Balanced section,under reinforced,over reinforced section

Here we discussed about the balanced section,Under reinforced and Over reinforced sections and what are the failure and their moment of resistance.. and also comparison between among three sections

1. Balanced, Under Reinforced and Over Reinforced Section Name - Navdeep L-2020-AE-051-BIV

2. Content Introduction Balanced section Under Reinforced section Over Reinforced Section Failure in Balanced, Under and Over Reinforced section Comparison Moment of resistance References

3. Introduction When it comes to designing RCC beams, there are several options to consider when it comes to the amount of reinforcement used we have three types of sections: 1) Balanced Section 2) Under Reinforced Section 3) Over Reinforced Section

4. Balanced Section Stress in concrete and steel reach their permissible value at the same time Percentage of steel corresponding to this section is called as balanced steel Neutral axis is called as critical neutral axis  

5. Under Reinforced Section Percentage of steel provided is less than that provided in balanced section Actual neutral axis will shift upwards i.e., nc > n Stress in steel first reaches it permissible value, while the concrete is under stressed

6. Over Reinforced Section Percentage of steel provided is greater than the balanced section Actual neutral axis shift downward i.e., n>nc Stress in concrete reaches its permissible value while steel is not fully stressed Concrete is brittle and it fails by crushing suddenly Steel is not fully utilised, the over reinforced section is uneconomical (steel is much costlier than concrete)

7. Failure in Balanced Sections Balanced failure Both the materials will fail at the same time due to same permissible value

8. Failure in Under Reinforced Section Ductile or Under Reinforced Failure The permissible strength of steel is less as compared to concrete The application of load on this particular member, the failure of steel takes place prior to the failure of concrete

9. Failure in Over Reinforced Section Brittle or Over Reinforced Failure Permissible strength of steel is greater as compared to concrete Application of load on such member, the failure of concrete will occur prior to the failure of steel

10. Comparison sr no. Balanced section Under Reinforced section Over Reinforced Section 1) Steel and Concrete both are fully stressed Steel is fully stressed Concrete is fully stressed 2) n = nc Neutral axis lies above the critical neutral axis n < nc Neutral axis lies below the critical neutral axis n > nc 3) Percentage of steel axis lies on the natural axis Percentage of steel is less than balanced section Percentage of steel is more than balanced section

11. Sr no. Balanced section Under Reinforced section Over Reinforced section 4) The moment is balanced at the natural axis The moment of resistance is less than balanced section The moment of resistance is more than a balanced section 5) Uneconomcial Economical Uneconomical 6) Sudden failure Safe failure Ductile failure Sudden failure Brittle failure – crushing failure 7) Not Preferred by designers Preferred by designers Not Preferred by designers continued......

12. Parameters Ast= Area of Steel in Tension Zone fst or σst= Stress in Steel fst.u or σst.u= Ultimate Stress in Steel fc or σc = Stress in Concrete fy = Yield strength of steel fck = Characteristics strength of concrete ϵc= Strain in concrete ϵst = Strain in Steel Nc or nc or Xu = Critical Neutral Axis N or n= Actual Neutral Axis D= Total Depth of Beam d= Effective depth of beam (from centroid of steel in tension zone to topmost fiber of concrete in compression zone).

13. Moment of resistance Balanced section Under Reinforced section Over Reinforced section (Moment of Resistance) Mr = Compressive Force*(d-0.42d) Mr= Tensile Force*(d-0.42d) (Moment of Resistance) Mr=fst.Ast(d-n/3) (Moment of resistance) Mr=b.n.(fst/2) *(d-n/3)

14. References Sr no. Slide number Reference 1) 3 ,7-9 https://civiltutorofficial.com/why-do-we-prefer-under-reinforced-sections-over-balanced-or-over-reinforced-sections/ 2) 4-6 https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=web&cd=&ved=0CAMQw7AJahcKEwjQhveztdH-AhUAAAAAHQAAAAAQAg&url=https%3A%2F%2Fcivilengineering.blog%2F2017%2F11%2F14%2Fbalanced-sections-under-reinforced-section-over-reinforced-section%2F&psig=AOvVaw2Oh-H4W6z-5abbhLF16LmN&ust=1682937637971857 3) 10-11 https://civilexperiences.com/balanced-sections-under-reinforced-section-over-reinforced-section/ 4) 12-13 https://civilideas374921463.wordpress.com/2021/09/11/balanced-section-under-reinforced-section-over-reinforced-section/

15. Thank You