Toward　estimating　accurately　the　distortional　response　of　box　girders,　in　this　article,　distortion　of　steel　box　girders　strengthened　with　intermediate　solid　diaphragms　under　eccentric　loads　is　analyzed　by　employing　the　so-called　initial　parameter　method.　A　new　model　of　high-order　statically　indeterminate　structure　was　established　with　three　orthogonal　redundant　forces　acting　at　the　junction　between　the　girder　and　diaphragms.　Emphasis　is　put　onto　the　interaction　between　the　girder　and　diaphragms,　where　a　hypothetical　bi-moment　B　indicating　all　longitudinal　redundant　force　components　for　diaphragm　was　proposed　besides　the　moment　M-pi　for　in-plane　shear　component.　Simplified　initial　parameter　method　solutions　for　distortional　angle　and　distortional　warping　stresses　and　displacements　were　derived　based　on　the　in-plane　and　out-of-plane　compatibilities　between　the　girder　and　diaphragms.　Taking　box　girders　with　three　and　five　intermediate　diaphragms　as　an　example,　the　proposed　initial　parameter　method　solutions　have　good　agreement　with　the　finite　element　analysis　ones.　Finally,　distortional　behavior　under　moving　eccentric　loads　is　investigated,　resulting　in　a　bowl-shaped　curve　for　moment　M-pi　and　an　approximate　trigonometric　function　for　bi-moment　B-pi.　Results　show　that　diaphragms　have　a　stronger　resistance　on　in-plane　distortional　shear　for　the　loads　in　midspan　than　on　ends.　Plus,　the　thick　diaphragm　holds　a　stronger　restraint　on　distortional　warping　deformations　and　stresses　than　the　thin　one.