Welded　features　in　the　tubular　joints　are　one　of　the　most　severe　sources　of　fatigue　failure　in　supporting　structure　for　offshore　wind　turbines　(OWTs).　Therefore,　fatigue　resistance　becomes　a　vital　design,　inspection　and　maintenance　criterion　for　tripod　supporting　structures.　This　paper　proposes　a　time-domain　fatigue　damage　assessment　approach　for　tripod　structures　by　establishing　a　detailed　finite　element　model　for　the　critical　zones　and　simplified　beam　model　for　the　remaining　regions.　The　stress　influence　matrix　(SIM)　is　formed　once　by　utilizing　multiple　finite　element　analyses.　Based　on　the　equivalent　static　loads　and　linear　superposition　principle,　the　time-variant　stress　can　be　efficiently　calculated.　By　comparing　the　fatigue　damage　caused　by　multiple　loads　to　that　caused　by　a　single　load　in　a　particular　direction,　we　conclude　that　the　advantage　of　the　proposed　method　over　the　conventional　stress　concentration　factors　method.　Afterwards,　we　investigate　the　effects　of　environmental　conditions　on　the　cumulative　fatigue　damage　of　critical　zones.　The　fatigue　resistances　of　various　structures　by　altering　angles　between　the　main　barrel　and　up　brace,　and　a　novel　structure　inspired　by　topology　optimization,　are　promptly　verified.　All　results　indicate　that　the　present　approach　can　determine　the　fatigue　damage　for　the　tripod　structure　with　precision　and　efficiency.　©　2023　Elsevier　Ltd