Analysis I — Static & Global Analysis

Methodology for global static structural analysis and code-based member unity checks aligned with API RP 2A-WSD and ISO 19902 standards.

1. Global Analysis Framework

Stick Model vs. Detailed Finite Element Model

Most offshore platforms employ a two-tier analysis approach:

• Stick Model (Global Analysis): Each structural member (leg, brace, riser) is represented as a single line element with properties (cross-section area, moments of inertia) assigned. Connectivity is simplified to joint nodes. Typical size: 500–5,000 elements. Fast to run; provides global load distribution and internal member forces. Used for preliminary design and iterative optimization.
• Detailed Finite Element Model: Critical connections, local stress concentrations, and complex geometries are resolved with 3D solid elements. Used to verify weld designs, check gusset plate capacity, and evaluate local stresses near cut-outs. Typical size: 50,000–500,000 elements. Computationally expensive; used for final detailed design and specific problem-solving.

Industry practice uses the stick model for overall design development and load-path studies, then references critical areas with refined local models for final certification.

2. Load Path and Structural Behavior

Typical Jacket Load Path

Environmental loads (wave, wind, current) applied to the topside (deck) are transferred downward through the jacket structure to the piles:

1. Deck (Topside): Receives distributed wave, wind, and gravity loads. Deck frame distributes loads to four leg tops via fixed or pinned connections.
2. Primary Load-Bearing Legs: Four vertical legs carry most of the vertical load (dead + live + dynamic amplified wave inertia). Legs also resist lateral (shear) forces from wind and wave drag, creating bending moments.
3. Bracing System: Diagonal and horizontal braces provide lateral stiffness and prevent sidesway. Braces also carry axial loads (tension/compression) that offset bending in legs. In storm waves, braces see cyclic tension/compression, driving fatigue.
4. Piles: Driven steel pipe piles, typically one per leg (sometimes two for large platforms), anchor the jacket to seafloor. Piles resist vertical load (axial), lateral load (bending in soft clay), and overturning moment.

Internal Force Types

The stick model output includes internal forces at each element:

• Axial Force (Fa): Tension (positive) or compression (negative) along the member axis.
• Shear Force (Vy, Vz): Force perpendicular to the member axis (in two perpendicular directions).
• Bending Moment (My, Mz): Moment about principal axes; induces bending stress.
• Torsional Moment (Mx): Twist about the member axis; rare in jackets but common in spars and risers.

3. API RP 2A In-Place Analysis Procedure

Analysis Steps

API RP 2A Section 5 prescribes a methodical approach:

1. Geometry and Properties: Define all members (legs, braces, deck frame, piles) with outer diameter D, wall thickness t, length L, and material properties (yield strength Fy, Young's modulus E).
2. Load Definition: Calculate environmental loads (wave, wind, current) for design conditions. Combine with dead and live loads per API RP 2A Table 5-2 (in-place load combination).
3. Structural Analysis: Run linear-elastic FEA to obtain member forces and moments. Modern software (SACS, SESAM, STAAD) automates meshing and load application.
4. Code Checks: For each member, calculate unity checks (UC) for axial, bending, combined stress, buckling, and hydrostatic loads. UC = actual stress / allowable stress; UC ≤ 1.0 is acceptable.
5. Global Stability Check: Verify that the structure does not sway excessively or buckle as a whole. Check P-Delta effects (second-order geometry effects) and overall frame instability.
6. Design Iteration: If UC > 1.0 for any member, increase member size or material grade; re-run analysis until all members pass.

4. Member Unity Check Formulas

Axial Stress Check

For a member under axial load:

For long slender members, buckling reduces capacity. API RP 2A Equation 6-11 modifies F_a,allowable based on slenderness ratio λ = L/r (L = effective length, r = radius of gyration).

Bending Stress Check

For bending about a principal axis:

Combined Axial and Bending Check

The interaction formula accounts for simultaneous axial and bending loads:

This bilinear interaction is conservative but simple to apply and widely used in industry. More refined checks account for the interaction via secant formula or LRFD provisions.

Hydrostatic Pressure Check

External water pressure reduces the buckling capacity of thin-walled cylinders. API RP 2A Equation 6-35 combines external pressure and axial compression:

5. Euler Buckling and Slenderness Effects

Elastic Buckling Stress

For a pin-ended slender column in pure compression:

The slenderness ratio λ = L/r is compared to a critical value λ_c = π·sqrt(E/Fy). For λ < λ_c, inelastic (Johnson) buckling dominates; for λ > λ_c, elastic (Euler) buckling applies. API RP 2A transitions between the two regions.

Typical Slenderness Values

Jacket legs and braces have vastly different slenderness:

• Large-diameter legs (D ≈ 0.76–1.2 m, thin wall): λ ≈ 40–100; often buckle inelastically.
• Small-diameter braces (D ≈ 0.2–0.5 m, thin wall): λ ≈ 80–200; buckling critical, requires careful design.

6. Stress Distribution and Global Stability

Stress Distribution in Jacket

A typical lateral load (wave or wind) produces:

• Windward Legs: Compression (from bending); reduced by gravity loads which offset some compression.
• Leeward Legs: Tension (from bending); additive to any gravity loads.
• Diagonals: Alternating tension/compression depending on orientation and loading direction.

The deck frame distributes shear loads to legs; moment-resisting connections (rigid gusset plates) create rigid joints, concentrating bending in the legs. Pinned connections distribute shear more evenly but may be weaker in tension.

P-Delta (Second-Order) Effects

As a column deflects laterally under load, the vertical gravity load creates an additional moment M_P-Delta = P·Δ, where Δ is the lateral deflection. This moment increases the bending stress, which increases deflection further—a feedback loop:

7. Software Tools and Workflow

Industry Standard Software

SACS (Structural Analysis and Design System) by Bentley: Dominant for jacket and GBS design. Proprietary FEA solver with extensive API RP 2A code checking. Integrated optimization and fatigue modules.

SESAM (Finite Element Analysis): DNV GL suite; widely used in Europe and Asia. Strong in nonlinear analysis and floating structure analysis.

STAAD.Pro: General-purpose FEA; suitable for smaller projects or preliminary analysis. Less specialized offshore functionality than SACS.

ANSYS / ABAQUS: Specialized advanced nonlinear FEA; used for complex local investigations and implicit dynamics.

Typical Analysis Workflow

1. Pre-processing: Define geometry, properties, boundary conditions (pile fixity), and loads in CAD-integrated environment.
2. Meshing: Automatic generation of node-element mesh. Refinement near critical areas (deck connections, brace-leg junctions).
3. Load application: Apply combined gravity, wave, wind loads per code requirements. Generate multiple load cases for different environmental scenarios.
4. Solver: Run linear-elastic analysis. Typical solution time: seconds to minutes on modern workstations.
5. Post-processing: Extract member forces; visualize stresses, deformations, and UC distribution. Identify governing members.
6. Code compliance: Software automatically computes UC for each member; highlights non-compliant elements.

8. Output Interpretation and Typical UC Values

Example UC Summary Table

Member Type	Typical UC (ASD)	Governing Load Case	Notes
Leg (axial)	0.4–0.6	Dead + Live load	Compression from weight; buckling checked
Leg (bending)	0.6–0.8	Design wave + wind	Lateral load creates bending; often governs
Leg (combined)	0.8–1.0	Worst-case combination	Axial + bending; iteration may be needed
Diagonal brace (tension)	0.5–0.9	Design wave	Typically lower UC; high redundancy
Diagonal brace (compression)	0.7–1.0	Design wave	Buckling critical for slender braces
Horizontal brace	0.4–0.7	Local connection loads	Lower utilization; often sized for fabrication

A well-designed platform typically exhibits UC ≈ 0.7–0.9 in primary members and UC ≈ 0.4–0.6 in secondary members, ensuring redundancy and robustness. Over-design (UC < 0.5 everywhere) is uneconomical; under-design (UC > 1.0) fails code requirements and must be remedied by member resizing or material upgrade.