1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
294
AXIAL DEFORMATION OF COLUMNS IN MULTI-STORY R.C.
BUILDINGS
Snehal D. Poojara1
, Dr. Paresh V. Patel2
1
Post Graduate Student, Department of Civil Engineering, Institute of Technology,
Nirma University, Ahmedabad, India
2
Professor, Department of Civil Engineering, Institute of Technology,
Nirma University, Ahmedabad, India
ABSTRACT
Axial shortening of columns in building structures results in differential shortening of them
and causes axial force redistribution among columns and walls. Differential shortening may also lead
to additional forces in the horizontal members like beams and slabs. Elastic deformation of columns
contributes a lot towards the axial shortening of columns and hence it needs to be considered in the
design and construction of medium to high-rise buildings. Sequence of the construction directly
affects the elastic deformation and hence to the axial as well as differential shortening of columns.
A parametric study is conducted and reported in this paper to investigate the influence of
various parameters such as structural element sizes and lumping of different numbers of floors.
Rigid frame buildings of 10, 20 & 30 stories are analyzed and designed to know the effect of axial
shortening on behavior of structures. The results obtained in this research can serve as an aid to the
structural engineers during preliminary design.
Keywords: Elastic Deformation, Construction Sequence, Axial shortening, Differential shortening
1. INTRODUCTION
Column shortening are the secondary effects which needs to be considered in the
construction and design of multi-story buildings. During the construction of a building, columns
would be subjected to a number of load increments. These load increments varies as the sequence of
the construction varies. Axial shortening of columns in building structures results in differential
shortening of them and causes axial force redistribution among columns and walls. Differential
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ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
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2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
295
shortening may also lead to additional forces in the horizontal members like beams and slabs.
Furthermore, axial shortening of column will also affect the finishes and partitions. For these
reasons, construction method and stages should be considered in design as well as at construction of
buildings. Elastic deformation of columns is a major contributor of the axial shortening of columns.
Axial shortening of columns increases with increasing height of the building. To take into account
the effect of construction sequence, live load should applied simultaneously and dead load should be
applied sequentially in the analysis and design of buildings.
1.1 Objective and Scope
The objective of the study is to examine the effect of axial deformations on behavior of
medium to high-rise buildings. The present study also aim to develop the understanding of the
factors that influence the behavior of a reinforced concrete buildings considering the secondary
effects i.e. axial deformation of columns. In the present study 10, 20, 30 story framed building is
analyzed considering the effect of axial deformation of columns.
1.2 Theoretical Background
Elastic shortening of columns is cumulative over the height of a structure. As the height of
the building increases, the resultant differential shortening become an important criteria which needs
to be overcome. Nonlinear components of axial shortening includes inelastic shortening due to creep
and shrinkage. The combination of elastic and inelastic components is unacceptable to satisfy
structural performance criterion. Differential axial shortening may cause cracking and deflection of
floor plates, beams and other structural components, damage to facades, finishes, claddings,
mechanical and plumbing components and other masonry walls [1]. It also increases the bending
moments and shear forces in framing [2].
Many researchers have presented the approximate procedures for predicting elastic as well as
inelastic shortening of columns in buildings. Allowance for differential shortening of vertical
elements should be allowed on construction site [3]. Effects of the size of lumping of floors in ultra-
tall buildings were presented [4]. They recommended an effective size for lumping of floors to be
about 1/15th
of the total number of stories in the building. The recommended lumping size is helpful
to achieve more than 95 % accuracy in results and about 80 % reduction in computing time.
2. METHODOLOGY OF THE WORK
2.1 General
To take into account the effect of sequential dead load, construction stage analysis is carried
out using software Extended Three Dimensional Analysis of Building Systems (ETABS). ETABS
separates the model into sub-models for each construction stage and assigns corresponding
construction dead loads. The results for each stage are then superimposed to carry out the final static
nonlinear construction stage analysis. Analysis for loads other than dead loads i.e. Live load is
carried out using one step static linear analysis.[5] Focus of this investigation is 10, 20 & 30 story
Rigid Frame Structures with varying Lumped Construction Sequence. The typical floor plan of
frame building is shown in fig. 1.

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
296
Fig 1: Schematic Plan of 10, 20 & 30 story buildings
To reduce the time taken by a computer program to perform an iterative analysis, lumping
size were increased from one floor (1F) up to five floor (5F) and effective size of lumping is found
from various models. The varied lumped construction sequence of buildings is shown in fig. 2. The
varied lumped construction sequence also represent the rate of construction i.e. one floor constructed
at a time or more floors constructed at a time.
Fig 2: Varied Lumped Construction Sequence of buildings

4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
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3. RESULTS AND DISCUSSION
Sequential Axial Dead Load in Columns, Axial Shortening of Columns & Differential
Shortening of Columns in 10,20,30 story Rigid Frame Structures are mentioned in the tables 1(a)
and 1(b).
Sequential Axial Dead Load and Axial Shortening values are taken for the Middle Column
i.e. (D-3) of the Structure whereas Differential Shortening in Columns is taken as the Difference of
the Exterior Column & First Interior Column i.e. Difference of axial shortening values of column
(A-3) & (B-3) as shown in Fig. 1.
Table 1(a): Construction Stage Analysis Results with smaller cross sections of columns
No. of Story 10 20 30
Column Sizes (mm) 450 x 450 750 x 750 1200 x 1200
Axial Force (kN) 1555.36 3039.64 6670.17
Sequential Axial Force (kN) 1563 3114.2 6776.97
Axial Shortening (mm) 2.9611 3.8517 4.7782
Diff. Shortening (mm) 0.9901 0.7148 0.615
Table 1(b): Construction Stage Analysis Results with larger cross sections of columns
No. of Story 10 20 30
Column Sizes (mm) 600 x 600 1000 x 1000 1450 x 1450
Axial Force (kN) 1677.97 3794.8 8324.17
Sequential Axial Force (kN) 1685.55 3842.71 8402.39
Axial Shortening (mm) 1.7917 2.6868 4.0709
Diff. Shortening (mm) 0.5649 0.4792 0.4779
3.1 Axial Shortening of Columns
The Construction Stage Analysis results for the axial shortening of middle interior column in
10, 20 & 30 story buildings with varied number of lumping of floors are shown in Fig. 3(a), 3(b),
3(c). Fig. 4 shows the axial shortening of columns with one floor lumping and the results obtained
from one step analysis for the sake of comparison of one step analysis and sequential analysis. It can
be observed that maximum axial deformation occurs at a level around mid-height of the building.
The maximum axial deformation of the building varies from 0.5 to 1.8 mm in 10-story building, 0.45

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
298
to 2.6 mm in 20-story building, 0.4 to 4.0 mm for 30 story building. These numbers indicate that for
rigid frame structure less than 20 stories, the column shortening effect can be ignored. Considered
column sizes are shown in Table 1(b).
Fig 3: Axial Shortening of columns in: (a) 10 story building, (b) 20 story building,
(c) 30 story building
Fig 4: Axial shortening of columns using Construction Stage Analysis (CSA) and One Step Analysis
(OSA) in 30 story building

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
299
3.2 Differential Shortening of Columns
The Construction Stage Analysis results for the differential axial shortening of columns in
10, 20 & 30 story buildings with varied number of lumping of floors are shown in Fig. 5(a), 5(b),
5(c).
Differential Axial Deformations of columns is taken as the absolute difference of the exterior
column and the first interior column. Axial force transfer takes place from the exterior column to the
subsequent interior columns and hence larger axial shortening occurs in the interior columns such
that maximum shortening is in the first interior column. Maximum differential axial deformation
occurs at a level around mid-height of the building. The maximum differential axial deformation of
the building varies from 0.2 to 0.55 mm in 10-story building, 0.1 to 0.50 mm in 20-story building,
0.05 to 0.45 mm for 30 story building. Considered column sizes are shown in Table 1(b).
Fig 5: Differential Shortening of columns in: (a) 10 story building, (b) 20 story building, (c) 30 story
building
3. CONCLUSIONS
Axial deformation of columns and differential column shortening in reinforced concrete rigid
frame buildings is investigated in this paper. The main observations of the present study have been
summarized in the following points:
- As the height of a building structure increases, axial shortening of columns become quite
significant and should not be disregarded.

7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 294-300 © IAEME
300
- The cross-sectional area plays an important role towards increasing or decreasing axial
deformation values. Higher the cross-sectional areas of columns, lesser will be the axial
deformations of columns.
- Axial shortening of the columns is important in short as well as in tall building if the
construction rate is higher. However, for lower construction rates, in short buildings this is not
significant.
- Axial deformation of columns in two floor, three floor, four floor and five floor lumped model
shows accuracy of the results around 95%, 91%, 87% & 84% respectively from which it can be
considered that two floor lumping is an effective size of lumping to achieve better accuracy of
results.
- Axial as well as differential shortening of adjacent columns in a building becomes highest near
the mid-height of the building.
REFERENCES
Journal Papers
1- Serror, M.H. and El-Din, A.E. (2012). “Assessment of Internal Forces due to Differential
5- Shortening of Vertical Elements in Typical Medium- to High-Rise Buildings” Journal of
American Science, Vol. 8, No. 12, 161-174
2- Fintel, M., and Khan, F. R. (1987). “Effects of column creep and shrinkage in tall structures
analysis for differential shortening of columns and field observation of structures.” ACI J.,
Vol. 1, 95-112
3- Jayasinghe, M.T.R., and Jayasena, W.M.V.P.K. (2004). “Effects of Axial Shortening of
Columns on Design and Construction of Tall Reinforced Concrete Buildings.” Pract.
Period. On Struct. Des. And Constr., ASCE, Vol. 9, No. 2, 70-78
4- Kim, H.S. and Shin, A.K. (2011). “Column Shortening Analysis with Lumped Construction
Sequences.” Elsevier/Procedia Engineering, Vol. 14, 1791-1798
Books
5- Taranath, B.S., (1998). “Steel, Concrete, and Composite Design of Tall Buildings” New
York, Mc Graw Hill.