Verified FE model with the corresponding tested FB-RC30 specimen.

#### 4.2.1. Performance of Bending Behaviour

In Figure 10, the moment vs. mid-span deflection curves of the analysed FE models are presented independently for each group. These curves showed elastic behaviour at the initial loading stage up to a certain limit, followed by plastic behaviour until the ultimate strength capacity of the CFST model was achieved. The models with varied tube thicknesses and depths showed a major influence on their moment–deflection curves at both the elastic and plastic loading stages, as shown in Figure 10a,d for the FE models in groups A and D, respectively. This is a logical flexural behaviour since the cross-section parameters (the steel area and moment of inertia) of the suggested CFST models were increased as a result of enhancements in their tubes' thicknesses and/or depths. However, the use of varied tube yield strengths did not bring about a major impact on the models' moment–deflection behaviours at the elastic stage, but a major effect was found at their plastic stage only, as shown in Figure 10c for the models in group C. Moreover, very limited improvement was recorded for the moment–deflection curves' behaviour when only the compressive strength of the infill material increased, as shown in Figure 10b.

#### 4.2.2. Performance of Stiffness

The stiffness values of the analysed FE models are given in Table 3. The *K<sup>i</sup>* and *K<sup>s</sup>* values improved significantly with the increases in the steel tube's thickness and/or the depth of the studied models (group A and D), while very limited improvements were recorded when only the concrete compressive strength was increased (models in Group C). For example, the FB2-A model achieved *<sup>K</sup><sup>i</sup>* and *<sup>K</sup><sup>s</sup>* values of 2375 kN·m<sup>2</sup> and 2125 kN·m<sup>2</sup> , respectively. These values were improved by about 50–55% (3575 kN·m<sup>2</sup> and 3285 kN·m<sup>2</sup> ) when only the tube's thickness increased from 1.5 mm to 3.0 mm (FB5-A). Moreover, the stiffness *<sup>K</sup><sup>i</sup>* and *<sup>K</sup><sup>s</sup>* values of the FB1-B model were improved by about 18–19% (2819 kN·m<sup>2</sup> and 2529 kN·m<sup>2</sup> ) when only the *fcu* value increased by about three times (from 14.6 MPa to 45 MPa).

**Figure 10.** Moment vs. mid-span deflection of CFST models with varied parameters: (**a**) group A; (**b**) group B; (**c**) group C; (**d**) group D. **Figure 10.** Moment vs. mid-span deflection of CFST models with varied parameters: (**a**) group A; (**b**) group B; (**c**) group C; (**d**) group D.

### 4.2.3. Performance of Bending Strength

4.2.2. Performance of Stiffness The stiffness values of the analysed FE models are given in Table 3. The *Ki* and *Ks* values improved significantly with the increases in the steel tube's thickness and/or the depth of the studied models (group A and D), while very limited improvements were recorded when only the concrete compressive strength was increased (models in Group C). For example, the FB2-A model achieved *Ki* and *Ks* values of 2375 kN·m2 and 2125 kN·m2, respectively. These values were improved by about 50–55% (3575 kN·m2 and 3285 kN·m2) when only the tube's thickness increased from 1.5 mm to 3.0 mm (FB5-A). Moreover, the stiffness *Ki* and *Ks* values of the FB1-B model were improved by about 18– 19% (2819 kN·m2 and 2529 kN·m2) when only the *fcu* value increased by about three times (from 14.6 MPa to 45 MPa). 4.2.3. Performance of Bending Strength The ultimate bending strength capacities (*Mu*) of the analysed FE models are given in Table 3. In addition, they are independently compared for each group in Figure 11. Generally, compared to all of the studied parameters, increasing the tube's thickness The ultimate bending strength capacities (*Mu*) of the analysed FE models are given in Table 3. In addition, they are independently compared for each group in Figure 11. Generally, compared to all of the studied parameters, increasing the tube's thickness (group A) led to major improvements in the suggested CFST models' *M<sup>u</sup>* values; these improvements were even more significant than the effects of tube's depth (Group D). Meanwhile, increasing the strength of the concrete infill led to limited improvements in their *M<sup>u</sup>* values. This can be considered a reasonable outcome since the tube's thickness directly increased the overall area of the steel cross-section, including the internal stiffeners (the lips of the C-sections) at the top and bottom beam's flanges. Similar outcomes have been recorded in other studies for the conventional CFST beams that were investigated here [10,14,61]. For example, the FB2-A control model with 1.5 mm thickness achieved an *M<sup>u</sup>* value of 55.4 kN·m; this value was increased to about 30.6% (72.4 kN·m) and 60.3% (88.8 kN·m) when only the tube's thickness was increased to 2.0 mm and 2.5 mm, respectively. Meanwhile, the same *M<sup>u</sup>* value (55.4 kN·m) for the FB1-B model, in which concrete infill of 14.6 MPa strength was used, was increased by about 12.2% (62.2 kN·m) when a three-times-higher compressive strength was used (55 MPa; model FB5-B).

(group A) led to major improvements in the suggested CFST models' *Mu* values; these improvements were even more significant than the effects of tube's depth (Group D). Meanwhile, increasing the strength of the concrete infill led to limited improvements in their *Mu* values. This can be considered a reasonable outcome since the tube's thickness

**Figure 11.** Effects of the *Mu* values of CFST models with varied parameters: (**a**) group A; (**b**) group B; (**c**) group C; (**d**) group D. **Figure 11.** Effects of the *M<sup>u</sup>* values of CFST models with varied parameters: (**a**) group A; (**b**) group B; (**c**) group C; (**d**) group D.

#### **5. Design Guidelines 5. Design Guidelines**

*5.1. Evaluation of the Obtained Flexural Stiffness 5.1. Evaluation of the Obtained Flexural Stiffness*

This section evaluates the currently known flexural stiffness values (*Ki* and *Ks*) obtained from existing experimental and numerical approaches. The theoretical expressions that are presented in the AIJ-1997 [62], EC4-2004 [63], and ANSI/AISC 360-10 [64] standards are used: This section evaluates the currently known flexural stiffness values (*K<sup>i</sup>* and *Ks*) obtained from existing experimental and numerical approaches. The theoretical expressions that are presented in the AIJ-1997 [62], EC4-2004 [63], and ANSI/AISC 360-10 [64] standards are used:

directly increased the overall area of the steel cross-section, including the internal stiffeners (the lips of the C-sections) at the top and bottom beam's flanges. Similar outcomes have been recorded in other studies for the conventional CFST beams that were investigated here [10,14,61]. For example, the FB2-A control model with 1.5 mm thickness achieved an *Mu* value of 55.4 kN·m; this value was increased to about 30.6% (72.4 kN·m) and 60.3% (88.8 kN·m) when only the tube's thickness was increased to 2.0 mm and 2.5 mm, respectively. Meanwhile, the same *Mu* value (55.4 kN·m) for the FB1-B model, in which concrete infill of 14.6 MPa strength was used, was increased by about 12.2% (62.2 kN·m) when a three-times-higher compressive strength was used (55 MPa; model FB5-B).

$$K = E\_S I\_S + \mathcal{C}1E\_\mathcal{C}I\_\mathcal{C} \tag{1}$$

where *Es* and *Is* are the modulus of elasticity and moment of inertia, respectively, for the steel part. *Ec* and *Ic* are the modulus of elasticity and moment of inertia, respectively, for the concrete part. The *C1* is a reduction factor for the concrete stiffness part, which is taken to be 0.6 in EC4 where *E<sup>s</sup>* and *I<sup>s</sup>* are the modulus of elasticity and moment of inertia, respectively, for the steel part. *E<sup>c</sup>* and *I<sup>c</sup>* are the modulus of elasticity and moment of inertia, respectively, for the concrete part. The *C1* is a reduction factor for the concrete stiffness part, which is taken to be 0.6 in EC4-2004, and 0.2 in AIJ-1997. However, in the ANSI/AISC 360-10 standard, the *C1* value is estimated to be 0.6 *+* 2*A<sup>s</sup> /(A<sup>s</sup> + Ac)*, but should not exceed 0.9. The *E<sup>c</sup>* value in Equation (1) is 9500 *(fck +* 8)1/3, 4700 *(fc)* 0.5 and 21,000 (*fc*/19.6)0.5 for the EC4-2004, AISC-2010 and AIJ-1997 standards, respectively. Furthermore, the theoretical methods developed by Han et al. [51] and Al Zand et al. [56] for the independent prediction of the values of flexural stiffness at the initial and serviceability levels (*K<sup>i</sup>* and *Ks*) were adopted.

The predicted values of flexural stiffness (*Kpredicted*), and the experimentally and numerically obtained values (*Kobtained*), are compared in Figure 12. Generally, the obtained flexural stiffness values at the initial loading stage (*K<sup>i</sup>* ) are slightly overestimated by the

**Model Designations** 

*λ (W/t)* 

*λst (Weff/t)* 

*Mu* **(kN.m)**

theoretical prediction, which is acceptable since it is within ±20% [50,52]. However, the AIJ-1997 standard achieves the lowest predicted stiffness values (*K-AIJ*) as compared to the other standards and methods, since this standard uses the lowest concrete stiffness redaction factor (*C1* = 0.2). Additionally, the EC4-2004 and ANSI/AISC 360-10 standards showed a more conservative prediction for the stiffness values (*K-EC4* and *K-AISC*) at the serviceability level (see Figure 12b), given that they use a single-expression formula (Equation (1)) to estimate the flexural stiffness value of the CFST members, unlike the expression methods of Han-2006 and Al Zand-2020, in which the flexural stiffness values of CFST beams are estimated at two different loading stages (two independent levels: *K<sup>i</sup>* and *Ks*). numerically obtained values (*Kobtained*), are compared in Figure 12. Generally, the obtained flexural stiffness values at the initial loading stage (*Ki*) are slightly overestimated by the theoretical prediction, which is acceptable since it is within ±20% [50,52]. However, the AIJ-1997 standard achieves the lowest predicted stiffness values (*K-AIJ*) as compared to the other standards and methods, since this standard uses the lowest concrete stiffness redaction factor (*C1* = 0.2). Additionally, the EC4-2004 and ANSI/AISC 360-10 standards showed a more conservative prediction for the stiffness values (*K-EC4* and *K-AISC*) at the serviceability level (see Figure 12b), given that they use a single-expression formula (Equation (1)) to estimate the flexural stiffness value of the CFST members, unlike the expression methods of Han-2006 and Al Zand-2020, in which the flexural stiffness values of CFST beams are estimated at two different loading stages (two independent levels: *Ki* and *Ks*).

2004, and 0.2 in AIJ-1997. However, in the ANSI/AISC 360-10 standard, the *C1* value is estimated to be 0.6 *+* 2*As/(As + Ac)*, but should not exceed 0.9. The *Ec* value in Equation (1) is 9500 *(fck +* 8)1/3, 4700 *(fc)*0.5 and 21,000 (*fc/*19.6)0.5 for the EC4-2004, AISC-2010 and AIJ-1997 standards, respectively. Furthermore, the theoretical methods developed by Han et al. [51] and Al Zand et al. [56] for the independent prediction of the values of flexural stiffness at the

The predicted values of flexural stiffness (*Kpredicted*), and the experimentally and

*Materials* **2021**, *14*, x FOR PEER REVIEW 17 of 26

initial and serviceability levels (*Ki* and *Ks*) were adopted.

**Figure 12.** Verification of the obtained flexural stiffness: (**a**) *Ki*; (**b**) *Ks.* **Figure 12.** Verification of the obtained flexural stiffness: (**a**) *Ki*; (**b**) *Ks.*

#### *5.2. Evaluation of the Obtained Flexural Strength 5.2. Evaluation of the Obtained Flexural Strength*

improvements in their flexural strength capacities [19].

*Mu-EC4*  **(kN.m)**

**Table 4.** Verification of the obtained *Mu* values of the tested specimens and analysed FE models.

*Mu-EC4*  **/***Mu*

FB-RC0 98.0 48.0 57.7 39.1 0.678 42.3 0.732 42.6 0.738 48.9 0.848 FB-RC30 98.0 48.0 53.7 37.3 0.694 39.3 0.731 37.2 0.692 46.7 0.870 FB-RC50 98.0 48.0 52.6 37.2 0.706 39.2 0.745 36.8 0.700 46.6 0.886 FB-RC70 98.0 48.0 51.5 37.1 0.720 39.1 0.759 36.5 0.709 46.5 0.903 FB1-A 148.0 73.0 38.1 25.8 0.678 27.2 0.713 27.1 0.711 30.1 0.789 FB2-A 98.0 48.0 55.4 37.2 0.671 39.2 0.707 37.1 0.670 46.7 0.842 FB3-A 73.0 35.5 72.4 48.2 0.665 51.7 0.714 48.6 0.671 61.4 0.848 FB4-A 58.0 28.0 88.8 58.8 0.663 64.8 0.730 61.7 0.695 75.1 0.846 FB5-A 48.0 23.0 105.0 69.3 0.660 78.5 0.747 68.0 0.647 88.6 0.844 FB1-B 98.0 48.0 55.4 37.2 0.671 39.2 0.707 37.1 0.670 46.7 0.842

*Mu-Han*  **(kN·m)** *Mu-Han /Mu*

*Mu-P1*  **(kN·m)**  *Mu-P1 /Mu*

*Mn*  **(kN·m)** 

*Mn /Mu*

The ultimate flexural strength (*Mu*) values obtained for the tested and analysed CFST models were evaluated, using the existing theoretical methods given by EC4-2004 [63], Han-2004 [61], and Al Zand-2020 [56], to verify the findings of the current study. In Table 4, the predicted *Mu* values of the currently investigated beams and models are compared, using the above theoretical methods (*Mu-EC4*, *Mu-Han* and *Mu-Zand*), with those obtained from the current experimental and numerical investigations, including six models analysed by The ultimate flexural strength (*Mu*) values obtained for the tested and analysed CFST models were evaluated, using the existing theoretical methods given by EC4-2004 [63], Han-2004 [61], and Al Zand-2020 [56], to verify the findings of the current study. In Table 4, the predicted *M<sup>u</sup>* values of the currently investigated beams and models are compared, using the above theoretical methods (*Mu-EC4*, *Mu-Han* and *Mu-Zand*), with those obtained

others [19]. Generally, the existing methods showed a conservative prediction of the *Mu* values of the investigated CFST beams and models, with reasonable coefficient of

CFST beams (section of beams without internal steel stiffeners). In Table 4, it can be seen that *Mu-EC4* achieved a mean value (MV) of 0.643. However, *Mu-Han* and *Mu-Zand* achieved higher MVs, which were 0.740 and 0.734, respectively, since these two methods took into account the effects of the total area of the steel (*As)* of the CFST beam's cross-section. The above comparison confirmed that the lips of the C-sections used in the Slender CFST beams investigated in this study behaved as internal steel stiffeners, which led to sufficient

from the current experimental and numerical investigations, including six models analysed by others [19]. Generally, the existing methods showed a conservative prediction of the *M<sup>u</sup>* values of the investigated CFST beams and models, with reasonable coefficient of variation (COV) values, since these methods were mainly developed for conventional CFST beams (section of beams without internal steel stiffeners). In Table 4, it can be seen that *Mu-EC4* achieved a mean value (MV) of 0.643. However, *Mu-Han* and *Mu-Zand* achieved higher MVs, which were 0.740 and 0.734, respectively, since these two methods took into account the effects of the total area of the steel (*As)* of the CFST beam's cross-section. The above comparison confirmed that the lips of the C-sections used in the Slender CFST beams investigated in this study behaved as internal steel stiffeners, which led to sufficient improvements in their flexural strength capacities [19].

**Table 4.** Verification of the obtained *Mu* values of the tested specimens and analysed FE models.

