Aluminim might weigh about 1/3 of what steel does but it's also just about 1/3 as strong. Typical numbers might be like 200MPa (megapascals, million kilograms per square meter) for steel but around 70MPa for aluminum. Plus aluminum work hardens (as stated by zeroaxe) and gets brittle. Additionally, as volkdent mentioned, aluminum fatigues even at extremely low stresses, where steel has an endurance limit (the lowest stress that contributes to fatigue) of something like 100MPa. Of course, all of these numbers change with the actual alloys chose, but for illustration they work well.

If you want a safe tube frame chassis, I would say just look to the FIA specs for their rollcages (since I would hope you will have one of those too if you're having to build a chassis). The specs have been develeoped for a lot more abuse than you will hopefully see, and hold up to bad crashes every day.

Peace of Christ