- Explain why structural analysis begins by formulating a mathematical model.
- Distinguish the flexibility method from the stiffness method by their primary unknowns.
- State the three assumptions shared by both formulation methods.
- Define static indeterminacy and connect it with the flexibility approach.
- Describe why structural procedures should be generic, systematic, repetitive, and programmable.
- Introductory familiarity with statically determinate structural models.
- Basic understanding of static equilibrium, forces, moments, and structural displacement.
The Computational View of Structural Analysis
The course develops general structural methods before moving to offshore applications and advanced studies.
Computer methods organize structural analysis into procedures that can be applied repeatedly and implemented on a digital computer. The first emphasis is on general structural systems rather than problems limited to offshore structures.
- Develop computational methods for general structural-analysis problems.
- Apply the methods to static and dynamic analysis of offshore structures.
- Extend structural analysis to fatigue and reliability studies.
Examples are supported by MATLAB code, hand solutions, calculator work, and comparisons between manual and computer results. Classical offshore problems are also demonstrated with standard structural software.
Begin with the Formulation
An analyzable structural problem requires a carefully organized mathematical model.
The first task in structural analysis is to formulate the problem. This requires a mathematical model of the structural system.
- Statically determinate structural model
- Statically indeterminate structural model
Determinate models are comparatively straightforward. Computer-oriented formulation is especially important for statically indeterminate models.
A useful formulation follows a standard process, applies broadly instead of belonging to one special problem, and repeats operations that a computer can carry out.
- Use a standard procedure.
- Keep the process generic rather than problem-specific.
- Arrange the work as repeatable, programmable operations.
- Construct the model so it can be solved with standard equations of statics.
Two structures differ physically, but both can be handled by the same ordered operations. Why is one computer procedure suitable for both?
Because the formulation is generic, systematic, and repetitive rather than being designed for only one structure.
Two Ways to Organize the Model
Flexibility and stiffness formulations differ mainly in the unknown quantities they select.
Structural problems may be organized through the flexibility method or the stiffness method. Both simplify formulation so the restrained model can be addressed through standard statics equations.
Flexibility: Actions as Unknowns
The flexibility method formulates the problem with actions as its unknown quantities.
- Axial force
- Shear force
- Bending moment
Stiffness: Displacements as Unknowns
The stiffness method instead selects displacement quantities as its unknowns.
- Translational displacement, represented by
δ - Rotational displacement, represented by
θ
The Essential Distinction
| Method | Primary unknown | Examples |
|---|---|---|
| Flexibility | Actions | Axial force, shear force, bending moment |
| Stiffness | Displacements | Translation and rotation |
Assumptions Shared by Both Methods
Both approaches use the same three idealizations concerning response, material behavior, and geometry.
Every formulation includes idealizations. The flexibility and stiffness methods rely on three common assumptions.
Linear Load–Displacement Behavior
Applied load and the resulting displacement are assumed to have a linear relationship. The displacement may be translational or rotational.
Material Within the Elastic Limit
The structural material must obey Hooke’s law and must not be stressed beyond its elastic limit.
Equilibrium from the Original Geometry
Static-equilibrium equations are developed from the undeflected model. Geometry changes produced by the loads are treated as negligible relative to the original geometry.
Which three assumptions support both the flexibility and stiffness formulations?
Load and displacement are linearly related; the material follows Hooke’s law without exceeding its elastic limit; and equilibrium is written using the undeflected geometry because load-induced geometric change is considered negligible.
Introducing Indeterminacy
Indeterminacy is divided into static and kinematic forms.
Indeterminacy is an important organizing idea in both methods of formulation.
- Static indeterminacy
- Kinematic indeterminacy
Static Indeterminacy and Released Actions
Static indeterminacy counts the actions released to obtain a stable, statically determinate system.
The relevant actions can be internal or external. Examples include shear force, axial force, and bending moment.
The target is a simpler reference system that is both stable and statically determinate. The needed actions are released during the mathematical formulation to reach that condition.
Degree of Static Indeterminacy
- Identify the actions that must be released.
- Use those releases to obtain a stable, statically determinate system.
- Develop the required independent equations using the released actions as unknowns.
- Analyze the system through the flexibility approach.
If an analysis starts by releasing force or moment quantities to produce a stable determinate system, which formulation is being used, and what determines its degree of static indeterminacy?
It uses the flexibility formulation. The degree equals the number of released actions and specifies the number of independent equations required in those unknown actions.
From Formulation to Computation
Programming is useful when the structural procedure is clearly defined and repeatable.
A digital computer is valuable because a systematic structural procedure can be programmed and reused. MATLAB codes accompany examples so that the same problems can be handled computationally.
Manual calculations remain part of the process. Solving by hand and then comparing the answer with the computer result provides a direct check between the two approaches.
- Solve the structural problem manually with a calculator.
- Solve the corresponding formulation with computer code.
- Compare the two answers.
Common misconceptions
Watch out: One of the two formulation methods is inherently more powerful than the other.
Instead: Flexibility and stiffness are described as equally powerful and numerically useful; any later preference is tied to practical programmability.
Watch out: Flexibility and stiffness unknowns may be crossed freely during formulation.
Instead: The chosen formulation must remain consistent: flexibility uses actions, while stiffness uses displacements.
Watch out: The main purpose of computer structural analysis is merely to produce an answer.
Instead: Its central purpose is to create a formulation that can be solved through systematic, reusable computer procedures.
Lesson recap
- Structural analysis begins by expressing the problem as a mathematical model.
- A computer-ready formulation is standard, generic, systematic, and repetitive.
- Flexibility treats actions—such as axial force, shear force, and bending moment—as unknowns.
- Stiffness uses translational and rotational displacements as unknowns.
- Both methods assume linear load–displacement behavior, Hooke’s law within the elastic limit, and equilibrium based on undeflected geometry.
- Static indeterminacy counts released actions and is therefore connected to the flexibility method.
- Hand and computer solutions are compared as part of computational structural-analysis practice.