2D Frame & Beam FEA — analysis report

Does this solution deserve to be believed? Reported for every run, independent of any design limit.

Every capacity below is the value entered by the engineer. No code resistance, partial factor or buckling reduction is applied by this tool.

What was analysed, how, and within what boundary. This tool performs a linear analysis — LA in the terminology of EN 1993-1-14 — and reports the analysis record content that part describes. No compliance with any standard is claimed.

The complete analysis model, as solved. Coordinates are global with X to the right and Y upward.

Loads are listed exactly as defined. Distributed loads state their direction and whether the intensity is measured along the member or projected, because the two differ on an inclined member.

Support reactions in the global frame — the forces the supports apply to the structure — per design situation, each with its own equilibrium sum so the check is never read apart from the numbers it checks.

Global nodal displacements per design situation. Rotations are in radians, positive counter-clockwise.

Member end actions in the local frame — the forces the joints apply to the member, and the starting point for a connection design. Local x runs from the I node to the J node.

Peak absolute value per member over every design situation, each naming the situation that governs it.

Axial force, shear and bending moment enveloped over every design situation, per member. Ordinates are signed and plotted positive-up — this is not the tension-face drafting convention; see the sign convention in the analysis basis. Quantities that are zero along the whole member are not plotted.

Bending moment and deflected shape for each member under each design situation. Deflection appears only here and never on the envelope: an enveloped deflected shape would be a curve that no single load case produces. 43 further diagrams are omitted here: this report plots at most 72 diagrams in total, to keep the document readable. Members are plotted worst-first by peak bending moment, and every member's values — including those not plotted — appear in full in the result tables above.

Evidence that this particular analysis is trustworthy, reported per run rather than asserted once.

Stated in full so that the absence of a number is never mistaken for a passing result.

• First-order linear elastic analysis. Equilibrium is formed on the undeformed geometry, material response is linear with no yielding, and displacements are assumed small enough that their effect on equilibrium is negligible. Second-order ($P\text{-}\Delta$ and $P\text{-}\delta$) effects, buckling and plasticity are not represented.
• All geometry, restraints and loading lie in a single plane, and every member bends about one axis. Out-of-plane behaviour — minor-axis bending, torsion, lateral–torsional buckling — is outside the model entirely and is not merely un-checked.
• Joints are rigid and dimensionless unless an end release is declared. Connection flexibility, panel-zone deformation, member end eccentricity and the physical size of the joint are not modelled.
• The equilibrium residual is formed by integrating the applied loading directly from the load definitions, independently of the fixed-end forces used to solve. It therefore tests the load derivation as well as the solution, rather than confirming the solver against itself.
• Internal actions are integrated from exact statics along each member using its solved end forces, not differentiated from element shape functions. For prismatic members under polynomial loading this makes the diagrams exact and independent of the mesh — one element per member gives the same answer as fifty.
• Members are straight and prismatic between their end nodes: area, second moment of area and material are constant along each member. A tapered or haunched member must be modelled as a series of prismatic members.
• The deflection limit is applied per member, with the span taken as that member's own length between its end nodes and the deflection taken perpendicular to the member axis. Where a physical span is modelled as several members, apply the limit to the assembled span yourself — the tool cannot know which members form one span.
• Every limit compared against is supplied by the engineer. The tool states the comparison it performed and reports the value used; it does not select, derive or endorse an allowable, and it performs no code member check.
• Stresses are the nominal beam-theory stresses through the depth. The equivalent stress is evaluated at the extreme fibres, at the neutral axis, and — on a section generated from a flanged outline — at the step where the flange gives way to the web; within any run of constant thickness the equivalent stress can only peak at one of that run's ends, so those points bound it. A section whose properties were typed in rather than derived from an outline carries no step for the tool to find, and only the first two are evaluated. Stress concentrations, residual stresses, local effects at load points and supports, connection stresses, and any three-dimensional stress state are outside a beam-element analysis.
• Where a section is generated from an outline, the effective shear area $A_s$ follows the usual conventions ($5A/6$ for a rectangle, the gross web area for an I-section, both webs for a rectangular hollow section, $A/2$ for a circular tube). $A_s$ affects only the average shear stress and the optional shear-flexibility term; the peak shear stress comes from $Q/t$, which is exact for the outline. Any derived value can be overwritten.

• MECH_DIRECT_STIFFNESSMatrix structural analysis — direct stiffness method
  Assembly of element stiffness matrices in a global frame, elimination of restrained degrees of freedom, and solution of $Ku=F$ by symmetric factorisation. Public-domain structural mechanics; no code coefficients are involved.
• MECH_BEAM_ELEMENTEuler–Bernoulli and Timoshenko beam theory
  Two-node plane frame element with linear axial and Hermitian bending interpolation, written in shear-flexible form with $\Phi =12EI/(G{A}_s{L}^2)$. Setting $\Phi =0$ recovers Euler–Bernoulli exactly, so one element formulation serves both theories.
• NAFEMS_R0064NAFEMS R0064
  Quality assurance procedures for engineering analysis. Referenced as the framing for the pre-solve model diagnostics and the equilibrium and mesh-independence records reported with every analysis.
• MECH_STATICSStatics — equilibrium of a rigid body
  $\sum F_x=0$, $\sum F_y=0$, $\sum M_z=0$. Used both to recover internal actions along a member from its end forces and to cross-check the solved reactions against the applied loading.
• ASME_VV10ASME V&V 10
  Standard for verification and validation in computational solid mechanics. Supplies the vocabulary for the distinction this pack relies on: comparing the solver against closed-form analytical solutions is code verification. Referenced for that framing only.
• USER_ALLOWABLESUser-supplied acceptance criteria
  Every limit this pack compares against — the deflection span ratio and the normal, shear and equivalent-stress allowables — is entered by the engineer and reported as theirs. Xarpis supplies no resistance value, partial factor or code limit of its own.
• MECH_ENGINEERS_BENDINGEngineer's theory of bending
  $\sigma =N/A\pm My/I$ at the extreme fibres of a prismatic section that remains plane and elastic. Public-domain mechanics of materials.
• MECH_SHEAR_FORMULAShear stress distribution in beams
  $\tau =VQ/(It)$ at the neutral axis, with ${\tau }_{avg}=V/A_s$ reported alongside it. Public-domain mechanics of materials; $Q/t$ is derived from the section outline, not tabulated.
• MECH_VON_MISESDistortion-energy (von Mises) equivalent stress
  ${\sigma }_{vm}=\sqrt{{\sigma }^2+3{\tau }^2}$ for the plane stress state carried by a beam element. Evaluated at the extreme fibre and at the neutral axis, because the two locations are governed by different quantities.
• EN_1993_1_14EN 1993-1-14 · 2025
  Design of steel structures — design assisted by finite element analysis. Defines the analysis taxonomy (LA, LBA, GNA, GNIA, MNA, GMNA, GMNIA) and the content an analysis record is expected to carry. This tool performs a linear analysis, LA in that terminology, and reports the analysis record content that part describes. Referenced for vocabulary and reporting structure only — no clause is implemented and no compliance is claimed.
• NAFEMS_QSS001NAFEMS QSS001
  Quality system supplement to ISO 9001 for finite element analysis. Referenced as the framing for publishing a benchmark register and a per-analysis quality record rather than asserting correctness.
• AISC_360_STABILITYAISC 360 Chapter C / Appendix 1
  Direct analysis and second-order elastic analysis. Named here only to state what this v1 does NOT do: no second-order analysis, no notional loads, no stiffness reduction. Roadmap reference, not an implemented basis.
• DNV_RP_C208DNV-RP-C208
  Determination of structural capacity by non-linear finite element methods. Named here only to state what this v1 does NOT do: no material or geometric non-linearity. Roadmap reference, not an implemented basis.