This article explains how to model structures realistically within static linear assumptions. It focuses on boundary conditions, load application, geometry simplifications, and model stability.
Structural engineers now rely heavily on software to analyse complex systems. Yet, software outputs only reflect the assumptions and models engineer’s input. When those assumptions lack physical realism, the results can mislead even experienced professionals. For this reason, idealisation and modelling decisions deserve deliberate and informed effort.
In linear static analysis, engineers simplify the real behaviour of a structure to suit hand-based logic and software frameworks. These simplifications, while valid within limits, create the risk of misrepresentation when applied mechanically or without context. Finite element analysis (FEA), though powerful, cannot substitute engineering judgement or structural principles.
This article explains how to model structures realistically within static linear assumptions. It focuses on boundary conditions, load application, geometry simplifications, and model stability. An understanding of the consequences of each modelling choice, allows engineers to use software more responsibly and produce outputs that reflect physical reality.
Idealisation in Structural Modelling
Idealisation as has been expatiated in a previous article (See: Idealization of Structures: How Engineers Visualise and Break Down Structural Systems) transforms a physical structure into a model fit for analysis. Engineers reduce the system to simpler elements: lines, nodes, plates, supports, and load vectors. They remove irregularities, assume perfect material properties, and neglect secondary effects like cracking, creep, or plasticity.
These simplifications create a model that behaves predictably under assumed conditions. The model follows the laws of static equilibrium and uses superposition where allowed. But real-world structures often respond differently, especially under large loads, sustained deformation, or sudden instability. Engineers must always recognise where assumptions deviate from real behaviour.
Idealisation also includes deciding what to model. Engineers may omit stairs, parapets, minor openings, or thin members. They must understand which elements carry significant load and which contribute only to stiffness or distribution. A good model captures the core structural action without excessive complexity or false accuracy.
Static Linear Analysis Assumptions
Linear static analysis works under a few strict assumptions:
- Materials behave elastically throughout loading.
- Geometry does not change as the structure deforms.
- Loads remain constant and do not move or change direction.
- Superposition applies – the total response equals the sum of individual load effects.
These assumptions allow for quick, reliable solutions using finite element methods. Most structures under service conditions follow these assumptions reasonably well. However, high stress levels, support displacements, or member instability can invalidate them.
Engineers must therefore verify that the structure remains within elastic limits. They must avoid using static linear analysis for buckling problems, collapse mechanisms, or cracked concrete zones unless verified with more advanced models.
Load Modelling: Consistency and Clarity
Loads should reflect how they act in reality. A line load on a beam must correspond to a uniformly distributed action, not a point force at midspan. Loads must match the correct type: point loads, line loads, surface pressures, or imposed displacements. Misplacing loads creates non-physical moments and shear responses.
In a finite element model, engineers often distribute gravity as nodal point loads or apply pressures to plates. Both work if the structure behaves accordingly. But applying line loads to rigid members or applying patchy surface loads to slabs without proper mesh resolution can create unrealistic force concentrations.
Every load case must represent a possible design situation. Group loads into self-weight, live loads, wind loads, seismic actions, and equipment loads. Combine them using code-based load combinations. Avoid unrealistic worst-case loadings by considering real likelihoods and support conditions.
Support Conditions and Boundary Restraints
Boundary conditions in a model carry more importance than most engineers realise. A pinned base in software implies zero rotation resistance, but in reality, foundations have stiffness. A fully fixed support implies infinite rotational restraint, which no actual base provides.
Support assumptions must match the design philosophy. For example, a portal frame base may be idealised as pinned for analysis but designed to resist some moment in practice. Over-restraint in the model can lead to underestimation of beam moments and overestimation of column forces.
Structural models must resist movement in all directions. Any unrestrained degree of freedom creates a mechanism or causes the structure to collapse in the model. Engineers must confirm that every point resist vertical, horizontal, and rotational movement adequately unless movement is deliberate.
Connections and Releases
Connections in models either transfer all forces or allow selective releases. A pinned connection transfers vertical shear but no moment. A rigid connection transfers moment and shear. Some joints fall in between: semi-rigid, partial fixity, or flexible.
FEA software allows users to release degrees of freedom manually. These releases should reflect actual connection behaviour. Careless use of releases leads to zero bending stiffness, unintended hinges, or floating nodes. These produce unrealistic force patterns or collapse.
Always specify which member provides continuity. In beam-to-column joints, the column usually continues and the beam receives the moment. Releasing the wrong member causes unintended rotations. Provide continuity through the stronger element unless a special design dictates otherwise.
Geometry Simplifications and Offsets
In real structures, members have depth and eccentricity. In models, they often reduce to lines and points. This creates offset between member centrelines and actual force paths. Failing to account for this offset leads to bending where only axial action was expected, or vice versa.
FEA software allows eccentric offsets to match true geometry. These create secondary effects that must be handled carefully. For example, an eccentric beam connected to a slab can attract unexpected torsion or produce high stress at joints. Simplifying geometry too much can remove these effects and underpredict forces.
Sometimes, engineers exaggerate geometry accuracy in models, introducing accidental axial loads or artificial moments. Excessive offsets without true stiffness adjustments can make a simple floor system appear to carry unintended loads. Geometry should match the expected behaviour, not just the drawn layout.
Model Stability and Load Paths
A stable model resists displacement in all directions. It must have enough supports and structural continuity to stop unintended mechanisms. Common model instability warnings include:
- Rigid body motion
- Excessive displacements
- Singular matrix errors
- Floating nodes or disconnected elements
These often result from missing supports, poor connectivity, or incorrect releases. Engineers must trace each load path: from slab to beam, from beam to column, and from column to base. Each element must have a destination for its load, and each connection must transfer forces effectively.
To avoid instability, engineers can apply dummy restraints, stiff links, or temporary supports. However, these must not distort the real behaviour. Validate that these additions do not attract load or affect internal forces.
Element Types and Mesh Quality
In FEA, different elements represent different behaviours:
- Beam elements carry axial, bending, shear, and torsion.
- Plate/shell elements handle in-plane and out-of-plane forces.
- Solid elements represent full 3D behaviour but require more computation.
Use the simplest element that accurately reflects behaviour. For a slab, use plate elements; for a frame, use beams. Avoid over-modelling unless investigating complex stress fields. A good mesh balances refinement and performance. Meshes should be finer where stress changes rapidly and coarser in uniform zones.
Always check mesh quality with shape checks, aspect ratios, and stress concentration visualisations. Mesh errors cause misleading peaks, inaccurate reactions, or poor convergence. Model validation includes verifying that the mesh responds logically to simple load cases.
Multiple Models for Multiple Purposes
No single model answers every design question. One model may serve to size beams and slabs; another may analyse lateral stability or foundation reactions. Attempting to cover all behaviours in one model leads to poor assumptions or excessive complexity.
Engineers should develop different models for different actions:
- Gravity models for vertical loads
- Lateral models for wind or seismic response
- Local models for stress concentrations or joint detailing
Each model reflects its own set of assumptions. Engineers must clearly document each model’s purpose and limitations.
Verification and Documentation
Every model must be checked against expectations. Before accepting outputs, engineers must:
- Manually verify reactions and internal forces
- Run simplified hand calculations
- Check deformation shapes under known loading
- Validate support reactions and moment signs
Document every load case, support condition, and modelling assumption. Include date, author, version, and purpose of the model. Clear documentation allows peer review and reduces liability.
Conclusion
Modelling for static linear analysis allows engineers to solve complex structural problems efficiently. However, the value of such analysis depends entirely on modelling accuracy, assumption clarity, and physical realism. Software does not replace engineering judgement — it magnifies it.
Each modelling choice carries consequence. When engineers remain intentional and informed, finite element models become powerful allies — not traps. This approach upholds the core duty of engineering: to design safe, efficient, and understandable structures.
Also See: Common Errors in Finite Element Analysis and How to Avoid Them
Sources & Citations
- Institution of Structural Engineers (IStructE). (2025). Good FEA Modelling for Static Linear Analysis. The Structural Engineer CPD Series, April 2023. (Original CPD source that inspired this article.)
- Cook, R.D., Malkus, D.S., Plesha, M.E., & Witt, R.J. (2002). Concepts and Applications of Finite Element Analysis (4th ed.). John Wiley & Sons. (Comprehensive reference on the theoretical foundations of FEA in engineering.)
- Hibbeler, R.C. (2017). Structural Analysis (10th ed.). Pearson Education. (Widely used textbook covering idealisation techniques and linear analysis principles.)
