The frame that will not solve
foundationA single-bay, single-storey portal frame modelled with beam elements. Both column bases are given vertical restraint only. Gravity load is applied to the rafter.
Symptoms
- The solver stops with a message about a singular matrix or a zero pivot
- No results are produced at all
- Adding more load makes no difference to the message
Work it out first, then open the diagnosis
- 1. First check
- Count the restrained directions before looking at anything else. In two dimensions you need at least three independent restraints; in three dimensions, six.
- 2. Likely cause
- No horizontal restraint. The frame is free to translate as a rigid body.
- 3. Confirmatory test
- Run a modal or stability analysis. A rigid-body mode at zero frequency, showing the whole frame sliding, names the direction exactly.
- 4. Correction
- Restrain the bases horizontally, as the real foundation does. If the real base genuinely slides, model a spring rather than nothing — a real foundation has friction, and zero is not a stiffness the mathematics will accept.
- 5. Independent verification
- The analysis runs, and the horizontal reactions sum to the applied horizontal load. Under pure gravity on a symmetric portal they should be equal and opposite.
- 6. The lesson
- The model needs restraint in directions the structure has no load in. The requirement comes from the arithmetic, not from the statics.