Effect of concrete creep and shrinkage on tall hybrid-structures and its countermeasures

Abstract

This paper aims to study the different vertical displacements in tall hybrid-structures and the corresponding engineering measures. First, the method to calculate the different vertical displacements in tall hybrid-structures is presented. This method takes into account the effects of construction process by applying loads sequentially story by story. Based on the concrete creep and shrinkage calculation formula in American Concrete Institute (ACI) code, with the assumption that loads are increased linearly in members, the creep and shrinkage effects of members are analyzed by adopting two parameters named average load-aged coefficient and average age-last coefficient. The effects of steel ratio on members creep are analyzed by age-adjusted module method (AEMM). The effects that core-tube were constructed in advance to outer steel frame were also considered. Then, based on the sample calculation, the measures to effectively reduce the different vertical displacements in hybrid-structures are proposed. This method is simple and practical in the calculation of different vertical displacements in tall and super-tall hybrid-structures.

Keywords

creep / shrinkage / construction process / hybrid-structure

Introduction

Hybrid structures, which effectively combine the advantages of steel structures and concrete structures, are used more and more in tall building structures because of its excellent performances, such as economic and anti-seismic effects. However, the effects of different vertical displacements on tall hybrid-structures have not been considered. It is well known that concrete has creep and shrinkage performances but steel has not. Therefore, the different vertical displacements in hybrid structures change not only at construction stage but also at operation stage, which will cause the redistribution of internal forces in hybrid structures. Thus, technical specification for concrete structures of tall building (JGJ 3-2002) in China demands that the effects of concrete creep and shrinkage should be considered in the design of hybrid structure [1].

Concrete creep and shrinkage in hybrid structures was investigated. Zhou et al. [2] studied the different vertical displacements in tall hybrid-structures considering vertical loads, creep, shrinkage, and difference in temperature of indoor and outdoor using the finite element procedure SAP2000. The vertical loads of each story were sequentially applied to whole structure during construction. Thus, it is an approximate method to simulate construction process. Xu et al. [3] proposed a simple and practical method to calculate the different vertical displacements. But the method did not take into account construction process. Yang et al. presented a method that did not consider the effects of horizontal member [4]. Some other researchers also investigated the effects of concrete creep and shrinkage on tall hybrid-structures [5-9].

By simulating real conditions that tall building are built up sequentially and structure stiffness is changed correspondingly, the effects of different vertical displacements on tall hybrid-structures under vertical loads was studied with consideration of the effects of construction process, concrete creep and shrinkage.

Analysis of concrete creep

Based on the ACI code [10], the followings conclusions are presented [11]:

Conclusion 1: With the assumption that axial force increases linearly, after applying the nth stress increment, the ultimate creep strain of concrete members can be calculated by

(1){ϵ}_{\mathrm{c}}(\infty ,t_{\mathrm{0}})=\mathrm{2.35}{\gamma }_{\mathrm{h}}{\gamma }_{\mathrm{\lambda }}{\gamma }_{\mathrm{a}\mathrm{v}}\sigma /E,

where \sigma is the total axial stress and \sigma =n\mathrm{\Delta }\sigma, {\gamma }_{\mathrm{a}\mathrm{v}} is the average age coefficient and can be calculated by

(2){\gamma }_{\mathrm{a}\mathrm{v}}=\mathrm{0.671}+\mathrm{0.179}{\mathrm{e}}^{-\mathrm{0.0518}t}+\mathrm{0.244}{\mathrm{e}}^{-\mathrm{0.0055}t},

where t is the nth load-aged.

Conclusion 2: With the assumption that axial force increases linearly, the ratio of concrete creep strain at time t_i to its ultimate creep strain caused by stress increment (i-1) \mathrm{\Delta }\sigma can be calculated by

(3){\gamma }_{\mathrm{l}}=\mathrm{0.711}-\mathrm{0.456}{\mathrm{e}}^{-\mathrm{0.0064}{t}_i}.

Analysis of concrete shrinkage

Based on the ACI code and only considering the major factors, the concrete shrinkage strain can be evaluated by

{ϵ}_{\mathrm{s}\mathrm{h}}(t)={\gamma }_t{ϵ}_{\mathrm{s}\mathrm{h},\infty },

(4){ϵ}_{\mathrm{s}\mathrm{h},\infty }=\mathrm{780}{\gamma }_{\mathrm{c}\mathrm{p}}{\gamma }_{\mathrm{\lambda }}{\gamma }_{\mathrm{h}}{\gamma }_t\times {\mathrm{10}}^{-\mathrm{6}},

where {\gamma }_t,{\gamma }_{\mathrm{cp}},{\gamma }_{\lambda }, and {\gamma }_h represent the same meaning as those in Ref. [11].

Determination of creep and shrinkage vertical displacements of concrete shear walls and columns

The final in-elastic vertical displacements at the level of the ith story in an n-story tall building are composed of:

(1) Creep displacement {\mathit{\Delta }}_{\mathrm{c}\mathrm{1}} is caused by loads applied before the slab at level i is cast.

(2) Creep displacement {\mathit{\Delta }}_{\mathrm{c}\mathrm{2}} is caused by loads applied after the slab at level i-1 is cast.

(3) Shrinkage displacement {\mathit{\Delta }}_{\mathrm{s}\mathrm{h}} is generated at time stage t_i\sim \infty, in which t_i is the time when the slab at level i is cast.

Determination of {\mathit{\Delta }}_{c1}

The ultimate creep vertical displacement of the jth story caused by loads applied before the ith slab is cast can be evaluated by

(5){\delta }_{\mathrm{c}\mathrm{1},j}=h_j{\displaystyle \sum _{k=j}^{i-\mathrm{1}}{\displaystyle \frac{\mathrm{\Delta }{\sigma }_k}{E}}\mathrm{2.35}{\gamma }_{\mathrm{h},j}}{\gamma }_{\mathrm{\lambda },j}{\gamma }_{\mathrm{a},j,k}(\mathrm{1}-{\gamma }_{\mathrm{t},j,k}),

where j varies from 1 to i-1, h_j is the height of level j, \mathrm{\Delta }{\sigma }_k is the stress increment at level k, {\gamma }_{\mathrm{h},j} is the correction factor due to the member size effects of the jth story, {\gamma }_{\mathrm{\lambda },j} is the correction factor due to ambient relative humidity, {\gamma }_{\mathrm{a},j,k} and {\gamma }_{\mathrm{t},j,k} are the correction factors of load-aged and age-last respectively.

If every stress increment is equal, Eq.(5) can be simplified as follows:

(6){\delta }_{\mathrm{c}\mathrm{1},j}=\mathrm{2.35}{h}_j{\gamma }_{\mathrm{h},j}{\gamma }_{\mathrm{\lambda },j}{\gamma }_{\mathrm{a}\mathrm{v},j}(\mathrm{1}-{\gamma }_{\mathrm{l},j}){\displaystyle \frac{\sigma }{E}},

where {\gamma }_{\mathrm{a}\mathrm{v},j} is the average age coefficient and can be evaluated by Eq. (2), in which the calculation time equals t_{i-\mathrm{1}}-t_j; {\gamma }_{\mathrm{l},j} can be obtained by Eq. (3), in which the calculation time equals t_i-t_j; \sigma is the sum of stress increment from level j to i-1. {\mathit{\Delta }}_{\mathrm{c}1} can be calculated by

(7){\mathit{\Delta }}_{\mathrm{c}\mathrm{1}}={\displaystyle \sum _{j=\mathrm{1}}^{i-\mathrm{1}}{\delta }_{\mathrm{c}\mathrm{1},j}}.

Determination of {\mathit{\Delta }}_{c2}

The ultimate creep vertical displacement of the jth story caused by loads applied after the slab at level i-1 is cast can be evaluated by

(8){\delta }_{\mathrm{c}\mathrm{2},j}=h_j{\displaystyle \sum _{k=i}^n{\displaystyle \frac{\mathrm{\Delta }{\sigma }_k}{E}}}\mathrm{2.35}{\gamma }_{\mathrm{h},j}{\gamma }_{\mathrm{\lambda },j}{\gamma }_{\mathrm{a},j,k}.

The meanings of the parameters in Eq. (8) are the sameas that in Eq. (5).

Similarly, if every stress increment is equal, Eq. (8) can be simplified as follows:

(9){\delta }_{\mathrm{c}\mathrm{2},j}=\mathrm{2.35}{h}_j{\gamma }_{\mathrm{h},j}{\gamma }_{\mathrm{\lambda },j}{\gamma }_{\mathrm{a}\mathrm{v},j}{\displaystyle \frac{\sigma }{E}},

where \sigma is the stress increment in members at slab level j caused by loads applied after slab at level i-1 is cast. Thus, {\mathit{\Delta }}_{c2} can be calculated by

(10){\mathit{\Delta }}_{\mathrm{c}\mathrm{2}}={\displaystyle \sum _{j=\mathrm{1}}^i{\delta }_{\mathrm{c}\mathrm{2},j}}.

Determination of {\mathit{\Delta }}_{\mathrm{sh}}

The ultimate shrinkage vertical displacement of the jth story generating from time t_i can be evaluated by

(11)\begin{array}{ll}{\delta }_{\mathrm{s}\mathrm{h},j}=h_j{ϵ}_{\mathrm{s}\mathrm{h},\infty ,j}(\mathrm{1}-{\gamma }_{\mathrm{t},j}),& j=\mathrm{1},\cdots ,i,\end{array}

where {ϵ}_{\mathrm{s}\mathrm{h},\infty ,j} is the ultimate whole shrinkage of members at level j, and {\gamma }_{t,j} is the shrinkage developed from t_j to t_i. Therefore, shrinkage displacement {\mathit{\Delta }}_{\mathrm{s}\mathrm{h}} can be calculated by

(12){\mathit{\Delta }}_{\mathrm{s}\mathrm{h}}={\displaystyle \sum _{j=\mathrm{1}}^i{\delta }_{\mathrm{s}\mathrm{h},j}}.

The ultimate creep and shrinkage vertical displacement of story at level i is the sum of {\mathit{\Delta }}_{\mathrm{c}\mathrm{1}}, {\mathit{\Delta }}_{\mathrm{c}\mathrm{2}} and {\mathit{\Delta }}_{\mathrm{s}\mathrm{h}}. The formula is as

(13)\mathit{\Delta }={\mathit{\Delta }}_{\mathrm{c}\mathrm{1}}+{\mathit{\Delta }}_{\mathrm{c}\mathrm{2}}+{\mathit{\Delta }}_{\mathrm{s}\mathrm{h}}.

The vertical displacements of adjacent vertical members can be obtained by Eq. (13). By subtracting one value from another, the different vertical displacements can be obtained.

Effects of steel ratio on concrete creep and shrinkage

Smith et al. [9] and Xu et al. [3] proposed the formulae to calculate the ultimate displacements of concrete creep and shrinkage, and the formulae to calculate the stresses of steel and concrete. The effects of steel ratio were considered in all formulae. These formulae are as follows:

\begin{array}{ll}\mathrm{\Delta }{\sigma }_{\mathrm{s}}={\displaystyle \frac{{\sigma }_{\mathrm{c}}{ϵ}_{\mathrm{c}}^{\prime }+{ϵ}_{\mathrm{s}\mathrm{h}}}{\rho {ϵ}_{\mathrm{c}}^{\prime }}}F,& \mathrm{\Delta }{\sigma }_{\mathrm{c}}=({\sigma }_{\mathrm{c}}+{\displaystyle \frac{{ϵ}_{\mathrm{s}\mathrm{h}}}{{ϵ}_{\mathrm{c}}^{\prime }}})F,\end{array}

(14)\mathrm{\Delta }{ϵ}_{\mathrm{c}}=\mathrm{\Delta }{\sigma }_{\mathrm{s}}/E_{\mathrm{s}}.

Based on AEMM and equilibrium conditions of displacement and internal forces, the values \mathrm{\Delta }{\sigma }_{\mathrm{s}}, \mathrm{\Delta }{\sigma }_{\mathrm{c}}, and \mathrm{\Delta }{ϵ}_{\mathrm{c}} are deduced. The corresponding formulae are given as follows:

(15)\mathrm{\Delta }{\sigma }_{\mathrm{s}}={\displaystyle \frac{n}{\mathrm{1}+\rho n(\mathrm{1}+\chi \phi )}}({\sigma }_{\mathrm{c}\mathrm{0}}\phi +E_{\mathrm{c}}{ϵ}_{\mathrm{s}\mathrm{h}}),

(16)\mathrm{\Delta }{\sigma }_{\mathrm{c}}={\displaystyle \frac{\rho n}{\mathrm{1}+\rho n(\mathrm{1}+\chi \phi )}}({\sigma }_{\mathrm{c}0}\phi +E_{\mathrm{c}}{ϵ}_{\mathrm{s}\mathrm{h}}),

(17)\mathrm{\Delta }{ϵ}_{\mathrm{c}}=\eta ({ϵ}_{\mathrm{c}}+{ϵ}_{\mathrm{s}\mathrm{h}}),

(18)\eta ={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\rho n(\mathrm{1}+\chi \phi )}},

where {\sigma }_{\mathrm{c}0} is the initial elastic stress in concrete members; \chi is the aging coefficient of concrete, which depends on the age at the time when concrete members begin to carry load and on duration of load; \phi is the creep coefficient; \eta is the steel ratio coefficient. These formulae are obtained as follows:

Assume that the deformation of concrete creep and shrinkage begins and develops when the axial stress {\sigma }_{\mathrm{c}\mathrm{0}} at the time t_{\mathrm{0}} is applied in reinforced concrete members. At time t(t\ge t_{\mathrm{0}}), the value of axial internal force in concrete sections is decreased by N. Under the equilibrium conditions of internal forces, the value of axial internal force in reinforcement sections is increased by N. Then, the decrease of reinforcement strain \mathrm{\Delta }{ϵ}_{\mathrm{s}} and the axial press stress {\sigma }_{\mathrm{c}}(t) of concrete section at time t can be evaluated by

(19)\begin{array}{ll}\mathrm{\Delta }{ϵ}_{\mathrm{s}}={\displaystyle \frac{N}{E_{\mathrm{s}}{A}_{\mathrm{s}}}},& {\sigma }_{\mathrm{c}}(t)={\sigma }_{\mathrm{c}\mathrm{0}}-{\displaystyle \frac{N}{A_{\mathrm{c}}}}.\end{array}

At t_{\mathrm{0}}- t, the compressive stress {\sigma }_{\mathrm{c}}(\tau ) in concrete continuously changed from {\sigma }_{\mathrm{c}\mathrm{0}} to {\sigma }_{\mathrm{c}}(t). Then, the concrete section strain at time t is

(20)ϵ(t,t_{\mathrm{0}})={\displaystyle \frac{{\sigma }_{\mathrm{c}\mathrm{0}}}{E_{\mathrm{c}}}}[\mathrm{1}+\phi (t,t_{\mathrm{0}})]+{\displaystyle {\int }_{t_{\mathrm{0}}}^t{\displaystyle \frac{\mathrm{1}}{E_{\mathrm{c}}(\tau )}}[\mathrm{1}+\phi (t,\tau )]{\displaystyle \frac{\mathrm{d}\sigma (\tau )}{\mathrm{d}\tau }}\mathrm{d}\tau }+{ϵ}_{\mathrm{s}\mathrm{h}}(t,t_{\mathrm{0}}).

Based on the AEMM, the concrete section strain at time t can be obtained by

(21)ϵ(t,t_{\mathrm{0}})={\displaystyle \frac{{\sigma }_{\mathrm{c}0}}{E_{\mathrm{c}}}}[\mathrm{1}+\phi (t,t_{\mathrm{0}})]+{\displaystyle \frac{{\sigma }_{\mathrm{c}}(t)-{\sigma }_{\mathrm{c}\mathrm{0}}}{E_{\phi }}}+{ϵ}_{\mathrm{s}\mathrm{h}}(t,t_{\mathrm{0}}),

(22)E_{\phi }={\displaystyle \frac{E(t_{\mathrm{0}})}{\mathrm{1}+\chi (t,t_{\mathrm{0}})\phi (t,t_{\mathrm{0}})}}.

Then, the strain increment of concrete sections is

(23)\mathrm{\Delta }{ϵ}_{\mathrm{c}}={ϵ}_{\mathrm{c}}(t,t_{\mathrm{0}})-{ϵ}_{\mathrm{c}\mathrm{0}}.

Under the equilibrium conditions of displacement between steel and concrete, the strain increment of concrete sections can be obtained by

(24)\mathrm{\Delta }{ϵ}_{\mathrm{c}}=\mathrm{\Delta }{ϵ}_{\mathrm{s}}.

Combining Eq. (19) and (20)- (24), Eq. (15) -(18) can be obtained.

Effects of different vertical displacement on horizontal members

The internal forces of beams at story level i, M_i and V_i, caused by the different vertical displacements of adjacent vertical members, can be calculated with the slope-deflection equation of beams. Applying M_i and V_i(i=1,…,n) to the node of beam reversedly, the internal forces caused by the different vertical displacements {\mathit{\Delta }}_i can be obtained.

Effects of concrete core-tube construction

In real construction, m-stories of concrete core-tube are constructed in advance to outer steel frame (see Fig.1). When the ith story of outer steel frame is built up, the ith story core-tube bears the loads at the ith floor and the self weight of m-stories above the ith floor.

In this instance, the stress increment \mathrm{\Delta }\sigma of level i can be divided into two parts. One part is the self-weight stress of concrete core-tube \mathrm{\Delta }{\sigma }_{\mathrm{w}}, and another part is the load stress \mathrm{\Delta }{\sigma }_{\mathrm{f}} at this story. Then the concrete creep vertical displacements of core-tube can be formulated by Eqs. (25) and (26), which are transformed from Eqs. (7) and (10).

(25){\mathit{\Delta }}_{\mathrm{c}\mathrm{1}}={\displaystyle \sum _{j=\mathrm{1}}^{i-\mathrm{1}}{\displaystyle \frac{\mathrm{2.35}}{E_j}}{h}_j{\gamma }_{\mathrm{h},j}{\gamma }_{\mathrm{\lambda },j}{\gamma }_{\mathrm{a}\mathrm{v},j}[\mathrm{\Delta }{\sigma }_{\mathrm{w}}(i+m-\mathrm{1})}(\mathrm{1}-{\gamma }_{\mathrm{l}\mathrm{1},j})+\mathrm{\Delta }{\sigma }_{\mathrm{f}}(i-\mathrm{1})(\mathrm{1}-{\gamma }_{\mathrm{l}\mathrm{2},j})],

(26){\mathit{\Delta }}_{\mathrm{c}\mathrm{2}}={\displaystyle \sum _{j=\mathrm{1}}^i{\displaystyle \frac{\mathrm{2.35}}{E_j}}{h}_j{\gamma }_{\mathrm{h},j}{\gamma }_{\mathrm{\lambda },j}\{[n-(i+m-\mathrm{1})]}\mathrm{\Delta }{\sigma }_{\mathrm{w}}{\gamma }_{\mathrm{a}\mathrm{v}\mathrm{1},j}+[n-(i-\mathrm{1})]\mathrm{\Delta }{\sigma }_{\mathrm{f}}{\gamma }_{\mathrm{a}\mathrm{v}2,j}\}.

The shrinkage of core-tube is still calculated by Eq. (12). But {\gamma }_{t,j} is evaluated by

(27){\gamma }_{t,j}=(t_{i+m}-t_j)/(\mathrm{35}+t_{i+m}-t_j).

Numerical example

A tall hybrid-structure is analyzed. Its plane layout is shown in Fig. 2. The structure has 60 stories and is 216 m in height. The height of each story is 3.6 m. The steel in outer steel frame is Q345B, and the concrete strengths in core-tube range from C50 to C30. The column sections of outer steel frame are rectangle and its beam sections are H shape. The sizes of the members are shown in Table 1. The uniform distributing vertical loads on every story are 2.22 kN/m². The ambient relative humidity is 40%. The moist curing time for concrete is 4 d. The construction velocity is 4 d for each story. The vertical steel ratio in core-tube is 0.4%.

The results are as follows:

(1) Comparison of vertical displacement and different vertical displacements

Without considering the effects of core-tube constructed in advance, the vertical displacements of shear-wall at place B of every story are shown in Fig. 3, and the different vertical displacements between column A and shear-wall B of every story are shown in Fig. 4. In Figs. 3 and 4, line A represents results without considering creep, shrinkage and construction process, line B represents results considering construction process but without taking into account creep and shrinkage, line C represents results considering creep, shrinkage and construction process. By comparing Figs. 3 and 4, it is easily found out that there are big different vertical displacements between adjacent column and shear-wall due to concrete creep and shrinkage in shear-wall, which may have great negative effect on the structure.

(2) Effects of steel ratio

The change of inelastic vertical displacement with steel ratio is shown in Fig. 5. It is obvious that the inelastic vertical displacement is decreased greatly with the increase of steel ratio.

(3) Effects of core-tube constructed in advance

When the number of stories of core-tube constructed in advance is m, which varies from 0 to 20, the concrete creep and shrinkage vertical displacements of shear-wall B are shown in Fig. 6. It is known from Fig.6 that when m is larger, the vertical displacement of shear-wall and the different vertical displacements between shear-wall and adjacent column is smaller. For example, when m equals 20, namely, the core-tube is constructed in advance 20 stories, the shear-wall inelastic vertical displacement at top story is 43.4 mm, which is about half of the displacement without considering the core-tube constructed in advance.

Measures to reduce different vertical displacements

In order to reduce the different vertical displacements in tall hybrid structures, some suggestions are made as follows:

Part 1: Measures of material selection

Higher strength concrete;

Smaller ratio of water to cement and proportioning of mortar;

Higher strength aggregate which has high elasticity modulus;

Quicker-hardening cement;

Reasonable concrete cast and curing.

Part 2: Design measures

Setting vertical members reasonably to guarantee that compressive stresses are equal or have a little difference;

To control compressive stress in vertical members at low levels;

To increase steel ratio of vertical members;

To increase the volume to face ratio of vertical members;

To adopt steel-tube concrete columns in outer steel frame;

Part 3: Construction measures

To construct some stories of concrete core-tube in advance to outer steel frame;

To set special connects which allow vertical sliding of beams in outer steel frame along the adjacent concrete members in construction stage;

Calculating the different vertical displacements and adjusting the lengths of steel columns.

Conclusions

A simple and practical method of calculating the different vertical displacements in tall hybrid-structure is presented. It considers the effects such as construction process, concrete creep and shrinkage, steel ratio and construction of core-tube, and so on.

Based on the results of numerical study and the characters of concrete creep and shrinkage, some suggestions to reducing the different vertical displacements are made from material selection, structure design and construction.

References

[1] China Technical Specification for Concrete Structures of Tall Building (JGJ3-2002). Beijing: China Architecture Industry Publishing House, 2002 (in Chinese)

[2] Zhou Xuhong, Huang Xiangxiang, Wang Yihong, Di Jin, Liu Yongjian. Calculation of the differential shortening of steel frame-reinforced concrete core-wall structure. Journal of Building Structures, 2005, 26(2): 66–73 (in Chinese)

[3] Xu Peifu, Fu Xueyi, Wang Cuikun, Xiao Congzhen. Structural Design for Complex Tall Buildings. Beijing: China Architecture Industry Press, 2003 (in Chinese)

[4] Yang Li, Guo Zhigong. How to consider the effect of creep and shrinkage in reinforced concrete tall building structure design. Industrial Construction, 1995, 25(4): 40–46 (in Chinese)

[5] Deng Zhiheng, Qin Ring. Influence of shrinkage and creep on high-rise building in construction process. Journal of Harbin University of C. E.& Architecture, 2002, 35(5): 28–31 (in Chinese)

[6] Luo Wenbin, Zhang Baoyin. Countermeasures for different vertical deformation of S+RC mixed structures. Journal of Building Structures, 2000, 21(6): 68–73 (in Chinese)

[7] Maru S, Asfaw M, Nagpal A K. Consistent procedure for creep and shrinkage effects in RC frames. Journal of Structural Engineering, 2001, 127(7): 726–732

[8] Sharma R K, Maru S, Nagpal A K. Simplified procedure for creep and shrinkage effects in reinforced concrete frames. Journal of Structural Engineering, 2004, 130(10): 1545–1552

[9] Smith B S, Coull A. Tall Building Structures: Analysis and Design, New York: John Wiley & Sons, Inc.. 1991

[10] ACI Committee 209. Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures. Detroit: ACI, 1997

[11] Xia Xinhong, Shen Pusheng, Fang Hui, Gong Huguang, Tang Zheng. Simplified method of creep and shrinkage analysis in reinforced concrete members bearing multi-axial forces. Journal of Huazhong University of Science and Technology (Urban Science Edition), 2006, 23(4): 48–50 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg