WORKING STRESS, ULTIMATE LOAD, AND LIMIT STATE METHODS-ALL YOU NEED TO KNOW

Working Stress method

This method of design was the oldest one. It is based on the elastic theory and assumes that both steel and concrete and elastic obey Hook’s law. It means that the stress is directly proportional to strain up to the point of collapse. Based on the elastic theory, and assuming that the bond between steel and concrete is perfect, permissible stresses of the materials are obtained. The basis of this method is that the permissible stresses are not exceeded anywhere in the structure when it is subjected to a worst combination of working loads.

In this method, the ultimate strength of concrete and yield strength or 0.2% proof stress of steel are divided by factors of safety to obtain permissible stresses. These factors of safety take into account the uncertainties in manufacturing of these materials. As per IS456, a factor of safety of 3 is to be used for bending compressive stresses in concrete and 1.78 for yield/proof strength of steel.

Advantages of the Working stress method of design:

1. This technique is simple in calculation and simple to understand.
2. This methodology provides the worst combination of loadings and higher efficiency throughout excessive conditions.
3. The serviceability requirements are sufficient for the working stress method.

Disadvantages of the working stress method are :

1. It assumes that concrete is elastic which is not true as the concrete behaves in-elastically even on a low level of stress.
2. It uses factors of safety for stresses only and not for loads. Hence, this method does not give true margin of safety with respect to loads because we do not know the failure load.
3. It does not use any factor of safety with respect to loads. It means, there is no provision for the uncertainties associated with the estimation of loads.
4. It does not account for shrinkage and creep which are time-dependent and plastic in nature.
5. This method gives uneconomical sections.
6. It pays no attention to the conditions that arise at the time of the collapse.
7. The working stress method is very simple and reliable but as per IS 456:2000, the working stress method is to be used only if it is not possible to use the limit state method of design. The working stress method is the basic method and its knowledge is essential for understanding the concepts of design.

Ultimate Load Method

In this method of design ultimate load or load at collapse is taken as the designed load. This collapse load is obtained by multiplying the working load with a suitable load factor. This method gives a fair idea of the exact margin of safety in terms of load.

The major disadvantage of the working stress method is that it does not give a true factor of safety against failure, to overcome it ultimate load method was invented. It is also called the load factor method or ultimate strength method, it is designed to overcome the shortcomings of the working load method.

Ultimate loads are obtained by magnifying the load at the working level by suitable load factors. In this method of design, stresses induced in the structure at the verge of failure (impending failure) are taken which means that the nonlinear part of the stress-strain curve is accounted for. Also to distinguish the importance of different loads, a term load factor is introduced.

 

Load factor= Ultimate load/working load

The concept of load factor gives freedom to assign different load factors based on the relative importance of the load which was a major drawback in the working stress method of design.

The concept of modular ratio is avoided in this method. This method usually gives lighter sections(economical designs of beams and columns) that are economical as compared to the Working Stress method of design.

Advantages of the Ultimate load method are :

(i)        The method is more realistic as compared to the working stress method because the ultimate load method takes into account the non-linear behavior of the concrete.

(ii)       This method gives exact margin of safety in terms of load, unlike the working stress method which is based on the permissible stresses which does not give any idea about the failure/collapse load.

(iii)     The sections designed by the ultimate load method are thinner and require less reinforcement. Hence the method is economical as compared to WSM.

Disadvantages  of the ultimate load method are :

(i)        This method gives very thin sections which lead to excessive deformations and cracking, thus making the structure unserviceable.

(ii)       No factors of safety are used for material stresses.

As the serviceability requirements are not satisfied at all in this method, the code replaced this method with the limit state method which takes into account the strength as well as serviceability requirements.

 

Limit State Method:

In the working stress method of design, the structure is designed at working loads only, and in the Ultimate load method of design, the structure is designed at ultimate load only. Limit State method of Design takes into account the safety at ultimate load and serviceability at service load.

In other words, this method of design is the combination of the working stress method of design and the ultimate load method of design. Different values of load factors are assigned for ultimate load and at working load. This method of design method is recommended as per Indian Standard Codes.

Limit State of Collapse

This limit state deals with the strength of the structure in terms of collapse, overturning, sliding, etc. Different limit states of collapse are Flexure, Compression, Shear, and Torsion.

Limit State of Serviceability

It deals with the deformation of the structure beyond which, the structure will become unserviceable. Different limit states of serviceability are Deflection, Vibration, Cracking, etc.

This method is based on the probabilities of variation in the loads and material properties. The limit state method takes into account the uncertainties associated with loads and material properties, and thus uses partial factors of safety to obtain design loads and design stresses.

The limit state method is based on predictions, unlike the working stress method which is deterministic in nature, and assumes that the loads, factors of safety and material stresses are known accurately. In the limit state method, the partial safety factors are derived using probability and statistics and are different for different load combinations, hence giving a more rational and scientific design procedure.

 

Advantages of the limit state method are :

1. It uses a modern way of designing a structure that encompasses a wide range of logical and technical considerations.
2. It includes separate considerations of different kinds of failure, types of material, and types of load.
3. This provides an economical design of the structure.

Disadvantages of the limit state method are :

1. It uses a possible approach for design so it cannot provide sufficient power and serviceability during the worst combination of loads and peak conditions.