CHAPTER 4 LIVE LOADS - C4-1 -
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

- C4-2 - Commentary on Recommendations for Loads on Buildings 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 18m 2 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 L e
is defined by :
L e
= max i
*
#
A
I i w ( x , y ) dxdy
#
A
I i dxdy
4
(4.2.1) where A is the influence area of the specific member, which is regarded as the floor area influencing the load on the member, I i
is the influence function defining the load effect on section i of the member,

CHAPTER 4 LIVE LOADS - C4-3 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 Q
0
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 Q
0
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 1m 2 (1m
X1m), 4m 2 (2m X 2m), 9m 2 (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 16m 2 (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 18m 2 , 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

- C4-4 - Commentary on Recommendations for Loads on Buildings designer, considering the probability of change, the use to which the building can be applied and the extra load.
Figure 4.2.1 The influence of the area on load intensities (furniture and people)
4.2.3
Conversion factor for equivalent uniformly distributed load
The members are analyzed elastically to investigate the influence on structure in normal use based on furniture disposition obtained from the survey. The equivalent uniformly distributed loads are calculated by the above analysis.
The finite difference method is applied to the analysis.
1) A reinforced concrete slab with four sides fixed and a poisson ratio of 0.167 is assumed. The boundary conditions of the girders are fixed. In considering the effect of actual loads on a slab, loads are assumed to be distributed uniformly on
25cm-square areas.

CHAPTER 4 LIVE LOADS - C4-5 -
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.
Figure 4.2.2
Definition of influence area

- C4-6 - Commentary on Recommendations for Loads on Buildings

CHAPTER 4 LIVE LOADS - C4-7 -
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 medium value 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 18m 2 because of the difficulty in adjusting the area for the equivalent uniformly distributed load analysis, which is not equal to 18m 2 , 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 load 2,3) 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 unit areas.

- C4-8 - Commentary on Recommendations for Loads on Buildings
Figure 4.2.3
The comparison of analyses between the equivalent uniformly distributed load and
the averaging live load intensities for square unit areas for office
4.2.4
Area reduction factor
As the area increases, the variation of live loads becomes smaller since the live loads is averaged over the area.
According to this recommendation, the design live load differs depending on the kind of member.
One reason is that the relationship between nominal live load intensity and equivalent uniformly distributed load are different for each member. Another reason is that the influence areas are different with slabs, beams and columns. In 4.2.3, k e
is defined as a conversion factor for converting the nominal live load intensity to the equivalent uniformly distributed load on the basis of an area of 18m 2 .
This section presents the reduction factor for reducing the equivalent uniformly distributed load for areas greater than 18m 2 . Figure 4.2.2 shows the influence area for evaluating the stress in structural members.
The area reduction factor is defined based on the following procedure. First, the type of probability distribution for averaged load intensity on square units is examined for four types of probability distribution: normal, log-normal, Gumbel (Extreme type I) and Gamma. The 99 percentile load, which is calculated based on each selected probability distribution type, is formulated as a function of the unit area.
The function of the area reduction factor is defined as :
L
1
= a + b
A f
/ A ref
(4.2.2)

CHAPTER 4 LIVE LOADS - C4-9 where L
1
indicates a reduced live load intensity (N/m 2 ), A f
is the influence area (m 2 ) and A ref
indicates the reference area (m 2 ).
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 4
X 4 (= 16)m 2 or 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 L
1
when A ref
= 18m 2 . The normalized formula for the reduction factor k a
is presented as : k a
= a t + b t
A f
/ A ref
(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 t , t 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.
Use
(1) dewellings
(2) hotel rooms
(3) offices ・ laboratories
(4) supermarkets
(5) computer rooms
(8) classrooms
Table 4.2.2 Parameters of reduction factor a
Equation (4.2.2)
449 b
2331
97
1075
1240
1750
1217
947
2066
4195
8417
366
Equation (4.2.3) a
0.45
b
2.34
0.30
0.69
0.56
0.47
0.93
2.96
1.32
1.88
2.25
0.28
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 that the load distribution over different floors can not be clearly described. When the multi-story reduction

- C4-10 - Commentary on Recommendations for Loads on Buildings 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
. Although the 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 4.2.7
8) .
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 buildings 8) . 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).
k n
= n n n
+ bv n
( n i
+ bv i
)
=
1 + bd i t ( n - 1) + 1 n
1 + bd i
(4.2.4) k n
= 0.6 +
0.4
n (4.2.5)
Table 4.2.3 shows the mean values, standard deviations and coefficients of variation of equivalent uniformly 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/m 2 and the standard deviations become smaller with increasing the number of floors supported.

CHAPTER 4 LIVE LOADS - C4-11 -
Table 4.2.3 Statistics of equivalent uniformly distributed load for columns
Floors
12
11
10
9
8
15
14
13
7
6
5
Equivalent uniformly distributed load for single storey columns
Mean value
Standard deviation
(N/m 2
412
642
451
430
227
606
592
858
721
557
305
) (N/m 2
151
217
210
195
68
181
247
346
190
203
86
)
Coefficient of variation
0.37
0.34
0.47
0.45
0.30
0.30
0.42
0.40
0.26
0.36
0.28
Number of floors supported
1
4
5
2
3
6
7
8
9
10
11
Equivalent uniformly distributed load for multiple storey columns
Mean value
Standard deviation
(N/m 2
412
526
502
484
432
462
480
527
549
550
527
) (N/m 2
151
148
124
132
109
105
105
86
74
77
74
)
Coefficient of variation
0.37
0.28
0.25
0.27
0.25
0.23
0.22
0.16
0.14
0.14
0.14
Temporary concentration of furniture often occurs with relocation or change of occupancy.
Temporary concentration of live loads produces excessive axial compression in columns. The live load reduction factor for multiple story columns has been investigated 9) , considering the live load concentration at plural stories.
The thick solid line in Figure 4.2.8 indicates the design live load intensity, and the thin solid lines show the expected live load intensity where the number of simultaneous occurrences of concentrated load changes from 2 to 6. In the figure, p ex
indicates the occurrence probability of k concentrated loads.
The 99 percentile loads based on the survey data (indicated by O in the figure) are calculated considering the effect of the difference of probability distributions.
Though there is a difference in the expected live load intensity for every number of floors supported, it is shown that the multi-story reduction factor in this recommendation is on a safe side and reasonable.

- C4-12 - Commentary on Recommendations for Loads on Buildings
Figure 4.2.8
Load intensity and occurrence probability of concentrated live loads
4.3 Live Loads Considering Concentration, Deflections or Cracks
The analyses described in section 4.2 are based on the surveyed data for normal use. As concentration or uneven distribution of loads may occur during normal use, they should be taken into account in the estimation. The data on the uneven distribution of loads are explained as follows.
4)
The effect of unevenly distributed loads on members is examined by the simulation analysis assuming the dynamic model. It is assumed that live loads are distributed uniformly on the slab. As the loading area is made smaller, i.e. the ratio of distribution unevenness is made greater, the effect on member stress is examined. The effect on the square slab ( l X l ) is estimated as an example. It is assumed that the square loading area moves on the slab. The fixed end moments are calculated.
5)
Figure 4.3.1 shows the results.
It is logical that, as the loading area gets smaller, the effect of distribution unevenness on the stress becomes greater. However, there is a limit to the actual concentration of furniture and the smallness of the loading area, so that the probability of greater unevenness of distribution is small. In structural design, it is important to determine the design load in view of the particular use.

CHAPTER 4 LIVE LOADS - C4-13 -
Figure 4.3.1
The effect of the uneven distribution of load on the fixed end moment of slabs
Where loads are distributed almost uniformly in normal use, the analysis of the equivalent uniformly distributed load gives nearly the same result as the averaged load intensities. Therefore, the conversion factor for uniformly distributed load needs to be determined so that the effect on each member is apparent. In this recommendation, it is estimated in consideration of the stochastic data of personnel loads based on the number of people on a floor in normal use and in consideration of uneven load distribution.
Especially where loads mainly consist of personnel, the stochastic values of the density of people, which is the number of people divided by the area on which they are located, are estimated from data of a survey of building users. The number of people in one event is regarded as one sample. If the total number of people in a event of N times is obtained, that number divided by N is regarded as one. This assumption only applies to the events in which almost the same number of people are gathered each time. Figure 4.3.2 shows the result.

- C4-14 - 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

CHAPTER 4 LIVE LOADS - C4-15 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 structurally supported 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 semiconductor 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 running 17,18,19,20) . The peak p
1
shown in the figure is attributable to the impact created when one’s heel makes initial contact with a slab. The peak p
1
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 p
1
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.

- C4-16 - Commentary on Recommendations for Loads on Buildings
Table 4.4.1 Slab Vibrations Caused by Human Movements
One step A Few steps by one person by several persons
Semi-synchronized a few Random by steps by several persons many persons, continuous
Synchronized by many persons, continuous
Walking
Running
Stepping up/down
Basics
Basics
Basics
Habitability of Habitability of officers, Habitability of residence (those etc. (those other than shopping malls, other than exciters), habitability of residence, offices, etc.
(exciters exciters), productivity and operability of facilities with precision equipment installed pedestrian decks, etc.
(during movements or still-standing) themselves)
Habitability of officers, etc.
(those other than exciters)
Habitability of staircase (those othe than exciters and exciters themselves)
Aerobics
Vertical footing or
"tatenori"
Basics
Basics
Habitability of neighboring rooms
(those other than exciters)
Habitability of the said building and neighboring buildings
(those other than exciters), structural safety of the said building
Jumping Basics, Ease to landing of use of ahtletic facilities
Semi-synchronized by several persons: Movement by 2-3 persons standing side by side nad unconciously
Random by many persons:
Synchronized by many persons:
Movement by various persons taking various positions and moving in various directions at various speeds
Movement taken by many persons all at once to music, etc.
Figure 4.4.2 shows the relationships between one’s stride/height, walking pace, foot-to-surface contact time, T
0
, (see Figure 4.4.1) and walking speed/height 19) . During normal walking, speed/height is approximately 0.7~0.9/s, stride/height approx. 0.4, pace approx. 0.5s, and T
0
approx.
0.6s. This means that the duration of time that both feet are in contact with the surface is approx.
0.1s. On the other hand, when running around the office, the upper limit of speed/ height is approx.
1.5/s. In this case, stride/height is approx. 0.525, pace approx, 0.35s, and T
0
approx. 0.3s.
Figure 4.4.3 shows the relationships between the magnitudes of the peak p
1
and p
2
, L
1
/ W and L
2
/ W
(where W refers to the exciter’s weight), the time for each load to reach its peak, T
1
and T
2
, and speed/height 19,20) . When walking at the normal speed/height, L
1
/ W distribution centers around 0.5, and its upper limit is about 1.0. T
1
, L
2
/ W and T
2
, distributions center around 0.012s, 1.2, and 0.15s, respectively. When running at the speed/height of about 1.5/s, L
1
/ W distribution centers around 1.5, and its upper limit is about 2.0. T
1
, L
2
/ W and T
2
, distributions center around 0.012s, 2.4 and 0.11s, respectively.

CHAPTER 4 LIVE LOADS - C4-17 -
Figure 4.4.1 Examples of Load Time Curve for Walking and Running 17,18,19,20)
Figure 4.4.2 Relationships between Stride/Height, Pace, T
0
and Speed/Height 19)
・
Figure 4.4.3 Relationships between L
1
/ W , T
1
, L
2
/ W , T
2 and Speed/Height 19 20)

- C4-18 - Commentary on Recommendations for Loads on Buildings
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 p
1
, etc. (see the acceleration time curve), and vibrations proportional to a double-peak patterned load (peak p
2
, p
3
, etc.) (see the deformation time curve).
Figure 4.4.5 Example of the Load Time Curve and Slab Vibration for Walking 17,18)

CHAPTER 4 LIVE LOADS - C4-19 -
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 doublepeak 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 + k
!
n = 1 a n sin (2 r nft + z n
) 3
Where: F ( t ) : time history waveform of load
W : exciter’s weight
t : time a n
: ratio of amplitude of n harmonic components to exciter’s weight f : forcing frequency z n
: 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

- C4-20 - Commentary on Recommendations for Loads on Buildings
Table 4.4.2 shows ranges of nf . a n
for various movements derived from several data. As for movements by one person, a
1
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, a
1
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 p
1
, etc., it is necessary to separately examine damped vibrations at the natural frequency of the slab excited by the peak p
1
, etc.
Table 4.4.2
Example of f , α n
for Walking and Running
One person walking
One person running
One person jumping to landing
Dancing by many persons
Jumping and dancing by many persons
Aerobics by many persons
Concert by many persons
Jumping to landing by many persons f (Hz)
1.6
~ 2.3
2.0
~ 3.3
2.0
~ 3.0
1.5
~ 3.0
1.5
~ 4.0
2.0
~ 2.75
1.5
~ 3.0
1.5
~ 3.0
α
1
0.38
~ 0.5
1.2
~ 1.4
1.07
~ 1.9
0.5
~ 2.0
1.5
0.25
0.7
~ 1.5
α
2
0.086
~ 0.2
0.33
~ 0.4
0.44
~ 0.69
0.2
~ 0.8
0.2
0.1
0.25
~ 0.6
α
3
0.057
0.1
~ 0.15
0.087
~ 0.31
0.05
~ 0.2
0.1
0.025
0.078
~ 0.15
α
4 about 0.05
(c) Impulsive Load
Design Recommendations for Composite Constructions of the Architectural Institute of Japan 25) 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 Japan 26) 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 p
1
, 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 p
1
, 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 p
1
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,

CHAPTER 4 LIVE LOADS - C4-21 it is 2.29N.s. With the maximum load taken as 600N (1.0 X the average weight 600N), the impulse is 4.58N.s.
4.4.2
Dynamic Effects of Operations of Machinery and Equipment
There is a wide variety of machinery and equipment that can be vibration sources including airconditioners for ordinary buildings, plants/equipment for industrial installations, production machines, etc. and it is difficult to estimate dynamic loads caused by them in a unified way. In practice, the vibration-forcing power is estimated from information available from manufacturers by understanding vibration-inducing mechanisms of individual machinery and equipment.
The following shows an outline of dynamic loads created by machinery and equipment 27,28,29) . In general, vibration-inducing mechanisms can be largely classified into rotary motions, reciprocating motions and impulsive motions. Rotary machines such as electric fans and motors are designed to eliminate unbalanced components caused by rotary motions. But in reality, with a complicated machine, it can be difficult to eliminate unbalanced components completely, resulting in a vibrationinducing force.
As for a multi-cylinder engine, though the force can be offset to some extent due to the phase relationship among different cranks, the unbalance inertial force and the unbalance inertial moment remain in any case, causing vibrations. Therefore, in designing fundamentals of an internalcombustion engine, it is important to understand its mechanism and predict the occurrence of possible vibrations.
In the case of a machine such as a forge or a caster in which a heavy object falls onto it or collides with it, the impulsive force generated in it causes vibrations. Though it is difficult to accurately measure the magnitude of the actual impulsive force, it is possible to express the time history waveform of the impulsive force with a half-sine wave pulse or a rectangular pulse by assuming the impulse as a case of freefall or collision.
Since it is possible to reduce the effects of the vibration-forcing power generated by the abovementioned machinery and equipment on buildings through appropriate counter-measures to vibrations, it is important to fully understand the characteristics of the vibration sources and reflect them in the design 30) .
For reference, Table 4.4.3 shows a summary of the types of plants/equipment that are potential vibration sources in ordinary buildings and the characteristics of those vibrations.
4.4.3
Dynamic Effects of Vehicular Traffic
When a car runs through an indoor parking space or along a road in front of a building, disturbances due to vibrations such as indoor floor slab vibrations may happen. Also, when a train runs above the ground or underground in close proximity to the building, vibrations caused by the running train propagate through the building structure and radiate as sound in certain areas inside the

- C4-22 - 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 to reflect 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.
3) Kinoshita, K., Kanda, J. : Equivalent Uniformly Distributed Loads for Office Buildings, Summaries 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,
1989.
8) Idota, H. and Ono, T. : Study on Live Load of Office Buildings using Measured Data, Summaries of Technical Papers of Annual Meeting AIJ, pp. 163-164 (in Japanese), 1991.
9) Idota, H., Ono, T. and Hayakawa, Y. : Live Load Reduction of Multiple-story Column for Office
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.

CHAPTER 4 LIVE LOADS - C4-23 -
13) Guidelines for the evaluation of Habitability to Building Vibration, AIJ, 1991 (in Japanese).
14) Bachmann, et a1. : Vibrations in Structures, Structural Engineering Documents, 3e, IABSE, 1987.
15) D.E. Allen : Building Vibrations from Human Activities, ACT Concrete International : Design and
Construction, 1990.
16) Takanashi, K. and Xiao-Hang Gao : Earthquake Resistant Design of Single Story
Frame with Sliding Floor Load, Summaries of Technical Papers of Annual Meeting AIJ, pp. 47-48
(in Japanese), 1989.
17) Yokoyama, Y : Study on excitation apparatus and perception apparatus for evaluating floor vibration caused by human walking, Establishment of dynamic excitation apparatus and perception apparatus, J. Struct. Constr. Eng., AIJ, No.466, December, 1994, pp.21-
29
18) Yokoyama, Y and Sato, M : Study on excitation apparatus and perception apparatus for evaluating floor vibration caused by human walking, Development of impactive excitation apparatus and verification of appropriateness of method to compute duration of vibration, J. Struct. Constr.
Eng., AIJ, No.476, October, 1995, pp.21-30
19) Yokoyama, Y, Ito, K, Matsunaga, K and Moritoki, H : The relationship between moving velocity and load caused by human walking and running, from a viewpoint of slipperiness and floor vibration, Summaries of technical papers of annual meeting, Tokai branch, AIJ, No.35,
February, 1997, pp.53-56
20) Yokoyama, Y and Matsunaga, K : Study on excitation apparatus for measurement of floor vibration caused by human tripping and computation method of vibration damping time, J. Struct.
Constr. Eng., AIJ, No.519, May, 1999, pp.13-20
21) Ono, H and Yokoyama, Y : Study on vertical vibration of building floors occurred by human actions and its indicating method from a viewpoint of human sense, In case of that the vibration source and receiver are the same, J. Struct. Constr. Eng., AIJ, No.381, November, 1987, pp.1-9
22) Ono, H and Yokoyama, Y : Evaluation method for vertical vibration on building floors caused by human activities from a viewpoint of comport, in case the same person causes and perceives the vibration, J. Struct. Constr. Eng., AIJ, No.394 December, 1988, pp.8-16
23) Yokoyama, Y and Ono, H : Indicating methods of floor vibrations caused by human activities based on human sensations, in the case of difference the vibration cause and the perceiver”, J.
Struct. Constr. Eng., AIJ, No.390, August, 1988, pp.1-9
24) Yokoyama, Y and Ono, H : Presentation of the evaluation method for floor vibration when a different person causes and perceives the vibration, Study on method for evaluation vibrations of building’s floors caused by human activities from a viewpoint of comport(part2), J. Struct. Constr.
Eng., AIJ, No.418, December, 1990, pp.1-8
25)Design Recommendations for composite constructions, Architectural Institute of Japan, 1985
26)AIJ Standard for structural calculation of reinforced concrete structures, Architectural Institute of
Japan, February, 1988

- C4-24 - 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.37-43
29) 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
30) Tano, M : Estimation of vibration isolation, Architectural acoustics and noise control, No.101,
March, 1998, pp.45-51