## Working Stress Method | Limit State Method

### What is working stress method?

**Working Stress Method** – In this method, the structure is analysed by the classical elastic theory: the stresses in the members are considered for normal working load condition, and no attention is given to the conditions that axis at the time structural collapse. The working loads are fixed by limiting the stresses in concrete and steel to a fraction of the stresses at which the material fails, when tested as cubes and cylinders of concrete and bars of steel. The ratio which the yield stress of the steel or the cube strength of the concrete bars to the corresponding permissible or working stress is usually called factor of safety, which is a stress factor of safety.

#### Assumption of Working Stress Method (W.S.M)

The elastic theory of bending is based on the following assumptions and forms the basis of R.C.C. structures, which is given in Appendix-B of IS 456:2000. List down the assumptions of working stress method.

- A section which is plane before bending remains plane after bending.
- The concrete and steel reinforcement are perfectly bonded.
- All tensile stresses are taken up by steel and none by concrete.
- The stress-strain relationship of steel and concrete under working loads is a straight line.
- The moduli of elasticity of steel (Es) and concrete (Ec) are constant.
- The modular ratio (m) has the value 280/3൳cbc where, ൳cbc is the permissible compressive strength of concrete in bending in N/mm2.
- There are no initial stresses in steel and concrete.

### What is Limit State Method?

**Limit State Method** – Limit state design is a method of designing structures based on a statistical concept of safety and the associated statistical probability of failure. This method is oriented towards the satisfaction of serviceability and durability requirements. This new method makes a judicious combination of the working stress philosophy as well as the ultimate load philosophy limit of safety and serviceability requirements before failure occurs is called a limit state. Two prominent types of limit states are considered in the design.

- Limit state of collapse (strength limit state)
- Limit state of serviceability.

#### Assumption of Limit State Method (L.S.M)

Following are the Assumption of Limit State Method (L.S.M)

- Plane sections normal to the axis remain plane after bending.
- The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending.
- For design purpose, the compressive strength of concrete shall be assumed to be 0.67 fck/ 𝛄m . where, fck – characteristic strength of concrete & 𝛄m =1.5.
- The tensile strength of the concrete is ignored.
- There is a perfect bond between steel & concrete up to failure.
- Partial factor of safety for steel is 1.15.
- The maximum strain in the tension reinforcement in the section at failure shall not be less than, f y/1.15Es + 0.002.

## Compare between working stress methods (W.S.M.) & Limit state method (L.S.M.) for design.

Sl. No. | Working Stress Method | Sl. No. | Limit State Method |
---|---|---|---|

01. | It is based on the behaviour of structure at working load. | 01. | It is based on the behaviour of structure in different limit states ensuring adequate safety against each limit state. |

02. | It is referred to as deterministic. | 02. | It is referred to as nondeterministic. |

03. | Factor of safety is applied to the yield or ultimate stress to get permissible stress. | 03. | Partial safety factors are applied to characteristics values to get design value. |

04. | It is based on linear stress distribution. | 04. | It is based on nonlinear stress distribution taking inelastic strain into consideration. |

05. | Actual safety against ultimate loads not known | 05. | It overcomes the drawbacks of the working stress method. |

### FAQ’s

Q 01. What is working stress method?

Answer – In this method, the structure is analysed by the classical elastic theory: the stresses in the members are considered for normal working load condition, and no attention is given to the conditions that axis at the time structural collapse.

Q 02. IS Code for Working Stress Method for design of R.C.C. Structure?

Answer – Appendix-B of IS 456:2000.

Q 03. IS Code for Working Stress Method

Answer – Appendix-B of IS 456:2000.

Q 04. What is Limit State Method?

Answer – This method design structures based on a statistical concept of safety and the associated statistical probability of failure. This method is oriented towards the satisfaction of serviceability and durability requirements.

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