Steel-reinforced　concrete　(SRC)　composite　structures　are　widely　employed　in　modern　buildings　because　of　their　elevated　load-carrying　capacity,　robust　stability　and　remarkable　resilience　to　corrosion　and　fire.　To　safely　utilize　SRC　composite　structures,　reliable　bonding　between　steel　and　concrete　is　crucial　in　designing　and　constructing　SRC　members　and　connections.　With　this　objective　in　mind,　the　current　study　aims　to　establish　accurate　models　for　estimating　the　characteristic　bond　stresses　(i.e.,　initial,　peak　and　residual　bond　stresses)　and　determining　the　necessary　anchorage　length　between　the　profiled　steel　and　the　adjacent　concrete.　To　realize　these　goals,　a　total　of　660　push-out　tests　and　their　results　were　compiled　from　existing　literature　for　model　development.　Probabilistic　bond　stress　models　were　created　by　integrating　existing　models　with　key　variables　related　to　the　mechanical　properties　and　geometrical　characteristics　of　concrete,　steel　section　and　stirrup.　Bayesian　theory　and　the　Markov　Chain　Monte　Carlo　(MCMC)　method　were　utilized　to　refine　and　select　the　most　precise　model.　The　evaluation　results　demonstrate　that　the　probabilistic　models　provide　more　accurate　predictions　for　initial,　peak　and　residual　bond　stresses　compared　to　existing　models.　With　the　assistance　of　this　reliable　analytical　technique,　the　established　model　for　peak　bond　strength　was　finally　applied　to　determine　the　minimum　required　anchorage　length　for　steel　within　concrete.　©　2023　Elsevier　Ltd