Project 1

The structure shown in the image is a tensile membrane structure with multiple masts, creating a series of cone-shaped (pinnacle or anticlastic) modules. To perform form-finding and structural analysis of such a structure, follow the steps below:

1. Define Geometry

Membrane Grid:

• Modular grid of membranes.

• Each module:

  • Central high point (mast top)

  • Edge nodes anchored to ground (low points)

  • Curved boundary cables forming saddle shapes.

Mast Arrangement:

• Central vertical masts (each module).

• Membrane is tensioned from mast tops to boundary anchors.

2. Boundary Conditions

Node Type	Support Conditions
Mast Bases	Pinned or fixed supports (XYZ)
Membrane Anchors	Fixed at the corners (XYZ locked)
Mast Tops	Connection to membrane via cable or joint

• Boundary nodes are fixed supports.

• Masts are vertical compression elements.

3. Membrane & Cable Definitions

Membrane:

• Use quadrilateral or triangular membrane elements.

• Assign initial prestress in warp and weft directions.

Edge/Valley Cables:

• Cable elements along membrane edges or valleys.

• Assign prestress or force density.

4. Prestress Application

• Warp direction (radial): 5–10 kN/m

• Weft direction (circumferential): 5–10 kN/m

• Edge cables: Pre-tension to balance upward mast force

5. Form-Finding Process

Use any of the following methods:

Force Density Method (FDM):

• Define q = Force/Length for all edges.

• Solve equilibrium for nodal positions.

Dynamic Relaxation:

• Iterative equilibrium simulation under mass, damping, and force.

Surface Evolver or Finite Element Software:

• Like SOFiSTiK, GSA, Rhino+Kangaroo, or Abaqus.

6. Structural Analysis

After form-finding:

1. Import geometry into structural analysis module.

2. Assign:

   • Membrane material (e.g., PVC-coated polyester or PTFE)

   • Elastic modulus, thickness

3. Apply loads:

   • Self-weight

   • Wind (positive and suction)

   • Snow, live loads (if applicable)

4. Check results:

   • Membrane stress (ensure tension only)

   • Mast compression

   • Cable tension

   • Support reactions

7. Output

• Form-found geometry (equilibrium shape)

• Membrane stress distribution

• Cable force profile

• Mast axial forces

• Support reactions

Summary Flow

Step	Action
Geometry	Grid of high-point modules
Supports	Ground anchors (fixed), mast bases
Form-Finding	FDM or Dynamic Relaxation
Prestress	In membrane and edge cables
Structural Analysis	Wind/snow loads, reaction forces, stress
Tools	Rhino+Kangaroo, SOFiSTiK, GSA, Abaqus

Workflow for Form-Finding & Structural Analysis of Multi-Mast Tensile Structures

Step 1: Define Geometry

1. Draw Base Grid:

   • Create a regular or irregular grid layout for the membrane units.

   • Decide on spacing (e.g., 5m x 5m) for modules.

2. Add Masts:

   • Place vertical mast at the center of each module.

   • Typical mast height: 3m–6m depending on curvature.

3. Create Membrane Surfaces:

   • Connect boundary corner points and the mast tops to define surface patches.

   • Use triangular or quadrilateral mesh generation.

Step 2: Define Supports

Location	Support Type	Conditions
Corner Nodes	Fixed Support	UX = UY = UZ = 0
Mast Base	Pinned or Fixed	UX = UY = UZ = 0
Mid-Edge Nodes	Fixed or Roller	Depending on design

Step 3: Assign Elements

• Membrane Elements:

  • Shell or membrane elements (triangular/quadrilateral).

  • Material: PTFE-coated fiberglass or PVC-coated polyester.

  • Define thickness (e.g., 1.2mm to 2mm).

• Cable Elements:

  • Edge cables or valley cables.

  • Define diameter, cross-sectional area, and modulus.

  • Pre-stress value: Typically 5–20 kN depending on span.

• Mast Members:

  • Circular hollow steel section (CHS).

  • Use compression-only or truss elements.

Step 4: Apply Prestress for Form-Finding

1. Membrane Prestress:

   • Assign initial stress in both directions.

   • Typical:

     • Warp (longitudinal): 5–10 kN/m

     • Weft (transverse): 5–10 kN/m

2. Cable Pretension:

   • Force: 10–20 kN (based on structure scale).

   • Define either directly (force) or indirectly (strain or force density).

Step 5: Perform Form-Finding

Objective: Find the tension-only equilibrium shape.

Methods (choose one based on software):

• Force Density Method (FDM) – for Rhino + Kangaroo, GSA

• Dynamic Relaxation – GSA, Rhino + Kangaroo, Tensyl

• Non-linear Finite Element Analysis – SOFiSTiK, Abaqus, Ansys

Convergence Criteria:

• Maximum residual force < 1% of total load

• Membrane is in pure tension (no compression)

Step 6: Structural Analysis

1. Import Form-Found Shape (locked geometry).

2. Apply Loads:

   • Dead load (self-weight of membrane and cables)

   • Live load (maintenance, access)

   • Wind load (positive/suction pressures from codes like IS 875-III or EN 1991-1-4)

   • Snow load (if applicable)

3. Analysis Type:

   • Non-linear static analysis (due to geometry and prestress dependency)

   • Use large deflection theory

Step 7: Post-Processing

Check and extract:

Checkpoint	Description
Membrane Stresses	Should be in tension; check max/min
Cable Forces	Check if within allowable limits
Mast Reactions	Axial compression forces
Support Reactions	Foundation force checks
Deformation	Acceptable under wind and live loads
Factor of Safety	Per codes (e.g., EN, ASCE, IS standards)

Deliverables

• Final Form-Found Shape

• Stress Distribution Plots (Membrane and Cable)

• Support Reactions

• Deformation Plots

• Bill of Materials (if needed)

• Design Report (optional)

Recommended Software Combinations

Software	Use
Rhino + Kangaroo	Visual form-finding & iteration
SOFiSTiK	Full FE form-finding and code-checks
GSA by Oasys	Membrane + cable tension structures
Abaqus	Advanced nonlinear analysis
RFEM 6 + RF-TENDON	Tensile structure form-finding