---------------------- | ---------------------------------- | --------------------------------------- | | Bolt behavior | Linear elastic (all bolts elastic) | Nonlinear inelastic (bolts can yield) | | Deformation compatibility | Not considered | Force-deformation relationship per bolt | | Accuracy at low e | Good (within 5-10%) | Excellent | | Accuracy at high e | Conservative (20-40% low) | Excellent | | Hand calculation | Easy — closed-form formulas | Requires tables (AISC 7-6 to 7-17) | | AISC 360-22 recognition | Permitted (J3.7 commentary) | Preferred method | | Software implementation | Simple matrix algebra | Iterative optimization |
For typical steel connection design, the IC method is used because the AISC Manual provides C values for common configurations, making hand calculation straightforward. For unusual bolt group geometries not covered by the AISC tables, the elastic method or a specialized software implementation of the IC method is required.
When to Use Each Method
- Use the IC method for final design of standard connections (shear tabs, clip angles, end plates) where the bolt group geometry is covered by AISC Manual Tables 7-6 through 7-17. This is the AISC-preferred approach and provides the most economical design.
- Use the elastic method for preliminary sizing (quick hand calc), for bolt groups with irregular geometry not in the AISC tables, and for checking existing connections where the original design basis is unknown and conservatism is desired.
- Always check both methods when the bolt group has an unusual combination of in-plane and out-of-plane eccentricity, or when the bolt group is very large (n > 12 bolts) where the C value tables may not cover the configuration.
Typical Bolt Group Coefficients (C Values)
For 3/4 in. dia. A325 bolts, s = 3 in., angle = 0 degrees (vertical load):
| Configuration | e_x = 3 in. | e_x = 6 in. | e_x = 9 in. | e_x = 12 in. |
|---|---|---|---|---|
| 1 column x 4 | 1.98 | 1.53 | 1.20 | 0.97 |
| 2 cols x 2 | 2.74 | 2.03 | 1.56 | 1.25 |
| 2 cols x 3 | 4.37 | 3.31 | 2.56 | 2.05 |
| 2 cols x 4 | 6.02 | 4.55 | 3.52 | 2.81 |
| 3 cols x 3 | 6.65 | 5.12 | 3.96 | 3.14 |
| 3 cols x 4 | 9.20 | 7.05 | 5.45 | 4.33 |
| 3 cols x 5 | 11.73 | 8.97 | 6.94 | 5.50 |
C values increase with more bolts (obviously) and with more columns (wider bolt group = larger polar moment of inertia). For horizontal load (angle = 90 degrees), C values differ — refer to the specific table for the load orientation.
Frequently Asked Questions
Why is the IC method preferred over the elastic method?
The IC method accounts for the ductility of bolts — when the most heavily loaded bolt begins to yield, it continues to carry its full ultimate load (R_ult) while deforming, allowing other bolts to pick up additional load. This load redistribution means the bolt group has significantly more capacity than the elastic method predicts. The elastic method assumes all bolts remain elastic, which is not how ductile steel bolts actually behave at ultimate load. AISC 360-22 Commentary J3.7 explicitly recognizes the IC method as the preferred approach.
What if my bolt group geometry is not in the AISC tables?
Options: (1) Use the elastic method as a conservative approximation (adds 20-40% conservatism). (2) Use the AISC Design Guide approach with equivalent eccentricity to approximate an irregular group as a regular group. (3) Implement the IC method iteratively (spreadsheet, MATLAB, Python) — the algorithm is described in AISC Design Guide 17 and numerous structural engineering textbooks. (4) Use this calculator, which implements the full IC method for arbitrary bolt group geometries.
Run This Calculator
Related References
- Bolt Holes Reference
- Bolt Spacing Requirements
- Bolt Pattern Design
- Bolted Connection Worked Example
- Welded Connection Calculator
- Steel Connection Design Guide
- Connection Checklist
- How to Verify Calculations
Disclaimer
This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.