Design Philosophies for design of RC structures

To have a properly designed structure which fulfils all the requirements like proper durability, functioning, etc. We follow certain design philosophies. Every philosophy has some set of assumptions, and based on the premises, some ideas are suggested. So, let us start one by one.

Working Stress Method (WSM) :
Now it is an outdated method, and it is used occasionally. Today, it is used in a place where the complete analysis of the structure is complex, and no risk is allowed like an overhead water tank, chimney, etc.
This traditional method has the following assumptions:
  • The material behaves elastically, means stress-strain linear relation will be applicable.
  • The adequate factor of Safety is applied so that the working load is well below the material strength.
Here, we raised a term factor of Safety ( FOS) which is given by 

                   FOS =  Strength of material / Allowable strength of the material

Since in this method, it is assumed that materials will behave elastically so all the forces and stresses can be calculated using techniques and concepts of Strength of Materials. However, using it for a composite section where steel and concrete both are present, one more assumption is taken to have simplicity in the analysis. The bond between steel and concrete is assumed perfect, and the strain in steel and concrete is considered equal at the interface.
By assuming this strain compatibility, we can indirectly relate the stress in concrete and stress in steel using the term modular ratio (m):
    
             m = Stress in steel / Stress in concrete
                  = (strain in steel * elastic modulus of steel) / (strain in concrete * elastic modulus of concrete)
                  = elastic modulus of steel / elastic modulus of concrete

Limitations of WSM:
  • In it, we are not able to understand the relative importance of different loads like wind load, snow load, earthquake load, etc. These loads act with various uncertainties, and thus we end designing over conservative structures.
  • While designing beams, one can end up with a beam of significant depth which may not be feasible sometimes.

The Ultimate Load Method (ULM) of Design:
This method is a slight improvement in WSM, where non-linear behaviour of steel and concrete are taken into consideration. In this method, the ultimate loads are considered where stresses generated produce failure. Safety of structures is taken into account, and it is ensured by a term called Load Factor.
                                   Load Factor = Ultimate Load / Service Load
This load factor leads us to a different Factor of Safety based upon requirements. Thus, the major drawback of  WSM is removed.

Limitations of ULM:
  • This method uses ultimate loads while designing, and thus, one cannot ensure that both safety and serviceability together will be satisfactory.
  • This method uses non-linear analysis which is troublesome to analyse.
The Limit State of Design (LSM):
This is the design method which takes care of safety at ultimate loads and serviceability at design load, and thus it is the most used method in today's era. This thing is done by applying different FOS for different kind of building loads, and all of them are decided by studying them with separate approaches. 
Limit state refers to the state of  " about to collapse" beyond which the structure cannot be used practically means either the serviceability criteria will fail or structure thoroughly will fail.

Limit State of Collapse:
This deals with the strength of the structure, and it is studied using the following parameters:
  • Flexure
  • Compression 
  • Shear
  • Torsion
Limit State of Serviceability:
This limit state deals with the deformation of structure to that extent when the fabric becomes unserviceable. It is studied using the following parameters.
  • Deflection 
  • Excessive Vibration 
  • Corrosion
  • Cracking
Important Note - If the structure has attained limit state of serviceability then after removal of loads it can achieve its original position. However, it is not the case with the limit state of collapse.

Load and Resistance Factor Design (LRFD):
LRFD is the simplest method of design to use. In only one condition just needs to be satisfied.

                         
Design Resistance should be greater than or equal to Design Load.
Design resistance is multiplied by a factor (phi) which takes care of all the uncertainties of the property of material characteristics values like elastic modulus and Poisson's ratio. The numerical value of the resistance factor is always less than one.
The design load is multiplied by a factor (gamma) which take cares of the possibility of overloading, and thus this value is always greater than one.

IS 456:2000 Recommendations for LSM of Design:
1. Characteristic strength and characteristic load: 
Characteristic strength has been covered in greater detail in my previous blog. Follow this link to read about it:
http://gk1711.blogspot.com/2020/07/characteristic-strength-of-concrete.html

The characteristic load is that load which has 95% probability of not being exceeded during its lifetime.

2. Partial Safety Factor for material:
The design strength is always less than the ultimate strength of the material, and thus FOS is implemented.
For concrete fck is characteristic strength, but in design, the characteristic strength is taken as 0.67*fck.
This reduction is there because while testing, we prepare the cubic specimen, but in reality, there are many different shapes, and sizes and this reduction is to account that. 
Now addition FOS of 1.5 is taken for concrete and of 1.15 for steel. 
             Thus, design stress in concrete = 0.67*fck / 1.5 = 0.446*fck
                       design stress in steel = fy / 1.15 = 0.87*fy
 

At serviceability limit state FOS is taken as 1. Because we want to analyse the actual deflection and cracking in the building.

3. Partial Safty Factor for loads:
It can be seen in Table 18 of IS 456:2000:

For different load combinations, it is given as:
  • 1.5( DL + LL )
  • 1.5( DL + EQ )
  • 0.9DL + 1.5EQ
  • 1.2(DL + LL + EQ)
For serviceability criteria it is given as:
  • 1.0(DL + LL)
  • 1.0(DL + EQ)
  • DL + 0.8LL + 0.8EQ
           
                       
















Comments

  1. UnknownJuly 9, 2020 at 4:20 PM

    good going brother...very informative

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  2. gsk1506July 9, 2020 at 4:30 PM

    awesome content presented in a very interesting way!!!

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    1. UnknownJuly 9, 2020 at 5:59 PM

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