Q.: What is size effect of concrete? What is its role in determining the material strength of concrete?***
A.: The characteristic strength of concrete is determined from the results of tests conducted on cube specimens of 150 mm dimension. The dimensions of concrete structures or in members of structure are different and widely varying. This has an effect on the strength of concrete in the structure. This is known as size effect.
         Due to the size effect, the characteristic strength of concrete is reduced to 2/3 of its value and then further divided by the partial safety factor of the concrete (γm = 1.5) to get the design strength of concrete (fd)..
                                    fd = (2/3)fck/ 1.5 =0.45fck

Q.: Give four reasons to justify the design of structures by limit state method.

A.: The four reasons are:
           (i) Concept of separate partial safety factors of loads of different combinations in the two limit state methods.
          (ii) Concept of separate partial safety factors of materials depending on their quality control during preparation. Thus, γm for concrete is 1.5 and the same for steel is 1.15. This is more logical than one arbitrary value in the name of safety factor.               
         (iii) A structure designed by employing limit state method of collapse and checked for other limit states will ensure the strength and stability requirements at the collapse under the design loads and also deflection and cracking at the limit state of serviceability. This will help to achieve the structure with acceptable probabilities that the structure will not become unfit for the use for which it is intended.
          (iv) The stress block represents in a more realistic manner when the structure is at the collapsing stage (limit state of collapse) subjected to design loads.

Q.: Why the partial safety factor of  concrete is taken (1.5) more than that of steel (1.15)?
A.: Because the steel for reinforcement is produced in steel plants and commercially available in specific diameters with expected better quality control than that of concrete (size effect of concrete).........

DESIGN OF CONCRETE STRUCTURES

Introduction
In any method of design, the following are the common steps to be followed:
(i) To assess the dead loads and other external loads and forces likely to be applied on the structure,
(ii) To determine the design loads from different combinations of loads,
(iii) To estimate structural responses (bending moment, shear force, axial thrust etc.) due to the design loads,
(iv) To determine the cross-sectional areas of concrete sections and amounts of reinforcement needed.

There are three methods of design:-
   (1) Working stress method,
   (2) Ultimate load method and
   (3)* Limit state method.
        
        Limit state method is one of the three methods of design as per IS 456:2000. The code has put more emphasis on this method by presenting it in a full section (Section 5), while accommodating the working stress method in Annex B of the code (IS 456). Considering rapid development in concrete technology and simultaneous development in handling problems of uncertainties, the limit state method is a superior method where certain aspects of reality can be explained in a better manner.

Limit State Method

What are limit states?
        Limit states are the acceptable limits for the safety and serviceability requirements of the structure before failure occurs. The design of structures by this method will thus ensure that they will not reach limit states and will not become unfit for the use for which they are intended. It is worth mentioning that structures will not just fail or collapse by violating (exceeding) the limit states. Failure, therefore, implies that clearly defined limit states of structural usefulness has been exceeded.
Limit state of collapse was found / detailed in several countries in continent fifty years ago. In 1960 Soviet Code recognized three limit states: (i) deformation, (ii) cracking and (iii) collapse.

How many limit states are there?
   (1) Limit state of collapse:- It deals with strength and stability of the structure under maximum design load..
 and
   (2) Limit state of serviceability:- It deals with deflection and cracking under service load; durability under working environment, stability, fire resistance etc...

Partial safety factors:-


The characteristic values of loads is the value of load and  is assumed that in ninety-five per cent cases the characteristic loads will not be exceeded during the life of the structures . However, structures are subjected to overloading also. Hence, structures should be designed with loads obtained by multiplying the characteristic loads with suitable factors of safety depending on the nature of loads or their combinations, and the limit state being considered. These factors of safety for loads are termed as partial safety factors (γf) for loads. Thus, the design loads are calculated as
                   (Design load Fd) = (Characteristic load F) (Partial safety factor for load γf)

Values of partial safety factor γf  for loads(DL, LL, WL, EL, etc )  are given in the IS code.

            Also, The characteristic strength of a material as obtained from the statistical approach is the strength of that material below which not more than five per cent of the test results are expected to fall . However, such characteristic strengths may differ from sample to sample also. Accordingly, the design strength is calculated dividing the characteristic strength further by the partial safety factor for the material (γm), where γm depends on the material and the limit state being considered. Thus,
                  
           Design strength of the materials(fd)= characteristic stength of the material/ partial safety factor 

      Clause 36.4.2 of IS 456:2000 states that partial safety factor for concrete and steel should be taken as 1.5 and 1.15, respectively when assessing the strength of the structures or structural members employing limit state of collapse. However, when assessing the deflection, the material properties such as modulus of elasticity should be taken as those associated with the characteristic strength of the material. It is worth mentioning that partial safety factor for steel (1.15) is comparatively lower than that of concrete (1.5) because the steel for reinforcement is produced in steel plants and commercially available in specific diameters with expected better quality control than that of concrete.
      Further, in case of concrete the characteristic strength is calculated on the basis of test results on 150 mm standard cubes. But the concrete in the structure has different sizes. To take the size effect into account, it is assumed that the concrete in the structure develops a strength of 0.67 times the characteristic strength of cubes. Accordingly, in the calculation of strength employing the limit state of collapse, the characteristic strength (fck) is first multiplied with 0.67 (size effect) and then divided by 1.5 (γm for concrete) to have 0.446 fck as the maximum strength of concrete in the stress block.***