In　the　past　20　years,　recycled　aggregate　concrete　(RAC),　as　a　type　of　low-carbon　concrete,　has　become　a　worldwide　focus　of　research.　However,　the　design　methodology　for　RAC　structural　components　remains　a　challenge.　Consequently,　demands　for　a　unified　design　of　natural　aggregate　concrete　(NAC)　and　RAC　components　have　been　presented.　Accordingly,　this　study　analyses　the　necessity　of　a　unified　design　theory　and　provides　an　in-depth　demonstration　of　the　strength　determination,　compressive　constitutive　relationship,　and　design　method　of　concrete　components.　The　coefficient　of　variation　of　RAC　strength　is　found　to　be　generally　higher　than　that　of　NAC　strength.　The　compressive　and　tensile　strengths　of　RAC　can　be　defined　and　determined　using　the　same　method　as　that　used　for　NAC.　The　uniaxial　compressive　constitutive　relationship　between　NAC　and　RAC　has　a　unified　mathematical　expression.　However,　the　elastic　modulus　of　RAC　decreases,　and　its　brittleness　exhibits　an　increasing　trend　compared　with　that　of　NAC.　Finally,　to　unify　the　design　formulae　of　RAC　and　NAC　components　for　bearing　capacity,　modification　factors　for　RAC　components　are　proposed　considering　safety　and　reliability.　Additionally,　the　feasibility　of　the　proposed　unified　time-dependent　design　theory　is　demonstrated　in　terms　of　conceptual　design　and　structural　measures　considering　the　effects　of　strength　degradation　and　reinforcement　corrosion.　It　is　believed　that　this　study　enriches　and　develops　the　basic　theory　of　concrete　structures.　(c)　2023　THE　AUTHORS.　Published　by　Elsevier　LTD　on　behalf　of　Chinese　Academy　of　Engineering　and　Higher　Education　Press　Limited　Company.　This　is　an　open　access　article　under　the　CC　BY-NC-ND　license　(http://creativecommons.org/licenses/by-nc-nd/4.0/).