The document discusses the design of doubly reinforced beams using the limit state method. Doubly reinforced beams are needed when the required depth is restricted but the beam needs to resist a higher bending moment. This is done by providing compression reinforcement in addition to tension reinforcement. The minimum compression steel is 0.4% of the section area and maximum is 4%. The yield stress of compression steel is taken as 0.87 times the yield stress in tension. The analysis involves assuming a neutral axis depth and checking force equilibrium.

1. DESIGN OF DOUBLY REINFORCED BEAM BY BY LIMIT STATE METHOD

2. TYPES OF BEAMS Doubly Reinforced beam Singly Reinforced beam

3. Need of doubly reinforced beam

4. NEED OF DOUBLY REINFORCED BEAM In practice, very frequently, it is desirable or even mandatory to have a section of restricted depth in order to comply with some architectural or structural requirements wherein the section has to carry a moment more than it can resist a balanced section. If the section is made arbitrarily made shallower than the balanced design, it results in over reinforced section and the concrete is over stressed, while steel is stressed to its permissible value. As it is mentioned in IS:456 do not permit the use of over reinforced section. In such cases it is preferable to design it as doubly reinforced beam where the reinforcement is also provided in compression to give additional strength to concrete.

5. MINIMUM AND MAXIMUM STEEL AS COMPRESSION STEEL IN BEAMS The minimum area of steel in compression = 0.4% of area in compression steel The maximum area of steel in compression = 4% of the total sectional area of the beam

6. YIELD STRESS IN COMPRESSION STEEL IS 456 ASSUMES THAT THE YIELD STRESS-STRAIN RELATIONSHIP FOR STEEL IN COMPRESSION AND TENSION REMAIN SAME Design yield stress = 0.87 ƒy

7. Z S Z C C C d’ C S 0.0035 d’ 0.002 b X u Є s d Є’ s Action of doubly reinforced beam T STRAIN DIAGRAM STRESS DISTRIBUTION

8. T = C C = C S M U = C C Z C + C S Z S C S = Compressive force due to concrete C C = Compressive force due to steel

9. ANALYSIS AND DESIGN OF DOUBLY REINFORCED BEAM Choose value of x, the depth of neutral axis. Assuming compressive strain of 0.0035 Total tension in steel, T = ƒ ast A st Total compression in steel, C = 0.36 ƒckbx

10. The total compression, C = C S + C C Check- if T = C, the assumed neutral axis is satisfactory . Moment of resistance of section M U = C C (d-k 2 x) + C S (d-d΄)

11. Thank you