For temporary roofs (and most other external scaffolds) you first need to calculate the wind load using EN 1991 or TG9:12. You then need to ascertain the most onerous load condition for each direction. Once you have established the wind loads,along with snow, live and dead loads, you would then check (as a minimum)
1. Overturning as a unit (if the support scaffold to roof connection is strong enough and the scaffold is free-standing).
2. Ledger or transverse brace loadings
3. Tension and compression in the supporting standards - anchors or kentledge may be required if free-standing.
4. Tie loading (if any)
5. Uplift at roof to scaffold connection
6. Gable end plan bracing (if any)
7. Longitudinal bracing loadings
8. Tension/compression in the standards and/or overturning in the longitudinal direction
9. Roof beam check against uplift (wind) and against downward forces (snow, live load, dead load)
10. Roof connection check
11. If using a duopitch roof in particular, you also need to check the horizontal forces induced by the roof angle which add to the tie or overturning loads.
TG9:12 recommends structural analysis software and it is by far the most accurate and safest way to design roofs and temporary buildings, especially duopitch roofs. For simple monopitch roofs a hand calculation may be sufficient but would still need to include all of the above.