# Analyses of Structural Robustness of Prefabricated Modular Buildings: A Case Study on Mid-Rise Building Configurations

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study Buildings Design

#### 2.1. Design of Modular Buildings

_{p}= 1.3), hazard factor (Z = 0.09) and sub-soil class C

_{e}, where they were considered to be on shallow soil [43]. The design load (E

_{d}) cases for ULS and SLS were determined using Equations (1)–(6) as given in AS 1170.0 [44]. Equations (1)–(4) were used to derive the design load at ULS, whilst Equations (5) and (6) were used to derive the design load at SLS.

_{u}and W

_{s}are the wind load at ULS and SLS, respectively. E

_{u}and E

_{s}are the earthquake load at ULS and SLS.

#### 2.2. Numerical Modeling

^{2}was applied on the floor to represent the self-weight of the floor slab. The super-imposed dead loads acting on the floors and ceilings of the building due to the finishes and services were assumed as 1.0 kN/m

^{2}and 0.5 kN/m

^{2}, respectively, in the FE models. Furthermore, a 4.5 kN/m line load was applied on the floor beams to represent the exterior walls and claddings of the building. A live load of 1.5 kN/m

^{2}was applied.

## 3. Robustness of Modular Buildings

#### 3.1. Non-Linear Static Analysis (NLS)

#### 3.2. Non-Linear Dynamic Analysis (NLD)

## 4. Results and Discussion

#### 4.1. Effect of Column Removal Location

#### 4.2. Effect of Span

#### 4.3. Estimation of Appropriate DAF

#### 4.4. Lateral Deformation Due to the Column Loss

#### 4.5. Effect of Damping Ratios

## 5. Conclusions

- The analyses revealed that 1% damping can be considered to assess the robustness of typical modular building types. Although a significant change in the element forces and displacements could not be observed, the highest forces and displacements were recorded in the models with 1% damping. Considering the three column loss scenarios analysed, the effect of the changes in damping ratio for building A was significant in the corner column loss scenario.
- It was observed from the analyses that the corner column removal scenario does not significantly reduce the robustness compared to the other two column removal scenarios (edge and interior column removal). It was further discovered that the corner column removal scenario has the ability of sharing the forces to the adjacent elements than the other two scenarios. The formation of several hinges in the frame indicates the participation of higher number of members in load sharing mechanism of the modular building systems considered.
- When the span of the module was doubled, the column loss in the corner showed the highest increment in axial forces (i.e., axial demand capacity ratios (DCR) of the columns). The increment in axial DCRs of edge, interior, and corner column losses are 23%, 24% and 30%, respectively. The increments of the bending capacity ratios of the beams adjacent to the collapsed columns for the aforementioned those cases were 56%, 75% and 88% respectively, and significantly affected the performance of the building under the interior column removal scenario than in the other two cases.
- The results from the nonlinear static analysis and nonlinear dynamic analysis indicate that the use of DAF of 2 for modular buildings was an over-estimation. When considering the axial forces in columns and the moments in the beams, a DAF value of 1.25 can be used, since the values obtained the dynamic analyses are in the range of 1.0 to 1.25. This may not be valid for all the layouts and heights. Therefore, further analyses with different parameters such as material properties and sectional details are required.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**The percentage of change in force in ground floor’s columns in CD1A by the column location.

Grid Y | Grid X (%) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | D | E | F | G | H | I | J | K | L | |

1 | - | 25 | 32 | 8 | 8 | 4 | 3 | 2 | 1 | 1 | −1 | −5 |

2 | 41 | −2 | 5 | 1 | 0 | 2 | 0 | 1 | −1 | 1 | −1 | −2 |

3 | 10 | −2 | 3 | 1 | 0 | 1 | −1 | 1 | −1 | 1 | −1 | −3 |

4 | 8 | −1 | 1 | 0 | −1 | 4 | 2 | 1 | −1 | 1 | −1 | −2 |

5 | 3 | 1 | 0 | 1 | −1 | 0 | −1 | 1 | −1 | 1 | −1 | −2 |

6 | −1 | 3 | −1 | 0 | −2 | −2 | −4 | −1 | −3 | −3 | −5 | −5 |

**Table A2.**The percentage of change in force in ground floor’s columns in ED1A by the column location.

Grid Y | Grid X (%) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | D | E | F | G | H | I | J | K | L | |

1 | 12 | - | 61 | 8 | 7 | 2 | 2 | 1 | 0 | 1 | 0 | −1 |

2 | 4 | 5 | −3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 2 | 3 | −3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −1 |

4 | 1 | 2 | −2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

6 | 2 | −2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −1 | −2 |

**Table A3.**The percentage of change in force in ground floor’s columns in ID1A by the column location.

Grid Y | Grid X (%) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | D | E | F | G | H | I | J | K | L | |

1 | −2 | 23 | −13 | −1 | −2 | 0 | −1 | 0 | −1 | 0 | 0 | −1 |

2 | −1 | 2 | 0 | 0 | −1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 0 | - | 89 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

4 | 0 | 4 | 1 | 0 | −1 | 0 | −1 | 0 | 0 | 0 | 0 | −1 |

5 | 0 | 1 | −1 | 0 | −1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

6 | 0 | 2 | −1 | 0 | −1 | −1 | 0 | 0 | 0 | 0 | 0 | −1 |

## Nomenclature

Symbols | |

A | Building A |

B | Building B |

C | Corner column loss |

D | Dynamic analysis |

C_{e} | Sub soil class (Shallow soil) |

E | Edge column loss |

E_{d} | Design load |

G | Dead load |

I | Interior column loss |

k_{p} | Probability factor |

Q | Live load |

R | Rotation |

RA | Building A before column removal under ULS loading condition |

RB | Building B before column removal under ULS loading condition |

S | Static analysis |

T | Fundamental frequency of the building |

U | Translation |

W | Wind Load |

Subscripts | |

s | Load at serviceability limit state |

u | Load at ultimate limit state |

Abbreviations | |

DAF | Dynamic Amplification Factor |

DCR | Demand Capacity Ratio |

FE | Finite Element |

HC | Horizontal Connection |

IO | Immediate Occupancy |

NLD | Non-linear dynamic analysis |

NLS | Non-linear static analysis |

SLS | Serviceability Limit State |

ULS | Ultimate Limit State |

VC | Vertical Connection |

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**Figure 6.**Column removal scenarios of Building A: (

**a**) CA; (

**b**) EA; (

**c**) IA; and Building B (

**d**) CB; (

**e**) EB; (

**f**) IB; and plan view of (

**g**) Building A; (

**h**) Building B with the removed column locations.

**Figure 7.**Percentage of change in force in ground floor’s columns in: (

**a**) CD1A; (

**b**) ED1A; and (

**c**) ID1A with Accidental Load case in Building A without column removal.

**Figure 8.**Column axial capacity ratios for corner column removal: (

**a**) Building A; and (

**b**) Building B.

**Figure 10.**Column axial capacity ratios for interior column removal: (

**a**) Building A; and (

**b**) Building B.

**Figure 11.**Beam moment capacity ratios for corner column removal: (

**a**) Building A; and (

**b**) Building B.

**Figure 13.**Beam moment capacity ratios for interior column removal: (

**a**) Building A; and (

**b**) Building B.

**Figure 14.**Formation of hinges in Building B in the dynamic analysis: (

**a**) Corner column removal (CB); (

**b**) Edge column removal (EB); and (

**c**) Interior column removal (IB).

**Figure 15.**The displacement at the top of the buildings in dynamic column removal of 1% damping: (

**a**) Building A; and (

**b**) Building B.

**Figure 16.**Effect of change of damping ratio on CA: (

**a**) Vertical displacement at removed column joint; and (

**b**) Lateral displacement at roof of the building.

Details | Building A | Building B |
---|---|---|

Floor area per one accommodation (m^{2}) | 18.7 | 18.7 |

Modular size (m) | 4 × 12 × 3 | 4 × 12 × 3 |

Column size (mm)/(Member Capacity (kN)) | SHS 150 × 150 × 8/(680) | SHS 150 × 150 × 8/(1050) |

Floor beam size (mm)/(Member Capacity (kNm)) | SHS 120 × 80 × 5/(20.5) | SHS 150 × 100 × 5/(33.5) |

Ceiling beam size (mm)/(Member Capacity (kNm)) | SHS 70 × 70 × 5/(8.5) | SHS 70 × 70 × 5/(8.5) |

Bracing size (mm)/(Member capacity (kN)) | SHS 80 × 80 × 6.3/(140) | SHS 80 × 80 × 6.3/(140) |

Floor | 20 mm thick cement board with floor purlins at 400 mm centre to centre | 20 mm thick cement board with floor purlins at 400 mm centre to centre |

Ceiling | Gypsum board | Gypsum board |

Inter module connection | Figures 4 and 5 [40] | Figures 4 and 5 [40] |

Foundation | Shallow foundation | Shallow foundation |

Building A (A) | Building B (B) | ||||||
---|---|---|---|---|---|---|---|

Corner Column Loss (CA) | Edge Column Loss (EA) | Interior Column Loss (IA) | Corner Column Loss (CB) | Edge Column Loss (EB) | Interior Column Loss (IB) | ||

Reference (1.2G + 1.5Q) | RA | RA | RA | RB | RB | RB | |

Static Analysis (S) | DAF = 1 | CS1A | ES1A | IS1A | CS1B | ES1B | IS1B |

DAF = 1.25 | CS1.25A | ES1.25A | IS1.25A | CS1.25B | ES1.25B | IS1.25B | |

DAF = 1.5 | CS1.5A | ES1.5A | IS1.5A | CS1.5B | ES1.5B | IS1.5B | |

DAF = 2 | CS2A | ES2A | IS2A | CS2B | ES2B | IS2B | |

Dynamic Analysis (D) | 0% | CD0A | ED0A | ID0A | - | - | - |

1% | CD1A | ED1A | ID1A | CD1B | ED1B | ID1B | |

2% | CD2A | ED2A | ID2A | - | - | - | |

5% | CD5A | ED5A | ID5A | - | - | - |

**Table 3.**Vertical displacement at the removed column joint in each column removal scenarios in Building A.

Column | RA | NLS | NLD | |||
---|---|---|---|---|---|---|

DAF = 1 | DAF = 1.25 | DAF = 1.5 | DAF = 2 | |||

A1-1 | −3.05 | −7.51 (CS1A) | −9.4 (CS1.25A) | −11.27 (CS1.5A) | −15.03 (CS2A) | −7.75 (CD1A) |

B1-1 | −3.07 | −4.2 (ES1A) | −5.25 (ES1.25A) | −6.3 (ES1.5A) | −8.4 (ES2A) | −4.28 (ED1A) |

B3-1 | −2.14 | −3.31 (IS1A) | −4.14 (IS1.25A) | −4.97 (IS1.5A) | −6.62 (IS2A) | −3.33 (ID1A) |

Axial Forces of Columns (kN) | Moments in Beams (kNm) | ||||||
---|---|---|---|---|---|---|---|

B1-1 | C1-1 | C1-2 | B1-2 | FB01 | FB02 | ||

Dynamic Analysis (D) | CD1A | −523.38 | −556.87 | −457.76 | −447.72 | 6.89 | 6.38 |

CD2A | −522.38 | −555.84 | −457.02 | −446.87 | 6.88 | 6.36 | |

CD5A | −520.64 | −553.98 | −455.81 | −445.32 | 6.87 | 6.34 |

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## Share and Cite

**MDPI and ACS Style**

Munmulla, T.; Navaratnam, S.; Thamboo, J.; Ponnampalam, T.; Damruwan, H.-G.H.; Tsavdaridis, K.D.; Zhang, G.
Analyses of Structural Robustness of Prefabricated Modular Buildings: A Case Study on Mid-Rise Building Configurations. *Buildings* **2022**, *12*, 1289.
https://doi.org/10.3390/buildings12081289

**AMA Style**

Munmulla T, Navaratnam S, Thamboo J, Ponnampalam T, Damruwan H-GH, Tsavdaridis KD, Zhang G.
Analyses of Structural Robustness of Prefabricated Modular Buildings: A Case Study on Mid-Rise Building Configurations. *Buildings*. 2022; 12(8):1289.
https://doi.org/10.3390/buildings12081289

**Chicago/Turabian Style**

Munmulla, Thisari, Satheeskumar Navaratnam, Julian Thamboo, Thusiyanthan Ponnampalam, Hidallana-Gamage Hasitha Damruwan, Konstantinos Daniel Tsavdaridis, and Guomin Zhang.
2022. "Analyses of Structural Robustness of Prefabricated Modular Buildings: A Case Study on Mid-Rise Building Configurations" *Buildings* 12, no. 8: 1289.
https://doi.org/10.3390/buildings12081289