Floor dynamics for truss system with light gauge steel and concrete
S.E Lee
Senior Researcher
Research Institute of Industrial Science & Technology
79-5 Young-chun Dongtan Hwasung Kyounggido R.of KOREA
[email protected]
ABSTRACT
The vibration of a structure has more influence if the structure is lighter and more flexible, and also if its damping ratio is
smaller. Problems related to vibration of structures are very unpredictable due to the fact that the structure itself is composed
of various materials and that the environmental vibration applied on the structure is irregular.
Evaluation of the vibrational influence on buildings range from serious vibration, which has great impact on the safety of the
structure, to micro vibration. Due to the fact that steel Framed house is a structure which uses light and flexible materials, its
vibration properties should be subjected to scrutinized evaluation.
Through this research, results of vibration measurement in 3 type of floor composed with single channel, truss channel and
truss B-type channel. Therefore, it would be possible to predict floor vibration of steel Framed house by making a comparative
analysis of such results.
Introduction
The floor structure of the light gauge steel framing system is generally used as a single structural member called a joist.
Nonetheless, its use as a joist member requires punching for installing a facilities line as a perennial consideration for the floor
structure. Note, however, that joist punching may cause work delays or fatal damage to the floor structure. Employing a flat
truss as a floor structure has several advantages, e.g., some space is provided for facilities to pass through, a floor structure
with the desired span can be formed using materials of a certain thickness according to the truss design. As such, trusses are
increasingly employed as floor structures.
Nonetheless, the materials used for trusses as structural members in the light gauge steel framing system are about 1.0mm
thick. Likewise, there is a need not only to evaluate the stiffness of the truss itself but also to consider the sheetings and
toppings in the stiffness evaluation. Therefore, this study analyzed the stiffness changes in relation to the base materials and
toppings according to the support and design conditions of flat trusses and evaluated the dynamic characteristics of the Floors
based thereon. Finally, this study sought to evaluate the dynamic characteristics of Floors based on the design and end
support conditions of truss floor structures.
Evaluation Method
Evaluating the vibration performance of a flat truss Floor requires correctly understanding its dynamic characteristics, e.g.,
natural frequency and damping ratio based on its structure and finishing. Likewise, understanding the dynamic characteristics
of the Floor requires a structural analysis or a field experiment. Specifically, determining the dynamic characteristics of a Floor
usually necessitates the use of several methods. One involves evaluating the serviceability of the Floor by measuring the
acceleration amplitude of the floor when walking as the working load is applied to the Floor; another method is the experiment
mode analysis approach, which is designed to aid in understanding the dynamic characteristics of the system by measuring
the input and output values at the same time using an impact hammer and an accelerometer. In evaluating the dynamic
characteristics of a Floor through structural analysis, properly modeling several variables affecting its dynamic characteristics
is very difficult. Thus, using only structural analysis to evaluate the dynamic characteristics of the floor is hardly a reliable
method. Using walking load to understand the dynamic characteristics of a Floor is the most common method of evaluating the
serviceability of the floor, which in turn enables determining the 1st natural frequency of the floor relatively correctly and
evaluating its serviceability through its acceleration amplitude according to the applied walking load. Note, however, that the
experiment method using the working load has limitations, e.g., impossibility of determining the damping ratio of the system,
high-order natural frequency, or vibration mode. Therefore, determining the dynamic characteristics of a Floor, its natural
frequency, its damping ratio, and/or its vibration mode requires performing experiment mode analysis. The experiment mode
analysis approach enables understanding the dynamic characteristics of the system correctly by obtaining the transfer function
through the correct measurement of input and output values.
Floor Modal Analysis
For the experiment modal analysis, three types of Floors were built according to the kinds of structural material and two types
of Floors by truss type. Specifically, grids were drawn at 300mm intervals. Afterward, nodes for the experiment mode analysis
were placed at 600mm intervals. There were a total of 54 nodes on each Floor, with the connection points fixed. All the nodes
were used for the excitement analysis. Since it was expected to show the largest displacement, the No. 28 node was selected
as the response-receiving node.
Table 1. Specifications of Experiment Equipment
Classification
Specifications
Accelerometer
DYTRAN SENSER 3161A
Scope of frequency
measurement
1Hz ~ 1500Hz
Accelerometer
DYTRAN SENSER 3161A
Sensitivity
5 V/g
Impact hammer
DYTRAN 5116A
Sensitivity
1 mV/Ib
FFT analyzer
Dynamic signal analyzer CVT 395
Channel
4 ch
Table 2. Target Floor Materials for Analysis
Section of materials
Floor Base and Finishing
Materials
Floor Type
Structural Materials
Deck_Joist
Joist 300JL16
C-type
300X50x1.6mm
Deckplate/concrete 70mm
Truss_C1
SE-type Truss 90SL12
C-type
90X40x1.2mm
Deckplate/concrete 70mm
Truss_C2
EE-type Truss 90SL12
C-type
90X40x1.2mm
Deckplate/concrete 70mm
Truss_P1
SE-type Truss 100PRY08
B-type
100X40x0.8m
Deckplate/concrete 70mm
Truss_P2
EE-type Truss 100PRY08
B-type
100X40x0.8mm
Deckplate/concrete 70mm
Figure 1. Nodes for the Floor Experiment Object
Web 090SL12 (connected to the top/bottom chords with (10) #48 screws)
Top chord 090SL12
Bottom chord 090SL12
(a) SE-type Flat Truss Using C-type Studs (length: 4.8m)
Web 090SL12 (connected to the top/bottom chords with (14) #48 screws)
Installing a web stiffener
Installing a web stiffener
Top chord 090SL12
Bottom chord 090SL12
(b) EE-type Flat Truss Using C-type Studs (length: 4.8m)
Figure 2. Two type Floor Truss
For the floor vibration tests, joist Floors, SE-type and EE-type flat truss Floors using C-type studs, and SE-type and EE-type
flat truss Floors using PRY materials were built as experiment objects. These Floors were made and installed by the
experiment laboratory at the Giheung Research Institute. After the installation of deck plates, 70mm concrete was poured into
all Floors except joist Floors with OSB installed. The Floors were installed on their supports in the form of simple beams. The
process of constructing free vibration experiment objects is shown below.
Figure 3. Experiment Objects Whose Deck and OSB Installation Has Been Completed
Analysis of the Dynamic Characteristics of Floor
① Natural Frequency
Comparative analysis was conducted on the dynamic characteristics of SE-type truss Floors assembled with stud materials
and those assembled with pry materials.
As a result of comparing the floor end connection methods and vibration performance of floors, C1 and P1 as SE-type trusses
showed first natural frequency of 13.3Hz; C2 and P2 as EE-type trusses showed first natural frequency of 12.5Hz and 11.8Hz,
respectively. (Table3)
Table 3. Comparison of Dynamic Characteristics by Truss Section
Deck_Joist
Truss_C1
Truss_P1
Truss_C2
Truss_P2
Natural
Damping
Natural
Damping
Natural
Damping
Natural
Damping
Natural
Damping
Frequency
Ratio
Frequency
Ratio
Frequency
Ratio
Frequency
Ratio
Frequency
Ratio
(Hz)
(%)
(Hz)
(%)
(Hz)
(%)
(Hz)
(%)
(Hz)
(%)
1st
mode
2nd
mode
3rd
mode
4th
mode
5th
mode
6th
mode
12.75
65.08
12.50
65.82
15.75
57.01
12.25
66.57
11.50
68.89
14.75
59.53
30.50
33.73
29.50
34.74
18.00
51.90
34.75
30.00
39.50
26.67
38.25
27.47
35.00
29.81
41.00
25.76
38.75
27.14
41.25
25.61
51.00
20.95
43.75
24.24
48.75
21.88
46.00
23.11
48.25
22.09
74.25
14.56
74.00
14.61
82.25
13.17
71.25
15.16
71.00
15.21
80.75
13.41
84.25
12.86
93.25
11.64
89.50
12.12
Comparative analysis was conducted on the dynamic characteristics of EE-type truss Floors assembled with stud materials
and those assembled with pry materials.(Table4)
Table 4. Vibration Mode of EE-type Trusses
Truss_C2
Truss_P2
1st natural frequency
1st natural frequency
2nd natural frequency
2nd natural frequency
3rd natural frequency
3rd natural frequency
② Analysis of dynamic characteristics
The natural frequencies of floor structures, i.e., first natural frequencies, second natural frequencies, and third natural
frequencies, were compared. As a result of evaluating the first natural frequencies of other types of Floors vs. the natural
frequency of joist Floor as the criterion, similar distributions were observed in general. On the other hand, as a result of
comparing the respective response amplitudes of Floors in their first natural frequencies wherein the performance of Floors is
influenced greatly vs. the joist Floor as the criterion, the amplitudes of Truss_C1, Truss_C2, and Truss_P1 showed smaller
values compared to the joist Floor; only the amplitude of Truss_P2 was found to be larger by about 12%.(Table5)
Table 5. Comparison of Vibration Amplitude in the First Natural Frequency of Each Floor Structure
Joist
Truss_C1
Truss_C2
Truss_P1
Truss_P2
Amplitude(mg)
6.3
2.09
4.15
5.78
7.03
Amplitude ratio
100%
33%
66%
92%
112%
Experiment on Serviceability Evaluation
There are two kinds of experiment for evaluating the serviceability of a Floor: vibration amplitude evaluation experiment by a
single person walking and impact load evaluation experiment by a single person jumping. For the vibration amplitude
evaluation by a single person walking, the largest acceleration amplitude is evaluated when a male adult weighing about 65kg
walks at a pace of 2Hz by analyzing the acceleration responses in the time domain followed by the natural frequency by
performing APS (auto power spectrum) on the measured values. The scope of frequency for measurement was 100Hz; a total
of 1024 sample data were used.
① Natural Frequency
The natural frequencies of the experiment objects were determined by analyzing the spectrum response values of acceleration
and displacement by a resident’s walking and impact excitement.
② Largest Vibration Response
The performance of a Floor was evaluated by assessing the largest vibration response in the data acceleration response
function of the time domain.
Acceleration Response (Frequency Domain)
Figure 4. Response of Walking load
Results of Serviceability Evaluation
Since the floor structure used as an experiment object had no wall in its upper part or inside the Floor unlike a real floor
structure, less binding strength and less stiffness of the end portions of the Floor placed on the beams compared to a real
Floor had to be taken into account during the evaluation of the serviceability of a Floor by walking load. As such, assessing the
results of an experiment conducted on Floors using walking load as design guideline applicable to the Floors of real structures
was deemed difficult. Therefore, the Floor performance of each type of floor structure was compared with that of other types by
comparing the vibration amplitudes arising from the walking load applied to them.( Figure 4.)
In terms of the natural frequency distribution of Floors, the distribution of first natural frequencies was 11.8Hz~13.3Hz; the
second natural frequencies and third natural frequencies were distributed at 16.8Hz~19.5Hz and 36.8Hz~42.6Hz, respectively.
There was no second natural frequency component observed in Truss_C1 and Truss_P2. The result of the analysis suggested
that the components of the second natural frequency showed a very small value at the No. 28 node as the measurement node
compared to third natural frequency components. (Table 6.)
The natural frequency components of floors were found to be similar in general.
Table 6. Analysis of the Natural Frequency of Floors Based on Walking Load (unit: Hz)
Joist
Truss_C1
Truss_C2
Truss_P1
Truss_P2
12.9
13.3
12.5
13.3
11.8
natural frequency
16.8
-
19.5
17.6
-
3 natural frequency
42.6
40.6
45.3
37.1
36.8
1st natural frequency
nd
2
rd
On the other hand, as a result of measuring the vibration amplitudes of Floors by walking load, the distribution of their vibration
amplitudes was 22.1mg~34.8mg. The vibration amplitudes were calculated to be at 64%~82% levels based on the vibration
amplitude of the joist Floor as the criterion. This suggested that the vibration performance of the truss Floor improved by
18%~36% compared to the joist Floor under the same condition.
Finally, as a result of evaluating the floor vibration performance of each truss type, the floor performance of the Floor using
Stud 90SL12 materials was found to be 10%~18% better than that of the truss Floor using 100pry08. (Table7,Figure 5)
Table 7. Vibration Amplitude of Each Floor Structure Based on Walking Load
Joist
Truss_C1
Truss_C2
Truss_P1
Truss_P2
Vibration amplitude (mg)
34.8
23.55
22.1
27.2
28.6
Amplitude ratio
100%
68%
64%
78%
82%
Figure 5. Cpmparison of Floor Performance by Walking Load
Summary of Results
① As a result of comparing the first, second, and third natural frequencies via experiment mode analysis, the distribution of
first natural frequencies was found to be 11.5Hz~12.75Hz, and that of second natural frequencies and third natural frequencies,
13.75Hz~18Hz and 34.75Hz~41Hz, respectively. In other words, compared to the natural frequencies of the Floor of joist
structure materials as the criteria, Truss_C1, Truss_C2, and Truss_P1 Floors showed similar natural frequency distributions in
general; the first, second, and third natural frequencies of Truss_P2 Floor were relatively small, accounting for 80%, 93%, and
88%, respectively. The dynamic characteristics of the Truss_P2 experiment object were found to be the most disadvantageous
in terms of serviceability, since the analysis results suggested that the 0.8mm thick materials used for Truss_P2 was relatively
thinner compared with the materials used for Truss_C1 (1.2mm) and those for the joist Floor (1.6mm); thus making Truss_P2
the least likely to secure the stiffness of connections with the concrete portion.
② As a result of comparing the vibration amplitudes of Floors in the first natural frequency via experiment mode analysis,
Truss_C1, Truss_C2, and Truss_P1 showed good vibration performance with small vibration amplitudes of 33%, 66%, and
92%, respectively, compared to the vibration amplitude of the joist Floor as the criterion. In contrast, the vibration performance
of Truss_P2 was found to be poor with vibration amplitude of 112% or 12% higher than that of the joist Floor.
③ As a result of evaluating the dynamic characteristics of Floors based on the walking load, the Floors had first natural
frequencies of 11.8Hz ~13.3Hz. Compared to the first natural frequency of the joist Floor as the criterion, Truss_C1, Truss_C2,
and Truss_P1 all showed 97% ~ 103%; Truss_P2 delivered the lowest vibration performance at 90%.
④ Compared to the vibration amplitude of the joist Floor as the criterion, the vibration amplitudes of the truss Floors evaluated
based on the walking load accounted for 64% ~ 82%. This suggests that the vibration performance of Floors using trusses
improves by 18%~36% compared to Floors using joists under the same conditions.
⑤ As a result of evaluating the vibration amplitudes of Floors by truss type, the floor performance of Floors using STUD
90SL12 materials was found to be 10% ~ 18% better than that of trusses using 100PRY08 materials. The analysis results
suggest that the connections between the truss using thicker 90SL12 materials and upper concrete are harder even as C type
and B type materials have the same moment of inertia.
⑥ As a result of comparing SE-type trusses showed first natural frequency of 13.3Hz; EE-type trusses showed first natural
frequency of 12.5Hz and 11.8Hz, respectively. The analysis results suggest that SE-type trusses have the most favorable
vibration performance.
As a result of analyzing the vibration performance of the joist and truss Floors, the moment of inertia in the floor structure
materials as well as the stiffness of the connections with the concrete portion as floor finishing material are found to have
considerable influence on the vibration performance of the floor particularly cold-formed steel Floors.
Finally, the results of this study suggest the need to research on the changes in the vibration performance of floors according
to the various methods of connecting the floor structure and finishing materials.
References
1. AISI, Specification for the Design of the cold Formed Steel Members , 1996
2. J. Mills and R. LaBoube, Self-drilling Screw Joints for Cold-Formed Channel Portal Frames, 2002
3. Y.B Kwon, G.D Kim and I.S Song, Structural Behavior of Cold-Formed PRY Section, KSSC Vol. 14-2, pp 357-364