Design Philosophy of Reinforced Concrete -- Complete Revision Notes
Every definition, assumption, formula, comparison table, diagram, mnemonic and exam-style answer you need for this chapter -- built for fast revision and mock practice.
On this page
- Why Do We Design Structures
- Reinforced Concrete Basics
- Working Stress Method (WSM)
- Limit State Method (LSM)
- Characteristic Load and Strength (with curve)
- Partial Safety Factors (added)
- Difference Between WSM and LSM
- Why LSM is Preferred + Applications
- Other Design Philosophies (added)
- Model Answers by Weightage
- MCQs
- Interview Questions
- Memory Box
- Full Mock Test (20 Questions)
- One-Page Summary Sheet
1. Why Do We Design Structures? (5 Marks)
Every structure must satisfy three basic requirements, regardless of which design method is used:
| Requirement | Meaning |
|---|---|
| (a) Safety | The structure should not collapse under design loads during its service life. |
| (b) Serviceability | The structure should remain usable and comfortable throughout its design life. Checks: deflection, cracking, vibration, durability. |
| (c) Economy | The structure should be safe without unnecessary material consumption -- safe AND cost-effective. |
Exam tip: always open a design-philosophy answer with these three requirements before moving to WSM/LSM -- markers look for this first.
2. Reinforced Concrete (RC) -- Why Combine Steel and Concrete?
| Material | Behaviour |
|---|---|
| Concrete | Strong in compression, weak in tension (tensile strength is only about 1/10th of compressive strength) |
| Steel | Strong in both tension and compression |
Steel is embedded in concrete so that concrete resists compression and steel resists tension. This combination forms Reinforced Cement Concrete (RCC). The two materials work together because they have almost the same coefficient of thermal expansion and concrete provides steel with corrosion protection and fire resistance.
3. Working Stress Method -- WSM (5 / 10 Marks)
Definition: The Working Stress Method is based on the assumption that the stresses developed under service (working) loads should not exceed the permissible stresses of the materials, keeping the structure within the elastic range.
Assumptions of WSM (added -- frequently asked)
- Plane sections before bending remain plane after bending (linear strain distribution).
- There is perfect bond between steel and concrete; no slip occurs.
- Concrete is assumed to take no tension -- all tensile stress is resisted by steel only.
- Stress-strain relationship for both concrete and steel is linear (elastic) within the working range.
- The modular ratio m relates the elastic behaviour of steel to concrete.
Permissible Stresses in Concrete -- WSM (added, typical IS 456 values)
| Grade of concrete | sigma_cbc, N/mm sq (bending compression) | sigma_c, N/mm sq (direct compression) |
|---|---|---|
| M15 | 5.0 | 4.0 |
| M20 | 7.0 | 5.0 |
| M25 | 8.5 | 6.0 |
| M30 | 10.0 | 8.0 |
Permissible stress in steel (added): sigma_st is generally taken as 140 N/mm sq for mild steel (Fe250) and 230 N/mm sq for HYSD bars (Fe415), used in tension.
Characteristics of WSM
- Uses service (working) loads directly, with no load factor.
- Based on linear elastic theory.
- Uses one overall factor of safety applied to material strength.
- Suitable for linear elastic behaviour; does not represent true ultimate strength.
| Advantages of WSM | Disadvantages of WSM |
|---|---|
| Simple calculations | Uneconomical -- section sizes and steel area tend to be larger |
| Easy to understand and apply by hand | Does not represent actual ultimate (failure) strength of the section |
| Good control of serviceability (deflection, cracking) since stresses are kept low | Does not account adequately for variability in loads and material strength |
| Historically well proven, still used for water-retaining structures | Single factor of safety cannot separately reflect uncertainty in load vs material |
4. Limit State Method -- LSM (5 / 10 Marks)
Definition: The Limit State Method is based on the concept that a structure should satisfy all relevant limit states during its design life with an acceptable level of safety, without becoming unfit for its intended use.
A limit state is the condition beyond which a structure no longer satisfies the design performance requirements -- either by collapsing or by becoming unserviceable.
Types of Limit States
| Type | Checks |
|---|---|
| (A) Limit State of Collapse | Flexure, shear, compression, torsion, overall stability |
| (B) Limit State of Serviceability | Deflection, cracking, durability, vibration |
LSM Stress Block (added -- companion diagram)
| Feature | WSM stress block | LSM stress block |
|---|---|---|
| Shape | Triangular (linear elastic) | Rectangular-parabolic (realistic non-linear) |
| Concrete stress used | Low permissible stress, sigma_cbc | Full strength utilised, up to 0.446 fck |
| Represents | Service condition, elastic range | Actual failure condition, ultimate range |
| Advantages of LSM | Disadvantages of LSM |
|---|---|
| Reflects true ultimate strength and realistic failure behaviour | Calculations are more involved than WSM |
| Separate, more rational treatment of uncertainty in loads and materials | Requires more careful detailing for ductility |
| More economical -- efficient use of concrete and steel | Serviceability must be checked as a separate step, not automatic |
| Provides explicit checks for both collapse and serviceability | Conceptually harder for beginners than simple elastic theory |
5. Characteristic Load and Characteristic Strength (5 Marks)
Characteristic load: a load that has only a small (95%) probability of not being exceeded during the structure's life. Typical loads: dead load, live load, wind load, earthquake load.
Characteristic strength: the value of material strength below which not more than a small percentage (commonly 5%) of test results are expected to fall.
Examples: M20 concrete has characteristic compressive strength of 20 MPa; Fe500 steel has characteristic yield strength of 500 MPa.
6. Partial Safety Factors (added -- high exam weightage)
Instead of using one overall factor of safety like WSM, LSM uses separate partial safety factors for loads and for materials. This allows a more realistic and independent treatment of the uncertainty in each quantity.
Partial Safety Factor for Materials, gamma_m
| Material | gamma_m (limit state of collapse) |
|---|---|
| Concrete | 1.5 |
| Steel | 1.15 |
Partial Safety Factor for Loads, gamma_f
| Load combination | DL | LL | WL / EL |
|---|---|---|---|
| DL + LL | 1.5 | 1.5 | -- |
| DL + LL + WL (or EL) | 1.2 | 1.2 | 1.2 |
| DL + WL (or EL), checking strength | 1.5 | -- | 1.5 |
| DL + WL (or EL), checking stability | 0.9 | -- | 1.5 |
7. Difference Between WSM and LSM (5 / 10 Marks)
| Working Stress Method | Limit State Method |
|---|---|
| Based on elastic theory | Based on ultimate strength and serviceability |
| Uses service (working) loads | Uses factored (ultimate) loads |
| Single overall factor of safety on material | Separate partial safety factors for loads and materials |
| Conservative and less economical | More economical |
| Less realistic representation of actual behaviour | More realistic representation of actual behaviour |
| Stress block is triangular (linear) | Stress block is rectangular-parabolic (non-linear) |
| Rarely used for modern RC design | Standard method for modern RC design (IS 456, NBC) |
8. Why is LSM Preferred? (5 / 10 Marks)
- Better reflects actual structural behaviour up to failure.
- Provides separate, explicit checks for both collapse and serviceability limit states.
- More economical use of concrete and steel through realistic stress distribution.
- Accounts for uncertainty in loads and materials independently, through partial safety factors.
- Widely adopted in modern design codes (IS 456:2000 in India, and the Nepal National Building Code, NBC).
Engineering Applications
LSM is used for the design of: residential buildings, high-rise buildings, bridges, water tanks, and industrial structures. WSM is still occasionally retained for water-retaining structures where crack-width control under service load is critical.
9. Other Design Philosophies (added -- for completeness)
Historically, RC design evolved through three broad philosophies:
| Method | Basis | Status |
|---|---|---|
| Working Stress Method (WSM) | Elastic theory, permissible stress | Older method, largely replaced |
| Ultimate Load Method (ULM) | Load factor applied to working load, section designed for ultimate (failure) strength only | Transitional method, did not separately check serviceability |
| Limit State Method (LSM) | Combines the strength focus of ULM with explicit serviceability checks, using partial safety factors | Current standard method |
LSM can be seen as ULM plus an explicit, independent serviceability check -- this is exactly why it is considered the most complete philosophy.
10. Model Answers by Weightage
Answer structure: (1) one line on the three basic design requirements (safety, serviceability, economy), (2) define WSM and state its principle flow, (3) define LSM and state its principle flow, (4) reproduce the comparison table in Section 7, (5) close with one line on why LSM is preferred (Section 8, point 1 and 3).
Answer: use the two advantage/disadvantage tables from Sections 3 and 4 side by side, then conclude that LSM's advantages outweigh its added complexity, which is why it is now the standard method.
Answer: give both definitions from Section 5, add the fk = fm - 1.65s relation, and mention the M20 / Fe500 examples for clarity.
Answer: list all five reasons from Section 8 as numbered points, expand each with one supporting sentence, and mention that IS 456:2000 and NBC both adopt LSM as the standard.
Answer: reproduce the comparison table in Section 7 directly -- this single table earns full marks for a 5-mark differentiate question.
11. MCQs
- A. Working Stress Method
- B. Limit State Method
- C. Ultimate Load Method only
- D. Plastic Design
- A. Plastic theory
- B. Elastic theory
- C. Yield theory
- D. Limit analysis
- A. Working Stress Method
- B. Limit State Method
- C. Both are identical
- D. Neither
- A. Tension only
- B. Compression only
- C. Both tension and compression equally
- D. Shear only
- A. 1.15
- B. 1.5
- C. 1.0
- D. 2.5
- A. 1.5
- B. 1.15
- C. 2.0
- D. 1.0
- A. 50 percent of the time
- B. 5 percent of the time
- C. 95 percent of the time
- D. Never
- A. Purely triangular
- B. Purely rectangular
- C. Rectangular-parabolic
- D. Trapezoidal
12. Interview Questions
- Why has the Working Stress Method largely been replaced by the Limit State Method?
- Why are separate safety factors used for loads and materials in LSM?
- What is the difference between collapse and serviceability limit states?
- Why is reinforced concrete stronger and more versatile than plain concrete?
- Can a structure satisfy the collapse limit state but fail the serviceability limit state? Explain with an example.
- (Added) Why is the partial safety factor for steel (1.15) smaller than that for concrete (1.5)?
- (Added) Why is the 1.65 factor used when computing characteristic strength from test data?
- Concrete: strong in compression, weak in tension. Steel: strong in tension and compression.
- Three design requirements: Safety, Serviceability, Economy.
- WSM: elastic theory, working loads, permissible stress, one factor of safety, triangular stress block.
- LSM: characteristic loads, partial safety factors, ultimate + serviceability checks, rectangular-parabolic stress block.
- gamma_m: concrete = 1.5, steel = 1.15.
- fk = fm - 1.65s (characteristic strength from test data).
- Modern RCC design follows LSM -- the standard method in IS 456 and the Nepal NBC.
Full Mock Test -- 20 Questions (Chapter 1)
Attempt all questions first, then expand each answer to check yourself.
1. What are the three basic requirements every structure must satisfy?
Safety, serviceability, and economy.
2. Why is steel embedded in concrete?
Concrete is weak in tension, so steel is added to resist the tensile forces while concrete resists compression.
3. Define Working Stress Method.
A method where stresses under service loads must not exceed the permissible stresses of the materials, keeping the structure elastic.
4. What theory is WSM based on?
Linear elastic theory.
5. What does WSM assume about concrete in tension?
Concrete is assumed to take no tension; all tension is resisted by steel.
6. Write the modular ratio formula.
m = 280 / (3 . sigma_cbc), or m = Es / Ec.
7. Define Limit State Method.
A method where a structure must satisfy all relevant limit states (collapse and serviceability) during its design life with an acceptable level of safety.
8. Name the two categories of limit states.
Limit state of collapse and limit state of serviceability.
9. What checks fall under the limit state of collapse?
Flexure, shear, compression, torsion, overall stability.
10. What checks fall under the limit state of serviceability?
Deflection, cracking, durability, vibration.
11. Define characteristic load.
A load that has only a small (5 percent) probability of being exceeded during the structure's life.
12. Define characteristic strength.
The value of material strength below which not more than 5 percent of test results are expected to fall.
13. Write the formula relating characteristic strength to mean strength.
fk = fm - 1.65s
14. What is the partial safety factor for concrete (gamma_m)?
1.5
15. What is the partial safety factor for steel (gamma_m)?
1.15
16. What is the load factor for DL + LL under the limit state of collapse?
1.5 on both dead load and live load.
17. Which stress block shape does WSM use, and which does LSM use?
WSM: triangular (linear elastic). LSM: rectangular-parabolic.
18. Name one advantage and one disadvantage of WSM.
Advantage: simple calculations. Disadvantage: uneconomical, does not reflect true ultimate strength.
19. Why is LSM considered more economical than WSM?
Because it uses the full realistic strength of concrete and steel up to near failure, rather than a conservative elastic permissible stress.
20. Which method is the current standard in IS 456 and the Nepal National Building Code?
Limit State Method (LSM).
One-Page Summary Sheet (last-minute revision)
| Topic | Key point to remember |
|---|---|
| Design requirements | Safety, Serviceability, Economy |
| Concrete vs Steel | Concrete strong in compression; Steel strong in tension and compression |
| WSM | Elastic theory, working loads, permissible stress, single factor of safety, triangular stress block |
| LSM | Characteristic loads, partial safety factors, ultimate + serviceability check, rectangular-parabolic stress block |
| Modular ratio | m = 280 / (3.sigma_cbc) |
| Characteristic strength | fk = fm - 1.65s (5 percent lower fractile) |
| gamma_m (materials) | Concrete = 1.5, Steel = 1.15 |
| gamma_f (DL+LL) | 1.5 on both dead load and live load |
| Why LSM preferred | Realistic behaviour, economy, separate load/material factors, standard in IS 456 and NBC |
Source notes covered the definitions, principles, characteristics, advantages, disadvantages and comparison of WSM and LSM. The following were added above because they are regularly tested in the Loksewa 7th level paper but were missing from the original notes: assumptions of WSM, modular ratio, typical permissible stress values, the WSM and LSM stress-block diagrams, the statistical definition and curve for characteristic strength, the full partial safety factor tables for loads and materials, and a short note on the historical Ultimate Load Method for context.
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