Gang Wang School of Civil Engineering Beijing Jiaotong University
Beijing, China
Abstract—In China, the safety of high falsework is a worrying problem, and human error is the uppermost reason for the collapse of falsework. In this paper, on the bases of test data of axial forces of vertical bars of the falsework in a construction site, a phenomenon of improper erection of vertical bar (IEVB) is described and analyzed. The effect of IEVB on structural reliability is discussed, and the results show that IEVB will make an order of magnitude increase in the failure probability. The reliability index of the high falsework does not meet the requirement of corresponding code, and more attentions should be paid to the construction of high falsework.
Keywords-Structural reliability; falsework; hidden defect; in-situ test; human error; test analysis.
I. INTRODUCTION People have generally paid a great deal of attention to
insuring the safety of structures during its service life by meeting safety requirements of Code. Unfortunately less attention has often been paid to the consideration of safety during construction. In some countries such as China, the most critical stage of structures is during construction, and most failures which have caused casualties and the loss of large amounts of money have occurred during construction according to the survey results of Walker (1981) and Smith (1977) who have surveyed 120 cases and 800 cases respectively. Among all the failures during construction stages, the most disastrous is the collapse of falsework. In China, during past 4 years there were 27 cases of serious collapses of falseworks which had made about one hundred workers lost their lives and more workers injured. These collapsed falseworks are all over 8 meters high, and are defined as high falsework. Now the safety of high falsework has become the focus of society’s attention.
In America, Canada, Japan and Taiwan, door-type tubular steel falsework is the most common type and Huang (2000), Peng(1996) and Weesner(2001) have studied the load-carrying capacity of this kind of structure using computational and/or experimental methods. In China, the above supports are not so popular because of the expensive price. Other two kinds of high formwork supports, steel tube supports with couplers and steel tube supports with bowl-buttons are most widely used in construction. Yuan(2006), Liu(2006) and the writer of this
paper, Xie(2008) have modeled steel tube supports with coupler, and studied the instability behavior.
In above studies, the falseworks were considered as temporary structures without any human errors. But in fact, according to formwork failures surveys (Hadipriono, 1986 and You, 2004), most of falsework failures are the result of human errors. Some human errors such as lacking of foot ties and braces can be observed easily by inspecting engineers, and it is possible for construction workers to correct them. However, other human errors are difficult to be found out in engineering inspections.
According to some in-situ tests, the writer has realized that there are always some kinds of hidden defects in high falsework. Among those unconspicuous defects, the improper erection of vertical bar (IEVB) which is very hard to be found out in the visual inspection process is the most serious one. In this paper, on the bases of test data of axial forces of vertical bars of the falsework in a construction site, the phenomenon of IEVB is described and analyzed. The effect of IEVB on structural reliability is discussed.
II. HIDDEN DEFECTS FOUND OUT FROM IN-SITU TEST DATA A Introduction of In-situ Measurement
The test was taken in a construction site named trade center of construction materials in Beijing. The investigated falsework is used to support the formwork of slab floor system. The frame beam has a depth of 1000mm and a width of 500mm, and the cross beam has a depth of 800mm and a width of 300mm. The depth of slab is 150mm. The falsework is 8 meters high with vertical cross braces which are inclined to the horizontal at 45°~60°, and its configuration is shown in Figure 1.
The main measuring points were placed on the top of the 5 vertical bars which were under the crossing of frame beam and cross beam, as shown in Figure 2. Typical construction errors such as inadequate falsework foundation had been detected and corrected during the initial visual inspection and the second visual inspection.
Once the process of the laying of formwork and steel bars ended, the strain gauges would be stuck on the measuring points of vertical bars. The DH3816 measurement system for
static strain was used to record strains. During the concrete placement, sampling rate was one sampling per five seconds.
Figure 1. Configuration of the falsework
Figure 2. Serial numbers of bars and measured points
B Unusual Phenomenon Observed During the In-situ Measurement
The axial forces at juxtaposition point ②, ③ and ④ on vertical bars 2, 3 and 4 which are arrayed along the axis of frame beam and the axial forces at juxtaposition point ①,③and⑤ on vertical bars 1,3 and 5 which are arrayed along the axis of the cross beam are shown in Figure 3 and Figure 4 respectively.
Figure 3. Histories of axial forces at juxtaposition point ②, ③ and ④ on bar
2, 3 and 4 respectively
Figure 4. Histories of axial forces at juxtaposition point ①,③ and ⑤ on bar 1, 3 and 5 respectively
From Figure3, it is found that the axial force of bar 4 is very small comparing to those of bar 2 and bar 3, so we can conclude that bar 4 has not been subjected to any load. It is in the state of IEVB.
From Figure 3 and Figure 4, it is also observed that when the concrete pouring is over, axial force of bar 3 is 27kN, which is almost 20% larger than the axial force of bar 2 and is twice as large as the axial forces of bar1 and bar 5. So the falsework is loaded very unevenly.
C Analysis of the Unusual Phenomenon In this paper, a 3m×3m partial falsework is used to
investigate the axial forces of vertical bars under dead load and live load. According to Technical code for Safety of forms in Construction (JGJ162-2008), without taking into account the action of wind load, the combination of load effects should be:
(1)
where is the effect of the characteristic value of concrete
weight C KGS
CG K ; is the effect of the characteristic value of construction live load (3kN/m
QKS2).
The axial forces of vertical bars without IEVB are shown in Figure 5. Once the IEVB of bar 4 is taken into account, the working state of falsework changed distinctly, and the axial forces of vertical bars with IEVB are shown in Figure 6.
From Figure 6, we can know that the IEVB of vertical bar 4 makes the axial forces of bar 3, bar 7, bar 12 and bar 13 increase by about 50% and axial force of bar 3 is almost 30% larger than the axial force of bar 2 and is nearly twice as large as the axial forces of bar 1 and bar 5. Results of the calculation analysis are in agreement with those of test.
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Figure 5. Axial forces of vertical bars without IEVB
Figure 6. Axial forces of vertical bars with IEVB of bar 4
III. RELIABILITY ANALYSIS METHOD OF FALSEWORK A Performance Function
Without regard to the action of wind load, the performance function can be expressed as:
(2)
where R= the resistance of falsework; S= load effect.
R can be expressed as:
(3)
where 1η = influence coefficient for the initial crookedness of vertical bar which is larger than L/1000, and L = length of vertical bar; 2η = influence coefficient for the undersize section
of vertical bar; 0R = resistance of falsework taking no account
of 1η and 2η , 0 R KR K R= , RK = the ratio of 0R to KR ,
KR is the characteristic value of R ; 1.2 1.4K GK QKR S S= + ,
GKS is characteristic value of the effect of dead load G .
1η and 2η can be calculated in terms of the formulations proposed by Xie (2008).
S can be expressed as:
(4)
where = load effect of G , , = the
ratio of to ; = effect of live load . GS G G GKS K S= GK
GS GKS QS Q
B Statistical Characteristics of Random Variables On the bases of the in-situ investigation and statistical
analysis of the wall-thickness cγ and initial crookedness a of vertical bars (Xie, 2008), as well as statistical data from other references, the statistical characteristics of main random variables are listed in Table 1.
TABLE I. STATISTICAL CHARACTERISTICS OF RANDOM VARIABLES
C Reliability Analysis Method In this paper, the Monte Carlo Simulation is adopted to
assess the reliability of system according to the following formulation:
[ ( ) 0] limf n
kP P g Xn→∞
= ≤ = (5)
where k= number of failures during the process of simulation; n= number of simulations.
Assuming a normal distribution for the performance function, and the corresponding reliability index can be estimated by
(6)
IV. EFFECT OF HIDDEN DEFECT ON STRUCTURAL RELIABILITY
Considering two states of falseworks, without IEVB and with IEVB, the failure probabilities of falseworks are
Random variable
Mean value
Standard deviation
Distribution type Source
cγ 3.02 (mm)
0.23 (mm)
normal distribution
Xie et al. (2008)
a 2.4L/1000 1.5L/1000 normal distribution
Xie et al. (2008)
RK 1.0773 0.106 lognormal distribution
Li et al. (1990)
Q 0.40892(kN/m2)
0.40892 (kN/m2)
exponential distribution
Zhang et al. (2002)
GK 1.06 0.07 normal distribution
Li et al. (1990)
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calculated. By running 106 Monte-Carlo simulations, the failure probabilities of two cases are estimated to be 0.0112 and 0.0912, the corresponding reliability indexes are 2.22 and 1.33 respectively.
V. CONCLUSIONS According to the test data of axial forces acting on vertical
bars of a high falsework, the unusual phenomenon of IEVB is found out. It can result in the falsework being loaded very unevenly. The results of the reliability analyses considering two states without IEVB and with IEVB show that IEVB will make about an order of magnitude increase in the failure probability. The reliability index of the high falsework with IEVB does not satisfy the requirement of corresponding code, and more attentions should be paid to the construction of high falseworks.
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