Titanium　alloys　have　shown　wide　application　potential　in　the　areas　such　as　aerospace　and　marine　because　of　their　comprehensive　properties,　including　high　specific　strength,　ductility,　corrosion　resistance,　and　damage　tolerance.　Given　the　rapid　development　of　new-generation　advanced　military　hardware　toward　large　scale,　high-speed,　light-weight,　and　structure-complicated　titanium　alloys　experience　increasingly　harsh　application　environments.　Thus,　developing　novel　high-strength　and　high-toughness　titanium　alloys　is　an　important　direction　in　the　field　of　titanium　research.　To　date,　the　compositional　design　of　titanium　alloys　is　performed　within　the　framework　of　some　empirical　rules　without　involving　strengthening　and　toughening　mechanisms.　This　kind　of　approach　can　hardly　achieve　an　accurate　and　efficient　material　design.　Based　on　the　abovementioned　background,　the　effect　of　alloying　on　the　precipitation　strengthening　of　the　α　+　β　dual-phase　titanium　alloy　was　studied　by　using　the　first-principles　exact　muffin-tin　orbital　method　in　combination　with　a　coherent　potential　approximation.　High-strength　and　high-toughness　titanium　alloys　obtain　its　high　strength　through　precipitation　strengthening　in　the　β-phase　matrix　with　α-phase　precipitates.　The　influence　of　alloying　on　the　precipitation　strengthening　is　crucial　to　the　understanding　and　prediction　of　alloy　strength　and　rational　alloy　design.　In　the　present　work,　the　elastic　moduli　and　lattice　constants　of　a　serial　binary　titanium　alloy　Ti-xM　(M　=　Al,　V,　Cr,　Mn,　Fe,　Co,　Ni,　Nb,　Mo,　Ta,　W)　against　the　composition　x　were　calculated　using　the　first-principles　method.　Based　on　which,　the　elastic　moduli　of　the　titanium　alloy　with　a　complex　composition　(such　as　Ti-Al-V　and　Ti55521)　were　evaluated　using　the　concept　of　elastic　Mo　equivalency.　Subsequently,　the　precipitation　strengthening　of　binary　titanium　alloys　and　the　Ti55521　alloy　was　evaluated　by　using　the　elastic　modulus　within　the　framework　of　the　modulus　strengthening　model.　Result　shows　that　alloying　elements,　such　as　Co,　Fe,　W,　Mo,　Ni,　and　Mn,　have　the　strongest　precipitation　strengthening　effect　for　the　same　particle　size　and　volume　fraction　of　α　precipitates,　followed　by　Cr,　Nb,　and　Ta,　whereas　V　is　the　weakest.　The　strengthening　effect　increases　with　the　content　of　alloying　element.　For　the　Ti55521　alloy　prepared　by　using　a　thermal　mechanical　process,　subsequent　short-time　aging　weakens　the　precipitation　strengthening　effect　compared　with　long-time　aging.　©　2024　Chinese　Academy　of　Sciences.　All　rights　reserved.