# Limit State Method,Working Stress Method and Ultimate Load Method

Limit State Method,Working Stress Method and Ultimate Load Method

**1) Limit States Method (LSM)**

- A limit state is a state of impending failure, beyond which a structure ceases to perform its intended function satisfactorily, in terms of either strength or serviceability; i.e., it either collapses or becomes unserviceable.
- Unlike WSM, which bases calculations on service load conditions alone, and unlike ULM, which bases calculations on ultimate load conditions alone, LSM aims for a comprehensive and rational solution to the design problem, by considering safety at ultimate loads and serviceability at working loads.
- LSM is described as a ‘semi-probabilistic’ method or a ‘Level 1 reliability’ method

** Partial load and material safety ****factor**

* Ultimate limit states – partial load factors:*

** UL = 1.5 (DL + LL)**

** UL = 1.5 (DL + QL) or (0.9DL + 1.5 QL)**

** UL = 1.2 (DL + LL + QL)**

* Ultimate limit states – material safety factors:*

** Concrete: gamma ****= 1.5**

** Steel: gamma**** = 1.15**

**Code Recommendations for Limit States Design**

** Characteristic Strength**

- 5 percentile strength
- to be taken as ‘specified yield strength’ in case of steel.

** Characterestic load**

- the load that “has a 95 percent probability of not being exceeded during the life of the structure”
- In the absence of statistical data regarding loads, the nominal values specified for dead, live and wind loads are to be taken from IS 875 (Parts 1–3) : 1987 and the values for ‘seismic loads’ (earthquake loads) from IS 1893 : 2002

**Partial Load Factors (main load combinations)**

*Ultimate limit states – partial load factors:*

** UL = 1.5 (DL + LL)**

** UL = 1.5 (DL + QL) or (0.9DL + 1.5 QL)**

** UL = 1.2 (DL + LL + QL)**

*Serviceability** limit states – partial load factors:*

** S****L = 1.****0**** (DL + LL)**

** S****L = 1.****0**** (DL + QL) **

** S****L = 1.****0 DL + 0.8**** (LL + QL)**

**2) Working Stress Method (WSM)**

- Traditional method of design
- Simple conceptual basis: The structural material behaves in a linear elastic manner, and that adequate safety can be ensured by suitably restricting the stresses in the material induced by the expected ‘working loads’ (service loads) on the structure.
- As the specified permissible (‘allowable’) stresses are kept well below the material strength (i.e., in the initial phase of the stress-strain curve), the assumption of linear elastic behaviour is considered justifiable.
- The ratio of the strength of the material to the permissible stress is often referred to as the
**factor of safety.** **Still in use for the design of bridges, chimneys, water tanks etc.**

Points in WSM

- Modular ratio is not a constant: increases with time due to creep of concrete.
- Assumption of linear elastic behaviour not always justifiable.
- WSM does not account for behaviour under loads that exceed service loads.
- WSM does not account for varying degrees of uncertainty in different loads under combined loading.
- Uneconomical section design

**3) Ultimate Load Method (ULM)**

- Evolved in the 1950s and became an alternative to WSM
- Also called the load factor method or the ultimate strength method
- The stress condition at the state of impending collapse of the structure is analysed, and the non-linear stress-strain curves of concrete and steel are made use of.
- No need for ‘modular ratio’.
- The safety measure in the design is introduced by an appropriate choice of the
**load factor**, defined as the ratio of the ultimate load (design load) to the working load.

**Advantages of ULM over WSM**

- The ultimate load method makes it possible for different types of loads to be assigned different load factors under combined loading conditions.
- This method generally results in more slender sections, and often more economical designs of beams and columns (compared to WSM), particularly when high strength reinforcing steel and concrete are used.

**Points in ULM**

- Satisfactory performance at ultimate loads does not guarantee serviceability at working loads (reduced stiffness due to slender sections).
- The use of the non-linear stress-strain behaviour for the design of sections becomes truly meaningful only if appropriate non-linear limit analysis is performed on the structure (significant inelastic behaviour and redistribution of stress resultants takes place at ultimate loads).

READ MORE

**Voids in Hydrated cement paste**

Some genuinely wonderful articles on this web site , thankyou for contribution.