Section-property inputs and the section helper remain metric. Check the units printed on each result or exported table.

Supports, releases and one-way behaviour

• Supports can restrain X, Y and rotation, use translational/rotational springs, or define an inclined single-axis restraint. See the fixity and spring reference for the input letters.
• A P release at either member end releases its bending moment. Releasing an unloaded, otherwise unused rotation is permitted; a load on a zero-stiffness degree of freedom remains a mechanism error.
• C and T members carry compression-only or tension-only axial force. They have no bending stiffness; transverse member loading is rejected. Apply loads through an appropriate frame member or the joints.
• One-way support actions limit the sign of the support reaction along its restraint axis. They do not specify the sign of the applied load. A model must retain a stable load path after an element or restraint disengages.

Loads and combinations

• Named cases accept nodal Fx, Fy and Mz, uniform or linearly varying member loads, and member point forces at a distance from the start node. Self-weight is generated from the section data.
• X and Y member distributed loads use actual member length. X projected and Y projected use the perpendicular coordinate projection: on a 3–4–5 member, a Y projected load acts over the 3 m horizontal run. The ⊥ local option acts perpendicular to the member. Concentrated forces have no projected-length multiplier.
• ULS (ultimate) and SLS (serviceability) use separate factor sets and result lists. Linear combinations can use superposition; one-way behaviour requires direct re-analysis. Check the factors in the Loading reference rather than assuming the 3D defaults apply.
• For a row with a numeric ULS factor and blank SLS factor, SLS uses −1 when ULS is negative and +1 otherwise. Enter an explicit zero to omit that case at SLS.
• Loads must resolve to existing members and point-load distances must lie on their target member. Cases combined on a staged structure must use compatible stage settings.

What the tool does not do

The documented released baseline excludes shear deformation, geometric stiffness and P–Δ effects, elastic buckling, dynamics, imposed support movements, temperature actions, moving loads and member design-code checks. Numerical-core support for prescribed constraints does not mean that a support-movement load input has been released.

Check member capacity, connection design, stability and the project design basis separately. A successful equilibrium or solver-residual check is a numerical check, not a design approval.

Verification and benchmarks

Existing repository regression checks compare the following models with analytical expectations. The values below describe those checks, not the unfinished worked examples above. E = 200,000 MPa and I = 8 × 10⁶ mm⁴ in these bending checks; density is zero.

• 3 m cantilever, 10 kN downward tip load: Uy = −PL³/(3EI) = −0.05625 m; Ry = 10 kN; base moment = 30 kNm. Absolute test tolerances: 10⁻⁸ m for Uy, 10⁻⁷ kN for reaction and 10⁻⁷ kNm for moment.
• 2 m axial bar, 120 kN tension, A = 6,000 mm²: extension PL/(EA) = 0.0002 m, reaction Rx = −120 kN. Absolute tolerances: 10⁻¹¹ m and 10⁻⁷ kN.
• 4 m simply supported beam, 5 kN/m downward: each reaction = wL/2 = 10 kN; maximum deflection 5wL⁴/(384EI) = 0.0104166666666667 m. Absolute tolerances: 10⁻⁶ kN and 10⁻⁸ m.

The suite also covers releases, springs, projected loads, one-way behaviour, force extrema, equilibrium and invalid models. These regression and closed-form checks do not constitute independent software certification.