With　consideration　of　the　different　failure　modes　and　the　influence　of　secondary　loading　for　FRP-strengthened　RC　beams,　the　Hognestad　constitutive　model　that　is　close　to　actual　stress-strain　situations　of　concrete　was　used　for　the　nonlinear　changes　in　the　compressive　zone　of　concrete.　The　coefficients　related　to　the　equivalent　stress　of　concrete　under　compression,　as　well　as　to　the　depth　of　compressive　zone　of　concrete,　were　deduced　based　on　the　Hognestad　model.　Then　the　formulas　of　ultimate　bending　moments　of　RC　beams　were　established　with　respect　to　three　different　failure　modes　i.e.,　FRP　tensile　failure,　reinforcement　yield　before　and　after　concrete　crushing.　Meanwhile,　the　maximum　and　the　minimum　FRP　amounts　for　beam　reinforcement　were　given　to　define　the　critical　conditions　between　different　failure　modes.　The　secondary　loading　effects　with　lag　strains　were　also　involved　in　the　context.　Lastly,　the　proposed　formulas　were　validated　by　using　some　tested　FRP-reinforced　RC　beams.　The　results　show　that　the　proposed　formulas　consider　different　failure　modes　and　the　influence　of　secondary　loading.　The　ultimate　loads　calculated　with　the　formula　are　in　agreement　with　the　experiments　results,　which　indicates　that　the　formula　can　be　used　to　design　the　FRP　reinforcement　and　analyze　the　corresponding　ultimate　load　of　RC　beams.　©　2019,　Central　South　University　Press.　All　right　reserved.