Reinforced Concrete (RCC) Design for SSC JE Civil: Limit State Method, Beams, Slabs, Columns, Cover and IS 456 Rules

Reinforced concrete (RCC) design is a high-scoring part of the SSC JE Civil syllabus because the questions are based on IS 456:2000 and a few standard formulas. This guide on RCC design for SSC JE covers the methods of design, the limit state parameters, the IS code rules for beams, slabs and columns, the nominal cover and development length, with solved examples, practice questions and FAQs.

Basics of Reinforced Concrete

• Concrete is strong in compression and weak in tension; steel bars carry the tension.
• The code of practice is IS 456:2000 (Plain and Reinforced Concrete); for steel, IS 800:2007.
• Grades of concrete: M20, M25, M30 etc., where the number is the characteristic compressive strength f_ck in N/mm² at 28 days (150 mm cube); minimum grade for RCC is M20.
• Grades of steel: Fe 250, Fe 415 and Fe 500 (the number is the yield strength f_y in N/mm²); Fe 415 and Fe 500 are high-yield strength deformed (HYSD) bars.
• Modulus of elasticity of concrete: E_c = 5000√f_ck N/mm²; for steel E_s = 2 × 10⁵ N/mm².
• Modular ratio in the working stress method: m = 280 / (3σ_cbc); for M20 (σ_cbc = 7), m = 13.33.

Methods of Design

Limit State Method: Key Values

Types of Sections

Beams

• Minimum tension steel: A_s/(bd) ≥ 0.85/f_y.
• Maximum tension steel: 4% of bD (the gross area).
• The effective span of a simply supported beam is the lesser of the clear span plus the effective depth, or the centre-to-centre distance of the supports.
• Shear: nominal shear stress τ_v = V_u/(bd); shear reinforcement is in the form of vertical stirrups or bent-up bars.
• Depth to span ratios: simply supported 20, continuous 26, cantilever 7 (for spans up to 10 m).
• Minimum clear spacing between bars: the largest of the bar diameter, the maximum size of aggregate + 5 mm and 20 mm.

Slabs

• A slab is one-way if l_y/l_x > 2 (main steel in the short span only), and two-way if the ratio ≤ 2.
• Distribution (secondary) steel in a one-way slab is 0.15% of the gross area for Fe 250 and 0.12% for Fe 415 and Fe 500.
• Maximum diameter of bars in slabs is not more than one-eighth of the total thickness of the slab.
• Maximum spacing of main bars is the smaller of 3d and 300 mm; of distribution bars 5d and 450 mm.
• Torsion reinforcement is needed at the corners of a simply supported two-way slab.

Columns

Nominal Cover

Development Length

L_d = φ σ_s / (4 τ_bd), where φ is the bar diameter, σ_s is the stress in the bar (0.87 f_y at the design load) and τ_bd is the design bond stress. For M20 with plain bars τ_bd = 1.2 N/mm², and for deformed bars it is increased by 60%.

Solved Examples

Example 1. Find M_u,lim for a beam of 250 mm width and 450 mm effective depth, with M20 concrete and Fe 415 steel.
M_u,lim = 0.138 × 20 × 250 × 450² = 139.7 kN m.

Example 2. Find the minimum tension steel for the same beam.
(0.85/415) × 250 × 450 = 230 mm².

Example 3. A slab is 3 m × 7 m, supported on all four sides. Is it one-way or two-way?
l_y/l_x = 7/3 = 2.33, which is more than 2, so it is a one-way slab.

Example 4. What is the minimum number of longitudinal bars in a circular column?
6.

Quick Tips

• Memorise the values of x_u,max/d for the three grades of steel.
• Remember the 0.85/f_y minimum steel in beams.
• Remember the slab rule l_y/l_x = 2.
• Learn the column steel limits 0.8% and 6%.

Quick Revision Points

• IS 456:2000 is the code for RCC.
• Limit state design uses γc = 1.5 and γs = 1.15.
• x_u,max/d = 0.48 for Fe 415.
• Under-reinforced beams fail in a ductile manner.
• Minimum steel in columns is 0.8%.

Practice Questions With Answers

1. Which IS code is used for RCC design?
   Answer: IS 456:2000
2. What is the partial safety factor for steel in LSM?
   Answer: 1.15
3. What is the value of x_u,max/d for Fe 415?
   Answer: 0.48
4. What is the maximum percentage of tension steel in a beam?
   Answer: 4% of bD
5. When is a slab one-way?
   Answer: When l_y/l_x is greater than 2
6. What is the minimum number of bars in a rectangular column?
   Answer: 4
7. What is the minimum grade of concrete for RCC?
   Answer: M20
8. Which section is preferred: under-reinforced or over-reinforced?
   Answer: Under-reinforced
9. What is the nominal cover for columns (minimum)?
   Answer: 40 mm
10. What is the design strength of steel in LSM?
    Answer: 0.87 f_y

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Civil Engineering notes page, read the previous topic Engineering Mechanics and the next topic Steel Structures Design.

Frequently Asked Questions

What is RCC?

Reinforced cement concrete, in which steel bars are placed in concrete to carry tension.

Which method is used in IS 456:2000?

The limit state method.

What is a balanced section?

A section in which steel and concrete reach their limiting stresses at the same time.

What is an under-reinforced section?

A section in which the steel yields before the concrete crushes.

What is the modulus of elasticity of concrete?

5000√f_ck N/mm².

What is the characteristic strength?

The strength below which not more than 5% of test results are expected to fall.

What is the difference between one-way and two-way slabs?

A one-way slab bends in one direction (ratio above 2), while a two-way slab bends in both directions.

What is development length?

The length of a bar needed to develop its full design stress through bond.

What is the minimum diameter of main bars in columns?

12 mm.

What is the pitch of lateral ties?

The least of the least lateral dimension, 16 times the smallest bar diameter and 300 mm.

Is RCC asked in SSC JE?

Yes. It is asked in SSC JE Civil papers every year.

What is the concrete cover for?

To protect steel from corrosion and fire and to provide the bond.