Capacity Design of CB Frames — User & Engineering Manual

1. Introduction

Capacity Design of CB Frames is a Windows application that automates the seismic capacity design of Concentric Braced Frames (CBF) directly within SAP2000. It reads your structural model, computes the capacity forces on all diagonal braces per AISC 341-16, writes those forces back into SAP2000 as point loads, generates the required load combinations, and prepares the model for a final steel design run — all with a single button click.

The tool is fully reversible: a second button restores the model to its exact pre-capacity-design state, removing every modification the tool made.

What problem does it solve?

In the capacity design philosophy, columns and connections must be designed to remain elastic while the diagonal braces yield and dissipate seismic energy. Computing the expected brace capacity forces, creating the corresponding load patterns, and updating load combinations is a tedious, error-prone process when done manually in SAP2000. Capacity Design of CB Frames eliminates this manual process entirely.

Supported Frame Types

Supported Loading Modes

2. System Requirements

3. Quick Start

Before You Run Capacity Design of CB Frames

Basic Workflow

1. Open Capacity Design of CB Frames. Double-click the executable. The main form appears.

2. Select frame type. Choose Ordinary Frames or Special Frames from the radio buttons at the top.

3. Select loading direction. Choose X Dir, Y Dir, or one of the bidirectional options.

4. Set the SAP2000 model. Either browse to a .sdb file, or check Attach to Instance if SAP2000 is already open.

5. Enter the earthquake load case name. Type the exact name of the seismic load case as it appears in SAP2000 (e.g., EQX).

6. Enter Omega₀. Default is 2.0. Adjust per project requirements.

7. Click "Prepare for capacity design". The progress bar shows status. When complete, a message confirms the number of braces found.

8. Return to SAP2000 and run steel design using the new capacity-design load combinations.

9. When done, click "Return to Original" to remove all Capacity Design of CB Frames modifications from the model.

4. User Interface Guide

Frame Type Selection

Direction Selection

Input Fields

Buttons

5. Step-by-Step Workflows

Workflow A — Ordinary CBF, Single Direction

1. Select Ordinary Frames and X Dir (or Y Dir).

2. Select SAP2000 file or check Attach to Instance.

3. Enter the earthquake load case name in EQ Case (X).

4. Set Omega₀ (default: 2.0).

5. Optionally enable Rho and/or P-Delta.

6. Click Prepare for capacity design. Wait for completion message.

7. In SAP2000: Run Analysis → Run Steel Design. The design will use CP_ and CN_ combinations.

8. Review results. When finished, click Return to Original.

Workflow B — Special CBF, Single Direction

1. Select Special Frames and X Dir.

2. Enter EQ case name, Omega₀, and optional Rho / P-Delta settings.

3. Click Prepare for capacity design. The tool also overrides column flexural capacities to prevent columns from being the governing element.

4. In SAP2000: Run Analysis → Run Steel Design. Combinations CP1_, CN1_, CP2_, CN2_ are now active.

5. Click Return to Original when done.

Workflow C — Bidirectional (100% + 30%)

1. Select frame type, then Both Dir (100% + 30%).

2. Fill in EQ Case X, EQ Case Y, EX_03 pattern name, and EY_03 pattern name.

3. Click Prepare for capacity design. The tool processes X-direction braces, then Y-direction braces, then generates combined combos C1_–C4_.

4. Run SAP2000 design as normal.

Workflow D — Bidirectional (100% + 100%)

1. Select Special Frames and Both Dir (100% + 100%).

2. Fill EQ Case X and EQ Case Y. EX_03 and EY_03 are not needed (they are automatically zeroed).

3. Click Prepare for capacity design. The tool creates 16 combinations per original seismic combo for special frames.

4. Run SAP2000 design.

6. Algorithm Overview

The core algorithm is executed in the following sequence. Each numbered step corresponds to a dedicated subroutine in the codebase:

7. Brace Identification

Capacity Design of CB Frames identifies diagonal braces purely by the geometry of their end joints. No member labels, groups, or section types are used. This makes the tool robust to any naming convention.

Identification Rules

What is NOT identified as a brace

8. Seismic Force Extraction

For each identified brace, the axial force from the earthquake load case is queried from SAP2000 and amplified by Omega₀:

The Omega₀ factor is applied here to amplify the elastic analysis result to an approximate inelastic demand level. Simultaneously, the SAP2000 design code preference for Omega₀ is set to 1.0 to prevent SAP2000 from applying it a second time during design checks.

9. Ordinary Frame Capacity Calculation

For Ordinary CBF, the capacity is derived from the SAP2000 steel design result rather than from explicit section property calculations.

Post-Buckling Capacity

Load Assignment (Ordinary)

The rationale: in the positive earthquake direction, a brace classified as "compression" buckles and carries only its post-buckling residual. In the reverse direction, the same brace is in tension and must carry the full seismic demand (Ω₀ × E).

10. Special Frame Capacity Calculation

For Special CBF, the capacity forces are computed from first principles using section properties and material data retrieved from SAP2000, following AISC 341-16 F2.3 and AISC 360-16 Chapter E.

Step 1 — Get Section Properties

For each brace: gross area A_g, radii of gyration r₂₂ and r₃₃, yield stress F_y, and elastic modulus E are retrieved. The critical slenderness uses the minimum radius of gyration:

Step 2 — Euler Critical Stress

Step 3 — Expected Yield Stress

Step 4 — Critical Stress (Buckling Curve)

Step 5 — Dual Compression Criteria

Load Assignment (Special)

The four cases represent the envelope of possible brace states during a seismic event: full compression, full tension, post-buckling (reduced compression), and tension again. Designing for all four ensures the connected members are safe under every phase of the seismic response.

11. Load Assignment to Joints

Capacity forces are applied as point loads at the end joints of each brace, in the global X, Y, or Z direction corresponding to the brace's axial direction.

This approach is load-direction independent — SAP2000 resolves the joint loads into axial, shear, and moment components based on member orientation. The load direction index used is 1 (local axis 1, i.e., the member axial direction).

12. Brace Stiffness Modification

After assigning the capacity loads, the axial stiffness of all diagonal braces is reduced by a factor of 1000:

Why?

Per AISC 341, during the capacity design analysis, diagonal braces should not participate in carrying gravity loads — the gravity load path runs through the columns and beams. Reducing axial stiffness to 0.1% of its original value effectively removes the brace from the gravity load path while keeping it visible in the model for design output purposes.

13. Load Combination Generation

Capacity Design of CB Frames scans all existing response combinations in SAP2000. For each combo that references the earthquake load case, it:

1. Creates new capacity-design combinations using the capacity load cases
2. Removes the original seismic combo from the steel strength design list
3. Adds all new capacity combos to the steel strength design list

Naming Convention

Combo Content

Each new combination is a copy of the original, with the earthquake load case term replaced by the corresponding capacity-design load case. All gravity load terms (dead, live, etc.) are preserved unchanged.

14. Return to Original

The restoration sequence is the exact reverse of the preparation sequence:

15. Engineering Background — Capacity Design Concept

Capacity design is the fundamental seismic design philosophy that underlies modern ductile structural systems. It deliberately creates a hierarchy of strength in the structure:

• Ductile fuse elements (braces) — designed to yield, buckle, and dissipate seismic energy through large inelastic deformations. These are the "sacrificial" members.
• Protected elements (columns, connections, foundations) — designed to remain elastic. Their demand is computed from the capacity of the fuse elements, not from the code-level seismic forces.

In a Concentric Braced Frame, the diagonal braces are the ductile fuses. Their capacity forces — not the elastic analysis forces — become the design demand for everything they connect to.

The Two-Phase Approach

Phase 1 (elastic analysis): Run SAP2000 with the earthquake load case to find which braces are in tension and which are in compression under a given earthquake direction. Classify each brace.

Phase 2 (capacity application): Replace the elastic seismic forces with the expected capacity forces of each brace. Compression braces: apply their compressive capacity. Tension braces: apply their tensile capacity. Also apply the post-buckling residual for the states where a brace has already buckled.

16. AISC 341-16 Provisions

Chapter F2 — Concentrically Braced Frames

F2.3(a) — Column Flexural Capacity Override (Special Frames)

AISC 341-16 F2.3, Exception (a), page 9.1-64 states that columns in SCBF may be exempt from certain combined force requirements if the flexural demands are limited. Capacity Design of CB Frames implements this by setting the SAP2000 design overwrite for M_n,major and M_n,minor to 1×10³⁰ kN·m, effectively removing the flexural limit so that columns are never the governing element in a capacity design check.

F2.3 — Expected Brace Capacities

AISC 341-16 requires that braces in SCBF be designed using expected material properties (R_yF_y instead of F_y) to account for material overstrength. The standard specifies R_y = 1.5 for ASTM A500 HSS and 1.1 for A36/A992 W-shapes. Capacity Design of CB Frames uses R_y = 1.5 as a conservative default applicable to typical brace sections.

Post-Buckling Capacity = 0.3 × P_n

When a brace buckles in compression, it does not lose all its capacity immediately. It retains a post-buckling residual force of approximately 30% of its pre-buckling compressive strength. This 0.3 factor comes from experimental research on brace behavior and is codified in AISC 341.

Ordinary vs. Special — Key Differences

17. AISC 360-16 Chapter E — Compression Equations

Background — Column Buckling Theory

A compression member can fail by yielding (short/stocky) or by elastic buckling (long/slender). The boundary between these regimes is defined by the ratio of the yield stress to the Euler elastic buckling stress.

Euler Elastic Buckling Stress

Critical Stress — Inelastic Buckling (E3-2)

When the member is stocky enough that it yields before elastic buckling occurs (4.71√(E/F_y) ≥ KL/r, equivalent to F_y/F_e ≤ 2.25):

Critical Stress — Elastic Buckling (E3-3)

When the member is slender and buckling occurs elastically (KL/r > 4.71√(E/F_y)):

Transition — 4KL/r vs. 2.25 Threshold

The code transition can be expressed equivalently as:

Capacity Design of CB Frames uses the second form (RyFy/F_e ≤ 2.25) which is algebraically equivalent and avoids computing a square root.

18. Key Factors & Constants

19. Parameter Reference

User Inputs

Computed Per-Brace Outputs

20. Load Combination Naming Convention

The following table shows exactly how the 16 combinations are built for the Special Frame + BiDir 100%+100% mode, for an original combo named DSEQX that uses EQ cases EQX and EQY:

21. Limitations & Assumptions

22. Troubleshooting / FAQ

Q: No braces were found. What's wrong?

Check that your model contains members with different Z-coordinates at each end. If using X-direction mode, the brace must also differ in X-coordinate. Pure vertical columns and horizontal beams are excluded by design.

Q: The progress bar stops mid-way. What happened?

The most common cause is a SAP2000 API error — for example, the earthquake load case name doesn't match exactly, or no steel design results exist. Check that steel design has been run before clicking "Prepare for capacity design". Use "Return to Original" to clean up partial changes before retrying.

Q: I accidentally closed the tool without clicking "Return to Original". How do I restore the model?

Re-open Capacity Design of CB Frames, load the same model and configuration, and click "Return to Original". The tool does not store a separate state file — it identifies its modifications by the naming convention of load patterns and combinations (prefixes: CP_, CN_, CP1_, CN1_, CP2_, CN2_, C1_–C16_).

Q: SAP2000 design results look unchanged after running "Prepare for capacity design". Why?

You must manually trigger a new analysis and design run in SAP2000 after Capacity Design of CB Frames has prepared the model. The tool modifies the model but does not run the final design automatically. Go to SAP2000 → Analyze → Run Analysis, then Design → Steel Frame Design → Start Design/Check.

Q: Can I use this with a non-AISC design code in SAP2000?

No. The tool uses AISC 360-specific SAP2000 design API indices (preference index 34 for Omega₀, overwrite indices 39 and 40 for column M_n). Other design codes use different index mappings and are not supported.

Q: Why is Omega₀ set to 1.0 in SAP2000 during the process?

The tool manually multiplies seismic forces by Omega₀ when computing BraceE. If SAP2000's internal Omega₀ preference were left at the user's value, SAP2000 would apply it a second time during the design check, resulting in a double-amplification. Setting it to 1.0 prevents this.

Q: The Rho factor — when should I enable it?

Enable Rho when your seismic load case in SAP2000 already includes the redundancy factor ρ in its scale factor (e.g., the load case was defined as ρ×E). Capacity Design of CB Frames will divide out the ρ before capacity design so that the brace capacity is computed based on the unreduced seismic demand.

23. Report Generation

After a successful capacity design run, Capacity Design of CB Frames can produce a fully formatted Word document (.docx) that records every action the tool took — inputs used, braces detected, capacity forces computed, loads applied, and model modifications made. The report serves as a traceable engineering record for peer review, project documentation, or quality assurance.

Availability

The Generate Word Report button is enabled only after Prepare for capacity design has completed successfully. It is grayed out at startup and resets to disabled each time you click Prepare for capacity design so that you cannot generate a report from a previous run by accident.

How to Generate a Report

1. Complete a successful capacity design run by clicking Prepare for capacity design and waiting for the completion message.

2. Click the 📄  Generate Word Report button that appears in the main form.

3. A Save As dialog opens. The default file name is CapacityDesignReport_YYYYMMDD_HHMM.docx. Choose a folder and file name, then click Save.

4. The tool writes the report. When complete, a dialog asks whether you want to open the file immediately. Click Yes to open it in your default Word viewer, or No to leave it on disk.

Report Structure

The report always contains the same seven sections regardless of frame type or loading direction. Sections that differ between Ordinary and Special frames are noted below.

Ordinary vs. Special Report Differences

Bidirectional Runs

When either bidirectional mode (100%+30% or 100%+100%) is used, Sections 2 through 5 split into sub-tables for X-direction braces and Y-direction braces. The X-direction braces are classified from the X earthquake load case and the Y-direction braces from the Y earthquake load case. Each sub-table is labelled with the relevant load case name.

Report Styling

The document uses the software's navy-and-gold colour scheme: a dark navy cover with a gold title, gold-accented section headings with a left border, alternating-stripe data tables with navy headers and gold header text, and muted italic caption text below each table. The page margins are approximately 1 inch top and bottom, 0.85 inch left and right.