## How does ETABS compute global force balance relative error? (Available in ETABS v9 only)

**Answer:** ETABS computes global force balance for Loads, Modes, Specs, and Combos to ensure that forces and moments within each Analysis Case are in equilibrium. This operation is not performed for time-history cases. Results are reported in .OUT and .LOG files, which should be reviewed to validate the model and analysis.

For each Analysis Case, resultants are computed at the global origin for forces and moments of the following types:

- Applied loads
- Inertial loads
- Spring forces
- Link forces
- Restraint forces (reactions)
- Constraint forces
- P-Delta forces

Total resultants are also summed from the combination of all these types. Zero total resultant indicates equilibrium for each DOF at the origin, though a solution of exactly zero cannot occur due to round-off. Accuracy may be gauged relative to the magnitude of contributing forces.

**GLOBAL FORCE BALANCE**reports resultant forces and moments in an output file.

**GLOBAL FORCE BALANCE RELATIVE ERRORS**reports equilibrium errors in a log file. These values are expressed as a percentage of the maximum possible equilibrium error, which is computed as follows:

- For each component (FX, FY, FZ, MX, MY, and MZ), absolute values are summed for each resultant, including applied loads, inertial loads, spring forces, link forces, reactions, constraint forces, and P-Delta forces.
- The maximum of absolute sums FX, FY, and FZ is determined.
- The maximum of absolute sums MX, MY, and MZ is determined.
- The maximum possible force-component error is determined as the larger value between maximum absolute force sum and maximum absolute moment sum divided by the average moment arm.
- The maximum possible moment-component error is determined as the larger value between maximum absolute moment sum and maximum absolute force sum multiplied by the average moment arm.

**NOTE:** This formulation assures that only numerically meaningful equilibrium errors are indicated.