8/3/2019 Chapter4_comlive Load Reduction Factor http://slidepdf.com/reader/full/chapter4comlive-load-reduction-factor 1/24 CHAPTER 4 LIVE LOADS 4.1 General 4.1.1 Definition Live loads are the weights of people, furniture, supplies, machines, stores, and so on, borne by the building during its use and occupancy. Live loads are distinguished from dead loads which are the weights of the building itself, the secondary members and the finishing materials. Live loads are movable and variable during the use and occupancy of the building, and sometimes cause dynamic effects. Therefore, they are easily affected by social transitions, such as the rapid advances in building services equipment and mechanization. The loads of small or movable pieces of equipment are considered as live loads, but equipment that belongs to the building and is fixed and heavy is regarded as dead load. Live loads are specified as the weight per unit area corresponding to the use of the floor. In terms of their concentration, they are estimated differently, depending on the kind of structural member. Live loads are produced by the gravity of people and equipment in the actions of people, and do not include environmental loads such as snow loads, wind loads and earthquake loads. In the design of buildings, the design live load must be calculated by considering the maximum load effect for the particular use caused by the specific disposition of people and equipment. This recommendation is based on data from recent surveys of live loads done in Japan. There are two problems with using these data for this recommendation. 1) Not all possible floor uses are surveyed. 2) Spatial scatter may be comprehended with enough data, but temporal scatter, especially that resulting from the concentration of people and furniture occurring only once in several years or even once in more than ten years, can not be determined with few or no data. For 1), it is impossible to survey all possible uses of a floor, because future human activity cannot be predicted. Therefore, design live loads for unspecified uses should be estimated from loads caused by similar uses. The classification of uses in this recommendation is based on available data for present typical uses. This recommendation applies to normal use of buildings. For special uses, the design live load should be reconsidered with reference to the estimation method of this recommendation. The disposition of furniture and people depends on the building's uses, which causes the relationship between the stochastic and the design values for the maximum load effect to vary. 2) is related to the decision on the level of the building's serviceability and safety in its structural design. As there have been few claims against live load in conventional structural design of existing buildings, it is considered that the current sustained live loads in practice could be referred to without serious danger or loss of serviceability. Therefore, in this recommendation, the basic value of live load is estimated on the basis of the sustained load data surveyed. In accordance with engineering judgment, the scenario of a rarely occurring concentration of people and furniture is considered, and safety is verified by the probabilistic model of simulation. This calculation assumes that the estimation of the CHAPTER 4 LIVE LOADS - C4-1 -
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basic value is adequate. In the future, if enough stochastic data from temporal variations are stored, it
is thought that it will be possible to reconsider the design live load directly from the probabilistic
model of the maximum value during the design lifetime, as is currently done for snow, wind and
earthquake loads.The design load for safety and serviceability is based on the basic value referred to above.
Therefore, the basic value of live load in this recommendation may be used as the design load in
allowable stress design for sustained loading.
If the levels of safety and serviceability are modified, the percentile determining the basic value
may be varied from 99 percent, for example, to 95 or 99.9 percent, from the stochastic value of the
surveyed data.
When a design load lower than the basic value is used, it should be carefully applied based on the
examination of the maximum value during its design lifetime, so that safety does not become too low.
When the design load in limit state design is estimated using the basic value in this
recommendation, it is necessary to determine the appropriate load factor. At the present time, there
may not be enough stochastic data, but designs in which serviceability in the normal state and safety
during design lifetime are determined, and they specify the relationship between performance and
quality which are ambiguous in conventional allowable stress design. Therefore, this recommendation
is expected to be applicable to limit state design.
4.2 Estimation of Live Loads
4.2.1 Equation for live loads
The basic value of live load is estimated as sustained load and calculated as a product of the basic
live load intensity which is obtained statistically, a conversion factor for equivalent uniformly
distributed load, a area reduction factor and a multi-story reduction factor.
The basic live load intensity is the 99 percentile value on the basis of the statistic data of the
average weight of people and furniture on an area of 18m2
for the particular use of a floor.
Considering temporal concentration, people and furniture should be estimated separately because of
their different dispositions. However, since there are not enough data, they are estimated together in
this recommendation.
The conversion factor for equivalent uniformly distributed load is estimated differently for
members such as slabs, beams, girders, columns and foundations, because the influence of their
disposition state on load effect is different. Generally, the equivalent uniformly distributed load Le is
defined by :
Le = maxi I i dxdy
A #
I i w ( x, y)dxdy A # * 4
(4.2.1)
where A is the influence area of the specific member, which is regarded as the floor area influencingthe load on the member, I i is the influence function defining the load effect on section i of the member,
- C4-2 - Commentary on Recommendations for Loads on Buildings
and w( x, y) is the load of people and furniture at coordinates ( x, y).
In considering Equation (4.2.1), the basic equation for load estimation expresses Q0 as a
representative value of the essentially ambiguous random variate X , and k e, k a and k n are factors given
as mean values if there is a stochastic basis. However, in this recommendation k e is defined for convenience as the ratio of the 99 percentile value of Q to Q0 where k a is given by the following
section 4.2.4 and k n is 1, and Q is estimated from the mean influence area for each member. Although
k e is generally different for beams, girders and columns, here the difference is insignificant, so the
same value is used.
4.2.2 Basic live load intensity
The basic live load intensity Q is estimated on the basis of surveys of several normal uses. The
scatter of the averaged load, that is, the live loads divided by the area on which they act, becomes
smaller as the assumed area becomes larger, because live loads are averaged over the area. Therefore,
the basic live load intensity should be determined considering the influence of area.
In calculating statistic values, the surveyed data are divided into square unit areas, such as 1m2
(1m
X1m), 4m2 (2m X 2m), 9m2 (3m X 3m), etc., and the averaged loads are calculated for each case. This
analysis is called the analysis of averaged live load intensities for square unit areas. The calculated
values are regarded as the statistic values of load intensity, and are estimated by the method of
moments to derive parameters of the probability distributions.
Four main probability distributions are applied: Normal, Log-normal, Gumbel (Type I extreme
distribution) and Gamma. Sometimes other distributions are applied, but have not significantly
influenced the result.
After the estimation of parameters, goodness of fit is examined by the normalized error, and the
probabilistic models for respective areas should be selected as the distribution which has the smallest
normalized error. One probability distribution is selected to specify the influence of the area on the
loads. The Gamma distribution is selected because it generally shows good fit for various uses, and the
percentile values are calculated.
The basic live load intensity is estimated as the 99 percentile value of load models. To investigate
the influence of the area on load intensities, the relationship between the percentile values and area is
expressed as a regressive equation.
For the detailed calculation method, see section 4.2.4. In considering the actual area of the building,
areas smaller than 16m2
(4m X 4m) are not used. Figure 4.2.1 shows examples of averaged weights
and regression curves. This figure shows that load intensities are influenced by the area.
The basic live load intensities must be specified as the values normalized to a specific area. In this
recommendation, they are normalized to an area of 18m2, based on the area of one slab, the
arrangement of frames and the mean surveyed area.
For particular up not specified in this recommendation basic live load intensity is estimated from
surveyed data based on the principles of this recommendation. These principles should be adopted in
all cases. Where the up may change, the basic live load intensity should be re-estimated by the
Load effects on bending moments and shear forces are analyzed for slabs (short or long direction
and support or mid span), load effects on bending moments (support or mid span) and shear forces are
analyzed for girders, and load effects on axial forces are analyzed for columns. The equivalent
uniformly distributed loads are examined in terms of fixed end moments for short directions of slabs,fixed end moments for girders, and axial forces for columns.
All analyses are based on the influence area. The influence area is defined as the floor area whose
load has an influence on the assumed member. For a slab it is equal to the tributary area and to the
panel area, and for a girder and a column it is defined in Fig.4.2.2. In this analysis, a girder means a
member which supports beams, and a beam means a member which does not support them. If there is
no available information about the location of beams, it is assumed for respective uses.
The stochastic analysis is made of the equivalent uniformly distributed load for each case of stress
and the averaged weight on each influence area. It is estimated according to the probabilistic model
which shows the best fit for respective stresses. The conversion factor for uniformly distributed load is
the ratio of the 99 percentile value of the equivalent uniformly distributed load to the averaged load on
the influence area. It is calculated for each member.
Table 4.2.1 shows the results of these calculations. The conversion factor for uniformly distributed
load is estimated on the basis of Table 4.2.1. The conversion factor for uniformly distributed load of
slabs is rounded off to 1.6, 1.8 or 2.0. That of frames is about 1.0 to 1.3, so 1.2 is adopted.
In conventional design, that of beams used to be the same as that of slabs or girders, or the mediumvalue between them. In this recommendation, the designer may adopt value according to his judgment.
That of a foundation is thought to be the same as that of a column, and is estimated considering the
effect of reduction for changing influence area indicated in section 4.2.4 and 4.2.5. Reduction may
also be applied to a multiple-story column.
In the equation for estimating the basic value, the basic live load intensity Q is multiplied by the
conversion factor for uniformly distributed load. Thus, it is impossible to estimate the equivalent
uniformly distributed load of the standardized area of 18m2 because of the difficulty in adjusting the
area for the equivalent uniformly distributed load analysis, which is not equal to 18m2, to the area for
the analysis of the averaged live load intensities for square unit areas. Therefore, it is assumed that the
relationship between the equivalent uniformly distributed load and its area is the same as that between
the averaged live load intensities for square units and its area. The product of the basic live load
intensity and the conversion factor for uniformly distributed load could be regarded as the equivalent
uniformly distributed load.
The conversion factor for equivalent uniformly distributed load is the ratio of the 99 percentile
value of the equivalent uniformly distributed load to that of the averaged weight over the influence
area of each member. Figure 4.2.3 compares the analyses of the equivalent uniformly distributed
load2,3) and the averaged live load intensities for square unit areas. The broken lines in the figure
connect the estimated values of the analyses for each member. The upper one indicates the 99
percentile values of the equivalent uniformly distributed load, and the lower one indicates that of the
averaged weight over the influence area. The solid line shows the result of the averaged live load
intensities for square unit areas. Their gradients are regarded as the same.
Where the area is small, the equivalent uniformly distributed loads have large scatter. According to
the above results, the estimated values for each up should be used, considering the characteristics of
the analysis of the equivalent uniformly distributed load and the averaged load intensities for square
where L1 indicates a reduced live load intensity (N/m2), Af is the influence area (m
2) and Aref indicates
the reference area (m2).
Parameters a and b in Equation(4.2.2) are estimated using the method of least squares in the
relation of the 99 percentile load to the unit area. The statistical data of square units with an area of 4X 4 (= 16)m
2or more are used for the parameter estimation.
Next, parameters a and b in Equation (4.2.2) are normalized by dividing Equation (4.2.2) by the
basic live load intensity, namely L1 when Aref = 18m2. The normalized formula for the reduction factor
k a is presented as :
ka= ta + Af / Aref
tb
(4.2.3)
The results of this analysis show that the Gamma distribution fits well for a probabilistic model of
square unit loads for every use. Table 4.2.2 shows the value of parameters a, b, and normalized
parameters ta, tb of the reduction factor for every use.
The area reduction factor should actually be derived using statistical data of the uniformly
distributed load, so the equivalent uniformly distributed load must be statistically analyzed to
formulate the load reduction factor. However, the reduction factor for changing the influence area is
defined using statistical results of square unit loads, because data of equivalent uniformly distributed
load is lacking.
Table 4.2.2 Parameters of reduction factor
a b
(1) dewellings 449 2331 0.45 2.34
(2) hotel rooms 97 947 0.30 2.96
(3) offices・ laboratories 1075 2066 0.69 1.32
(4) supermarkets 1240 4195 0.56 1.88
(5) computer rooms 1750 8417 0.47 2.25
(8) classrooms 1217 366 0.93 0.28
Equation (4.2.3)
b
Usea
Equation (4.2.2)
4.2.5 Multi-story reduction factor
The axial compression stress in building columns caused by live loads is the cumulative stress of
the live loads on every floor that the column supports. Therefore, the variation of axial compression in
a multi-story column caused by live loads becomes smaller than the variation of axial compression in
a single story column as the number of floors supported increases, because the variation on every floor
is averaged. Thus, in calculating the axial compression caused by live loads, the design live load can
be reduced according to the number of stories supported by the column.
However, this load reduction doesn't apply where loads are produced mainly by people for two
reasons. One is that the temporary concentration of human load can easily occur, and the other is thatthe load distribution over different floors can not be clearly described. When the multi-story reduction
factor k n is used, the influence area of a single story column is used as the influence area to calculate
the reduction factor k n.
The variation of equivalent uniformly distributed load for a single column varies according to the
size of the tributary area of the column. The value of k n becomes smaller with increasing δ i. Althoughthe tributary area of a column greatly varies with its position and the building's use, δ i is assumed to be
0.4 in determining the reduction factor, considering the actual dimensions of the tributary area of the
column based on the statistical results of square unit loads for office buildings shown in Figure 4.2.78)
.
Figure 4.2.7 Relationship between unit area and coefficient of variation by unit analysis
The correlation coefficient ρ of live loads between two different floors is determined to be 0.119,
based on survey results for office buildings8). The reliability index, denoted by β , is 2.33 for a 99%
limit value based on the second moment method. Substituting these values into Equation (4.2.4),
removing the square by the relation (a + b) ] 1/ 2 ( a + b ), and rounding the coefficients, the
multi-story reduction factor k n is derived as shown in Equation. (4.2.5).
kn =n ( n i + bvi )
nn + bvn
=1 + bdi
1 + bd in
t (n - 1) + 1
(4.2.4)
kn = 0.6 +n
0.4
(4.2.5)
Table 4.2.3 shows the mean values, standard deviations and coefficients of variation of equivalentuniformly distributed loads of columns obtained by survey results for office buildings
8). Both the mean
values and standard deviations vary considerably for single story columns at every floor, but for me
multiple story columns the mean values converge to 540 N/m2
and the standard deviations become
smaller with increasing the number of floors supported.
- C4-10 - Commentary on Recommendations for Loads on Buildings
Figure 4.3.2 The result of the analysis of personnel loads
During the design lifetime of buildings, live loads vary with time. As explained above, live loads
for a building in normal use, i.e. sustained live loads, have been analyzed. Over the design lifetime, the
variation of live loads may be shown as in Fig. 4.3.3.
For example, in an office building, the occupancy may change several times during the design
lifetime, and the live loads vary each time. During one occupancy, transient loads may occur. If the
live load is determined synthetically based on this frequency, the design lifetime maximum live load
can be estimated.6),7)
Figure 4.3.3 The state of loading during the design lifetime of office buildings
4.4 Dynamic Effects of Live Loads
With regard to the dynamic effects of live loads, the effects of movements of people and objects
must be considered when it is necessary to evaluate the serviceability performance of buildings in
relation to vibrations, such as habitability for occupants, counter-vibration measures for precision
equipment, etc. It is also desirable to consider the influence of ambient environment and the source
(or sources) of vibrations located on other floor slabs inside the buildings.Long-span floor slabs have often been adopted recently in office buildings and stores. As human
- C4-14 - Commentary on Recommendations for Loads on Buildings
traffic and plants/equipment may cause vibrations in long-span floor slabs, the structural design of
these buildings is developed in consideration of the dynamic effects of their occupants, machinery and
equipment in order to provide satisfactory habitability suitable for specific uses of the buildings.
Moreover, seats in stadiums or halls where a large number of people gather are often structurallysupported by cantilever beams. When a large audience jumps in the air all at once in a rock concert,
for example, extraordinarily large dynamic loads may be applied, resulting in a resonance
phenomenon. Having said this, it is also desirable to consider the dynamic effects during the design
development stage.
On the other hand, as plants/equipment such as manufacturing or testing machines sensitive to the
effects of vibrations may be installed in facilities having ultra-precision environments including semi-
conductor fabrication plants or research laboratories, it is often necessary to control slab responses to
the dynamic effects of humans, machinery and equipment. In such cases, the degree of amplitude of
vibrations imperceptible to humans is so important that highly precise techniques must be applied to
assume dynamic loads and predict slab responses.
Hereinafter, the dynamic effects of such live loads as those caused by human movements,
operations of plants/equipment, and vehicular traffic are presented on the basis of currently available
research results.
4.4.1 Dynamic Effects of Human Movements
・Outline
Slab vibrations due to various human movements cause problems in diverse ways. Table 4.4.1
shows typical vibration-forcing activities and points of evaluation for them in consideration of actual
problems caused by slab vibrations due to human movements.
・Characteristics of Dynamic Loads Due to Human Movements
Figure 4.4.1 describes examples of the load-time curve for walking and running17,18,19,20)
. The
peak p1 shown in the figure is attributable to the impact created when one’s heel makes initial contact
with a slab. The peak p1 does not always appear, though; the incidence is in the range of 80~95% for
walking and 70~85% for running. Walking loads other than the peak p1 show a double-peak pattern.The first peak is due to one’s heel making contact with the slab and the second due to one’s foot
leaving the slab in preparation for the next step. On the other hand, in running, both movements
occur as a continuous movement, so running loads show a single-peak pattern.
Figure 4.4.4 Typical Example of Load Time Curve for Walking and Running
Figure 4.4.4 summarizes the information presented above by showing typical examples of loads
generated by walking and running.
・Characteristics of Slab Vibrations Due to Human Movements
Figure 4.4.5 shows examples of slab vibrations due to one-step walking by one person (the
deformation time curve and the acceleration time curve)17,18)
, together with the load time curve. Slab
vibrations due to walking generally show complex and complicated characteristics of damped
vibrations at a natural frequency of a slab excited by the peak p1, etc. (see the acceleration time curve),and vibrations proportional to a double-peak patterned load (peak p2, p3, etc.) (see the deformation
time curve).
Figure 4.4.5 Example of the Load Time Curve and Slab Vibration for Walking17,18)
- C4-18 - Commentary on Recommendations for Loads on Buildings
An assessment on human sensitivity toward slab vibrations due to walking is influenced both by
damped vibrations at the natural frequency of the slab and by vibrations proportional to the double-
peak patterned load
21,22,23,24)
. Therefore, it is difficult to properly evaluate the dynamic effects of human movements from the viewpoint of habitability without establishing a load model that enables
us to examine vibrations with two different frequency components.
・ Dynamic Load Model
(a) Time History Waveform
The time history waveform set on the basis of the load time curve for human movements serves as
the most basic dynamic load model. Figure 4.4.6 shows a typical time history waveform for walking.
The waveform shown in the figure is developed by setting the walker’s weight, W , as 600N and
superposing sections supported by both legs (0.1s each) in the typical load time curve shown in Figure
4.4.4.
(b) Fourier Series
The vibration-forcing power caused by continuous human movements generally involves many
components of a forcing frequency and its harmonics. The time history waveform consisting of the
components of the forcing frequency and its harmonics of continuous movements is generally
expressed by the following equation using the Fourier series.
F (t ) = W 1 + an sin(2rnft + zn )n = 1
k
!) 3
Where: F (t ) : time history waveform of load W : exciter’s weight
t : time
an : ratio of amplitude of n harmonic components to exciter’s weight
f : forcing frequency
zn : phase gap between n harmonic components and first harmonic components
n : harmonic number
k : upper limit of target n harmonic
Figure 4.4.6 Example of Time History Waveform for Walking
Table 4.4.2 shows ranges of nf . an for various movements derived from several data. As for
movements by one person, a1 is approx. 1/2~1/3 the gap between the maximum and minimum values
of actual loads. In the case of movements by many persons, a1 for each person still tends to be
smaller due to the effects of phase differences among individual movements.The dynamic load model using the Fourier series is basically used for a slab with a relatively low
natural frequency in order to calculate and evaluate the amplitude of resonance that is induced
between a forcing frequency or its harmonics and its natural frequency by subtly changing the forcing
frequency, f , according to its natural frequency. This model may also be used for a slab whose
natural frequency is not low to predict vibrations due to aerobics, “tatenori” or other movements.
However, as for walking and running, since this dynamic load model does not involve components of
the load equivalent to the peak p1, etc., it is necessary to separately examine damped vibrations at the
natural frequency of the slab excited by the peak p1, etc.
(c) Impulsive Load
Design Recommendations for Composite Constructions of the Architectural Institute of Japan25)
indicates that an impulsive force created by one person walking is “almost equal to the impact
generated by a 3kg object freefalling from a height of 5cm”. On the other hand, All Standards for
Structural Calculation of Reinforced Concrete Structures (1998 edition) of the Architectural Institute
of Japan26)
indicates that the effective impulsive force due to walking is about 3N.s of the impulse (the
half-sine wave with a maximum load of 118N and an action time of 0.04s). This impulse almost
corresponds to the aforementioned 3kg and 5cm.
Any dynamic load model based on an impact with the above-mentioned impulse of about 3N.s is
applicable to the peak p1, etc. and the momentum of the response to be calculated can be regarded as
the maximum amplitude in the early stage of damped vibrations at a natural frequency of a slab
excited by the peak p1, etc. In other words, this load model does not involve components of the
double-peak pattered load, and vibrations proportional to the double-peak pattered load must be
separately studied.
In this connection, when the impulse is calculated by transforming the load time curve up to the
peak p1 into the 1/4 sine wave with a maximum load of 300N (0.5 X the average weight 600N) and an
action time of 0.012s in accordance with the typical example of walking loads shown in Figure 4.4.4,
f (Hz) α 1 α 2 α 3 α 4
One person walking 1.62.3 0.380.5 0.0860.2 0.057 about 0.05
One person running 2.03.3 1.21.4 0.330.4 0.10.15
One person jumping to landing 2.03.0 1.071.9 0.440.69 0.0870.31
Dancing by many persons 1.53.0 0.5 0.2 0.05
Jumping and dancing by many persons 1.54.0 2.0 0.8 0.2
Aerobics by many persons 2.02.75 1.5 0.2 0.1
Concert by many persons 1.53.0 0.25 0.1 0.025
Jumping to landing by many persons 1.53.0 0.71.5 0.250.6 0.0780.15
Table 4.4.2 Example of f ,αn for Walking and Running
- C4-20 - Commentary on Recommendations for Loads on Buildings
building. This is a problem with solid borne sound.
When a car runs inside a building, its dynamic effects on the floor slab differ, depending on the
type of car itself, its running speed, floor conditions, and the type of framework of the slab.
Therefore, it is extremely difficult to accurately assess the dynamic effects of a running car and toreflect them in the design. Instead, a simplified way to assess the dynamic effects of a running car is
to regard the dynamic effects as the ratio of the dynamic deflection of the floor slab due to the running
car to the static deflection due to the car’s own weight. In designing a floor slab, a formula has been
developed to calculate the additional static load of the car based on this ratio. In most cases, a ratio
in the range of 1.2~1.3 is used.
References
1) Tsuboi, Y. : Theory of Plates, Maruzen, 1960 (in Japanese). .
2) Ishikawa, T., Hisagi, A. : A Study on Evaluation of Live Load, Journal of Structural Engineering,
Vol.38B, pp.31-38 (in Japanex with English abstract), 1992.
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of Technical Papers of Annual Meeting Architectural Institute of Japan, pp. 1023-1024 (in
Japanese), 1984.
4) Ishikawa, T., Hisagi, A. : A Study on the Effect of Extraordinary Live Load on
Evaluation value, Summaries of Technical Papers of Annual Meeting Architectural Institute of
Japan, pp. 217-218 (in Japanese), 1992.
5) Komori, S., Hayashi, M. : The Effects of Partial Load on the Fixed End Slab being Unevenly
Distributed; The Simple Design of the Fixed End Slab that is Supposed Partial Load, Proceeding
of the 7th Architectural Research Meetings (CHUGOKU and KYUSHU) Architectural Institute of
Japan, pp. 129-136 (in Japanese), 1987.
6) Kanda, J., Kinoshita, K. : A Probabilistic Model for Live Load Extremes in Office Buildings,
Proc.4, ICOSSAR, 1985.
7) Kanda, J., Yamamura, K. ; Extraordinary Live Load Model in Retail Premises, Proc. 5, ICOSSAR,
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8) Idota, H. and Ono, T. : Study on Live Load of Office Buildings using Measured Data, Summaries
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Buildings Part 2, Summaries of Technical Papers of Annual Meeting AU, pp. 215-216 (in
Japanese), 1992.
10) Uchida, S., Uno, H., et a1. : Effect of Floor Hardness on Human Sensation, Summaries of
Technical Papers of Annual Meeting AIJ, pp. 225-226 (in Japanese), 1968.
11) Yamaoka, H., Aoki, M., et a1. : Live Load Survey for Buildings Part 3, Summaries of Technical
Papers of Annual Meeting AIJ, pp. 745-746 (in Japanese), 1976.
12) Kunihiro, H., Aoki, M., et a1. : Live Load Survey for Buildings Part 4, Summaries of
Technical Papers of Annual Meeting AIJ, pp. 853-854 (in Japanese), 1977.
- C4-22 - Commentary on Recommendations for Loads on Buildings
27) Yamahara, H : Design of Vibration isolation for preserving environment, Shokokusya, December,
1974
28) Mugikura, K : Prediction of exciting force of equipment and floor impedance, Architectural
acoustics and noise control, No.101, March, 1998, pp.37-4329) Tano, M, Andou, K, Minemura, A and Magikura, K : Experimental study on the exciting force of
fans for building equipment, Simplified methods for determing the exciting force of fans(Part 2),
J. Archit. Plann. Environ. Eng., AIJ, No.427, September, 1991, pp. 49-55
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March, 1998, pp.45-51
- C4-24 - Commentary on Recommendations for Loads on Buildings