High　temperature　has　a　significant　impact　on　the　mechanical　properties　of　steel　structural　members,　which　can　develop　a　potential　collapse.　Currently,　various　studies　have　been　concentrating　on　the　post-fire　mechanical　properties　of　different　steels,　while　few　of　them　considered　the　corresponding　constitutive　model.　Therefore,　in　this　paper,　the　classical　Johnson-Cook　constitutive　equation　is　selected　as　a　benchmark　and　is　modified　to　fit　the　conditions　in　which　the　effects　of　heating　and　cooling　on　the　mechanical　properties　of　fire-affected　steel　are　considered.　To　this　end,　three　commonly　used　structural　steels,　namely　Q345B,　Q460　and　Q690D,　are　selected　in　this　paper.　First,　the　specimens　were　heated　to　different　target　temperatures,　and　then　naturally　cooled　down　to　the　ambient　temperature　in　the　air.　After　cooling　from　the　exposure　temperatures,　the　subsequent　tensile　tests　were　performed　on　the　fire-affected　specimens　to　capture　the　failure　modes　and　study　the　residual　mechanical　properties.　To　verify　the　proposed　constitutive　model,　an　Abaqus　subroutine　(UMAT)　program　was　developed　in　this　study.　The　experimental　data　of　water-cooled　specimens　obtained　in　our　previous　studies　were　also　selected　to　further　test　the　feasibility　of　this　new　model.　The　results　show　that　the　exposure　temperature　and　steel　grade　have　significant　effects　on　the　residual　mechanical　properties　of　the　structural　steel　specimens　when　the　target　temperature　exceeds　700　°C.　Meanwhile,　the　modified　Johnson-Cook　constitutive　is　able　to　predict　the　stress　–strain　behavior　precisely,　regardless　of　the　cooling　method.　The　results　obtained　in　this　study　are　helpful　for　both　further　research　and　engineering　application　when　doing　a　numerical　study　of　the　fire-affected　steel　structures.　©　2022　Elsevier　Ltd