**6. Discussion of the two-bay, three-story model analysis results**

With the finite element model validated based on the performance of a single-bay, singlestory infilled frame, the modeling approach can next be applied to a multi-bay, multistory system. The same modeling features presented in previous sections were used to model the two-bay, three-story frame shown in **Figure 18**. The panel dimensions and material properties were the same as those for the single-bay, single-story case. The steel frame members,

**Figure 18.** Two-bay, three-story model description [53].

**Figure 17.** Load-deflection relation for single-bay, single-story case study with "multilinear" response for fuse element [53].

**Figure 16.** Load-deflection relation for single-bay, single-story case study with "trilinear" response for fuse element [53].

42 New Trends in Structural Engineering

**Figure 19.** ANSYS models for two-bay, three-story case study: (a) bare steel frame; (b) single-diagonal strut method; and (c) three-diagonal strut method [53].

however, were modified to make them appropriate for a three-story structure. The masonry infill walls were assumed to be conventional CMU blocks (200 mm x 200 mm × 400 mm).

the elements used consist of 110 BEAM3 elements for the frame, 50 COMBIN30 elements for nonlinear joints, 606 PLAIN42 elements for masonry infill, 108 CONTACT12 elements for wall and frame connections, 12 COMBIN39/40 elements for fuse, 12 COMBIN40 elements for

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The loading applied to the four models described consisted of imposing incremental horizontal in-plane displacement at the third floor level in a displacement-controlled mode. The resulting load-deflection diagrams for all four models are plotted in **Figure 23**. The results

gap modeling, and 12 COMBIN39 elements for tie-downs.

**Figure 22.** ANSYS model for two-bay, three-story infilled frame with fuse elements [53].

Models were developed for two-bay, three-story systems for three cases of bare frame, infilled frame without fuse, and infilled frame with fuse elements. The bare frame model shown in **Figure 19(a)** employed nonlinear beam-column joints shown in the figure by COMBIN39 elements. The model with masonry infill without fuse shown in **Figure 19(b** and **c)** consisted of two cases of single-diagonal strut and three-diagonal strut representation of the infill wall. **Figure 20** shows the moment-rotation section behavior assumed for beam and column sections. For the single-strut case, the force-deformation behavior model shown in **Figure 21** was used, while for the three-strut case, the models proposed in Ref. [57] were considered. The finite element model for the infilled frame with fuse elements is shown in **Figure 22**, where

**Figure 20.** Moment-rotation response for joints [53].

**Figure 21.** Force-deformation response for diagonal strut of single-diagonal strut model [53].

the elements used consist of 110 BEAM3 elements for the frame, 50 COMBIN30 elements for nonlinear joints, 606 PLAIN42 elements for masonry infill, 108 CONTACT12 elements for wall and frame connections, 12 COMBIN39/40 elements for fuse, 12 COMBIN40 elements for gap modeling, and 12 COMBIN39 elements for tie-downs.

The loading applied to the four models described consisted of imposing incremental horizontal in-plane displacement at the third floor level in a displacement-controlled mode. The resulting load-deflection diagrams for all four models are plotted in **Figure 23**. The results

**Figure 22.** ANSYS model for two-bay, three-story infilled frame with fuse elements [53].

**Figure 20.** Moment-rotation response for joints [53].

44 New Trends in Structural Engineering

**Figure 21.** Force-deformation response for diagonal strut of single-diagonal strut model [53].

however, were modified to make them appropriate for a three-story structure. The masonry infill walls were assumed to be conventional CMU blocks (200 mm x 200 mm × 400 mm).

Models were developed for two-bay, three-story systems for three cases of bare frame, infilled frame without fuse, and infilled frame with fuse elements. The bare frame model shown in **Figure 19(a)** employed nonlinear beam-column joints shown in the figure by COMBIN39 elements. The model with masonry infill without fuse shown in **Figure 19(b** and **c)** consisted of two cases of single-diagonal strut and three-diagonal strut representation of the infill wall. **Figure 20** shows the moment-rotation section behavior assumed for beam and column sections. For the single-strut case, the force-deformation behavior model shown in **Figure 21** was used, while for the three-strut case, the models proposed in Ref. [57] were considered. The finite element model for the infilled frame with fuse elements is shown in **Figure 22**, where

**Figure 23.** Load-deflection relation for single-bay, single-story system [53].

shown are consistent with the type of response observed for the single-bay, single-story in **Figure 9**. The results for the infilled frame with fuse element are also shown with three different fuse capacities. **Figure 24** shows the enlarged plot of the fuse-equipped system compared to the bare frame model, while **Figure 25** shows the sequence of fuse breakages. As expected, the load-deflection diagram for the system with fuse shows that after the breakage of the last fuse, the response closely follows the bare frame diagram. It should be added that such deflection will continue until the clearance between the frame and the infill wall is overcome, at which point the frame will directly bear against the infill wall, and the overall system will again experience high stiffness due to re-engagement and participation of infill wall.

applied incrementally. The resulting load-deflection diagram is shown in **Figure 26** and the sequence of fuse breakage is graphically shown in **Figure 27**. **Figure 26** shows that upon the breakage of the last fuse (third story), the response follows that of the bare frame. The results in **Figure 26** show the beneficial effects of using fuse on increasing the stiffness and thus reducing in-plane deflection. Desirable sequence of fuse failure can be obtained by appropriate distribu-

**Figure 25.** Behavior and failure mechanism of two-bay, three-story infilled steel frame with fuse system [53].

**Figure 24.** Load-deflection relation for two-bay, three-story infilled steel frame with "brittle-failure" fuse elements [53].

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In addition to described analytical studies, parametric studies were conducted to determine the effect of varying the structural frame joint rigidities, member strengths, as well as the

tion of fuses with predetermined varying capacities over the height.

The displacement-controlled load application is useful to understand the behavior of the system as each fuse breaks, and in general for experimental tests studies to collect detailed data at each displacement increment. To simulate more realistic earthquake loading conditions and also for design purposes, however, load-controlled application can be a better choice. The twobay, three-story model of the infilled frame with fuse elements was subjected to such a loadcontrolled case. Consistent with the first-mode deflection and story lateral loads, in-plane loads of F/2, F/3, and F/6 were considered at the third, second, and first floor levels, respectively, and

**Figure 24.** Load-deflection relation for two-bay, three-story infilled steel frame with "brittle-failure" fuse elements [53].

**Figure 25.** Behavior and failure mechanism of two-bay, three-story infilled steel frame with fuse system [53].

**Figure 23.** Load-deflection relation for single-bay, single-story system [53].

46 New Trends in Structural Engineering

shown are consistent with the type of response observed for the single-bay, single-story in **Figure 9**. The results for the infilled frame with fuse element are also shown with three different fuse capacities. **Figure 24** shows the enlarged plot of the fuse-equipped system compared to the bare frame model, while **Figure 25** shows the sequence of fuse breakages. As expected, the load-deflection diagram for the system with fuse shows that after the breakage of the last fuse, the response closely follows the bare frame diagram. It should be added that such deflection will continue until the clearance between the frame and the infill wall is overcome, at which point the frame will directly bear against the infill wall, and the overall system will

again experience high stiffness due to re-engagement and participation of infill wall.

The displacement-controlled load application is useful to understand the behavior of the system as each fuse breaks, and in general for experimental tests studies to collect detailed data at each displacement increment. To simulate more realistic earthquake loading conditions and also for design purposes, however, load-controlled application can be a better choice. The twobay, three-story model of the infilled frame with fuse elements was subjected to such a loadcontrolled case. Consistent with the first-mode deflection and story lateral loads, in-plane loads of F/2, F/3, and F/6 were considered at the third, second, and first floor levels, respectively, and applied incrementally. The resulting load-deflection diagram is shown in **Figure 26** and the sequence of fuse breakage is graphically shown in **Figure 27**. **Figure 26** shows that upon the breakage of the last fuse (third story), the response follows that of the bare frame. The results in **Figure 26** show the beneficial effects of using fuse on increasing the stiffness and thus reducing in-plane deflection. Desirable sequence of fuse failure can be obtained by appropriate distribution of fuses with predetermined varying capacities over the height.

In addition to described analytical studies, parametric studies were conducted to determine the effect of varying the structural frame joint rigidities, member strengths, as well as the

Next, by changing the size of the frame members, for a rigid frame, the member size effect on fuse equipped infilled frame performance were studied. Such behavior for the two-bay, threestory frame with different member sizes is shown in **Figure 30**. The initial design consisted of W12x53 for columns and W10x30 for beams, and the variation includes two cases of heavier and two cases of lighter sections. The results of the analysis show that heavier frame members provide stiffer and stronger system as a whole and that with stronger frames, fuse breaks at lower displacements. The results also show that the strength of the fuse elements should be consistent with that of frame, that is, a frame with higher ultimate load capacity should be

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**Figure 29.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different

used with fuse elements with larger capacity.

**Figure 28.** Three-linear moment-rotation response for joints [53].

connection rigidity (stiffness) [53].

**Figure 26.** Load-deflection relation for two-bay, three-story infilled steel frame with "brittle-failure" fuse elements (load control) [53].

**Figure 27.** Behavior and failure mechanism of two-bay, three-story infilled steel frame with fuse system (load control) [53].

location and stiffness of fuse elements. The moment-rotation model used for beam-column connection is shown in **Figure 28**, where the initial stiffness is Kj = Mpl/φel. By varying the rotation φel values from 0.0001 rad for a rigid frame to 100 rad for a pinned frame, the effects of joint stiffness on the response were evaluated. The results of the analysis for the two-bay, three-story frame are shown in **Figure 29**, which shows that by reducing the stiffness of the joints, the frame becomes more flexible. However, the effect on fuse performance is minor.

Next, by changing the size of the frame members, for a rigid frame, the member size effect on fuse equipped infilled frame performance were studied. Such behavior for the two-bay, threestory frame with different member sizes is shown in **Figure 30**. The initial design consisted of W12x53 for columns and W10x30 for beams, and the variation includes two cases of heavier and two cases of lighter sections. The results of the analysis show that heavier frame members provide stiffer and stronger system as a whole and that with stronger frames, fuse breaks at lower displacements. The results also show that the strength of the fuse elements should be consistent with that of frame, that is, a frame with higher ultimate load capacity should be used with fuse elements with larger capacity.

**Figure 28.** Three-linear moment-rotation response for joints [53].

**Figure 26.** Load-deflection relation for two-bay, three-story infilled steel frame with "brittle-failure" fuse elements (load

**Figure 27.** Behavior and failure mechanism of two-bay, three-story infilled steel frame with fuse system (load control) [53].

location and stiffness of fuse elements. The moment-rotation model used for beam-column connection is shown in **Figure 28**, where the initial stiffness is Kj = Mpl/φel. By varying the rotation φel values from 0.0001 rad for a rigid frame to 100 rad for a pinned frame, the effects of joint stiffness on the response were evaluated. The results of the analysis for the two-bay, three-story frame are shown in **Figure 29**, which shows that by reducing the stiffness of the joints, the frame becomes more flexible. However, the effect on fuse performance is minor.

control) [53].

48 New Trends in Structural Engineering

**Figure 29.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different connection rigidity (stiffness) [53].

**Figure 30.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different frame Strengths [53].

The effect of varying the vertical position of fuse elements with respect to the top of the wall was also examined. Four positions consisting of the wall top corner, 300 mm, 600 mm, and 900 mm below the top corner were chosen. The results of the analysis of the two-bay, threestory frame are illustrated in **Figure 31**, which show that the lower the position of fuse element, the larger the frame drift at fuse breakage points. The results also show that by lowering the position of the fuse, the initial stiffness of the entire system will be reduced and the fuse breaks at larger deflection. It can be concluded that higher positions enhances the effectiveness of the fuse function. Finally, in order to examine the effect of the fuse stiffness on the overall response, four different stiffness values were chosen for fuse elements and the results of the analysis of the two-bay, three-story frame are shown in **Figure 32**, which show that for fuse with lower stiffness, the load and deflection at fuse breakage increases. It can therefore be concluded that the stiffness of the fuse element can have a notable effect on the response of infilled frame.

**Figure 32.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different stiffness

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The study presented has shown that existing commercial software (such as ANSYS or other similar software) can be used to effectively model complex use of masonry walls. The study has shown how various finite elements can be used to model masonry, structural fuse, as well as infilled frame for analysis under in-plane lateral loading. The available library of finite elements seems to be well-developed for this purpose. Aside from concluding the appropriateness of existing of modeling capabilities to capture various behavioral aspects of masonry

**7. Concluding remarks**

for fuse elements [53].

**Figure 31.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with varying location for fuse element [53].

**Figure 32.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different stiffness for fuse elements [53].

The effect of varying the vertical position of fuse elements with respect to the top of the wall was also examined. Four positions consisting of the wall top corner, 300 mm, 600 mm, and 900 mm below the top corner were chosen. The results of the analysis of the two-bay, threestory frame are illustrated in **Figure 31**, which show that the lower the position of fuse element, the larger the frame drift at fuse breakage points. The results also show that by lowering the position of the fuse, the initial stiffness of the entire system will be reduced and the fuse breaks at larger deflection. It can be concluded that higher positions enhances the effectiveness of the fuse function. Finally, in order to examine the effect of the fuse stiffness on the overall response, four different stiffness values were chosen for fuse elements and the results of the analysis of the two-bay, three-story frame are shown in **Figure 32**, which show that for fuse with lower stiffness, the load and deflection at fuse breakage increases. It can therefore be concluded that the stiffness of the fuse element can have a notable effect on the response of infilled frame.

### **7. Concluding remarks**

**Figure 30.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with different frame

**Figure 31.** Load-deflection relation for two-bay, three-story infilled steel frame with fuse system with varying location

Strengths [53].

50 New Trends in Structural Engineering

for fuse element [53].

The study presented has shown that existing commercial software (such as ANSYS or other similar software) can be used to effectively model complex use of masonry walls. The study has shown how various finite elements can be used to model masonry, structural fuse, as well as infilled frame for analysis under in-plane lateral loading. The available library of finite elements seems to be well-developed for this purpose. Aside from concluding the appropriateness of existing of modeling capabilities to capture various behavioral aspects of masonry infills used in conjunction with fuse elements, some conclusions and remarks can also be mentioned related to the proposed use of fuse concept to mitigate damage to masonry infill walls and/or infilled frames. The concept of using structural fuse elements as sacrificial components in masonry construction is practical and should be given consideration for follow-up R&D studies and more refined design and detailing for practical application. The use of finite element modeling for parametric study of the proposed concept has shown that the effect of frame joint stiffness on the overall mode of behavior is not as much as the stiffness of the frame members. The latter affects the design of the fuse capacity, and for a given frame stiffness, the overall behavior will be sensitive to the fuse capacity. The finite element model analysis also showed that higher positions of the fuse element add efficiency to fuse element performance. While the presented study focused on proof of the concept for masonry infill within steel frames, the concept is equally applicable for concrete frames as well. In fact, variations of the presented concept can be expanded to develop energy dissipating fuse systems for application to steel and concrete frames as well as light frame construction infilled with other materials than masonry.

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## **Author details**

Ali M. Memari<sup>1</sup> \* and Mohammad Aliaari<sup>2</sup>

\*Address all correspondence to: memari@engr.psu.edu

1 Department of Architectural Engineering and Department of Civil and Environmental Engineering, Penn State University, PA, USA

2 IMEG Corporations, Pasadena, CA, USA

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[6] Klingner RE, Rubiano NR, Bashandy T, Sweeney S. Evaluation and analytical verification of Infilled frame test data. TMS Journal, The Masonry Society. 1997;**15**(2):33-41

infills used in conjunction with fuse elements, some conclusions and remarks can also be mentioned related to the proposed use of fuse concept to mitigate damage to masonry infill walls and/or infilled frames. The concept of using structural fuse elements as sacrificial components in masonry construction is practical and should be given consideration for follow-up R&D studies and more refined design and detailing for practical application. The use of finite element modeling for parametric study of the proposed concept has shown that the effect of frame joint stiffness on the overall mode of behavior is not as much as the stiffness of the frame members. The latter affects the design of the fuse capacity, and for a given frame stiffness, the overall behavior will be sensitive to the fuse capacity. The finite element model analysis also showed that higher positions of the fuse element add efficiency to fuse element performance. While the presented study focused on proof of the concept for masonry infill within steel frames, the concept is equally applicable for concrete frames as well. In fact, variations of the presented concept can be expanded to develop energy dissipating fuse systems for application to steel and concrete frames as well as light frame construction infilled with other materi-

1 Department of Architectural Engineering and Department of Civil and Environmental

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**Section 2**

**Novel Structural Elements**


**Novel Structural Elements**

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[53] Aliaari M. Development of seismic Infill Wall isolator subframe (SIWIS) system PhD

[54] Aliaari M, Memari AM. Development of a seismic design approach for infill walls equipped with structural fuse. Open Civil Engineering Journal. 2012;**6**(1):249-263

[56] Seah CK. A universal approach for the analysis and design of masonry infilled frame structures. PhD Thesis, Univ. of New Brunswick, Fredericton, N.B., Canada; 1998 [57] El-Dakhakhni WW, Elgaaly M, Hamid AA. Three-strut model for concrete masonryinfilled steel frames. Journal of Structural Engineering, ASCE. 2003;**129**:177-185

[58] Richardson J. The behavior of masonry infilled steel frames. MS Thesis, University of

Thesis, Pennsylvania State University, University Park, PA; 2005

New Brunswick, Fredericton, N.B., Canada; 1986

[55] ANSYS Users' manuals – Version 6.1. (2002), ANSYS Inc., Canonsburg, PA

634. DOI: 10.3390/buildings4040605

56 New Trends in Structural Engineering

**Chapter 3**

Provisional chapter

**Prefabricated Steel-Reinforced Concrete Composite**

DOI: 10.5772/intechopen.77166

In conventional concrete-encased steel composite columns, a steel section is placed at the center of the cross section. Thus, the contribution of the steel section to the overall flexural capacity of the column could be limited. For better efficiency and economy, particularly under biaxial moment, the steel section needs to be placed at the corners, rather than at the center of the cross section. Recently, a prefabricated steel-reinforced concrete column has been developed to utilize the advantages of the reinforced concrete column and the steelconcrete composite column. In the composite column, four steel angles are placed at the corners of the cross section, and transverse bars and plates are used to connect the angles by welding or bolting. The composite column has been widely applied to industrial buildings that require large sized columns and fast construction. In this chapter, the newly developed composite column is introduced, and basic mechanism, structural perfor-

Keywords: metal and composite structures, composite column, steel angle, weld

Nowadays, the demand for huge buildings, long-span structures, and skyscrapers has increased. As a result, (1) sectional performance of compressive members, and (2) fast and safe construction method become important. Figure 1(a) shows a conventional concrete-encased steel (CES) composite column using a wide-flange steel section at the center of the cross section. Generally, the wide-flange steel is placed at the center of the cross section, and then longitudinal bars and tie bars are placed in construction site. Thus, the contribution of the steel

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

connection, bolt connection, compression test, flexural test, cyclic test

Prefabricated Steel-Reinforced Concrete Composite

**Column**

Column

Hyeon-Jong Hwang

Hyeon-Jong Hwang

Abstract

1. Introduction

Additional information is available at the end of the chapter

mance, and field application case are discussed.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77166

#### **Prefabricated Steel-Reinforced Concrete Composite Column** Prefabricated Steel-Reinforced Concrete Composite Column

DOI: 10.5772/intechopen.77166

Hyeon-Jong Hwang Hyeon-Jong Hwang

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77166

#### Abstract

In conventional concrete-encased steel composite columns, a steel section is placed at the center of the cross section. Thus, the contribution of the steel section to the overall flexural capacity of the column could be limited. For better efficiency and economy, particularly under biaxial moment, the steel section needs to be placed at the corners, rather than at the center of the cross section. Recently, a prefabricated steel-reinforced concrete column has been developed to utilize the advantages of the reinforced concrete column and the steelconcrete composite column. In the composite column, four steel angles are placed at the corners of the cross section, and transverse bars and plates are used to connect the angles by welding or bolting. The composite column has been widely applied to industrial buildings that require large sized columns and fast construction. In this chapter, the newly developed composite column is introduced, and basic mechanism, structural performance, and field application case are discussed.

Keywords: metal and composite structures, composite column, steel angle, weld connection, bolt connection, compression test, flexural test, cyclic test

#### 1. Introduction

Nowadays, the demand for huge buildings, long-span structures, and skyscrapers has increased. As a result, (1) sectional performance of compressive members, and (2) fast and safe construction method become important. Figure 1(a) shows a conventional concrete-encased steel (CES) composite column using a wide-flange steel section at the center of the cross section. Generally, the wide-flange steel is placed at the center of the cross section, and then longitudinal bars and tie bars are placed in construction site. Thus, the contribution of the steel

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Figure 1. Comparison of CES column and PSRC columns. (a) CES composite column, (b) PSRC composite column (weld connection), (c) PSRC composite column (bolt connection)

section to the overall flexural capacity of the column could be limited. Further, the need for rebar and formwork construction requires considerable construction time. Particularly, in mega structures such as semiconductor factory and warehouse using long and large sized columns, fast and safe construction methods are necessary.

In order to improve structural capacity and cost efficiency, a prefabricated steel-reinforced concrete (PSRC) composite column has been used. As shown in Figure 1(b) and (c), the prefabricated steel angles at the four corners replace the conventional wide-flange steel, and the steel angles are weld connected or bolt connected with transverse bars or plates [1–5]. The weld connection should follow the details prescribed in welding standards [6, 7]. The steel angles resist axial load and flexural moment. The transverse bars and plates provide shear resistance, concrete confinement, and bond resistance between the steel angles and concrete. Because the steel cage of angles and transverse reinforcement are prefabricated off site, field rebar work is unnecessary. Further, the self-erectable steel cage can provide sufficient strength and rigidity to support the construction loads of beams and slabs that are superimposed on the PSRC composite column.

concrete form is preattached to the steel cage and it can be permanently used after concrete pouring (Figure 3). Thus, field work related to reinforcing bar placement and concrete form work is excluded, which improves the construction safety and saves the construction time at

Prefabricated Steel-Reinforced Concrete Composite Column

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61

The prefabricated steel angle composite columns strongly depend on the transverse reinforcement that connects the corner steel angles. The transverse reinforcement provides (1) shear transfer between the steel angles, (2) bond between the steel angles and concrete, (3) buckling resistance for the steel angles, and (4) lateral confinement for the core concrete. To satisfy the requirements of (3) and (4), close spacing as well as sufficient strength are required for the

working in high place.

2. Structural performance of PSRC column

Figure 3. Semiconductor FAB (bolt-connected PSRC composite column).

Figure 2. Semiconductor FAB (weld-connected PSRC composite column).

2.1. Contribution of transverse reinforcement

Figures 2 and 3 show field application of weld-connected and bolt-connected PSRC composite columns, respectively. Generally, the PSRC composite column with 20 m height and 1.5 m 1.5 m to 2.0 m 2.0 m sectional area is used for two- or three-story construction at the same time. In the case of the weld-connected PSRC composite column, the steel cage of angles and transverse reinforcement is moved to construction site, and then concrete form is installed (Figure 2). On the other hand, in the case of the bolt-connected PSRC composite column, Prefabricated Steel-Reinforced Concrete Composite Column http://dx.doi.org/10.5772/intechopen.77166 61

Figure 2. Semiconductor FAB (weld-connected PSRC composite column).

Figure 3. Semiconductor FAB (bolt-connected PSRC composite column).

section to the overall flexural capacity of the column could be limited. Further, the need for rebar and formwork construction requires considerable construction time. Particularly, in mega structures such as semiconductor factory and warehouse using long and large sized

Figure 1. Comparison of CES column and PSRC columns. (a) CES composite column, (b) PSRC composite column (weld

In order to improve structural capacity and cost efficiency, a prefabricated steel-reinforced concrete (PSRC) composite column has been used. As shown in Figure 1(b) and (c), the prefabricated steel angles at the four corners replace the conventional wide-flange steel, and the steel angles are weld connected or bolt connected with transverse bars or plates [1–5]. The weld connection should follow the details prescribed in welding standards [6, 7]. The steel angles resist axial load and flexural moment. The transverse bars and plates provide shear resistance, concrete confinement, and bond resistance between the steel angles and concrete. Because the steel cage of angles and transverse reinforcement are prefabricated off site, field rebar work is unnecessary. Further, the self-erectable steel cage can provide sufficient strength and rigidity to support the construction loads of beams and slabs that are superimposed on the

Figures 2 and 3 show field application of weld-connected and bolt-connected PSRC composite columns, respectively. Generally, the PSRC composite column with 20 m height and 1.5 m 1.5 m to 2.0 m 2.0 m sectional area is used for two- or three-story construction at the same time. In the case of the weld-connected PSRC composite column, the steel cage of angles and transverse reinforcement is moved to construction site, and then concrete form is installed (Figure 2). On the other hand, in the case of the bolt-connected PSRC composite column,

columns, fast and safe construction methods are necessary.

connection), (c) PSRC composite column (bolt connection)

60 New Trends in Structural Engineering

PSRC composite column.

concrete form is preattached to the steel cage and it can be permanently used after concrete pouring (Figure 3). Thus, field work related to reinforcing bar placement and concrete form work is excluded, which improves the construction safety and saves the construction time at working in high place.

#### 2. Structural performance of PSRC column

#### 2.1. Contribution of transverse reinforcement

The prefabricated steel angle composite columns strongly depend on the transverse reinforcement that connects the corner steel angles. The transverse reinforcement provides (1) shear transfer between the steel angles, (2) bond between the steel angles and concrete, (3) buckling resistance for the steel angles, and (4) lateral confinement for the core concrete. To satisfy the requirements of (3) and (4), close spacing as well as sufficient strength are required for the transverse reinforcement. However, the transverse bars welded to steel angles or the transverse plates bolt-connected to steel angles may cause premature tensile fracture of the connection, which should be considered in design.

Cover concrete provides local buckling resistance and fire resistance for the steel angles. However, when the transverse bars are not closely spaced, the PSRC composite columns are vulnerable to premature spalling of the cover concrete due to smooth surface of steel angles. Particularly, when the columns are subjected to high axial compression force, the load-carrying capacity and deformation capacity of the PSRC composite columns can be degraded by early spalling of the cover concrete. Further, under cyclic lateral loading, the PSRC composite columns are expected to be more susceptible to such damages as the ductility demand increases.

#### 2.2. Compressive strength

#### 2.2.1. Design method

The nominal compressive strengths Pn of a PSRC composite column under concentric axial loading can be evaluated by current design code equations for a concrete-encased steel composite column. For example, AISC 360–10 [8] specifies the nominal compressive strength based on plastic stress and column length effect.

$$P\_n = P\_{no} \cdot 0.658^{(P\_0/P\_e)} \tag{1}$$

$$P\_{no} = 0.85f\_c' \left(A\_g - A\_s - A\_{sr}\right) + F\_y A\_s + f\_{yr} A\_{sr} \tag{2}$$

$$P\_{\varepsilon} = \pi^2 \left( E I\_{\text{eff}} \right) / \left( \text{KL} \right)^2 \tag{3}$$

Figure 5(a), performance points A and B indicate pure compressive strength Pno and moment strength Mn, respectively. Performance points C indicates the compressive strength Pnc corresponding to the moment Mn. Performance points D indicates the maximum moment strength corresponding to Pnc/2. Considering the slenderness effect of columns, each performance point should be decreased by multiplying the slenderness reduction factor λ to the compressive strength (where λ = ratio of Pn to Pno). Further, using the strain-compatibility

Figure 5. Section analysis methods of PSRC column under eccentric axial loading: (a) P-M interaction diagram and

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Figure 6 shows the test setup for the concentric axial loading and eccentric axial loading tests. The eccentricity can be controlled using the distance between the column center and loading center. During the test, the load-carrying capacity, axial shortening, and horizontal expansion were measured to evaluate the structural performance of the PSRC composite columns.

Figure 7(a) compares the axial load-strain relationships of a CES and PSRC composite columns using steel ratio of 2.0% under concentric axial compression force [3–5]. The axial load behavior of the PSRC composite column was similar to that of the CES composite column. The

method, P-M interaction diagram can be estimated (Figure 5(b)).

Figure 4. Stress–strain relationships of concrete and steel for numerical analysis.

2.2.2. Structural test

(b) strain-compatibility method.

$$EI\_{\rm eff} = E\_s I\_s + 0.5E\_s I\_{sr} + C\_1 E\_c I\_c \tag{4}$$

$$\mathcal{L}\_1 = 0.1 + 2A\_s/(A\_c + A\_s) \le 0.3\tag{5}$$

where Pno = maximum compressive strength of the composite column; Pe = elastic buckling strength of the column; fc' = concrete strength; Fy and As = yield strength and area of the steel section, respectively; fyr and Asr = yield strength and area of the longitudinal bars, respectively; EIeff = effective flexural stiffness of the composite column; KL = effective buckling length; Es = elastic modulus of steel; Ec = elastic modulus of concrete (= 4700√fc'); Is, Isr, and Ic = secondorder moments of inertia of the steel section, reinforcing bar, and concrete, respectively, with respect to the centroid of the column section; and Ac = concrete area.

For better evaluation of the load-carrying capacity of a PSRC composite column, numerical analysis using the stress–strain relationship of confined concrete, unconfined concrete, and steel can be used as shown in Figure 4 [1, 3]. The numerical analysis can be performed using strain compatibility method [9]. The stress–strain relationship of confined and unconfined concrete can be determined from various existing models [10–12].

The nominal compressive strengths Pn of a PSRC composite column under eccentric axial loading can be evaluated by assuming plastic stress distribution of the composite section. In

Figure 4. Stress–strain relationships of concrete and steel for numerical analysis.

Figure 5. Section analysis methods of PSRC column under eccentric axial loading: (a) P-M interaction diagram and (b) strain-compatibility method.

Figure 5(a), performance points A and B indicate pure compressive strength Pno and moment strength Mn, respectively. Performance points C indicates the compressive strength Pnc corresponding to the moment Mn. Performance points D indicates the maximum moment strength corresponding to Pnc/2. Considering the slenderness effect of columns, each performance point should be decreased by multiplying the slenderness reduction factor λ to the compressive strength (where λ = ratio of Pn to Pno). Further, using the strain-compatibility method, P-M interaction diagram can be estimated (Figure 5(b)).

#### 2.2.2. Structural test

transverse reinforcement. However, the transverse bars welded to steel angles or the transverse plates bolt-connected to steel angles may cause premature tensile fracture of the connection,

Cover concrete provides local buckling resistance and fire resistance for the steel angles. However, when the transverse bars are not closely spaced, the PSRC composite columns are vulnerable to premature spalling of the cover concrete due to smooth surface of steel angles. Particularly, when the columns are subjected to high axial compression force, the load-carrying capacity and deformation capacity of the PSRC composite columns can be degraded by early spalling of the cover concrete. Further, under cyclic lateral loading, the PSRC composite columns

The nominal compressive strengths Pn of a PSRC composite column under concentric axial loading can be evaluated by current design code equations for a concrete-encased steel composite column. For example, AISC 360–10 [8] specifies the nominal compressive strength based

<sup>c</sup> Ag � As � Asr

where Pno = maximum compressive strength of the composite column; Pe = elastic buckling strength of the column; fc' = concrete strength; Fy and As = yield strength and area of the steel section, respectively; fyr and Asr = yield strength and area of the longitudinal bars, respectively; EIeff = effective flexural stiffness of the composite column; KL = effective buckling length; Es = elastic modulus of steel; Ec = elastic modulus of concrete (= 4700√fc'); Is, Isr, and Ic = secondorder moments of inertia of the steel section, reinforcing bar, and concrete, respectively, with

For better evaluation of the load-carrying capacity of a PSRC composite column, numerical analysis using the stress–strain relationship of confined concrete, unconfined concrete, and steel can be used as shown in Figure 4 [1, 3]. The numerical analysis can be performed using strain compatibility method [9]. The stress–strain relationship of confined and unconfined

The nominal compressive strengths Pn of a PSRC composite column under eccentric axial loading can be evaluated by assuming plastic stress distribution of the composite section. In

Pe <sup>¼</sup> <sup>π</sup><sup>2</sup> EIeff

Pn <sup>¼</sup> Pno � <sup>0</sup>:658ð Þ <sup>P</sup>0=Pe (1)

<sup>þ</sup> FyAs <sup>þ</sup> <sup>f</sup> yrAsr (2)

EIeff ¼ EsIs þ 0:5EsIsr þ C1EcIc (4)

C<sup>1</sup> ¼ 0:1 þ 2As=ð Þ Ac þ As ≤ 0:3 (5)

<sup>=</sup>ð Þ KL <sup>2</sup> (3)

are expected to be more susceptible to such damages as the ductility demand increases.

which should be considered in design.

62 New Trends in Structural Engineering

2.2. Compressive strength

on plastic stress and column length effect.

Pno ¼ 0:85f

respect to the centroid of the column section; and Ac = concrete area.

concrete can be determined from various existing models [10–12].

0

2.2.1. Design method

Figure 6 shows the test setup for the concentric axial loading and eccentric axial loading tests. The eccentricity can be controlled using the distance between the column center and loading center. During the test, the load-carrying capacity, axial shortening, and horizontal expansion were measured to evaluate the structural performance of the PSRC composite columns.

Figure 7(a) compares the axial load-strain relationships of a CES and PSRC composite columns using steel ratio of 2.0% under concentric axial compression force [3–5]. The axial load behavior of the PSRC composite column was similar to that of the CES composite column. The

composite columns, the P-M interaction curves of design codes were similarly predicted at the load level of 0.2Pn to 0.5Pn, regardless of the assumption for the stress distribution. Further, the maximum flexural strength predictions of the PSRC composite columns were greater than those of the CES composite columns, because of the steel angles placed at the four corners of the column. This result indicates that when the same amount of the steel is used for composite columns, the flexural strength of PSRC composite columns can be greater than that of CES

The ultimate flexural strength of a PSRC composite column can be evaluated by performing a section analysis based on either plastic stresses (i.e., plastic stress method) or strain-induced stresses (i.e., strain-compatibility method); the stresses of the steel angles, reinforcing bars, and concrete are determined by linear strain distribution and the stress–strain relationships of the materials [1]. Figure 8 shows the stress distributions at the PSRC cross section by two methods. For the plastic stress method (Figure 8(a)), plastic stresses of concrete, steel angles, and

method (Figure 8(b)), strain-induced stresses of angles, reinforcing bars, and concrete can be

ε

where σs, σr, σ<sup>c</sup> = strain-induced stresses of angles, re-bars, and concrete, respectively; ε = strain which is linearly proportional to the distance from the neutral axis; εco = strain corresponding

stress and strain are negative values. Perfect bond (or full composite action) between steel

Figure 8. Section analysis methods of PSRC column: (a) plastic stress method and (b) strain-compatibility method.

, Fy, and Fyr, respectively. For the strain-compatibility

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�Fy ≤ σ<sup>s</sup> ¼ Esε ≤ Fy (6)

�Fyr ≤ σ<sup>r</sup> ¼ Esε ≤ Fyr (7)

<sup>ε</sup>co � �<sup>2</sup> ! for � <sup>ε</sup>cu <sup>≤</sup> <sup>ε</sup> <sup>≤</sup> <sup>0</sup> (8)

<sup>c</sup>; and εcu = ultimate strain of concrete. In σs, σr, σc, and ε, compressive

composite columns under general design compression load (= 0.2Pn ~ 0.5Pn).

0

determined assuming linear distribution of strain over the entire cross section.

σ<sup>c</sup> ¼ f 0 c 2ε εco þ

0

2.3. Flexural strength

2.3.1. Flexural design method

to the concrete strength f

reinforcing bars can be used as 0.85fc

Figure 6. Test setup of compressive loading tests: (a) concentric axial loading and (b) eccentric axial loading.

Figure 7. Axial load-carrying capacities of CES and PSRC columns: (a) concentric axial loading and (b) eccentric axial loading.

contribution of the steel angles to the lateral confinement increased the peak strength Pu and the deformation capacity in the PSRC composite column. Under concentric axial force, local buckling of the steel angles was not observed. After the peak strengths, significant cracking and subsequent concrete spalling occurred. Particularly, the early spalling can be initiated at the corners of the cross section because of the smooth surface of the angle. Thus, to secure robust axial load behavior of the PSRC composite columns under high axial load, it is recommended that the spacing of transverse reinforcement be decreased to half of the requirement of CES composite columns.

Figure 7(b) compares the P-M interaction curves of design codes [8, 13, 14] with the test results of CES and PSRC composite columns under eccentric load with a low eccentricity ratio of e/h = 0.1 and 0.3. As the eccentricity ratio increased, the structural behavior changed from compression to flexure. The peak strength of the CES composite column was less than that of the PSRC composite column with e/h = 0.3. This is because the effective compressive area of the steel and concrete sections was increased in the PSRC composite column with large eccentricity. In the PSRC

composite columns, the P-M interaction curves of design codes were similarly predicted at the load level of 0.2Pn to 0.5Pn, regardless of the assumption for the stress distribution. Further, the maximum flexural strength predictions of the PSRC composite columns were greater than those of the CES composite columns, because of the steel angles placed at the four corners of the column. This result indicates that when the same amount of the steel is used for composite columns, the flexural strength of PSRC composite columns can be greater than that of CES composite columns under general design compression load (= 0.2Pn ~ 0.5Pn).

#### 2.3. Flexural strength

contribution of the steel angles to the lateral confinement increased the peak strength Pu and the deformation capacity in the PSRC composite column. Under concentric axial force, local buckling of the steel angles was not observed. After the peak strengths, significant cracking and subsequent concrete spalling occurred. Particularly, the early spalling can be initiated at the corners of the cross section because of the smooth surface of the angle. Thus, to secure robust axial load behavior of the PSRC composite columns under high axial load, it is recommended that the spacing of transverse reinforcement be decreased to half of the require-

Figure 7. Axial load-carrying capacities of CES and PSRC columns: (a) concentric axial loading and (b) eccentric axial

Figure 6. Test setup of compressive loading tests: (a) concentric axial loading and (b) eccentric axial loading.

Figure 7(b) compares the P-M interaction curves of design codes [8, 13, 14] with the test results of CES and PSRC composite columns under eccentric load with a low eccentricity ratio of e/h = 0.1 and 0.3. As the eccentricity ratio increased, the structural behavior changed from compression to flexure. The peak strength of the CES composite column was less than that of the PSRC composite column with e/h = 0.3. This is because the effective compressive area of the steel and concrete sections was increased in the PSRC composite column with large eccentricity. In the PSRC

ment of CES composite columns.

loading.

64 New Trends in Structural Engineering

#### 2.3.1. Flexural design method

The ultimate flexural strength of a PSRC composite column can be evaluated by performing a section analysis based on either plastic stresses (i.e., plastic stress method) or strain-induced stresses (i.e., strain-compatibility method); the stresses of the steel angles, reinforcing bars, and concrete are determined by linear strain distribution and the stress–strain relationships of the materials [1]. Figure 8 shows the stress distributions at the PSRC cross section by two methods. For the plastic stress method (Figure 8(a)), plastic stresses of concrete, steel angles, and reinforcing bars can be used as 0.85fc 0 , Fy, and Fyr, respectively. For the strain-compatibility method (Figure 8(b)), strain-induced stresses of angles, reinforcing bars, and concrete can be determined assuming linear distribution of strain over the entire cross section.

$$-F\_y \le \sigma\_s = E\_s \varepsilon \le F\_y \tag{6}$$

$$-F\_{yr} \le \sigma\_r = E\_s \varepsilon \le F\_{yr} \tag{7}$$

$$
\sigma\_{\varepsilon} = f\_{\varepsilon}' \left( \frac{2\varepsilon}{\varepsilon\_{\alpha}} + \left(\frac{\varepsilon}{\varepsilon\_{\alpha}}\right)^2 \right) \text{ for } -\varepsilon\_{\varepsilon u} \le \varepsilon \le 0 \tag{8}
$$

where σs, σr, σ<sup>c</sup> = strain-induced stresses of angles, re-bars, and concrete, respectively; ε = strain which is linearly proportional to the distance from the neutral axis; εco = strain corresponding to the concrete strength f 0 <sup>c</sup>; and εcu = ultimate strain of concrete. In σs, σr, σc, and ε, compressive stress and strain are negative values. Perfect bond (or full composite action) between steel

Figure 8. Section analysis methods of PSRC column: (a) plastic stress method and (b) strain-compatibility method.

angles and concrete is assumed for the section analysis. For confined concrete, the stress–strain relationship of the confined concrete can be used.

#### 2.3.2. Shear design method

The shear resistance of a PSRC composite column is provided by concrete, transverse reinforcement, and steel angles. Since the dimensions of the angle cross section are significantly less than that of the entire cross section, the contribution of the angles to the shear strength is neglected. Thus, the nominal shear strength Vn of a PSRC composite column can be calculated, on the basis of current RC design code [13].

$$V\_{\
u} = \frac{1}{6} \sqrt{f\_c'}bd + A\_{st}F\_{yt}\frac{d}{s} \le \frac{5}{6} \sqrt{f\_c'}bd\tag{9}$$

Bn ¼ α 0:85f

the transverse reinforcement.

three points need to be measured.

Figure 10. Test setup of flexural loading tests.

2.3.4. Structural test

0 <sup>c</sup> <sup>2</sup>dbt ð Þ lwt ls

where dbt = diameter or thickness of a transverse reinforcement projected from the angle surface; lwt = weld length of a transverse bar or projected length of a transverse plate from the angle surface; ls = shear span length of the PSRC composite column; and α = a factor addressing the confinement effect on the bearing area (≤2.0). After spalling of concrete cover at large inelastic flexural deformation, concrete bearing disappears and is replaced by dowel action of

Figure 10 shows the test setup for the flexural loading tests to investigate the flexural and shear strengths, shear transfer between steel angle and concrete, and strength at the joint between steel angle and transverse reinforcement. The columns are simply supported, and two-point loading is applied at the center of the columns. To estimate the curvature, deflections at least

Figure 11(a) shows the moment-curvature relationships at the center span of a CES column and a PSRC column with a cross section of 500 mm � 500 mm (i.e., 2.0% steel ratio) [1]. In the PSRC column using the same steel ratio of the CES column, the peak strength was 56.7% greater than that of the CES column for the following reasons: (1) the yield strength of the steel angles used for the PSRC column was 15.9% greater than that of the wide-flange steel section used for the CES column and (2) the angles placed at the four corners of the cross section can develop 35.2% higher nominal flexural capacity than the center wide-flange steel section. In the PSRC column, the load-carrying capacity was suddenly decreased when bond failure (i.e., concrete bearing failure) occurred in the bottom angles in the shear span (Figure 12(b)). After the bond failure, dowel action of the transverse bars developed, causing significant bond-slip deformation. Ultimately, it failed due to the fracture of the transverse bars and spalling of web concrete, which was the typical bond-shear failure mode of the PSRC composite column.

Figure 11(b) compares the effect of transverse reinforcement spacing on the moment-curvature relationship of PSRC composite columns with a smaller cross section of 400 mm � 400 mm

s

(10)

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Prefabricated Steel-Reinforced Concrete Composite Column

where b = width of the cross section; d = effective depth of the cross section; and Ast, Fyt, and s = area, yield stress, and spacing of the transverse reinforcement, respectively.

#### 2.3.3. Bond strength design method

Figure 9 shows the details of the weld- or bolt-connection between the steel angles and transverse reinforcement. Before spalling of concrete cover, the shear transfer between the steel angles and concrete is provided by friction of the angle surface and concrete bearing of the transverse reinforcement projected from the angle surface. Conservatively neglecting the frictional resistance, the nominal bond strength Bn of a steel angle is provided by the concrete bearing of the transverse reinforcement [1].

Figure 9. Bond strength between steel angle and concrete.

Prefabricated Steel-Reinforced Concrete Composite Column http://dx.doi.org/10.5772/intechopen.77166 67

$$B\_{\rm tr} = \alpha \left[ 0.85 f\_c'(2d\_{bt}l\_{wt}) \right] \left( \frac{l\_s}{s} \right) \tag{10}$$

where dbt = diameter or thickness of a transverse reinforcement projected from the angle surface; lwt = weld length of a transverse bar or projected length of a transverse plate from the angle surface; ls = shear span length of the PSRC composite column; and α = a factor addressing the confinement effect on the bearing area (≤2.0). After spalling of concrete cover at large inelastic flexural deformation, concrete bearing disappears and is replaced by dowel action of the transverse reinforcement.

#### 2.3.4. Structural test

angles and concrete is assumed for the section analysis. For confined concrete, the stress–strain

The shear resistance of a PSRC composite column is provided by concrete, transverse reinforcement, and steel angles. Since the dimensions of the angle cross section are significantly less than that of the entire cross section, the contribution of the angles to the shear strength is neglected. Thus, the nominal shear strength Vn of a PSRC composite column can be calculated,

bd þ AstFyt

where b = width of the cross section; d = effective depth of the cross section; and Ast, Fyt, and

Figure 9 shows the details of the weld- or bolt-connection between the steel angles and transverse reinforcement. Before spalling of concrete cover, the shear transfer between the steel angles and concrete is provided by friction of the angle surface and concrete bearing of the transverse reinforcement projected from the angle surface. Conservatively neglecting the frictional resistance, the nominal bond strength Bn of a steel angle is provided by the concrete

d s ≤ 5 6

ffiffiffiffi f 0 c q

bd (9)

relationship of the confined concrete can be used.

on the basis of current RC design code [13].

bearing of the transverse reinforcement [1].

Figure 9. Bond strength between steel angle and concrete.

2.3.3. Bond strength design method

Vn <sup>¼</sup> <sup>1</sup> 6

ffiffiffiffi f 0 c q

s = area, yield stress, and spacing of the transverse reinforcement, respectively.

2.3.2. Shear design method

66 New Trends in Structural Engineering

Figure 10 shows the test setup for the flexural loading tests to investigate the flexural and shear strengths, shear transfer between steel angle and concrete, and strength at the joint between steel angle and transverse reinforcement. The columns are simply supported, and two-point loading is applied at the center of the columns. To estimate the curvature, deflections at least three points need to be measured.

Figure 11(a) shows the moment-curvature relationships at the center span of a CES column and a PSRC column with a cross section of 500 mm � 500 mm (i.e., 2.0% steel ratio) [1]. In the PSRC column using the same steel ratio of the CES column, the peak strength was 56.7% greater than that of the CES column for the following reasons: (1) the yield strength of the steel angles used for the PSRC column was 15.9% greater than that of the wide-flange steel section used for the CES column and (2) the angles placed at the four corners of the cross section can develop 35.2% higher nominal flexural capacity than the center wide-flange steel section. In the PSRC column, the load-carrying capacity was suddenly decreased when bond failure (i.e., concrete bearing failure) occurred in the bottom angles in the shear span (Figure 12(b)). After the bond failure, dowel action of the transverse bars developed, causing significant bond-slip deformation. Ultimately, it failed due to the fracture of the transverse bars and spalling of web concrete, which was the typical bond-shear failure mode of the PSRC composite column.

Figure 11(b) compares the effect of transverse reinforcement spacing on the moment-curvature relationship of PSRC composite columns with a smaller cross section of 400 mm � 400 mm

Figure 10. Test setup of flexural loading tests.

The moment-curvature relationship and failure mode of the PSRC composite column with greater transverse reinforcement spacing of 200 mm were similar to those of the PSRC composite column with transverse reinforcement spacing of 100 mm. It failed due to tensile fracture of the angles in the uniform moment span (Figure 12(d)). In the PSRC composite column with the greatest transverse reinforcement spacing of 300 mm, bond failure occurred in the bottom angles. After the bond failure, the load-carrying capacity was significantly decreased due to spalling of web concrete caused by dowel action of the transverse reinforcement. Ultimately, it failed due to

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Figure 13 shows the test setup of cyclic loading tests for CES and PSRC composite columns. Using two oil jacks, a uniform axial load corresponding to about 22% of compressive capacity

Figure 14 compares the cyclic behaviors of the CES and PSRC composite columns using steel ratio of 2.2%. In the CES composite column, the load-carrying capacity gradually decreased after the peak strength. Although spalling of the cover concrete occurred at the lateral drift of 3.0–4.0% in the plastic hinge region, the load-carrying capacity was not significantly decreased. However, after the spalling of the cover concrete, post-yield buckling occurred in the longitudinal bars. Ultimately, it failed at the drift ratio of 7.0% because of a low cycle fatigue fracture of the longitudinal bars. In the PSRC composite column, the peak strength was 20% greater than that of the CES composite column because of the higher yield strength and the location of the steel angles. Spalling of the cover concrete occurred at the drift ratio of 3.0%, and significant shear cracks occurred in the plastic hinge region because of the increased shear demand. The angles and transverse reinforcement were exposed because of the spalling of cover concrete at the drift ratio of 5.0%. The exposed angles and longitudinal bars were subjected to local

are applied, and a cyclic lateral load is applied using an actuator to the column.

fracture of the transverse reinforcement (Figure 12(e)).

2.4. Seismic performance

Figure 13. Test setup of cyclic loading tests.

Figure 11. Moment-curvature relationships at the center span of CES and PSRC columns: (a) CES and PSRC columns; (b) PSRC columns according to transverse bar spacing.

Figure 12. Failure modes of CES and PSRC columns. (a) CES column, (b) PSRC column, (c) PSRC column @ 100 mm tie, (d) PSRC column @ 200 mm tie, (e) PSRC column @ 300 mm tie

(i.e., 3.1% steel ratio). When the transverse reinforcement at a spacing of 100 mm was used, the load-carrying capacity was degraded due to spalling of cover concrete in the uniform moment span, but was slightly recovered due to the strain hardening of the steel angles. Ultimately, it failed due to the tensile fracture of the bottom angle in the uniform moment span (Figure 12(c)). The moment-curvature relationship and failure mode of the PSRC composite column with greater transverse reinforcement spacing of 200 mm were similar to those of the PSRC composite column with transverse reinforcement spacing of 100 mm. It failed due to tensile fracture of the angles in the uniform moment span (Figure 12(d)). In the PSRC composite column with the greatest transverse reinforcement spacing of 300 mm, bond failure occurred in the bottom angles. After the bond failure, the load-carrying capacity was significantly decreased due to spalling of web concrete caused by dowel action of the transverse reinforcement. Ultimately, it failed due to fracture of the transverse reinforcement (Figure 12(e)).

#### 2.4. Seismic performance

Figure 13 shows the test setup of cyclic loading tests for CES and PSRC composite columns. Using two oil jacks, a uniform axial load corresponding to about 22% of compressive capacity are applied, and a cyclic lateral load is applied using an actuator to the column.

Figure 14 compares the cyclic behaviors of the CES and PSRC composite columns using steel ratio of 2.2%. In the CES composite column, the load-carrying capacity gradually decreased after the peak strength. Although spalling of the cover concrete occurred at the lateral drift of 3.0–4.0% in the plastic hinge region, the load-carrying capacity was not significantly decreased. However, after the spalling of the cover concrete, post-yield buckling occurred in the longitudinal bars. Ultimately, it failed at the drift ratio of 7.0% because of a low cycle fatigue fracture of the longitudinal bars. In the PSRC composite column, the peak strength was 20% greater than that of the CES composite column because of the higher yield strength and the location of the steel angles. Spalling of the cover concrete occurred at the drift ratio of 3.0%, and significant shear cracks occurred in the plastic hinge region because of the increased shear demand. The angles and transverse reinforcement were exposed because of the spalling of cover concrete at the drift ratio of 5.0%. The exposed angles and longitudinal bars were subjected to local

Figure 13. Test setup of cyclic loading tests.

(i.e., 3.1% steel ratio). When the transverse reinforcement at a spacing of 100 mm was used, the load-carrying capacity was degraded due to spalling of cover concrete in the uniform moment span, but was slightly recovered due to the strain hardening of the steel angles. Ultimately, it failed due to the tensile fracture of the bottom angle in the uniform moment span (Figure 12(c)).

Figure 12. Failure modes of CES and PSRC columns. (a) CES column, (b) PSRC column, (c) PSRC column @ 100 mm tie,

Figure 11. Moment-curvature relationships at the center span of CES and PSRC columns: (a) CES and PSRC columns;

(b) PSRC columns according to transverse bar spacing.

68 New Trends in Structural Engineering

(d) PSRC column @ 200 mm tie, (e) PSRC column @ 300 mm tie

Figure 14. Lateral load-drift relationships of CES and PSRC columns: (a) CES column and (b) PSRC column.

buckling during repeated cyclic loading. As a result, the load-carrying capacity was degraded. However, despite the local buckling of angles and longitudinal bars, tensile fracture did not occur at the joint between the angles and transverse reinforcement.

> inside the U-shaped section (Figure 16(b)), and the strut-and-tie action between the concrete (outside of the U-shaped section) and the band plates (Figure 16(c)) [2]. The shear strength Vws

> Figure 16. Joint shear strength mechanisms. (a) Web shear yielding (Vws), (b) Concrete diagonal strut (Vcs), (c) Strut and tie

Figure 15. Beam-column joint details: (a) interior beam-column joint and (b) exterior beam-column joint.

where tw = web thickness; and hwj = effective horizontal length of the web in the joint in the

0

0

The shear strength Vcs of the direct concrete strut is defined as follows:

bic hc ≤ 0:5f

bic hc ≤ 0:5f

ffiffiffiffi f 0 c q

ffiffiffiffi f 0 c q

Vws ¼ ð Þ� 2 0:6Fytwhwj (11)

<sup>c</sup> bic hb for the interior joint (12)

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<sup>c</sup> bic hb for the exterior joint (13)

of the two web plates is defined as follows:

action (Vst), (d) Effective width bo for interior joint, (e) Joint shear demand.

Vcs ¼ 1:7

Vcs ¼ 1:2

direction of the shear.

#### 2.5. Beam-column joint

#### 2.5.1. Design method

Figure 15 shows a U-shaped composite beam-PSRC composite column connection. In order to minimize the workability problem during concrete pouring, only the web plate of the U-section is passed through the joint, and the top and bottom flanges are connected to the top and bottom band plates in the joint. Under high axial compressive force and cyclic lateral loading, premature cover concrete spalling of the joint may deteriorate the connection's strength and deformation capacity.

Figure 16 shows the three mechanisms that contribute to the joint shear strength: web shear yielding of the U-shaped steel section (Figure 16(a)), direct strut action of the in-filled concrete

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Figure 15. Beam-column joint details: (a) interior beam-column joint and (b) exterior beam-column joint.

Figure 16. Joint shear strength mechanisms. (a) Web shear yielding (Vws), (b) Concrete diagonal strut (Vcs), (c) Strut and tie action (Vst), (d) Effective width bo for interior joint, (e) Joint shear demand.

inside the U-shaped section (Figure 16(b)), and the strut-and-tie action between the concrete (outside of the U-shaped section) and the band plates (Figure 16(c)) [2]. The shear strength Vws of the two web plates is defined as follows:

$$V\_{\rm us} = (2) \cdot 0.6 F\_y t\_w h\_{wj} \tag{11}$$

where tw = web thickness; and hwj = effective horizontal length of the web in the joint in the direction of the shear.

The shear strength Vcs of the direct concrete strut is defined as follows:

buckling during repeated cyclic loading. As a result, the load-carrying capacity was degraded. However, despite the local buckling of angles and longitudinal bars, tensile fracture did not

Figure 14. Lateral load-drift relationships of CES and PSRC columns: (a) CES column and (b) PSRC column.

Figure 15 shows a U-shaped composite beam-PSRC composite column connection. In order to minimize the workability problem during concrete pouring, only the web plate of the U-section is passed through the joint, and the top and bottom flanges are connected to the top and bottom band plates in the joint. Under high axial compressive force and cyclic lateral loading, premature cover concrete spalling of the joint may deteriorate the connection's strength and deformation

Figure 16 shows the three mechanisms that contribute to the joint shear strength: web shear yielding of the U-shaped steel section (Figure 16(a)), direct strut action of the in-filled concrete

occur at the joint between the angles and transverse reinforcement.

2.5. Beam-column joint

70 New Trends in Structural Engineering

2.5.1. Design method

capacity.

$$V\_{cs} = 1.7\sqrt{f\_c'}b\_{ic}h\_c \le 0.5f\_c'b\_{ic}h\_b \quad \text{for the interior joint} \tag{12}$$

$$V\_{\infty} = 1.2\sqrt{f\_c'}b\_{ic}h\_c \le 0.5f\_c' \, b\_{ic}h\_b \quad \text{for the exterior joint} \tag{13}$$

where bic = width of the in-filled concrete, hc = depth of the PSRC composite column; and hb = overall depth of the composite beam including the concrete slab.

The shear strength Vst of the strut-and-tie action is defined as follows:

$$V\_{st} = 0.4\sqrt{f\_c'}b\_o h\_o \tag{14}$$

$$b\_o = b\_{af} - b\_{ic} - \mathcal{D}t\_w \tag{15}$$

where bo = effective width of the joint concrete; ho = effective length of the joint concrete in the direction of shear; baf = distance between the corner angles in the direction orthogonal to the shear; and bic and tw = width of the in-filled concrete and web of the U-shaped section, respectively.

For the strut-and-tie mechanism in Eq. (14), the tension force caused by the concrete strut should be resisted by the top and bottom band plates. Thus, the required cross-sectional area Abp of each band plate is calculated as follows:

$$A\_{bp} \geq \frac{V\_{st}}{2F\_{ybp}}\tag{16}$$

where 2Fybp = yield strength of the top and bottom band plates.

The joint shear capacity and demand can be expressed as moments, from the static moment equilibrium at the joint (Figure 16(e)).

$$
\sum M\_{\rm nc} - \sum V\_b h\_o / 2 \le \phi M\_{\rm nc} \tag{17}
$$

plates were not connected to the bottom flange of the U-section, the band plates were not damaged even after cover concrete spalling. However, a gap occurred between the end of the U-section and the column face under positive moments, which was attributed to an anchorage slip of the web plates showing plastic strains inside the joint. As the anchorage slip increased, development of the beam's flexural capacities was delayed, which caused significant pinching in the cyclic behavior. The top band plates welded to the top flange of the U-section were pulled out under a negative moment. In the exterior beam-column joint, after the peak strengths, the load-carrying capacity was significantly degraded because of cover concrete spalling in the PSRC composite column and because of local buckling and fracture of the web

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Figure 17. Lateral load-drift relationships: (a) interior beam-column joint and (b) exterior beam-column joint.

In this chapter, a prefabricated steel-reinforced concrete (PSRC) composite column using steel angles was introduced. Using current design codes, the structural capacities of PSRC composite columns can be evaluated, and it shows better performance than those of a conventional

in the composite beam. The steel angles of the column were completely exposed.

3. Conclusions

concrete-encased steel (CES) composite column.

$$
\sum M\_{\rm uc} = \sum M\_{bp} + \sum V\_b h\_c / 2 - V\_c h\_b \tag{18}
$$

$$M\_{nc} = V\_{ws}d\_w + V\_{cs}(0.75h\_b) + V\_{st}d\_b \tag{19}$$

where (ΣMuc - ΣVb ho/2) and Mnc = joint shear demand and capacity, respectively; ΣMpb and ΣVb = sums of the plastic moments and shear demands, respectively, of the composite beams framing into the joint; Vc = column shear demand; dw = center-to-center distance between the top and bottom flanges; 0.75hb = approximate moment arm for the composite beam section; and db = center-to-center distance between the top and bottom band plates.

#### 2.5.2. Structural test

Figure 17 shows the cyclic lateral load-story drift ratio relationships of U-shaped steel composite beam-PSRC composite column joints. The composite beam has 330 mm width and 700 mm height including slab. The PSRC composite column has 800 mm � 800 mm crosssectional area. In the interior beam-column joint, cover concrete spalling in the PSRC composite column occurred in the vicinity of the U-section, whose web plate buckled, and severe diagonal cracking occurred in the joint face. The fracture was initiated at the weld joint between the web and the bottom flange and then propagated vertically. Because the band

Figure 17. Lateral load-drift relationships: (a) interior beam-column joint and (b) exterior beam-column joint.

plates were not connected to the bottom flange of the U-section, the band plates were not damaged even after cover concrete spalling. However, a gap occurred between the end of the U-section and the column face under positive moments, which was attributed to an anchorage slip of the web plates showing plastic strains inside the joint. As the anchorage slip increased, development of the beam's flexural capacities was delayed, which caused significant pinching in the cyclic behavior. The top band plates welded to the top flange of the U-section were pulled out under a negative moment. In the exterior beam-column joint, after the peak strengths, the load-carrying capacity was significantly degraded because of cover concrete spalling in the PSRC composite column and because of local buckling and fracture of the web in the composite beam. The steel angles of the column were completely exposed.

#### 3. Conclusions

where bic = width of the in-filled concrete, hc = depth of the PSRC composite column; and

where bo = effective width of the joint concrete; ho = effective length of the joint concrete in the direction of shear; baf = distance between the corner angles in the direction orthogonal to the shear; and bic and tw = width of the in-filled concrete and web of the U-shaped section,

For the strut-and-tie mechanism in Eq. (14), the tension force caused by the concrete strut should be resisted by the top and bottom band plates. Thus, the required cross-sectional area

The joint shear capacity and demand can be expressed as moments, from the static moment

where (ΣMuc - ΣVb ho/2) and Mnc = joint shear demand and capacity, respectively; ΣMpb and ΣVb = sums of the plastic moments and shear demands, respectively, of the composite beams framing into the joint; Vc = column shear demand; dw = center-to-center distance between the top and bottom flanges; 0.75hb = approximate moment arm for the composite beam section;

Figure 17 shows the cyclic lateral load-story drift ratio relationships of U-shaped steel composite beam-PSRC composite column joints. The composite beam has 330 mm width and 700 mm height including slab. The PSRC composite column has 800 mm � 800 mm crosssectional area. In the interior beam-column joint, cover concrete spalling in the PSRC composite column occurred in the vicinity of the U-section, whose web plate buckled, and severe diagonal cracking occurred in the joint face. The fracture was initiated at the weld joint between the web and the bottom flange and then propagated vertically. Because the band

and db = center-to-center distance between the top and bottom band plates.

Vst 2Fybp

Abp ≥

ffiffiffiffi f 0 c q

boho (14)

(16)

bo ¼ baf � bic � 2tw (15)

<sup>X</sup>Muc �XVbho=<sup>2</sup> <sup>≤</sup>ϕMnc (17)

<sup>X</sup>Muc <sup>¼</sup> <sup>X</sup>Mbp <sup>þ</sup>XVbhc=<sup>2</sup> � Vchb (18)

Mnc ¼ Vwsdw þ Vcsð Þþ 0:75hb Vstdb (19)

Vst ¼ 0:4

hb = overall depth of the composite beam including the concrete slab. The shear strength Vst of the strut-and-tie action is defined as follows:

respectively.

72 New Trends in Structural Engineering

Abp of each band plate is calculated as follows:

equilibrium at the joint (Figure 16(e)).

2.5.2. Structural test

where 2Fybp = yield strength of the top and bottom band plates.

In this chapter, a prefabricated steel-reinforced concrete (PSRC) composite column using steel angles was introduced. Using current design codes, the structural capacities of PSRC composite columns can be evaluated, and it shows better performance than those of a conventional concrete-encased steel (CES) composite column.

• The axial load-carrying capacity and deformation capacity of PSRC composite columns are comparable to, or even better than, those of conventional CES composite columns. In the PSRC composite column under axial compression, the corner angles and the transverse reinforcement provide adequate lateral confinement to the concrete.

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[3] Hwang HJ, Eom TS, Park HG, Lee SH. Axial load and cyclic lateral load tests for composite columns with steel angles. Journal of Structural Engineering. 2016;142(5):04016001.

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