Why is the characteristic compressive strength fck reduced to 0.67 fck?
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I agree with the reason given by CB Sowmya, but only partially.
We don’t assume concrete strength to be 2/3rd of the characteristic strength, but there’s a logical reason behind it. She’s only stated the shape factor with the correct 20% decrease in strength, but there is also a size factor.
What happens is, first of all, due to slenderness, concrete cylinders have shown to have 80% of the characteristic strength corresponding to 150mm cubes. But also, even concrete cubes of sizes exceeding 450mm show only 85% the strength as compared to the standard 150mm ones. Since the concrete members will neither be cubes and not just 450mm, we need to take into account both the factors.
So, the new compressive strength becomes 0.8*0.85*fck = 0.68 fck. Now, 0.68 fck is very close to 0.67 fck or fck/1.5. So, for a rounder figure, we take it as 0.67 fck.
Note: This 1.5 isn’t the factor of safety. (FoS). A factor of 1.5 is further applied for design and the design strength becomes 0.67 fck / 1.5 = 0.446 fck.
The main reason for the decrease in characteristic strength is the quality control.why? Because in concrete, we can not achieve full or 100% strength as per our requirement due to casting in the site. However, there is weathering action and atmospheric effect on concrete, loss of water from it, etc. So concrete characteristic strength can be achieved up to 0.67fck according to is 456:2000. Whereas in the case of steel, due to casting in the lab, there are controlled conditions that can be achieved, so its characteristic strength can be achieved better than concrete i.e., fy.
By applying Fos, we are taking the design strength of concrete as .67fk/1.5 = 0.45fck.
It is the main reason.
The characteristic strength of concrete is the compressive strength below, in which not more than 5% of the test results should fall. It is generally represented as fck.
But during analysis, we reduce the characteristic strength of concrete and include a factor of safety 0.67. As a result, fck becomes 0.67fck.
In order to understand the reason, let us look into how concrete is tested for the characteristic strength in the first place.
A given concrete mix is prepared and cast into cube molds of side 150 mm. After sufficient curing, the cubes are tested for its compressive strength. In those test results, the compressive strength below which not more than 5% of the test results fell is taken as the characteristic strength. Let’s take that as fck.
If the same design mix was cast into a cylindrical mold of 150 mm diameter and 300 mm length and given the same curing, then it would have yielded only 80% of the compressive strength of that of the cubes, i.e., 0.8 fck. This because of the side effect due to the slenderness ratio in the cylinder.
There has been a 20% reduction in strength for a mere slenderness ratio, though both the specimens were monitored in the same laboratory conditions.
Answering your question, in reality, concrete is versatile. It can be cast into a number of shapes and sizes. In order to overcome the size effect on the concrete, in design, we assume that concrete can carry only 2/3rd of its characteristic strength. Thus we reduce fck to 0.67 fck.
Because fck that is adopted for laboratory work only which is fully controlled conditions and specified size but when we concern with building or other structure we have no such limits and control condition for that reason we will adopt for 1.5 for that is fck/1.5 = 0.667 fck that is material fos and again further FOS for design 1.5 as per IS 456 is applied so final design stress will be 0.667fck/1.5 = 0.444fck.