*2.3. Monotonic Cycle Loading Test* 2.3.1. Test Device and Loading System

*2.3. Monotonic Cycle Loading Test* 

#### 2.3.1. Test Device and Loading System This test loading device adopts the CMT microcomputer controlled electro-hydraulic

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This test loading device adopts the CMT microcomputer controlled electro-hydraulic servo universal testing machine in the Structure Laboratory of Zhengzhou University, and the measuring range of force sensor is 2000 kN. The test adopts four-point bending loading, and the force were applied to the trisection point of the beam by the distributing beam. All test data are automatically collected by the test software of Power Test V3.4. The loading device is shown in Figure 6. The measuring points of strain of reinforcements are arranged in the middle of the span. servo universal testing machine in the Structure Laboratory of Zhengzhou University, and the measuring range of force sensor is 2000 kN. The test adopts four-point bending loading, and the force were applied to the trisection point of the beam by the distributing beam. All test data are automatically collected by the test software of Power Test V3.4. The loading device is shown in Figure 6. The measuring points of strain of reinforcements are arranged in the middle of the span.

(**b**)

**Figure 6.** Test setup for quasi-static cyclic tests. (**a**) Sketch of the test loading device. (**b**) Photograph of the test setup. **Figure 6.** Test setup for quasi-static cyclic tests. (**a**) Sketch of the test loading device. (**b**) Photograph of the test setup.

#### 2.3.2. Loading Protocol 2.3.2. Loading Protocol

Using variable amplitude displacement control loading mode. Firstly, the test specimen should be preloaded once before the formal loading, in order to check whether the loading equipment and instruments can work normally. The value of preloading should be less than the design cracking load *P*cr. Then, the vertical ultimate displacement Δ in the middle of the span should be determined by monotonic loading test on the specimen of SJ-5. The results of monotonic loading test on the specimen of SJ-5 shows that the Δ is about 15 mm. Therefore, in the formal loading, the displacement of the initial loading cycle is 1.5 mm, and then the displacement of each cycle increases by 1.5 mm progressively. Using variable amplitude displacement control loading mode. Firstly, the test specimen should be preloaded once before the formal loading, in order to check whether the loading equipment and instruments can work normally. The value of preloading should be less than the design cracking load *P*cr. Then, the vertical ultimate displacement ∆ in the middle of the span should be determined by monotonic loading test on the specimen of SJ-5. The results of monotonic loading test on the specimen of SJ-5 shows that the ∆ is about 15 mm. Therefore, in the formal loading, the displacement of the initial loading cycle is 1.5 mm, and then the displacement of each cycle increases by 1.5 mm progressively. The monotonic cycle loading protocol is shown in Figure 7.

The monotonic cycle loading protocol is shown in Figure 7.

**Figure 7.** Monotonic cycle loading protocol. **Figure 7.** Monotonic cycle loading protocol.

#### **3. Test Results and Analysis** *Materials* **2021**, *14*, x FOR PEER REVIEW 8 of 19

**3. Test Results and Analysis**  *3.1. Failure Process*

*3.1. Failure Process*  (1) SJ-1 (Strengthened by Steel reinforced concrete)

(1) SJ-1 (Strengthened by Steel reinforced concrete) Six cracks were observed in the pure bending section of the specimen. As the load increased, the width of the cracks increased, and finally part of the concrete was crushed. After unloading, the number of cracks and the crack widths remain basically unchanged, Six cracks were observed in the pure bending section of the specimen. As the load increased, the width of the cracks increased, and finally part of the concrete was crushed. After unloading, the number of cracks and the crack widths remain basically unchanged, and the ultimate bearing capacity was 32.16 kN. The failure mode of the specimen after unloading is shown in Figure 8a. It can be clearly seen from Figures 8 and 9 that there are no obvious cracks at the connection interface between the enlarged section and existing beam section of all specimens, which indicates that the bonding performance between the enlarged section and existing beam section is reliable. After strengthening, the enlarged section and existing beam section are commonly worked together and deformed harmoniously.

ened section at the bottom of the beam until the end of loading. In the existing beam sec-**Figure 8.** Failure modes of specimens. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4. **Figure 8.** Failure modes of specimens. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

tion, there were still main cracks that appeared. With the increase of loading cycle, the (2) SJ-2 (Strengthened by SMA reinforced concrete)

number of micro-cracks in the strengthened section of the specimen increased, but the width of these cracks increased slowly. Finally, more than 70 micro-cracks were counted in the pure bending section of the strengthened section. The crack distribution of specimen SJ-3 was shown in the Figure 9. After unloading, most of micro-cracks were closed, only 3 cracks were still observed, and the ultimate bearing capacity of the specimen was 25.31 The failure mode of specimen SJ-2 was similar to that of SJ-1, and the number of vertical cracks observed by SJ-2 is slightly reduced. After unloading, the maximum crack width at the beam bottom decreased, some small cracks were closed, and the ultimate bearing capacity was 27.17 kN. The failure mode of the specimen after unloading is shown in Figure 8b.

Due to the characteristics of ECC, there was no obvious main crack in the strength-

kN. The failure mode of the specimen after unloading is shown in Figure 8c. (3) SJ-3 (Strengthened by SMA reinforced ECC)

**Figure 9.** The crack distribution of SJ-3.

SJ-1 and SJ-2 are the worst.

strengthening beams.

seen that:

bar.

(4) SJ-4 (Strengthened by steel reinforced ECC) ECC material was also used in specimen SJ-4, so the development of cracks during Due to the characteristics of ECC, there was no obvious main crack in the strengthened section at the bottom of the beam until the end of loading. In the existing beam section,

The load–displacement curves for all the specimens are shown in Figure 10. By comprehensively comparing the load–displacement curves of the four specimens, it can be

(1) Comparing the number of loading cycles of the load–displacement curves of the four specimen, it can be found that the number of loading cycles of beams strengthened by ECC is more than that of beams strengthened by concrete, indicating that strengthening with ECC can significantly improve the ductility of specimens. Among all tested members, the ductility of SJ-3 is the best, followed by SJ-4, and the ductility of

(2) The ultimate bearing capacities of SJ-1 and SJ-4 are higher than that of the other two specimens, because both SJ-1 and SJ-4 are reinforced by steel bars. The total tensile capacity of steel reinforcements is slightly greater than that of SMA bars, and the bond strength of ribbed steel bar in concrete or ECC is better than that of the SMA

(3) The residual deformation of SJ-2 and SJ-3 after unloading is smaller than the other two specimens. However, the self-recovery performances of SJ-2 and SJ-3 are still not obvious, and the super-elasticity of SMA is not significantly displayed while

ure mode of the specimen after unloading is shown in Figure 8d.

loading was basically similar to SJ-3, mainly a large number of fine micro-cracks. With the

bending section of the strengthened section. The width of the cracks was small, and it appeared as obvious multiple micro-cracking when it failed. After unloading, the crack width was basically unchanged, and the ultimate bearing capacity was 30.16 KN. The fail-

there were still main cracks that appeared. With the increase of loading cycle, the number of micro-cracks in the strengthened section of the specimen increased, but the width of these cracks increased slowly. Finally, more than 70 micro-cracks were counted in the pure bending section of the strengthened section. The crack distribution of specimen SJ-3 was shown in the Figure 9. After unloading, most of micro-cracks were closed, only 3 cracks were still observed, and the ultimate bearing capacity of the specimen was 25.31 kN. The failure mode of the specimen after unloading is shown in Figure 8c. (**c**) (**d**) **Figure 8.** Failure modes of specimens. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

(**a**) (**b**)

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It can be clearly seen from Figures 8 and 9 that there are no obvious cracks at the

connection interface between the enlarged section and existing beam section of all specimens, which indicates that the bonding performance between the enlarged section and existing beam section is reliable. After strengthening, the enlarged section and existing

beam section are commonly worked together and deformed harmoniously.

**Figure 9.** The crack distribution of SJ-3. **Figure 9.** The crack distribution of SJ-3.

## (4) SJ-4 (Strengthened by steel reinforced ECC)

*3.2. Load–Displacement Curves*  The load–displacement curves for all the specimens are shown in Figure 10. By comprehensively comparing the load–displacement curves of the four specimens, it can be seen that: (1) Comparing the number of loading cycles of the load–displacement curves of the four ECC material was also used in specimen SJ-4, so the development of cracks during loading was basically similar to SJ-3, mainly a large number of fine micro-cracks. With the increase of the load, the number of micro-cracks in the strengthened section of the specimen increased obviously. Finally, more than 40 micro-cracks were counted in the pure bending section of the strengthened section. The width of the cracks was small, and it appeared as obvious multiple micro-cracking when it failed. After unloading, the crack width was basically unchanged, and the ultimate bearing capacity was 30.16 KN. The failure mode of the specimen after unloading is shown in Figure 8d.

specimen, it can be found that the number of loading cycles of beams strengthened by ECC is more than that of beams strengthened by concrete, indicating that strengthening with ECC can significantly improve the ductility of specimens. Among all tested members, the ductility of SJ-3 is the best, followed by SJ-4, and the ductility of It can be clearly seen from Figures 8 and 9 that there are no obvious cracks at the connection interface between the enlarged section and existing beam section of all specimens, which indicates that the bonding performance between the enlarged section and existing beam section is reliable. After strengthening, the enlarged section and existing beam section are commonly worked together and deformed harmoniously.

#### SJ-1 and SJ-2 are the worst. *3.2. Load–Displacement Curves*

(2) The ultimate bearing capacities of SJ-1 and SJ-4 are higher than that of the other two specimens, because both SJ-1 and SJ-4 are reinforced by steel bars. The total tensile capacity of steel reinforcements is slightly greater than that of SMA bars, and the The load–displacement curves for all the specimens are shown in Figure 10. By comprehensively comparing the load–displacement curves of the four specimens, it can be seen that:


capacity of steel reinforcements is slightly greater than that of SMA bars, and the bond strength of ribbed steel bar in concrete or ECC is better than that of the SMA bar.

(3) The residual deformation of SJ-2 and SJ-3 after unloading is smaller than the other two specimens. However, the self-recovery performances of SJ-2 and SJ-3 are still not obvious, and the super-elasticity of SMA is not significantly displayed while strengthening beams. *Materials* **2021**, *14*, x FOR PEER REVIEW 9 of 19

**Figure 10.** Load displacement curves (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4. **Figure 10.** Load displacement curves (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

*3.3. Skeleton Curves 3.3. Skeleton Curves*

The skeleton curves of 4 specimens are shown in Figure 11. By comprehensively comparing those skeleton curves, it can be seen that: The skeleton curves of 4 specimens are shown in Figure 11. By comprehensively comparing those skeleton curves, it can be seen that:


(3) After reaching the ultimate bearing capacity, the bearing capacity of SJ-3 decreases significantly slower than that of the other three members, followed by SJ-4, and SJ-1 decreases the fastest. It indicates that the ductility of SJ-3 and SJ-4 is significantly im-

proved while being strengthened by ECC.

(3) After reaching the ultimate bearing capacity, the bearing capacity of SJ-3 decreases significantly slower than that of the other three members, followed by SJ-4, and SJ-1 decreases the fastest. It indicates that the ductility of SJ-3 and SJ-4 is significantly improved while being strengthened by ECC. *Materials* **2021**, *14*, x FOR PEER REVIEW 10 of 19

**Figure 11.** Skeleton curves. **Figure 11.** Skeleton curves.

#### *3.4. Maximum Crack Width*

*3.4. Maximum Crack Width*  The curves of maximum crack width distribution during loading and unloading are The curves of maximum crack width distribution during loading and unloading are shown in Figure 12. The following conclusions can be drawn from the comparison between those curves:


ment of crack width in the tensile zone of the beam section.

(3) By comparing the values of maximum crack width for all specimens, the maximum

crack widths of SJ-3 and SJ-4 are much smaller than the other 2 specimens, which are

of SJ-3 can be continuously loaded until the vertical displacement in mid-span reaches 42 mm (the 28th loading cycle). The maximum crack width of SJ-3 at this time is only 1078 μm, which is still less than the maximum crack widths of SJ-1 and SJ-2. It proves that using ECC as reinforcement layer can effectively control the develop-

**Figure 12.** The curves of maximum fracture width under loading and unloading. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4. **Figure 12.** The curves of maximum fracture width under loading and unloading. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

#### *3.5. Number of Cracks 3.5. Number of Cracks*

The curves of number of cracks for each specimen is shown in Figure 13. By comparing the results of data analysis, it can be found that: The curves of number of cracks for each specimen is shown in Figure 13. By comparing the results of data analysis, it can be found that:


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#### the bonding performance between SMA and concrete is poor, so the super-elasticity of SMA is not effective under this situation. the bonding performance between SMA and concrete is poor, so the super-elasticity of SMA is not effective under this situation.

**Figure 13.** The curves of number of cracks under loading and unloading. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4. **Figure 13.** The curves of number of cracks under loading and unloading. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

#### *3.6. Mid-Span Deflection 3.6. Mid-Span Deflection*

The curves of mid-span deflection for all the specimens are shown in Figure 14. By comparing these curves, it can be seen that as the loading cycle increases, the mid-span deflection of the specimen increases linearly. After unloading, the mid-span deflections of the four specimens recover, while the self-recovery performance of SJ-3 is obviously the best, followed by SJ-2 and SJ-4, and the value of recovered mid-span deflection for SJ-1 is the minimum. The maximum recovery rates for all components are 28.4% for SJ-1, 42.7% for SJ-2, 26.1% for SJ-3, and 27.1% for SJ-4, respectively. It indicates that: (1) The mid-span deflection of the strengthened beam can be actively recovered by use of shape memory effect and super-elasticity of SMA; (2) The self-recovered value of mid span deflection of beams strengthened with ECC is obviously better than that of concrete beams, which proves that the failure mode of fine cracks of ECC can provide good conditions for selfrecovery of the strengthened beams after unloading; (3) The recovery value of mid span deflection of ECC members is large, but due to the low stiffness of ECC members, the recovery rate is less than that of concrete members; (4) The recovery value of mid span The curves of mid-span deflection for all the specimens are shown in Figure 14. By comparing these curves, it can be seen that as the loading cycle increases, the mid-span deflection of the specimen increases linearly. After unloading, the mid-span deflections of the four specimens recover, while the self-recovery performance of SJ-3 is obviously the best, followed by SJ-2 and SJ-4, and the value of recovered mid-span deflection for SJ-1 is the minimum. The maximum recovery rates for all components are 28.4% for SJ-1, 42.7%for SJ-2, 26.1% for SJ-3, and 27.1% for SJ-4, respectively. It indicates that: (1) The mid-span deflection of the strengthened beam can be actively recovered by use of shape memory effect and super-elasticity of SMA; (2) The self-recovered value of mid span deflection of beams strengthened with ECC is obviously better than that of concrete beams, which proves that the failure mode of fine cracks of ECC can provide good conditions for self-recovery of the strengthened beams after unloading; (3) The recovery value of mid span deflection of ECC members is large, but due to the low stiffness of ECC members, the recovery rate is less than that of concrete members; (4) The recovery value of mid span deflection of ECC

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#### members is large, but due to the low stiffness of ECC members, the recovery rate is less than that of concrete members deflection of ECC members is large, but due to the low stiffness of ECC members, the recovery rate is less than that of concrete members

**Figure 14.** The curves of mid-span deflection. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4. **Figure 14.** The curves of mid-span deflection. (**a**) SJ-1; (**b**) SJ-2; (**c**) SJ-3; (**d**) SJ-4.

#### *3.7. Energy Consumption Capacity 3.7. Energy Consumption Capacity*

The energy consumption capacity of the specimen can be determined by the area enveloped by the load–displacement curve of each level of loading. The curves of energy consumption capacity for all the specimens are shown in Figure 15. It can be seen that the energy consumption capacity of the specimen SJ-3 is the highest. Before the 22nd cycle, the energy dissipation capacity is mainly borne by ECC, which is in the strain-hardening stage. At the 23rd cycle, the ECC layer began to failure, the energy consumption capacity is mainly borne by SMA at this moment, and it is significantly reduced. Before the specimen is completely failed, the values of energy consumption for all specimens are basically the same. This is because the steel bars inside the original beam section are still retained after strengthening of the beams. With the reinforcement of the enlarged section, all the reinforcements at the bottom section of the beam do not yield obviously during the tests. Therefore, there is no obvious difference in the energy consumption capacity between each specimen. The energy consumption capacity of the specimen can be determined by the areaenveloped by the load–displacement curve of each level of loading. The curves of energy consumption capacity for all the specimens are shown in Figure 15. It can be seen that the energy consumption capacity of the specimen SJ-3 is the highest. Before the 22nd cycle, the energy dissipation capacity is mainly borne by ECC, which is in the strain-hardening stage. At the 23rd cycle, the ECC layer began to failure, the energy consumption capacity is mainly borne by SMA at this moment, and it is significantly reduced. Before the specimen is completely failed, the values of energy consumption for all specimens are basically the same. This is because the steel bars inside the original beam section are still retained after strengthening of the beams. With the reinforcement of the enlarged section, all the reinforcements at the bottom section of the beam do not yield obviously during the tests. Therefore, there is no obvious difference in the energy consumption capacity between each specimen.

**Figure 15.** The curves of energy consumption capacity. **Figure 15.** The curves of energy consumption capacity.

#### *3.8. Mechanical Performance of Reinforcements 3.8. Mechanical Performance of Reinforcements*  Figure 16 shows the load–strain relationship between the reinforcement in the en-

*3.8. Mechanical Performance of Reinforcements*  Figure 16 shows the load–strain relationship between the reinforcement in the enlarged section and the steel bar in original section. It can be concluded from the analysis of those results that: (1) The strain development of the original reinforcements is basically similar, which shows that all the strengthening methods of the specimens can give full play to the material properties of the original reinforcements, and the mechanical performances of the strengthened specimens are good. (2) The strain development of reinforcements in the enlarged section is also relatively stable in the elastic stage. With the increase Figure 16 shows the load–strain relationship between the reinforcement in the enlarged section and the steel bar in original section. It can be concluded from the analysis of those results that: (1) The strain development of the original reinforcements is basically similar, which shows that all the strengthening methods of the specimens can give full play to the material properties of the original reinforcements, and the mechanical performances of the strengthened specimens are good. (2) The strain development of reinforcements in the enlarged section is also relatively stable in the elastic stage. With the increase of load, the reinforcement of SJ-1 yields first, followed by SJ-2 and SJ-4, and the reinforcement of SJ-3 yields last. This shows that ECC in the enlarged section can bear part of the tensile force, which makes the reinforcements in the tensile area yield later so as to improve its recovery ability. larged section and the steel bar in original section. It can be concluded from the analysis of those results that: (1) The strain development of the original reinforcements is basically similar, which shows that all the strengthening methods of the specimens can give full play to the material properties of the original reinforcements, and the mechanical performances of the strengthened specimens are good. (2) The strain development of reinforcements in the enlarged section is also relatively stable in the elastic stage. With the increase of load, the reinforcement of SJ-1 yields first, followed by SJ-2 and SJ-4, and the reinforcement of SJ-3 yields last. This shows that ECC in the enlarged section can bear part of the tensile force, which makes the reinforcements in the tensile area yield later so as to improve its recovery ability.

4 **Figure 16.** The load–strain relationship between the reinforcement. (**a**) The steel bar in existing beam section; (**b**) The reinforcements in enlarged section. **Figure 16.** The load–strain relationship between the reinforcement. (**a**) The steel bar in existing beam section; (**b**) The reinforcements in enlarged section.

2013) [45], the flexural bearing capacity of the existing beam section should be determined

(**a**) (**b**)

0

**Figure 16.** The load–strain relationship between the reinforcement. (**a**) The steel bar in existing beam

According to the "Code for design of strengthening concrete structure" (GB50367-

2013) [45], the flexural bearing capacity of the existing beam section should be determined

1

2

3

5

0 5 10 15 20 25 30 35

Load (kN)

section; (**b**) The reinforcements in enlarged section.

**4. Flexural Capacity Formula** 

according to Formula (1):

*4.1. Basic Formula* 

**4. Flexural Capacity Formula** 

according to Formula (1):

*4.1. Basic Formula* 

0 5 10 15 20 25 30 35

Load (kN)

0

1

2

3

4

5

Strain (×103με)

6

7

8

9

10

#### **4. Flexural Capacity Formula** *h*0, *h*01*—*Effective height of section after strengthening and before strengthening (mm), as

Figure 17.

*4.1. Basic Formula*

According to the "Code for design of strengthening concrete structure" (GB50367-2013) [45], the flexural bearing capacity of the existing beam section should be determined according to Formula (1): shown in Figure 17. *x—*Height of compression zone of the section concrete (mm) *f*y0, *f'*y0*—*Design value of tensile and compressive strength of steel bars in existing structure

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$$M \le a\_5 f\_{\mathfrak{H}} A\_i(h\_0 - \frac{\chi}{2}) + f\_{\mathfrak{H}} A\_{\mathfrak{H}}(h\_{\mathfrak{H}} - \frac{\chi}{2}) + f\_{\mathfrak{H}}' A\_{\mathfrak{sl}}'(\frac{\chi}{2} - d') \tag{1}$$
  $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\mathfrak{h}$   $\mathfrak{h}$   $\chi$   $\chi$   $\mathfrak{h}$   $\chi$   $\chi$   $\mathfrak{h}$   $\mathfrak{h}$   $\chi$   $\chi$   $\chi$   $\mathfrak{h}$   $\mathfrak{h}$   $\chi$   $\chi$   $\mathfrak{h}$   $\chi$   $\chi$   $\chi$   $\chi$   $\mathfrak{h}$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$   $\chi$ 

*M—*Design value of bending moment after strengthening of member (kN·m)

*α*s*—*Strength utilization factor of reinforcements in enlarged section, taken as *α*s = 0.9

*A*s*—*The cross-sectional area of the reinforcements in enlarged section (mm2), as shown in

*f*y*—*Design value of tensile strength of reinforcements in enlarged section (N/mm2)

<sup>≤</sup> *x xx <sup>M</sup> <sup>α</sup> fA h f A h f A a* '' '

s y s 0 y0 s0 01 y0 s0 ( - )+ ( - )+ ( - ) 2 22 (1)

where:

where:

*M*—Design value of bending moment after strengthening of member (kN·m) *α*s—Strength utilization factor of reinforcements in enlarged section, taken as *α*<sup>s</sup> = 0.9 *f* <sup>y</sup>—Design value of tensile strength of reinforcements in enlarged section (N/mm<sup>2</sup> ) *A*s—The cross-sectional area of the reinforcements in enlarged section (mm<sup>2</sup> ), as shown in Figure 17. ments (mm2), as shown in Figure 17. *a*'*—*The distance from the resultant force point of longitudinal compressive reinforcements to the edge of compression zone of the beam (mm), as shown in Figure 17.

**Figure 17.** Dimensions of strengthened beam. **Figure 17.** Dimensions of strengthened beam.

*h*0, *h*01—Effective height of section after strengthening and before strengthening (mm), as shown in Figure 17.

*4.2. Flexural Capacity of ECC Reinforced Beams x*—Height of compression zone of the section concrete (mm)

Through the verification of the test results, it is found that when ECC is used to *f* y0, *f'*y0—Design value of tensile and compressive strength of steel bars in existing structure member (N/mm<sup>2</sup> )

strengthen the tensile zone of the beam, due to the excellent tensile performance of ECC, *A*s0, *A'*s0—The cross-sectional area of the tensile reinforcements and compressive reinforcements (mm<sup>2</sup> ), as shown in Figure 17.

the contribution of ECC to the bending capacity of the strengthened beam must be considered. Therefore, formula 1 needs to be revised. The revised formula is shown as For*a*'—The distance from the resultant force point of longitudinal compressive reinforcements to the edge of compression zone of the beam (mm), as shown in Figure 17.

#### mulas (2) and (3). *4.2. Flexural Capacity of ECC Reinforced Beams*

≤ × '' ' <sup>1</sup> s y s 0 y0 s0 01 y0 s0 t,ecc ( - )+ ( - )+ ( - )+ ( - - ) 2 2 2 22 *x xx x <sup>h</sup> <sup>M</sup> <sup>α</sup> fA h f A h f A a F h* (2) Through the verification of the test results, it is found that when ECC is used to strengthen the tensile zone of the beam, due to the excellent tensile performance of ECC, the contribution of ECC to the bending capacity of the strengthened beam must be considered. Therefore, formula 1 needs to be revised. The revised formula is shown as Formulas (2) and (3).

$$M \le a\_5 f\_y A\_5 (h\_0 - \frac{\mathfrak{x}}{2}) + f\_{y0} A\_{50} (h\_{01} - \frac{\mathfrak{x}}{2}) + f'\_{y0} A'\_{50} (\frac{\mathfrak{x}}{2} - d') + F\_{\text{l.c.t}} \times (h - \frac{\mathfrak{x}}{2} - \frac{h\_1}{2}) \tag{2}$$
 
$$\dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots$$

lationship curve of the ECC shown in Figure 18 [46]

$$F\_{l, \text{eff}} = f\_{l, \text{eff}} \times b \times h\_1 \tag{3}$$

*h*1*—*The height of enlarged section strengthened by ECC (mm), *h*1 = 40 mm in these tests

where: *Materials* **2021**, *14*, x FOR PEER REVIEW 16 of 19

> *f* t,ecc—Equivalent strength of ECC (N/mm<sup>2</sup> ), Use value of σtc in the tensile stress–strain relationship curve of the ECC shown in Figure 18 [46]

*b*—Section width (mm)

*h*1—The height of enlarged section strengthened by ECC (mm), *h*<sup>1</sup> = 40 mm in these tests

**Figure 18.** ECC tensile stress–strain curve.

**Figure 18.** ECC tensile stress–strain curve. *4.3. Verification of the Revised Formula*

By using the parameters of material properties in Tables 4 and 5, the theoretical value of flexural bearing capacity of each specimen can be calculated through the revised formula.

*4.3. Verification of the Revised Formula*  **Table 4.** Yield strength of longitudinal reinforcement.


**Table 5.** Concrete strength.

beams.


**Material SMA Tensile Longitudinal Bar Compressed Longitudinal Bar**  Yield Strength (MPa) 296.17 397.17 397.17 The theoretical values and the experimental value of flexural bearing capacity for all 4 specimens are shown in Table 6, where *M*cu is the calculated theoretical value of the bearing capacity of the beam strengthening with increasing section area, *M*tu is the experimental value of the bearing capacity of the beam strengthening with increasing section area, which can be determined by the loading when the reinforcements are yielded, and *M*cu/*M*tu is the ratio of the theoretical value to the experimental value.

**Material Concrete ECC** 

Compressive strength (MPa) 17.48 18,021

The theoretical values and the experimental value of flexural bearing capacity for all

4 specimens are shown in Table 6, where *M*cu is the calculated theoretical value of the

bearing capacity of the beam strengthening with increasing section area, *M*tu is the exper-

imental value of the bearing capacity of the beam strengthening with increasing section

area, which can be determined by the loading when the reinforcements are yielded, and

**Table 6.** The theoretical values and the experimental values of bending capacity for the strengthened

It can be seen from Table 6 that the bending capacity calculated by Formula (2) for all

the specimens are in good agreement with the test value, and the errors are all within 10%,

indicating that the accuracy of the revised formula can be guaranteed. The values of *M*cu

are always less than the value of *M*tu, representing that the theoretical values calculated

by Formula (2) are much safer compared with the actual value, and the revised formula

can be well applied to beam strengthening with increasing section of ECC.

*M*cu/*M*tu is the ratio of the theoretical value to the experimental value.

**Specimen Number Reinforcement Material** *M***cu (kN·m)** *M***tu (kN·m)** *M***cu/***M***tu**

SJ-1 Steel-Concrete 2.75 2.96 0.92

SJ-2 SMA-Concrete 2.51 2.76 0.91

SJ-3 SMA-ECC 2.51 2.78 0.90

SJ-4 Steel-ECC 2.75 2.93 0.94

Tensile strength (MPa) - 5.1

**Table 5.** Concrete strength.


**Table 6.** The theoretical values and the experimental values of bending capacity for the strengthened beams.

It can be seen from Table 6 that the bending capacity calculated by Formula (2) for all the specimens are in good agreement with the test value, and the errors are all within 10%, indicating that the accuracy of the revised formula can be guaranteed. The values of *M*cu are always less than the value of *M*tu, representing that the theoretical values calculated by Formula (2) are much safer compared with the actual value, and the revised formula can be well applied to beam strengthening with increasing section of ECC.

#### **5. Conclusions**


The purpose of this paper is to reveal the bending capacity, failure mode, and selfrecovery capacity of concrete beams strengthened with SMA/ECC enlarged section based on full-scale beam specimens with small dimensions. In the follow-up research, the influence of different design parameters, such as section size, flexure reinforcement ratio, and material strength, etc., on the flexural performance of concrete beams strengthened with SMA/ECC enlarged section will be further analyzed theoretically and experimentally to

improve the design principle of the strengthening method and provide a theoretical basis for design of strengthening works.

**Author Contributions:** Conceptualization, H.Q. and X.Z.; methodology, Q.Z. and E.D.; software, Q.Z., E.D. and J.G.; validation, X.Z. and J.G.; formal analysis, Q.Z.; investigation, Q.Z. and X.Z.; resources, E.D.; data curation, Q.Z.; writing—original draft preparation, X.Z.; writing—review and editing, H.Q.; visualization, J.G.; supervision, X.Z.; project administration, H.Q.; funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, Grant number 51987631, 51478438; The Key Research Projects of Henan Higher Education Institutions, Grant number 20A560002.

**Conflicts of Interest:** The authors declare no conflict of interest.
