2.5.3 Essay

2.6.5.2. Part 2: For the descending part of tension stiffening model relationcurve " Tension-softening":

A load-ԑ for the tested specimen is shown in Fig. (4.43), where the average of three specimens P-16-5, P-16-6 and P-16-7 is used as an example. The average of three specimens Ø12, the average of three specimens Ø 16 and the results of specimens Ø 18 are used in this study. in the same Fig., the response of steel alone is a straight line. The shaded area simulate the FBLWC contribution in the pre-cracking and the post-cracking ranges. At the given load P and the corresponding ԑm, the force carried by the Conc. Pc can be determined from the test results as eq.(4.7):

Thus, the effective tensile σ ft , for this given average ԑm, can be determined as following eq. (4.8). ft = Pc / (Ac + n.As) (4.8) Using equations (4.5), (4.7) and (4.8), the effective tensile σ is calculated for all the tested specimens with single steel bar in the middle of the prism with variable reinforcement ratio. And all the

The tested proposed σ-ԑ relationcurve can be represented by the following linear function up to average ԑ. The relation is taking into account the different reinforcement ratio of the three specimens, as shown in eq. (4.io). ft = fcr+ ρ x 865 (ԑcr- ԑm) (4.9) where ft is the effective tensile σ of the Conc. at any given ԑ in tension ԑm. fcr is the cracking strength of Conc. at which the first crack is initiated. And ρ is the reinforcement ratio. The effectiveness of this relationship in simulating the behavior of various segments can be determined by using this relationcurve as input for any numerical analysis solution for foam balls lightweight Conc. of Ain Shams University and comparing the output with measured values.

4.2.6.6. Determination of actual tensile σ-ԑ relationcurve of foam balls lightweight