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Figure 3.12. Comparison of "basic" and "approximate" design curves

In clause 3.1.6 (4) of EC2 as well the possibility is offered to work with a rectangular stress distribution, see fig. 12. This requires the introduction of a factor A for the depth of the compression zone and a factor n for the design strength, see Fig. 3.13.

Figure 3.13. Rectangular stress distribution

Figure 3.13. Rectangular stress distribution

As a basis for the derivation of X and n the parabolic-rectangle stress strain relation is used, see Fig. 3.11. As an example the values X and n are calculated for the strength classes C50 and lower. For concrete's in the strength classes < C50 the characteristic strains are £c2 = 2.0 %o and £c2u = 3.5%. Now a rectangular stress block is searched for, which gives the same resulting force at the same location.

Figure 3.14. Derivation of rectangular stress block from the parabolic-rectangle stress distribution for concrete strength class < C50

For the parabolic-rectangle stress distribution the resulting force is 0.81 xbfcd and the distance of this force to the top is 0.415x, where x is the height of the compression area.

In order to obtain a rectangular stress block with its resultant at the same position, the depth of the compression area should be Ax = 2*0.415x = 0.83x, so A = 0.83.

In order to get the same magnitude of the resultant, the maximum stress is defined as ifcd.

The resultant force for the rectangular stress block is (Ax)b(nfcd). Since this force should be equal to

0.83xbfcd, the value of | follows from | = 0.81/A = 0.98

Carrying out this calculation for all concrete strength classes, with the values for £c3 and £c3u taken from table 3.5 [table 3.1 EC2], the values | and X shown in fig. 3.15 are obtained.

calculated

----apprewmation

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