Structural Design of Concrete Structures
Domain overview
This section tests limit-state design of reinforced concrete members to the governing code, including flexure, shear, bond, deflection, durability and ductile detailing. You must distinguish characteristic and design values and show checks, not just final steel areas.
Core rules
- Use factored loads and design strengths: concrete fcd = 0.67fck/γc and steel fyd = fy/γs; γc and γs are code-specified.
- For a singly reinforced rectangular section, Mu = 0.36fck b xu(d−0.42xu) and Ast = 0.5fck/fy [1−√(1−4.6Mu/(fck b d²))]bd.
- Keep xu/d below the code limit for under-reinforced, ductile behaviour; check minimum and maximum steel.
- Shear design needs τv = Vu/(bd), concrete capacity τc, and stirrups for the excess; detailing rules control spacing and anchorage.
Worked example
A 250 mm × 450 mm effective beam (b=250, d=450) uses fck=25 MPa and fy=500 MPa for Mu=120 kN·m. First check singly reinforced capacity: with xu,max/d≈0.46, Mu,lim≈0.133fckbd²≈169 kN·m, so 120 kN·m is feasible. Then 4.6Mu/(fckbd²)=4.6×120×10⁶/(25×250×450²)=0.436. Ast=0.5×25/500×[1−√(1−0.436)]×250×450≈700 mm². Check minimum steel (about 0.85bd/fy≈191 mm²) and provide bars, then check shear and deflection.
Traps
Using overall depth instead of effective depth, omitting the minimum-steel check, treating a singly reinforced section as adequate beyond Mu,lim, and ignoring ductile detailing at joints.