# Development of an Efficient Steel Beam Section for Modular Construction Based on Six-Sigma

Authors: Tae-Hyu Ha; Bong-Ho Cho; Hongjin Kim; Dae-Jin Kim
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

This study presents a systematic approach for the development of an efficient steel beam section for modular construction based on Six-Sigma. Although the Six-Sigma is frequently implemented in manufacturing and other service industries, it is a relatively new concept in the area of building design and construction. As a first step in this approach, market studies and surveys are conducted to obtain the opinions of potential customers. Then the opinions of customers are converted into quality characteristics for the steel beam using the quality function deployment methodology. A steel hollow flanged channel is chosen as the main modular beam shape, and the design concept is derived and developed by applying the Pugh matrix methodology. A pilot test was performed to validate the effectiveness of the developed beam section. The results indicated that the developed channel beam section showed excellent performance and retained high accuracy in fabrication, thus resulting in a significant reduction of steel consumption.


---

## Body

## 1. Introduction

Modular construction is an industrialized construction system, with a process that mainly consists of the factory production of preengineered building units, the delivery of the fabricated units to the construction site, and their fast assembly [1]. The structural system of steel frame modular buildings can be largely classified into two types. The first is the beam-column frame system and is suitable for use in school buildings or military barracks, which require relatively large open space [2]. The second is the load-bearing wall system, and dormitories or bachelor officer quarters are good applications of this type as they can be built with a series of transportable unit room modules [3, 4].In general, the modular unit of the beam-column frame system is constructed by connecting structural members such as corner columns, internal columns, floor beams, and ceiling beams by bolting or welding. Figure1 illustrates an example of standard modules for elementary schools in Korea. The dimensions are 9.8 m (length), 7.5 m (column to column span), 3 m (width), and 3.2 m (height). Table 1 provides the composition ratio of the main structural members used in this standard module. In the beam-column frame system, the upper beam of the lower level unit is connected with the lower beam of the upper level unit. This connection scheme is called the double beam system. As a result, beam members make up a larger portion of the structural components of the standard module, which is 81% as shown in Table 1. The beam members play an important role as they not only contribute greatly to the overall construction cost of modular buildings, but also may affect various factors such as story height and floor vibration. Therefore, the selection of adequate beam members is essential to improving the cost efficiency and performance of modular buildings.Table 1
Composition ratio of main structural members used in the standard module.
Component
Shape
Weight ratio (%)
Longitudinal floor beams
Built-up rectangular hollow section
41
73
81
Longitudinal ceiling beams
Rectangular hollow section
32
Transverse floor and ceiling beams
Roll-formed C shape
7
Columns
Square hollow section
19Figure 1
Standard modular unit and structural members.
(a)
Framed modular unit
(b)
Structural members of the modular unitSix-Sigma was first developed by Motorola in the 1980s [5] and became well known in the 1990s when Jack Welch made it central to his business strategy at General Electric. Since the late 1990s, most manufacturing companies in Korea have applied the Six-Sigma for productivity enhancement, process improvement, and new product development. While the Six-Sigma has been applied to construction management and housing design on several occasions such as [5, 6], this is one of very few studies where the Six-Sigma concept is employed to develop new steel structural members for modular construction.In general, Six-Sigma projects follow either the DMAIC or DFSS methodology. The DMAIC focuses on improving an existing business process, while the DFSS aims at creating new products or process designs. Based on this discussion, this study proposes a systematic approach for the development of a steel modular beam section that can be used in the beam-column frame system and validates its effectiveness through a pilot test.


## 2. QFD Methodology and Derivation of CTQ

### 2.1. QFD Methodology

The philosophy of the Six-Sigma approach emphasizes the reflection of customers’ needs in the development of production processes. In order to achieve this, the identification and categorization of potential customers are required, and the importance of each customer group needs to be evaluated. In the Six-Sigma methodology, these customer requirements are referred to as the voice of customers (VOCs), which are obtained through surveys and interviews and utilized as basic data for product development. According to the results of the interviews, module manufacturers require a decrease in manufacturing cost as well as a shortening of order-delivery period, while designers expect various construction-related requirements to be satisfied. The VOC of the building owner is mainly focused on the excellent performance of the manufactured modules.This study adopts the quality function deployment (QFD) methodology to convert customers’ needs into quality characteristics for the products to be developed. The QFD methodology, first proposed by Akao in the 1960s [7], is a tool that can provide a quantitative evaluation on the relation between customer requirements and product characteristics using a correlation matrix [8, 9]. Figure 2 illustrates the house of quality (HOQ), which is required to conduct QFD.Figure 2
HOQ required to conduct QFD.In general, the QFD methodology follows a number of procedures: (1) determination of required quality; (2) importance rating for customers’ needs; (3) identification of quality characteristics; (4) correlation analysis between the required quality and quality characteristics; (5) technical evaluation; (6) interrelation analysis of the quality characteristics if required; (7) target specification setup for the quality characteristics. In this study, the required quality is determined from the VOCs obtained from the first round of interviews, and then the quality characteristics are prioritized based on the evaluations of customers and experts. Finally, the target values and importance ratings for the quality characteristics are assigned.In this study, QFD methodology is used for the development of a new steel modular beam section. The results of priority ratings for the VOCs, where the requirements of both customers and product developers are considered, are provided in Table2. The item labeled “customers’ required quality” in Table 2 is a reorganization of the VOCs of each customer group for QDF analysis, and its priority ratings are determined based on the results of the customer surveys. From the results of the table, items with high priority are found to have “low manufacturing cost,” “small steel quantity,” “small manufacturing deformation,” and “short time for stocking after order.” In the determination of the priority rating in Table 2, the importance of customers’ requirements and satisfaction with existing products are determined from the surveys. The “planning quality” and “sales point” in Table 2 are the indicators for the attainable quality and sales quantity from the perspective of developers, respectively.Table 2
Priority rating for the customer requirements.
Customers’ required quality
(1) Importance rating
(2) Satisfaction rating
(3) Possible quality levels
(4) Level-up ratio
(5) Sales Point
(6) Absolute priority
Priority Ratios
Ratings
Small steel quantity
4.6
2.8
4
1.4
○
7.7
10%
2
Low manufacturing cost
4.6
2.6
5
1.9
◎
13.1
17%
1
Easy structural design
3.6
3.4
4
1.2
4.3
5%
7
Easy architectural design
3.6
3.4
4
1.2
4.3
5%
7
Easy connection
3.6
3.4
4
1.2
4.3
5%
7
Transportation with low-bed trailer
3.6
3.2
4
1.3
4.7
6%
5
Transportation with cargo truck
3
3
3
1
3
4%
15
Easy installation of plumbing equipment
3.4
3.2
4
1.3
4.4
6%
6
A short time for stocking after order
3.6
2.8
4
1.4
○
6
8%
4
The stock is secured in advance
3
2.6
3
1.2
○
4.3
5%
7
Small manufacturing deformation
3.8
3
4
1.3
◎
7.4
9%
3
Less surface defects
3.6
2.8
3
1.1
4
5%
12
Easy application of high-strength steel
3
2.8
3
1.1
3.3
4%
14
Structural safety
3.6
3.6
4
1.1
4
5%
12
Less floor vibration
4.2
4
4
1
4.2
5%
11
(1) Importance rating: values obtained from customer survey (1~5).
(2) Satisfaction rating: values obtained from customer survey (1~5).
(3) Quality levels that may be obtained from the viewpoint of developers (1~5).
(4) Level up ratio: (3)/(2).
(5) Sales point from the viewpoint of developers (◎: 1.5, ○: 1.2).
(6) Absolute priority: (1)∗(4)∗(5).


### 2.2. Derivation of CTQ

From a correlation analysis between the required qualities and quality characteristics, parameters that are critical to quality (CTQ) from the customers’ perspective can be derived. The quality characteristics are given different weight values (◎: 5 points, ○: 3 points, and △: 1 point) depending on the relationship with the corresponding customer requirements. The overall importance can be calculated by summing up the multiplications of the weighted value and absolute importance in Table 3. The quality characteristics with high importance score can be selected as the potential CTQs.Table 3
Correlation analysis between the required qualities and quality characteristics.
Customers’ required quality
Quality characteristic
Price of beams
Contribution to competitiveness of modules
Structural performance of bema
Quality of manufacturing
Absolute priority
Priority ratios
Ratings
Surface area per unit length
Welding length per unit length
Span length
Thickness of webs
Diameter of web opening
Number of webs
Thickness of flanges
Number of openings
Height of ceiling and floor beams
Weight of floor beams per unit area of plan
Moment of inertia per sectional area of beam
Section modulus per sectional area of beam
Lever arm of bolts at the end plate
Number of axes of symmetry
Radius of curved section
Low cost of beams
Small steel quantity
○
○
△
◎
◎
○
7.7
10%
2
Low manufacturing cost
○
◎
○
○
13.1
17%
1
Easy design of modular building
Easy structural design
◎
◎
○
◎
4.3
5%
7
Easy architectural design
◎
◎
○
○
○
◎
○
○
4.3
5%
7
Easy fabrication and transportation
Easy connection
◎
◎
◎
○
4.3
5%
7
Transportation with low-bed trailer
◎
○
4.7
6%
5
Transportation with cargo truck
◎
○
3
4%
15
Easy installation of plumbing equipment
◎
◎
4.4
6%
6
Short time for stocking
A short time for stocking after order
○
◎
○
6
8%
4
The stock is secured in advance
◎
4.3
5%
7
High quality of manufacturing
Small manufacturing deformation
○
◎
◎
7.4
9%
3
Less surface defects
○
4
5%
12
Easy application of high-strength steel
◎
◎
○
3.3
4%
14
Structural performance
Structural safety
◎
◎
4
5%
12
Small floor vibration
○
◎
4.2
5%
11
Absolute priority
126
194
116
62
92
90
46
110
95
138
182
72
101
80
48
100%
Priority ratios
8.1%
12.5%
7.5%
4.0%
5.9%
5.8%
3.0%
7.1%
6.1%
8.9%
11.7%
4.6%
6.5%
5.1%
3.1%
Ratings
4
1
5
13
9
10
15
6
8
3
2
12
7
11
14This process of deriving CTQs is important in the Six-Sigma methodology, which reflects the customers’ needs as much as possible. The VOC does not contain any direct statements on the quality characteristic, but it can be converted into designable quality characteristics through QFD analysis. Table3 lists the importance ratings derived from the correlation analysis on the required quality and quality characteristics.From the QFD analysis, the quality characteristics with high importance are found to be “weld length per unit length,” “moment of inertia per sectional area of beam,” and “weight of floor beams per unit area of plan.” These items are selected as CTQs in the following step and expressed quantitatively. Among the 15 quality characteristics, the top 3 items are selected as CTQs and defined as shown in Table4, which shows their definitions, measurement methods, current, and target levels. The target levels are determined using the existing built-up RHS (rectangular hollow sections) and channels as references.Table 4
CTQ definitions and target levels.
CTQ
Definition
Measuring method
⁢Current level
Target level
Built-up RHS
Channel
Welding length per unit length
Welding length per 1 m beam length
Measuring welding length
4
0
Less than 2
Moment of inertia per sectional area of beam
Moment of inertia divided by sectional area of beam
Calculation of moment of inertia and sectional area of beams
127 cm2 (7.5 m span)
132 cm2 (7.5 m span)
Larger than 150 cm2 (7.5 m span)
Weight of floor beams per unit area of plan
Total weight of beams used for modules divided by plan area of module
Calculation of weight of beams after redesign of modules
0.30 kN/m2 (7.5 m span)
0.25 kN/m2 (7.5 m span)
Less than 0.28 kN/m2 (7.5 m span)


## 2.1. QFD Methodology

The philosophy of the Six-Sigma approach emphasizes the reflection of customers’ needs in the development of production processes. In order to achieve this, the identification and categorization of potential customers are required, and the importance of each customer group needs to be evaluated. In the Six-Sigma methodology, these customer requirements are referred to as the voice of customers (VOCs), which are obtained through surveys and interviews and utilized as basic data for product development. According to the results of the interviews, module manufacturers require a decrease in manufacturing cost as well as a shortening of order-delivery period, while designers expect various construction-related requirements to be satisfied. The VOC of the building owner is mainly focused on the excellent performance of the manufactured modules.This study adopts the quality function deployment (QFD) methodology to convert customers’ needs into quality characteristics for the products to be developed. The QFD methodology, first proposed by Akao in the 1960s [7], is a tool that can provide a quantitative evaluation on the relation between customer requirements and product characteristics using a correlation matrix [8, 9]. Figure 2 illustrates the house of quality (HOQ), which is required to conduct QFD.Figure 2
HOQ required to conduct QFD.In general, the QFD methodology follows a number of procedures: (1) determination of required quality; (2) importance rating for customers’ needs; (3) identification of quality characteristics; (4) correlation analysis between the required quality and quality characteristics; (5) technical evaluation; (6) interrelation analysis of the quality characteristics if required; (7) target specification setup for the quality characteristics. In this study, the required quality is determined from the VOCs obtained from the first round of interviews, and then the quality characteristics are prioritized based on the evaluations of customers and experts. Finally, the target values and importance ratings for the quality characteristics are assigned.In this study, QFD methodology is used for the development of a new steel modular beam section. The results of priority ratings for the VOCs, where the requirements of both customers and product developers are considered, are provided in Table2. The item labeled “customers’ required quality” in Table 2 is a reorganization of the VOCs of each customer group for QDF analysis, and its priority ratings are determined based on the results of the customer surveys. From the results of the table, items with high priority are found to have “low manufacturing cost,” “small steel quantity,” “small manufacturing deformation,” and “short time for stocking after order.” In the determination of the priority rating in Table 2, the importance of customers’ requirements and satisfaction with existing products are determined from the surveys. The “planning quality” and “sales point” in Table 2 are the indicators for the attainable quality and sales quantity from the perspective of developers, respectively.Table 2
Priority rating for the customer requirements.
Customers’ required quality
(1) Importance rating
(2) Satisfaction rating
(3) Possible quality levels
(4) Level-up ratio
(5) Sales Point
(6) Absolute priority
Priority Ratios
Ratings
Small steel quantity
4.6
2.8
4
1.4
○
7.7
10%
2
Low manufacturing cost
4.6
2.6
5
1.9
◎
13.1
17%
1
Easy structural design
3.6
3.4
4
1.2
4.3
5%
7
Easy architectural design
3.6
3.4
4
1.2
4.3
5%
7
Easy connection
3.6
3.4
4
1.2
4.3
5%
7
Transportation with low-bed trailer
3.6
3.2
4
1.3
4.7
6%
5
Transportation with cargo truck
3
3
3
1
3
4%
15
Easy installation of plumbing equipment
3.4
3.2
4
1.3
4.4
6%
6
A short time for stocking after order
3.6
2.8
4
1.4
○
6
8%
4
The stock is secured in advance
3
2.6
3
1.2
○
4.3
5%
7
Small manufacturing deformation
3.8
3
4
1.3
◎
7.4
9%
3
Less surface defects
3.6
2.8
3
1.1
4
5%
12
Easy application of high-strength steel
3
2.8
3
1.1
3.3
4%
14
Structural safety
3.6
3.6
4
1.1
4
5%
12
Less floor vibration
4.2
4
4
1
4.2
5%
11
(1) Importance rating: values obtained from customer survey (1~5).
(2) Satisfaction rating: values obtained from customer survey (1~5).
(3) Quality levels that may be obtained from the viewpoint of developers (1~5).
(4) Level up ratio: (3)/(2).
(5) Sales point from the viewpoint of developers (◎: 1.5, ○: 1.2).
(6) Absolute priority: (1)∗(4)∗(5).


## 2.2. Derivation of CTQ

From a correlation analysis between the required qualities and quality characteristics, parameters that are critical to quality (CTQ) from the customers’ perspective can be derived. The quality characteristics are given different weight values (◎: 5 points, ○: 3 points, and △: 1 point) depending on the relationship with the corresponding customer requirements. The overall importance can be calculated by summing up the multiplications of the weighted value and absolute importance in Table 3. The quality characteristics with high importance score can be selected as the potential CTQs.Table 3
Correlation analysis between the required qualities and quality characteristics.
Customers’ required quality
Quality characteristic
Price of beams
Contribution to competitiveness of modules
Structural performance of bema
Quality of manufacturing
Absolute priority
Priority ratios
Ratings
Surface area per unit length
Welding length per unit length
Span length
Thickness of webs
Diameter of web opening
Number of webs
Thickness of flanges
Number of openings
Height of ceiling and floor beams
Weight of floor beams per unit area of plan
Moment of inertia per sectional area of beam
Section modulus per sectional area of beam
Lever arm of bolts at the end plate
Number of axes of symmetry
Radius of curved section
Low cost of beams
Small steel quantity
○
○
△
◎
◎
○
7.7
10%
2
Low manufacturing cost
○
◎
○
○
13.1
17%
1
Easy design of modular building
Easy structural design
◎
◎
○
◎
4.3
5%
7
Easy architectural design
◎
◎
○
○
○
◎
○
○
4.3
5%
7
Easy fabrication and transportation
Easy connection
◎
◎
◎
○
4.3
5%
7
Transportation with low-bed trailer
◎
○
4.7
6%
5
Transportation with cargo truck
◎
○
3
4%
15
Easy installation of plumbing equipment
◎
◎
4.4
6%
6
Short time for stocking
A short time for stocking after order
○
◎
○
6
8%
4
The stock is secured in advance
◎
4.3
5%
7
High quality of manufacturing
Small manufacturing deformation
○
◎
◎
7.4
9%
3
Less surface defects
○
4
5%
12
Easy application of high-strength steel
◎
◎
○
3.3
4%
14
Structural performance
Structural safety
◎
◎
4
5%
12
Small floor vibration
○
◎
4.2
5%
11
Absolute priority
126
194
116
62
92
90
46
110
95
138
182
72
101
80
48
100%
Priority ratios
8.1%
12.5%
7.5%
4.0%
5.9%
5.8%
3.0%
7.1%
6.1%
8.9%
11.7%
4.6%
6.5%
5.1%
3.1%
Ratings
4
1
5
13
9
10
15
6
8
3
2
12
7
11
14This process of deriving CTQs is important in the Six-Sigma methodology, which reflects the customers’ needs as much as possible. The VOC does not contain any direct statements on the quality characteristic, but it can be converted into designable quality characteristics through QFD analysis. Table3 lists the importance ratings derived from the correlation analysis on the required quality and quality characteristics.From the QFD analysis, the quality characteristics with high importance are found to be “weld length per unit length,” “moment of inertia per sectional area of beam,” and “weight of floor beams per unit area of plan.” These items are selected as CTQs in the following step and expressed quantitatively. Among the 15 quality characteristics, the top 3 items are selected as CTQs and defined as shown in Table4, which shows their definitions, measurement methods, current, and target levels. The target levels are determined using the existing built-up RHS (rectangular hollow sections) and channels as references.Table 4
CTQ definitions and target levels.
CTQ
Definition
Measuring method
⁢Current level
Target level
Built-up RHS
Channel
Welding length per unit length
Welding length per 1 m beam length
Measuring welding length
4
0
Less than 2
Moment of inertia per sectional area of beam
Moment of inertia divided by sectional area of beam
Calculation of moment of inertia and sectional area of beams
127 cm2 (7.5 m span)
132 cm2 (7.5 m span)
Larger than 150 cm2 (7.5 m span)
Weight of floor beams per unit area of plan
Total weight of beams used for modules divided by plan area of module
Calculation of weight of beams after redesign of modules
0.30 kN/m2 (7.5 m span)
0.25 kN/m2 (7.5 m span)
Less than 0.28 kN/m2 (7.5 m span)


## 3. Product Design Using Pugh Matrix Methodology

### 3.1. Function Analysis and Pugh Matrix

The core functions of the steel modular beam section are determined and its optimal design is developed utilizing the CTQs derived in the previous phase. Table5 describes the main processes required for the manufacturing of the steel modular beam section and classifies the functions required in each process into one of three functions, namely, the basic function (necessary), attractive function (delighter), and discriminative function (primary satisfier). The basic functions must be satisfied, while the attractive and differentiated functions can be optionally considered in the design process.Table 5
Classification of key functions for the steel modular beam section.
Main process
Manufacturing beams
Assembly of modules
Transportation and installing
Ensuring structural performance
Must be functions
—
Welding end-plateConnecting beam and columnConnecting beam and slabConnecting beam and ceiling trackConnecting beam and wall track
Transportation of modules
Flexural strength of beamShear strength of beamMinimize deflection of beamMinimize floor vibrationEarthquake and wind resistanceFire resistance
Delighter functions
—
—
Plumbing equipment penetration
—
Primary satisfier functions
Minimize a space for stock
—
—
—Key functions can be determined from a correlation analysis between the quality characteristics and associated functions by applying the same method used to create CTQs in Table3. Table 6 shows the relationship between the quality characteristics and the key functions. From this relationship, “minimize deflection and vibration of beam,” “flexural strength of beam,” “earthquake and wind resistance,” and “piping equipment penetration” are selected as key functions.Table 6
Correlation between the quality characteristics and key functions.
Quality characteristic
Key function
Assembly of modules
⁢Ensuring structural performance
⁢Secondary function
Welding end-plate
Connecting beam and column
Connecting beam and slab
Connecting beam and ceiling track
Connecting beam and wall track
Flexural strength of beam
Minimize deflection and vibration of beam
Earthquake and wind resistance
Fire resistance
Plumbing equipment penetration
Transportation of modules
Price of beam
Surface area per unit length
◎
Welding length per unit length
◎
○
Contribution to competitiveness of module
Span length
◎
Thickness of webs
◎
◎
Diameter of web opening
○
◎
Number of webs
○
◎
○
○
Thickness of flanges
◎
Number of openings
○
◎
Height of ceiling and floor beams
◎
◎
Weight of floor beams per unit area of plan
Structural performance of beam
Moment of inertia per sectional area of beam
◎
Section modulus per sectional area of beams
◎
◎
Lever arm of bolts at the end plate
◎
◎
◎
Quality of manufacturing
Number of axes of symmetry
◎
○
Radius of curved section
○
◎
Priority ratio
6.5%
9.5%
8.6%
6.7%
4.7%
16.7%
19.7%
11.9%
0.6%
10.1%
4.8%
Rating
8
5
6
7
10
2
1
3
11
4
9After derivation of the key functions, an optimal design concept satisfying the derived key functions needs to be developed. In order to achieve this, various methods can be used such as the benchmarking of advanced technologies, brainstorming by experts, TRIZ, and mind mapping. In this study, various solutions that can satisfy the key functions are created, and several possible design options are obtained by combining these solutions. Finally, the Pugh matrix is employed to select the optimal design among the designs obtained.Table7 lists the available solutions for each of the key functions of the steel modular beam section. The table indicates that there are two solutions for “piping equipment penetration” and “connecting beam and slab,” four solutions for structural functions, specifically “flexural strength of beam,” “minimize deflection and vibration of beam,” and “earthquake and wind resistance,” and one solution for all of the remaining functions. These solutions can be combined to produce an optimal design concept. By combining the solutions listed in Table 7, seven design concepts are derived. They satisfy various functions required for the floor and ceiling beams of the modular beam-column frame system and show different characteristics with regard to manufacturing cost, steel consumption, and availability for both of ceiling and floor beams. Their characteristics are summarized in Table 8.Table 7
Available solutions for each of the key functions.
Key functions
⁢Solutions
Piping equipment penetration
Install reinforcing device at penetrationSolution A
Penetrate without reinforcingSolution B
Transportation of modules
Limiting module height less than 3.3 m
Welding end-plate
Limiting flange width less than 120 mm
Connecting beam and column
Ensuring bolting space at end-plate
Connecting beam and slab
Integrate beam and slab supportSolution a
Separate beam and slab supportSolution b
Connecting beam and ceiling track
Connect track to web of beam with screw
Connecting beam and wall track
Ensuring flange width of 60 mm
Flexural strength of beam
Use hollow flange (flange thickness = web thickness)Solution I
Use hollow flange (flange thickness > web thickness)Solution II
Use open flange (flange thickness = web thickness)Solution III
Use open flange (flange thickness > web thickness)Solution IV
Minimize deflection and vibration of beam
Earthquake and wind resistanceTable 8
Design concepts obtained by combinations of the available solutions.
Combination of solutions
SolutionsA + a + I
SolutionsA + b + I
SolutionsA + a + II
SolutionsA + b + II
SolutionsB + a + III
SolutionsB + b + III
SolutionsB + b + IV
Design concepts
Manufacturing cost
Very high
High
Very high
Very high
Middle
Middle
Very high
Steel quantity
Very low
Low
Very low
Very low
Low
High
Low
Compatibility between floor and ceiling beam
Not compatible
Compatible
Not compatible
Compatible
Not compatible
Compatible
CompatibleIn order to select the optimal design among the candidates listed in Table8, a Pugh matrix is created in Table 9. In this methodology, a relative evaluation is performed on each candidate by comparing it with the reference design for each of the key criteria. The built-up RHS is chosen as the reference design for this comparison. Thus, if a candidate shows better performance than the reference design, it is denoted as +. If the candidate is worse than or is equal to the reference design, it is denoted as − or S, respectively. The candidate with the greatest difference between the sum of pluses and that of minuses is chosen as the optimal design. The results in Table 9 indicate that design concept 2 is the optimal design. Thus, it is selected as the prototype for the steel modular beam section.Table 9
Selection of the optimal design using the Pugh matrix methodology.
Better +Same SWorse −
Reference
Concept 1
Concept 2
Concept 3
Concept 4
Concept 5
Concept 6
Concept 7
Key criteria
Weight
Manufacturing cost
5
S
+
+
S
S
+
+
−
Fire proofing cost
4
S
−
−
−
−
−
−
−
Steel quantity
4
S
+
+
+
+
−
−
+
Easy fabrication
3
S
+
+
+
+
+
+
+
New investment
5
S
−
−
−
−
+
+
−
Compatibility
4
S
−
+
−
+
−
+
−
Creativity
3
S
+
+
+
+
S
S
S
Sum of +
0
4
5
3
4
3
4
2
Sum of −
0
3
2
3
2
3
2
4
Sum of S
7
0
0
1
1
1
1
1
Weighted sum of +
0
15
19
10
14
13
17
7
Weighted sum of −
0
13
9
13
9
12
8
18The prototype has hollow flanges in both the upper and lower parts of the section as shown in Table9. It can be manufactured by a roll forming method, in which thin steel sheets are passed through several rolls and are consecutively bent at room temperature. The cross-sectional shape is illustrated in Figure 3. The steel beam member with the cross-sectional shape shown in Figure 3 is hereafter referred to as the modular construction optimized (MCO) beam for convenience.Figure 3
Cross-sectional shape of the MCO beam and its roll forming simulation.


### 3.2. Detailed Design of MCO Beams

In this section, a detailed design of the MCO beam is discussed considering the manufacturing process. With the detailed design components, the cross-section has a variable portion as well as an invariable portion as shown in Figure4. Although MCO beams manufactured through the roll forming process require smaller manufacturing costs than general built-up beams, a variety in depth is also necessary for their applications to modular buildings with diverse spans. Therefore, the upper and lower hollow flange parts are designed as the invariable portion and produced using a single roll. In contrast, the thickness and width of the web section are variable. The design requirements for each design factor of the MCO beam are listed in Table 10. SPA-H steel is used for manufacturing the MCO beams since it has high durability as well as a high tensile strength of 490 MPa.Table 10
Design requirements for each design factor of the MCO beam.
Design factor
Design requirement
Invariable section
Flange width
(i) Limit the flange width to less than the column width (column width: 125 mm or 150 mm)(ii) Require the minimum flat flange width (50 mm) to be connected to the wall stud
Radius of curved section
(i) Minimum radius of curved section less likely to cause a crack
Flange height
(i) Flange to thickness ratio is larger than 61 (h
f > (h − 61t)/2)
Welding length
(i) Prevent local buckling
Variable section
Thickness of steel plate
(i) Variable sections for variable floor loads and spans
Web height
(i) Variable sections for variable floor loads and spans(ii) Able to penetrate pipesFigure 4
Cross-sectional design of the MCO beam.The design procedures for the MCO beam with invariable cross-section (hollow flange) can be summarized as follows.Step 1 (setting up the range of the flange width as shown in Figure5).
(i) If the minimum width of the column is 125 mm, the flange width is in the range of 100~120 mm.
(ii) The minimum width of the horizontal flat flange portion must be at least 50 mm.Figure 5
Range of the flange width.Step 2 (determination ofr
1 and r
2 shown in Figure 6).
These parameters are constant regardless of the steel plate thickness if the same roll forming process is used.(i)
Bending capacity of SPA-H steel: if the bending angle is 180 degrees, the inner radius must be at least 1.5 times the flange thickness.
(ii)
The maximum steel plate thickness is limited to 10 mm.
(iii)
If the bending angle ofr
1 is in the range of 90 to 180 degrees, r
1 = 15 mm.
(iv)
If the bending angle ofr
2 is 90 degrees, r
2 = 12 mm.Figure 6
Determination ofr
1 and r
2.Step 3 (determination of the flange width).
(i) If the steel plate thickness is 10 mm andr
1 and r
2 are 15 and 12 mm, respectively, the flat flange width is in the range of 53 to 73 mm, thus satisfying the condition in Step 1.
(ii) The flange width is determined as 120 mm, which is the maximum value allowed by the condition in Step1, considering its easy attachment onto ceilings and floor tracks.Step 4 (determination ofr
3).
This value is constant if the same roll forming process is used regardless of the flange thickness.(i)
If bending angle ofr
3 is less than 90 degrees, r
3 = 12 mm, which is the same as r
2.Step 5 (setting up the range of the flange height shown in Figure7).
(i) If it is assumed that the upper and lower flanges are parallel to each other and the flange thickness is 10 mm,h
f
,
m
i
n
1 = 10 + 15 + 15 + 10 = 50 mm.
(ii) The flange height can be calculated by considering the maximum beam height of 400 mm and minimum steel plate thickness of 4.5 mm and applying the maximum width-thickness ratio of 61 to prevent elastic local buckling ash
f
,
m
i
n
2 = (400 − 61 × 4.5)/2 = 63 mm.Figure 7
Determination of the flange height.Step 6 (final selection of invariable dimensions of the upper hollow flange).
(i) Front welding is performed on the steel plate connection as shown in Figure8.Figure 8
Invariable dimensions of the upper hollow flange of the MCO beam.The following design conditions for the variable portion of the MCS beam cross-section are assumed for three module spans of 6, 7.5, and 8.1 m: floor beam load in the range of 2~5 kN/m2, floor beam live load in the range of 2~5 kN/m2, ceiling beam load in the range of 0.3~0.5 kN/m2, and ceiling beam live load in the range of 0.5~1 kN/m2. Various cross-sectional shapes for the MCO beam are designed by changing the steel plate thickness and web height as design variables, while satisfying the requirements on the dimensions of the cross-section discussed above. As shown in Table 11, 6 steel plate thickness values and 7 web heights are used as design values. The effective moment of inertia for the cross-sections in the table ranges from 1,530 to 18,218 cm4. A total of 42 of the designed MCO beam cross-sectional shapes are given in Figure 9.Table 11
Design requirements and values on the variable sectional portion of the MCO beam.
Design factors
Design requirements
Design values
Thickness of steel plate
Use standard steel products
(i) 4.5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm
Depth of beam
Apply modular coordinate
(i) Floor beam: 270 mm, 300 mm, 330 mm, 360 mm, 390 mm(ii) Ceiling beam: 200 mm, 240 mmFigure 9
Developed cross-sectional shapes for the MCO beam.


## 3.1. Function Analysis and Pugh Matrix

The core functions of the steel modular beam section are determined and its optimal design is developed utilizing the CTQs derived in the previous phase. Table5 describes the main processes required for the manufacturing of the steel modular beam section and classifies the functions required in each process into one of three functions, namely, the basic function (necessary), attractive function (delighter), and discriminative function (primary satisfier). The basic functions must be satisfied, while the attractive and differentiated functions can be optionally considered in the design process.Table 5
Classification of key functions for the steel modular beam section.
Main process
Manufacturing beams
Assembly of modules
Transportation and installing
Ensuring structural performance
Must be functions
—
Welding end-plateConnecting beam and columnConnecting beam and slabConnecting beam and ceiling trackConnecting beam and wall track
Transportation of modules
Flexural strength of beamShear strength of beamMinimize deflection of beamMinimize floor vibrationEarthquake and wind resistanceFire resistance
Delighter functions
—
—
Plumbing equipment penetration
—
Primary satisfier functions
Minimize a space for stock
—
—
—Key functions can be determined from a correlation analysis between the quality characteristics and associated functions by applying the same method used to create CTQs in Table3. Table 6 shows the relationship between the quality characteristics and the key functions. From this relationship, “minimize deflection and vibration of beam,” “flexural strength of beam,” “earthquake and wind resistance,” and “piping equipment penetration” are selected as key functions.Table 6
Correlation between the quality characteristics and key functions.
Quality characteristic
Key function
Assembly of modules
⁢Ensuring structural performance
⁢Secondary function
Welding end-plate
Connecting beam and column
Connecting beam and slab
Connecting beam and ceiling track
Connecting beam and wall track
Flexural strength of beam
Minimize deflection and vibration of beam
Earthquake and wind resistance
Fire resistance
Plumbing equipment penetration
Transportation of modules
Price of beam
Surface area per unit length
◎
Welding length per unit length
◎
○
Contribution to competitiveness of module
Span length
◎
Thickness of webs
◎
◎
Diameter of web opening
○
◎
Number of webs
○
◎
○
○
Thickness of flanges
◎
Number of openings
○
◎
Height of ceiling and floor beams
◎
◎
Weight of floor beams per unit area of plan
Structural performance of beam
Moment of inertia per sectional area of beam
◎
Section modulus per sectional area of beams
◎
◎
Lever arm of bolts at the end plate
◎
◎
◎
Quality of manufacturing
Number of axes of symmetry
◎
○
Radius of curved section
○
◎
Priority ratio
6.5%
9.5%
8.6%
6.7%
4.7%
16.7%
19.7%
11.9%
0.6%
10.1%
4.8%
Rating
8
5
6
7
10
2
1
3
11
4
9After derivation of the key functions, an optimal design concept satisfying the derived key functions needs to be developed. In order to achieve this, various methods can be used such as the benchmarking of advanced technologies, brainstorming by experts, TRIZ, and mind mapping. In this study, various solutions that can satisfy the key functions are created, and several possible design options are obtained by combining these solutions. Finally, the Pugh matrix is employed to select the optimal design among the designs obtained.Table7 lists the available solutions for each of the key functions of the steel modular beam section. The table indicates that there are two solutions for “piping equipment penetration” and “connecting beam and slab,” four solutions for structural functions, specifically “flexural strength of beam,” “minimize deflection and vibration of beam,” and “earthquake and wind resistance,” and one solution for all of the remaining functions. These solutions can be combined to produce an optimal design concept. By combining the solutions listed in Table 7, seven design concepts are derived. They satisfy various functions required for the floor and ceiling beams of the modular beam-column frame system and show different characteristics with regard to manufacturing cost, steel consumption, and availability for both of ceiling and floor beams. Their characteristics are summarized in Table 8.Table 7
Available solutions for each of the key functions.
Key functions
⁢Solutions
Piping equipment penetration
Install reinforcing device at penetrationSolution A
Penetrate without reinforcingSolution B
Transportation of modules
Limiting module height less than 3.3 m
Welding end-plate
Limiting flange width less than 120 mm
Connecting beam and column
Ensuring bolting space at end-plate
Connecting beam and slab
Integrate beam and slab supportSolution a
Separate beam and slab supportSolution b
Connecting beam and ceiling track
Connect track to web of beam with screw
Connecting beam and wall track
Ensuring flange width of 60 mm
Flexural strength of beam
Use hollow flange (flange thickness = web thickness)Solution I
Use hollow flange (flange thickness > web thickness)Solution II
Use open flange (flange thickness = web thickness)Solution III
Use open flange (flange thickness > web thickness)Solution IV
Minimize deflection and vibration of beam
Earthquake and wind resistanceTable 8
Design concepts obtained by combinations of the available solutions.
Combination of solutions
SolutionsA + a + I
SolutionsA + b + I
SolutionsA + a + II
SolutionsA + b + II
SolutionsB + a + III
SolutionsB + b + III
SolutionsB + b + IV
Design concepts
Manufacturing cost
Very high
High
Very high
Very high
Middle
Middle
Very high
Steel quantity
Very low
Low
Very low
Very low
Low
High
Low
Compatibility between floor and ceiling beam
Not compatible
Compatible
Not compatible
Compatible
Not compatible
Compatible
CompatibleIn order to select the optimal design among the candidates listed in Table8, a Pugh matrix is created in Table 9. In this methodology, a relative evaluation is performed on each candidate by comparing it with the reference design for each of the key criteria. The built-up RHS is chosen as the reference design for this comparison. Thus, if a candidate shows better performance than the reference design, it is denoted as +. If the candidate is worse than or is equal to the reference design, it is denoted as − or S, respectively. The candidate with the greatest difference between the sum of pluses and that of minuses is chosen as the optimal design. The results in Table 9 indicate that design concept 2 is the optimal design. Thus, it is selected as the prototype for the steel modular beam section.Table 9
Selection of the optimal design using the Pugh matrix methodology.
Better +Same SWorse −
Reference
Concept 1
Concept 2
Concept 3
Concept 4
Concept 5
Concept 6
Concept 7
Key criteria
Weight
Manufacturing cost
5
S
+
+
S
S
+
+
−
Fire proofing cost
4
S
−
−
−
−
−
−
−
Steel quantity
4
S
+
+
+
+
−
−
+
Easy fabrication
3
S
+
+
+
+
+
+
+
New investment
5
S
−
−
−
−
+
+
−
Compatibility
4
S
−
+
−
+
−
+
−
Creativity
3
S
+
+
+
+
S
S
S
Sum of +
0
4
5
3
4
3
4
2
Sum of −
0
3
2
3
2
3
2
4
Sum of S
7
0
0
1
1
1
1
1
Weighted sum of +
0
15
19
10
14
13
17
7
Weighted sum of −
0
13
9
13
9
12
8
18The prototype has hollow flanges in both the upper and lower parts of the section as shown in Table9. It can be manufactured by a roll forming method, in which thin steel sheets are passed through several rolls and are consecutively bent at room temperature. The cross-sectional shape is illustrated in Figure 3. The steel beam member with the cross-sectional shape shown in Figure 3 is hereafter referred to as the modular construction optimized (MCO) beam for convenience.Figure 3
Cross-sectional shape of the MCO beam and its roll forming simulation.


## 3.2. Detailed Design of MCO Beams

In this section, a detailed design of the MCO beam is discussed considering the manufacturing process. With the detailed design components, the cross-section has a variable portion as well as an invariable portion as shown in Figure4. Although MCO beams manufactured through the roll forming process require smaller manufacturing costs than general built-up beams, a variety in depth is also necessary for their applications to modular buildings with diverse spans. Therefore, the upper and lower hollow flange parts are designed as the invariable portion and produced using a single roll. In contrast, the thickness and width of the web section are variable. The design requirements for each design factor of the MCO beam are listed in Table 10. SPA-H steel is used for manufacturing the MCO beams since it has high durability as well as a high tensile strength of 490 MPa.Table 10
Design requirements for each design factor of the MCO beam.
Design factor
Design requirement
Invariable section
Flange width
(i) Limit the flange width to less than the column width (column width: 125 mm or 150 mm)(ii) Require the minimum flat flange width (50 mm) to be connected to the wall stud
Radius of curved section
(i) Minimum radius of curved section less likely to cause a crack
Flange height
(i) Flange to thickness ratio is larger than 61 (h
f > (h − 61t)/2)
Welding length
(i) Prevent local buckling
Variable section
Thickness of steel plate
(i) Variable sections for variable floor loads and spans
Web height
(i) Variable sections for variable floor loads and spans(ii) Able to penetrate pipesFigure 4
Cross-sectional design of the MCO beam.The design procedures for the MCO beam with invariable cross-section (hollow flange) can be summarized as follows.Step 1 (setting up the range of the flange width as shown in Figure5).
(i) If the minimum width of the column is 125 mm, the flange width is in the range of 100~120 mm.
(ii) The minimum width of the horizontal flat flange portion must be at least 50 mm.Figure 5
Range of the flange width.Step 2 (determination ofr
1 and r
2 shown in Figure 6).
These parameters are constant regardless of the steel plate thickness if the same roll forming process is used.(i)
Bending capacity of SPA-H steel: if the bending angle is 180 degrees, the inner radius must be at least 1.5 times the flange thickness.
(ii)
The maximum steel plate thickness is limited to 10 mm.
(iii)
If the bending angle ofr
1 is in the range of 90 to 180 degrees, r
1 = 15 mm.
(iv)
If the bending angle ofr
2 is 90 degrees, r
2 = 12 mm.Figure 6
Determination ofr
1 and r
2.Step 3 (determination of the flange width).
(i) If the steel plate thickness is 10 mm andr
1 and r
2 are 15 and 12 mm, respectively, the flat flange width is in the range of 53 to 73 mm, thus satisfying the condition in Step 1.
(ii) The flange width is determined as 120 mm, which is the maximum value allowed by the condition in Step1, considering its easy attachment onto ceilings and floor tracks.Step 4 (determination ofr
3).
This value is constant if the same roll forming process is used regardless of the flange thickness.(i)
If bending angle ofr
3 is less than 90 degrees, r
3 = 12 mm, which is the same as r
2.Step 5 (setting up the range of the flange height shown in Figure7).
(i) If it is assumed that the upper and lower flanges are parallel to each other and the flange thickness is 10 mm,h
f
,
m
i
n
1 = 10 + 15 + 15 + 10 = 50 mm.
(ii) The flange height can be calculated by considering the maximum beam height of 400 mm and minimum steel plate thickness of 4.5 mm and applying the maximum width-thickness ratio of 61 to prevent elastic local buckling ash
f
,
m
i
n
2 = (400 − 61 × 4.5)/2 = 63 mm.Figure 7
Determination of the flange height.Step 6 (final selection of invariable dimensions of the upper hollow flange).
(i) Front welding is performed on the steel plate connection as shown in Figure8.Figure 8
Invariable dimensions of the upper hollow flange of the MCO beam.The following design conditions for the variable portion of the MCS beam cross-section are assumed for three module spans of 6, 7.5, and 8.1 m: floor beam load in the range of 2~5 kN/m2, floor beam live load in the range of 2~5 kN/m2, ceiling beam load in the range of 0.3~0.5 kN/m2, and ceiling beam live load in the range of 0.5~1 kN/m2. Various cross-sectional shapes for the MCO beam are designed by changing the steel plate thickness and web height as design variables, while satisfying the requirements on the dimensions of the cross-section discussed above. As shown in Table 11, 6 steel plate thickness values and 7 web heights are used as design values. The effective moment of inertia for the cross-sections in the table ranges from 1,530 to 18,218 cm4. A total of 42 of the designed MCO beam cross-sectional shapes are given in Figure 9.Table 11
Design requirements and values on the variable sectional portion of the MCO beam.
Design factors
Design requirements
Design values
Thickness of steel plate
Use standard steel products
(i) 4.5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm
Depth of beam
Apply modular coordinate
(i) Floor beam: 270 mm, 300 mm, 330 mm, 360 mm, 390 mm(ii) Ceiling beam: 200 mm, 240 mmFigure 9
Developed cross-sectional shapes for the MCO beam.


## 4. Design Verification and Pilot Test

As the final stage of the DFSS methodology, MCO beam rolls are produced using the roll forming facilities of a local company in Korea, and their formability and welding workability are assessed. Figure10 shows the procedure for a pilot production of the MCO beam sections developed. A long strip in coiled steel is passed through sets of rolls until a shape with upper and lower hollow flanges is obtained. Then the production of the MCO beam section is completed by performing welding on the roll formed shape. Figure 11 shows an example of the assembled modular unit with the produced MCO beams.Figure 10
Pilot production process for the developed MCO beam.Figure 11
Assembled modular unit with the produced MCO beams.The results of CTQ and productivity assessments on the final products are summarized in Table12. The deformation level of the MCO beam that occurs during its production is less than 5 mm per 10 m. While some deformation may take place during secondary machining such as welding of brackets and end plates, additional correction can be performed in the process of module assembly, resulting in an error less than 3 mm per unit module. To confirm that the produced beams have a sufficient moment of inertia per unit cross-sectional area, a total of 150 cases are tested for various floor spans and loading conditions. The results of the test show that the average floor span is 183.38 cm2 and the standard deviation is 16 cm2. Thus, the average is well above the design target, which is 160 cm2. For three spans of 6, 7.5, and 8.1 m, floor beams with optimal cross-sections are selected, and then the weight of the floor beams per unit area is evaluated for each case. It can be seen from the results of the table that target values are met for all of the three cases.Table 12
Design targets and test results for the produced MCO beams.
Design factors
Design targets
Test results
Verification of CTQ
Welding length per unit length (m/m)
Less than 2
2
Moment of inertia per unit sectional area of beam (cm2)
Larger than 150
Average 183.86
Weight of floor beams per unit area (kN/m2)
6 m span
Less than 0.25
0.18
7.5 m span
Less than 0.28
0.25
8.1 m span
Less than 0.35
0.32
Pilot test
Pilot production of beam
Flexural deformation is less than 0.05%
Less than 0.05%
Pilot assembly of module
Tolerance of 3 mm
Less than 3 mm


## 5. Concluding Remarks

In this study, a systematic approach was presented for the development of an efficient steel beam section for modular construction based on Six-Sigma. As the first step of this approach, market studies and surveys are conducted to obtain the opinions of potential customers. Then the opinions of the customers were converted into the quality characteristics for the channel-shaped steel beam using the quality function deployment methodology. A steel hollow flanged channel was chosen as the main modular beam shape, and the design concept was derived and developed by applying the Pugh matrix methodology. A pilot test was performed to validate the effectiveness of the developed beam section. The main conclusions of this study are as follows:(1)
To reflect customers’ needs in the development of production processes, the QFD methodology was applied, and “welding length per unit length,” “moment of inertia per sectional area of beam,” and “weight of floor beams per unit area of plan” were selected as CTQs. Quantitative target values for these items were also set up.
(2)
Seven design concepts were developed from an analysis on the key functions of the steel modular beam to satisfy the derived CTQs. The Pugh matrix methodology was applied to derive the optimal design of the steel modular beam, which has hollow flanges at the top and bottom.
(3)
In the final product design, the cross-section of the MCO beam has the upper and lower hollow flange parts as the invariable portion and the web section as the variable portion. The results of the pilot production of the MCO beam indicate that the weight of the floor beams per unit area can be reduced to an average of 0.25 kN/m2 for the standard 7.5 m span, which is 18% less than the corresponding value for the built-up RHS beam. All the modules assembled with the MCO beam products show an error less than 3 mm per unit module, thus satisfying the target value.
(4)
Based on the DFSS methodology of Six-Sigma, this study proposed a methodology which can effectively reflect customers’ needs, such as the reduction of manufacturing cost, less material usage, and reduced structural deformation of modular units, in the product design. It is expected that the proposed method can be utilized to develop other types of structural modular beams and can satisfy the diverse requirements of different customer groups.



---

*Source: 9687078-2016-11-24.xml*