**5. Comparison of the theoretical, numerical, and experimental results**

Specimen 2JGL-5-2. These fracture characteristics of 2JGL-5-2 were similar to those of the previous specimen. Their fracture characteristics differed in two ways: (1) the magnitudes of load at characteristic points were higher than those observed for 2JGL-1-1. For example, the primary fractures opened again when the load was 60 kN and new fractures arose extensively in the shear-bending segment as the load was reached and (2) the four peaks were more obvi-

The phenomena described above are consistent with the stress contour plots (**Figure 7**), dem-

Ductility is an important indicator considered in seismic design for beams. It is usually mea-

*μ* = *u*/*y* (14)

where △*y* is the displacement when the longitudinal rebars in the beam begin yielding and △*u* is the displacement when the load is decreased to 90% of the maximum load. The ductility

**Table 5** reveals that the RC beams had much higher ductility than the unreinforced beams. The specimens with small tendon cross-sectional areas and small initial tendon forces exhibited slightly higher ductility than the specimens with larger tendon cross-sectional areas and

The analysis performed earlier suggests that after being reinforced by DWM external prestressing, the SSB exhibited slightly increased stiffness, improved fracture strength, yield strength, and ultimate strength and significantly increased ductility. This is because the mechanical behavior of the RC beam was constrained by the external prestressing force.

**1.** It took longer times for the primary microfractures in the concrete to become through-

**2.** The beam formed an inverted arch. When an external load was applied, a part of the load

**3.** At a point during the experiment, reinforcement system composed of the external prestressing tendons, web members, and beam-bottom anchorage created a "net bag," which enclosed the working segment of the SSB and caused redistribution of stress at

**4.** Throughout the experiment, the web members served as an elastic support for the beam bottom and resulted in redistribution of internal force in the SSB. The support force pro-

vided by the elastic support tended to increase with increasing external load.

ous in the load-deflection curve for 2JGL-5-2 (See 2JGL-5-2 in **Figure 12**).

onstrating the reliability of the analytic method.

sured by displacement-based ductility coefficient, *μ*, [13]:

coefficients of the test beams are presented in **Table 5**.

would serve to offset the arch displacement.

*4.2.4. Ductility of RC beam*

96 New Trends in Structural Engineering

greater initial tendon forces.

**4.3. Summary**

going fractures.

cross-section.

**Figure 14** compares the theoretical, numerical, and experimental load-deflection curves for specimens JGL-1-1 and JGL-5-2.

Due to the fundamental assumptions mentioned earlier, the theoretical values for the stage of elastic deformation were slightly smaller than corresponding experimental and numerical values, thus ensuring the safety of the specimens. This demonstrates that the theoretical results can accurately describe the mechanical behavior of the specimens and the calculation method is reliable. For the stage of plastic deformation, the theoretical values were significantly greater than the experimental and numerical values, indicating that the theoretical calculation cannot provide reliable guidance.

The experimental data were highly consistent with the numerical data for both elastic deformation and plastic deformation stages, demonstrating the validity of the numerical method proposed.

**Figure 15** compares the structural performance extracted from all experimental curves with the structural performance of the beam models observed in numerical analysis. The findings are as follows:


**Figure 14.** Comparison of theoretical, simulated, and experimental values.

**References**

pp. 12-15. (in Chinese)

2005;**27**(9-10):945-957

Chinese)

Edition). 2002;**19**(4):86-91. (in Chinese)

and Buildings. 2004;**157**(4):263-278

Journal. 2007;**40**(12):28-37 (in Chinese)

Science & Technology (BISSTECH 2015)

2013;**30**(2):89-95. (in Chinese)

2014;**47**(10):1617-1631

[1] Yu S. Engineering Structural Detection and Reinforcement. Beijing: Science Press; 2005.

Mechanical Performance of Simple Supported Concrete Beam-Cable Composite Element...

http://dx.doi.org/10.5772/intechopen.76517

99

[2] Ting ZY, Jisheng Q, Hengwei H. Survey on research of external pre-stressed concrete beams. Journal of Huazhong University of Science and Technology (Urban Science

[3] Lou TJ, Lopes AV, Lopes SMR. Influence of span-depth ratio on behavior of externally

[4] Ahmed G, Beeby AW. Factors affecting the external pre-stressing stress in externally strengthened pre-stressed concrete beams. Cement and Concrete Composites.

[5] Jinsheng D, Guangda Q. Ultimate stress in external tendons-comments on the existing

[6] He Z, Zhao L, Wang J. A unified algorithm for calculating stress increment of external tendons based on deflection. China Civil Engineering Journal. 2008;**41**(9):90-96. (in

[7] Ghallab A, Beeby AW. Calculating stress of external pre-stressing tendons. Structures

[8] Wu G, Wu Z, Yang W, Jianbiao J, Yi C. Experimental study on flexural strengthening of RC beams with pre-stressed high strength steel wire ropes. China Civil Engineering

[9] Yu S, Wang Y, Aipeng LI. Internal force analysis of external pre-stressed cable of tilted

[10] Zhu H, Yang Y, Fan W. External Prestressing Bridge Reinforcement Technology Review. International Conference on Engineering Technology and Application (ICETA 2015) [11] Astawa MD, Raka IGP, Tavio. Moment Contribution Capacity of Tendon Prestressed Partial on Concrete Beam-column Joint Interior According to Provisions ACI 318-2008 Chapter 21.5.2.5 (c) Due to Cyclic Lateral Loads. The 3rd Bali International Seminar on

[12] Xu L, Xu F, Hao Z, Wenke Q. The design and test study on pre-stressed railway concert beam -bridge strengthened by externally draped CFRP tendon. Engineering Mechanics.

[13] Vasudevan G, Kothandaraman S. Experimental investigation on the performance of RC beams strengthened with external bas at soffit. Materials and Structures.

pre-stressed concrete beams. ACI Structural Journal. 2012;**109**(5):687-695

typical methods. Engineering Mechanics. 2010;**27**(9):63-68 (in Chinese)

belly poles. Engineering Mechanics. 2011;**28**(5):143-148. (in Chinese)

**Figure 15.** Comparison of simulation value and test value of related specimens. (a) Dip 200 All values contrast and (b) dip 250 All values contrast.
