Giovanni Malagnino Consulting

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    Engineering model guide

    Help & Technical Documentation

    Use this guide to choose the correct calculation model, prepare inputs and interpret what a result does—and does not—demonstrate.

    Getting started

    Choose the model that matches the operation

    This application contains two independent engineering models. They share pipe catalogues, units and reporting conventions, but they do not share the same mechanics or acceptance criterion. Select the model from the physical operation—not from the result you hope to obtain.

    QuestionPipe LoweringIn-service Deflection
    Intended operationLowering or differential end offsets of a fixed-end spanTemporary central movement of an operating steel pipe in a symmetric excavation
    Loads and axial stateSelf-weight; free sliding or initially straight restrained ends; optional groundWeight, gauge pressure, temperature and additional wall force; effective tension may be tensile or compressive
    SupportsEqually spaced vertical unilateral supports; optional rigid horizontal groundNone, equidistant pairs or custom temporary supports; permanent mode adds staged backfill interaction
    Governing resultBiaxial bending stress when free; combined axial plus biaxial normal stress when restrainedConservative Von Mises beam bound over the complete intervention path
    Not coveredPressure, temperature, local pipe details and code complianceHDPE, plastic steel, irreversible soil behavior, local contact design and normative compliance

    Getting started

    Read the verdict before the number

    Valid / converged
    The numerical checks required by that solver completed. This is not a physical-validity or code-compliance statement.
    Criterion met / not met
    The reported model stress is respectively at or below, or above, the selected strict threshold. There is no hidden mechanical margin.
    Uncertain
    The numerical uncertainty overlaps the threshold. It takes precedence over a pass/fail label.
    Unresolved
    A failed, uncertain, interrupted or unsampled region has not been classified and must not be treated as failing or impossible.
    Numerical failure
    The requested output could not be represented or solved reliably. The application does not substitute another model or a convenient mesh result.
    Out of domain
    A documented model-scope screen was exceeded. No result within this model is claimed.
    Instability risk
    The in-service initial effective compression reaches its Euler screen; the model stops without a post-buckling solution.
    Search results, represented values and certification language
    • An exploratory range contains verified samples and estimated boundaries; it is not proof that all admissible regions were found.
    • A represented length or height is a separately solved view used for charts and details. It can be changed without rerunning the search.
    • A search candidate is recomputed before publication. Failed or uncertain samples remain visible as unresolved coverage.
    • “Lowest computed stress” and “largest admissible value found” are observations, not demonstrated global optima.
    • A support count is certified minimal only in the explicitly documented case where a verified candidate uses zero supports.

    Getting started

    Units, stale results and report snapshots

    • The unit switch changes representation only; it does not restart a completed calculation.
    • Editing a mechanical input invalidates results and export availability until the new request completes.
    • Background calculations are isolated by request. Obsolete work is cancelled or ignored so it cannot overwrite a newer result.
    • PDF exports use one coherent completed-request snapshot: inputs, derived values, result and displayed unit system belong together.
    • A PDF records the model calculation; it is not a sealed design document or normative certificate.

    Model guide

    Pipe Lowering

    Fixed-end biaxial beam analysis with optional vertical supports, ground contact and axial end restraint.

    Pipe Lowering

    Geometry, properties and sign conventions

    The reference coordinate runs from the left clamp at x = 0 to the right clamp at x = L. Vertical elevation z is positive upward, lateral offset is y, and distributed weight q acts downward. Both end rotations are fixed; the right end is imposed at vertical offset hv and lateral offset hl.

    Input familyMeaningImportant convention
    Pipe and coatingOutside diameter, analysis wall thickness and coating propertiesThe coating contributes weight and outside radius; it does not add steel stiffness
    MaterialYoung’s modulus, density, grade or custom yield and allowable percentageThe displayed allowable is a user-selected model threshold, not a code check
    GeometryL, signed hv and signed hlL is the longitudinal reference distance, not the inclined chord
    Supports0–20 equally spaced installed supportsInstalled does not mean active: unilateral supports may lift off
    GroundMinimum pipe-axis elevationEnter physical ground elevation plus outside coated radius; the solver does not add the radius again
    Cross-section and weight equations
    Di=Do−2t,A=π4(Do2−Di2),I=π64(Do4−Di4),c=Do2D_i=D_o-2t,\quad A=\frac{\pi}{4}(D_o^2-D_i^2),\quad I=\frac{\pi}{64}(D_o^4-D_i^4),\quad c=\frac{D_o}{2}

    Uniform hollow circular steel section

    Internally, mechanics-v2 uses millimetres, newtons and MPa. The application bridge converts displayed length and modulus units before solving.

    Pipe Lowering

    Free sliding and restrained ends are different models

    Free sliding

    The beam is linear in both bending planes and carries no axial force. Vertical contact does not restrain lateral or axial motion. The governing stress is the biaxial extreme-fibre bending stress evaluated at the same position.

    Restrained

    The initially straight, unprestressed pipe has fixed axial end separation. Moderate rotation creates tension that couples vertical deflection, lateral deflection and contact. The governing criterion combines N/A with biaxial bending; a free solution is never substituted.

    Restrained compatibility and stress criterion
    N=EA2L∫0L(z′2+y′2) dxN=\frac{EA}{2L}\int_0^L\left(z'^2+y'^2\right)\,dx

    Coupled axial tension for the Pipe Lowering restrained model

    σmax⁡=max⁡x(NA+cIMv(x)2+Ml(x)2)≤σallow\sigma_{\max}=\max_x\left(\frac{N}{A}+\frac{c}{I}\sqrt{M_v(x)^2+M_l(x)^2}\right)\leq\sigma_{allow}

    Governing combined normal-stress criterion

    This is a small-strain, moderate-rotation von Kármán model—not exact large-rotation kinematics, a pressure model or a Von Mises code assessment.

    Pipe Lowering

    Supports and ground contact

    Installed supports

    Supports are equally spaced vertical obstacles along the straight end-to-end support line. They carry upward reaction only, allow lift-off and provide no lateral, rotational or axial restraint. Results distinguish installed supports from the subset actually in contact.

    Optional ground

    The ground is rigid, horizontal and frictionless over the full length. The solver enforces non-penetration in the vertical plane and reports ground, combined support/ground and clamp reactions separately. Contact zones shown in charts are graphical estimates; reported ground reactions are nodal forces, not pressures.

    Contact and refinement methods
    • Unilateral contact is solved with an active set and no penalty stiffness.
    • Free, fixed-L ground cases first try the fast path. The exact no-ground solution is accepted only when exact member minima clear the ground by more than the penetration tolerance.
    • Otherwise the mesh is refined; stress, reactions, displacements and exact between-node member minima participate in acceptance.
    • Two consecutive precision-loss refinement levels stop the calculation. Non-representable derived output is a numerical failure, not a fallback mesh result.

    Pipe Lowering

    Calculation modes

    ModeWhat remains fixedWhat is reported
    Fixed LEntered L, hv, hl and installed supportsOne full solution, including a valid result even when its stress criterion is not met
    Find hL, hl, section, load and installed supportsEstimated signed hv ranges and a separately solved represented height
    Find L rangehv, hl, section, load and installed supportsAdmissible length ranges; ground or restrained searches use an explicit exploratory domain
    Min. supportsGeometry, properties and search settingsCounts examined in order under one global budget, plus a final verification of the first candidate

    All four modes support free or restrained axial behavior, with or without ground. The represented value controls the detailed plots and tables but does not rewrite the original input or prove that a search range is complete.

    Necessary search bounds Hcap, Hax and Lax
    • Hcap bounds free-mode Find h from the allowable curvature and clamped end slopes.
    • Hax bounds restrained Find h from axial compatibility and the combined-stress threshold.
    • Lax is the corresponding necessary lower length for restrained Find L.
    • These are necessary exclusions only. They do not prove admissibility, replace a full solve or define universal mechanical limits.

    Pipe Lowering

    Numerical evidence and limitations

    Free searches without ground retain their analytical regime paths. Ground and restrained searches share exploratory samplers and classifiers; Find L samples logarithmic length. Failed, uncertain and budget-limited regions remain unresolved.

    • Mesh refinement and equilibrium/contact checks establish numerical acceptance only.
    • Search budgets cover sampling and final verification; partial coverage remains visible when a budget ends.
    • For restrained analyses, axial strain and transverse slope are indicators, not automatic physical certification thresholds.
    • Pressure, temperature, plasticity, ovalization, local buckling, welds, defects, fatigue, dynamics and soil capacity are outside this model.
    • Complex routing, bends, tees and local support/contact stresses require separate engineering analysis.

    Model guide

    In-service Deflection

    Elastic movement of a uniform pressurized steel pipe in a symmetric excavation. Choose temporary return or a separate maintained-deviation sequence with backfill.

    In-service Deflection

    Operation and input model

    This module is independent from Pipe Lowering. It represents a straight, uniform, elastic steel pipe with ideal clamps at both buried ends. The full excavated length is twice the entered half-length. Pressure and temperature remain constant during construction; permanent mode adds explicit future operating cases.

    Input groupWhat the model uses
    Pipe and steelOutside diameter, uniform analysis thickness, E, Poisson ratio, thermal expansion and yield at operating temperature
    Operating conditionsInternal gauge pressure, operating temperature and steel/fluid/coating weight
    FluidKnown custom density or gas density from absolute pressure, temperature, molar mass and user-supplied compressibility Z
    InterventionHalf-length, vertical/horizontal/combined direction, signed angle and displacement amplitude measured from the original straight axis
    Initial statesOne to twelve named hypotheses, each with reference temperature and additional wall force
    CriterionEditable percentage of yield; default values are conveniences, not normative limits
    Fluid density and coating conventions
    ρ=(pgauge+patm)106(M/1000)Z R (TC+273.15)\rho=\frac{(p_{gauge}+p_{atm})10^6(M/1000)}{Z\,R\,(T_C+273.15)}

    Selected-gas density at operating conditions

    Z = 1 is an ideal-gas assumption, not an automatic real-gas equation of state. The natural-gas initial molar mass is a methane approximation; use known mixture properties or custom density when unsuitable. Coating adds dead weight but no structural stiffness.

    Permanent maintained deviation

    Elastic construction and backfill sequence

    Select Permanent maintained deviation for a separate direct calculation. The initial pipe remains the steel reference configuration: neither support adjustment nor backfill erases stress.

    Quick setup pre-fills editable examples and offers uniform, successive-half or ends-first backfill layouts. Open a zone for its values and soil-response examples. Infobubbles explain units, signs, examples and limitations. Fill empty fields preserves existing entries; deliberate blanks stay blank until that action is used.

    Flexible/intermediate/stiff soil examples are sensitivity cases, not material classifications. Stress and position verdicts remain not evaluated until starting values have been checked against project information. New operating cases initially copy construction conditions. Identity and applicability confirmations still require your input.

    • Keep initial supports at their original height, or unload them under equipment control before moving the pipe. Loaded supports must be unloaded before reuse.
    • Install symmetric vertical pairs at the calculated shape, without added preload, or enter common absolute heights for all scenarios. Common heights can create a calculated preload.
    • Release equipment before or after backfill. Vertical supports allow lateral rebound and do not lock the imposed position.
    • Enter documented axial, lateral, downward and uplift soil curves and separate backfill/construction loads. Zones activate in explicit stages; temporary pairs are lowered and removed in the specified order.
    • Each future pressure/temperature case starts from the final loaded state. Enter its fluid density and confirm material properties at all temperatures.

    Stress, final centre position and soil resistance limits have separate results. Position tolerances apply in controlled directions, including computed operating transitions. Convergence failures, missing data or soil limits prevent verified retention. Scenario-fitted support heights do not validate one common physical setting.

    In-service Deflection

    Wall force and effective tension must remain separate

    Pressure, temperature and additional wall force define the initial wall force. Subtracting the pressure-area term gives effective tension, which controls beam geometric stiffness. Unlike the Pipe Lowering restrained model, the initial effective force may be tensile or compressive.

    Initial force and compatibility equations
    Nwall,0=2νpAi−EAα(T−Tref)+Nextra,N0=Nwall,0−pAiN_{wall,0}=2\nu pA_i-EA\alpha(T-T_{ref})+N_{extra},\qquad N_0=N_{wall,0}-pA_i

    Initial wall force and effective tension (tension positive)

    N=N0+EA2D∫0D(z′2+y′2) dx,Nwall=N+pAiN=N_0+\frac{EA}{2D}\int_0^D\left(z'^2+y'^2\right)\,dx,\qquad N_{wall}=N+pA_i

    Effective and wall force during the intervention

    The additional axial input excludes the pressure and thermal terms already modeled. A value of zero is still an explicit hypothesis; it does not make the initial state known.

    In-service Deflection

    Intervention path and temporary supports

    1. Initially, soil support balances the pipe weight.
    2. Weight is transferred uniformly to the pipe and installed temporary supports until the excavated state is reached.
    3. The central actuator engages at the excavated midpoint and ramps controlled components to the target measured from the original axis.
    4. The elastic, frictionless return retraces the sampled actuation path to the excavated state.
    5. Uniform support restoration returns the model to its initial straight state.

    Temporary support layouts

    Choose none, equidistant pairs from 2 to 20, or 1 to 20 custom positions. Each fixed obstacle acts upward at the original pipe-axis level, permits lift-off and free horizontal/axial sliding, and does not restrain rotation. Custom positions are stored as fractions of total length and scale during length searches. The actuator position is reserved.

    Contact event resolution

    Support nodes are inserted exactly into the nonuniform Hermite mesh. An active set removes tensile constraints and admits penetrated obstacles. Observed contact-state changes are locally refined; an unresolved event prevents a pass, but the method does not prove that no unsampled event exists.

    In-service Deflection

    Calculation and exploratory search modes

    ModePurposeSearch interpretation
    Direct calculationEvaluate the entered half-length, movement and support layoutAll initial-state scenarios follow the complete intervention path
    Find lengthExplore half-lengths within entered boundsLogarithmic samples and observed transitions; candidate is rechecked
    Find displacementExplore amplitudes up to the entered upper boundLinear samples and observed transitions; upper bound reached is not a mechanical maximum
    Find support countTest 0, 2, 4… up to the selected ceilingOne global budget; first passing count is recomputed for every scenario

    A candidate passes only when every initial-state hypothesis produces a completed, decidable path below the custom threshold. Failed, uncertain, out-of-domain and budget-limited samples stay unresolved. Searches do not claim monotonicity or a global optimum.

    In-service Deflection

    Stress bound, domain screens and refinement

    The reported criterion is a conservative Von Mises beam bound. It combines the section maximum of pressure, wall-force and bending normal stress with a conservative transverse beam-shear bound. The normal and shear maxima may occur at different positions within an element.

    σVM,bound=max⁡r ⁣(σnormal(r)2+3τpressure(r)2)+3τbeam,bound2\sigma_{VM,bound}=\sqrt{\max_r\!\left(\sigma_{normal}(r)^2+3\tau_{pressure}(r)^2\right)+3\tau_{beam,bound}^2}

    Conservative elastic beam bound (conceptual form)

    • The strict custom threshold is applied only after numerical uncertainty is considered.
    • Yield exceedance stops the elastic path; the module does not calculate plastic redistribution.
    • Model-domain screens require full length / outside diameter ≥ 10 and maximum resultant slope ≤ 0.1.
    • These scope screens are not code acceptance limits.
    Mesh and path refinement evidence

    The full span and intervention path are refined together through the documented element and increment levels. Acceptance requires two successive changes within the relative tolerance for maximum stress, maximum actuator force and excavated displacement, with absolute floors. Contact envelopes and event resolution are included when supports are present. The final stress change contributes to the reported uncertainty; convergence is not a guaranteed physical-error bound.

    In-service Deflection

    Results, presets and reporting

    • Scenario comparison identifies the governing hypothesis and status.
    • Detailed results show excavated and target profiles, governing phase, actuator forces, end reactions and moments, wall/effective force, critical element and separate normal/shear locations.
    • With supports, select any sampled intervention stage to inspect its profile, reaction, gap and contact state; peak support and transverse loads remain available separately.
    • Diagnostics expose refinement history, stress uncertainty, slope and axial residual rather than hiding incomplete paths.

    Presets and JSON transfer

    In-service presets form a separate, versioned local library containing the complete input set—not results or reports. They are stored on the current browser/device and site address, are not synchronized automatically, and can be moved with JSON export/import. Unsupported or malformed files are rejected without replacing current inputs. Loading clears obsolete results; review inputs and calculate again.

    PDF snapshot

    The report records the completed request, selected displayed support stages and current display units. A unit-only change does not rerun mechanics. Export is unavailable when edited inputs no longer match the completed request.

    In-service Deflection

    Explicit exclusions and evidence limits

    • Steel only: no HDPE, plastic steel or material aging model.
    • No plasticity, post-buckling, torsion, ovalization, local sling/contact stress, defects, weld concentration or fatigue assessment.
    • No moving excavation front, support capacity, local bearing or evolving settlement check. The temporary branch excludes surrounding-soil interaction; the permanent branch uses the documented reversible soil laws described above.
    • The temporary reverse path assumes elastic, frictionless behavior without impact, hysteresis or construction dynamics.
    • Analytical benchmarks and automated regression tests support implementation evidence; no independent commercial FE benchmark or field calibration is claimed.
    • Optional CSA Z662:2023 checks assess minimum nominal wall (4.3.11.2) and the anchored pressure/temperature design state (4.7.1), with the temperature factor from 4.3.9. Separate design inputs and scope confirmations are required. They do not assess lifting, bending/stability (4.7.2), or Annex C, and never govern searches. ASME and European checks and overall normative compliance verdicts are not implemented.

    Engineering Disclaimer

    This calculator is provided as an engineering tool for preliminary analysis purposes. Results should be independently verified by a qualified professional engineer.

    Do not use these calculations for final design or construction without proper professional review and approval.