6.pushover

International Journal of Civil, Structural, Environmental and Infrastructure Engineering Research and Development (IJCSEIERD) ISSN 2249-6866 Vol. 2 Issue 4 Dec - 2012 45-54 Š TJPRC Pvt. Ltd.,

PUSHOVER ANALYSIS OF UNSYMMETRICAL FRAMED STRUCTURES ON SLOPING GROUND 1

N. JITENDRA BABU, 2K.V.G.D BALAJI & 3S.S.S.V GOPALARAJU 1

2

Assistant Professor, K L University, Guntur, India

Professor, GITAM University, Visakhapatnam - 530 045, Andhra Pradesh, India 3

Professor & Head GITAM University, Hyderabad, India

ABSTRACT This paper deals with the non-linear analysis of various symmetric and asymmetric structures constructed on plain as well as sloping grounds subjected to various kinds of loads. Different structures constructed on plane ground and inclined ground of 30o slope is considered in the present study . Various structures are considered in plan symmetry and also asymmetry with difference in bay sizes in mutual directions. The analysis has been carried out using SAP-2000 and ETABS software. Pushover curves have been developed and compared for various cases. It has been observed that the structures with vertical irregularity are more critical than structures with plan irregularity.

KEYWORDS: Pushover Analysis, Symmetrical and Unsymmetrical Structures INTRODUCTION The nonlinear static procedure or pushover analysis is increasingly used to establish the estimations of seismic demands for building structures. Since structures exhibit nonlinear behavior during earthquakes, using the nonlinear analysis is inevitable to observe whether the structure is meeting the desirable performance or not (ATC 40).

The pushover procedure consists of two parts. First, a target displacement for the building is established. The target displacement is an estimation of the top displacement of the building when exposed to the design earthquake excitation.

Then a pushover analysis is carried out on the building until the top displacement of the building equals to the target displacement and the second one force controlled type in which the total amount of force acting is estimated and applied to the structure and the analysis is carried out.

In order to consider the torsion effects in the nonlinear static analysis of the asymmetric buildings is carried out by defining the target displacement for each resisting element until failure (Emrah erduran(2008)). The base shear is applied in incremental order until the target displacement is reached.

The main objective of the thesis is to consider the effect of the changes in the structures modal properties of asymmetric-plan buildings during the pushover analysis (Chatpan Chintanapakde (2004))and the application of the displacement based adaptive pushover procedure (Kazem

shakeri(2012)).

The analysis part of structures is carried out in ETABS, SAP and STAAD. Results obtained in all the cases are compared with remaining two cases and found satisfactory results, so as to carry out the analysis in ETABS and SAP. Nonlinear analysis has been carried out for structures with irregularities in both plan and elevation which undergo torsion effect due to vertical irregularity. The various results obtained from the analysis are presented.

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N. Jitendra Babu, K.V.G.D Balaji & S.S.S.V Gopalaraju

LINEAR STATIC ANALYSIS Linear analysis of all the considered structures is carried out using ETABS software. The general loads are considered for all the buildings and only single slab at the roof level is considered for all the structures. Six different cases are considered in the study and all the cases are analysed.

Case 1: Three Floored Regular Symmetric Plan Building •

A symmetric structure with 3.6m span and 4 bays in both X and Y directions elevated to three stories is developed.

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The columns are of 230mm x 600mm and the beams are of 230mm x 450mm size.

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A 150mm thick slab is assigned only to the top floor.

•

The self weight of the structure is considered and the slab weight is considered only of the top floor.

•

The top floor slab weight is only considered because in sloped cased the difference between the shortest and the longest column is about 3 floors.

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Hence the sloped structure may lie between the values obtained in single and multi-storied structures

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The failure beams and columns after running the linear static analysis are obtained and me in red colour in the below fig 1.

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All the outer most corner columns have failed and also all outer columns in the second floor have failed

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All the beams in top floor failed in the first and last bays along YZ plane.

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The outer beams have failed in top floor second, third and fourth bays along YZ plane and also first and fifth bays of second floor along YZ plane.

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The beams in the outer part of first and fifth bays in first, second and third floors have failed and also outer beams in second and fourth bays of top floor also failed along XZ plane

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The end beams in the outer bays in XZ plane are also subjected to failure in the second floor.

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Remaining all the beams and columns are designed and the reinforcement details are viewed on top of the members.

Fig. 1: Failure Members in Case 1

Pushover Analysis of Unsymmetrical Framed Structures on Sloping Ground

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Case 2: Three Floored Regular Asymmetric Plan Building •

In this case an asymmetric structure with 3.6m span and 4.2m with 4 bays in both Y and X directions respectively elevated to three stories is developed.

•

The columns are of 230mm x 600mm and the beams are of 230mm x 450mm size.

•

The self weight of the structure is considered and the slab weight is considered only of the top floor.

•

The top floor slab weight is only considered because in sloped cased the difference between the shortest and the longest column is about 3 floors.

•

Hence the sloped structure may lie between the values obtained in single and multi-storied structures

•

The failure beams and columns after running the linear static analysis are obtained as marked in red colour in the below fig 2.

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All the outer most corner columns have failed and also all exterior two columns in the second floor have failed

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The beams in top floor failed in the first and last bays along YZ plane.

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The outer beams have failed in top floor second, third and fourth bays along YZ plane and also first and fifth bays of second floor along YZ plane.

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The beams in the outer part of first, second, fourth and fifth bays in first, second and third floors have failed and also outer beams in second and fourth bays of top floor also failed along XZ plane

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The end beams in the outer bays in XZ plane are also subjected to failure in the second floor.

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Remaining all the beams and columns are designed and the reinforcement details are viewed on top of the members.

Fig. 2: Failure Members in Case 2

Case 3: Single Floored Asymmetric Plan Building on Sloping Ground •

A sloped structure is developed with a ground slope of 30 degrees.

•

Four bays in both Y and X directions are developed with bay sizes 3.6m and 4.2 in Y and X directions respectively.

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In Y directions all the columns of each bay are of equal size but in X direction the sizes of the columns vary with respect to each bay.

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N. Jitendra Babu, K.V.G.D Balaji & S.S.S.V Gopalaraju

Connecting beams are provided for columns of second third and fourth bays in X direction with a height difference of 3m from ground level downwards.

•

Above the ground level a single story is considered with slab load and the total dead load of the structure is considered.

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Linear static analysis is carried out and structure is designed.

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Failure beams and columns are represented in red colour in the below fig 3.

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All the outermost corner columns are subjected to failure.

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All the beams in top floor of fifth bay along XZ plane also failed.

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Beams in top floor along YZ plane in 2nd, 3rd,4th and 5th bays have been failed.

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In YZ-plane along X-direction exterior beams in 3rd and 4th bays have been failed.

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Also the other beams notified in red colour in the fig are subjected to failure.The beams in the longest side of the sloped ground are subjected to failure due to the torsion effect caused due to variation in the lengths of the columns.

Fig. 3: Failure Members in Case 3

NON-LINEAR STATIC ANALYSIS OF STRUCTURE In the previous (Diagrams Fig.No:1 to Fig No: 3) it has been observed that the failure beams and columns of different cases subjected to linear static analysis.

Now we run the non-linear static analysis of the structures which are considered in the previous cases and the different nodes subjected to failure and belonging to various regions are specified in different colours.

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In the figures below different nodes subjecting to different levels of elastic zone are represented with respective colors mentioned at the bottom of the figures.

•

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The elastic zone is categorized into three parts ( fig 4) as described in ATC 40 •

Immediate Occupancy (IO)

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Life safety (LS)

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Collapse prevention (CP)

The Immediate Occupancy to Life Safety zone (IO- LS) is mentioned in dark blue in colour, Life Safety to Collapse Prevention zone (LS- CP) is mentioned in light blue in colour and Collapse Prevention zone is mentioned in green colour.

Pushover Analysis of Unsymmetrical Framed Structures on Sloping Ground

49

All the nodes beyond Collapse Prevention zone are mentioned in yellow, orange and red colours depending on their severity and the nodes below Immediate Occupancy zone are mentioned in pink colour.

Fig. 4: Deformation Case1: Three Floored Regular Symmetric Plan Building •

In the second case a symmetric structure with 3.6m span and 4 bays in both X and Y directions elevated to three stories is developed.

•

The columns are of 230mm x 600mm and the beams are of 230mm x 450mm size.

•

A 150mm thick slab is assigned only to the top floor.

•

The self weight of the structure is considered and the slab weight is considered only of the top floor.

•

The top floor slab weight is only considered because in sloped cased the difference between the shortest and the longest column is about 3 floors.

•

Hence the sloped structure may lie between the values obtained in single and multi-storied structures.

•

A pushover case is considered in which the load in applied in negative X direction.

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Failure nodes are shown in the below fig 5.

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In this case only few nodes in the first floor are subjected to failure and those nodes are represented in orange colour which implies that they lie beyond the CP zone.

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All the nodes in the foundation level are represented in dark blue in colour which implies that they lie in the IOLS zone.

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And remaining all the node represented in light blue colour implies their occurrence in the LS-CP zone of the pushover curve.

Fig. 5: Nodes Corresponding to Different Zones for Case 1

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N. Jitendra Babu, K.V.G.D Balaji & S.S.S.V Gopalaraju

Case 2: Three Floored Regular Asymmetric Plan Building •

In this case, an asymmetric structure with 3.6m span and 4.2m span in Y and X directions respectively with 4 bays elevated to three stories is developed.

•

The columns are of 230mm x 600mm and the beams are of 230mm x 450mm size.

•

The self weight of the structure is considered and the slab weight is considered only of the top floor.

•

The top floor slab weight is only considered because in sloped cased the difference between the shortest and the longest column is about 3 floors.

•

Hence the sloped structure may lie between the values obtained in single and multi-storied structures.

•

Nonlinear static analysis is carried out and failure nodes are shown in fig 6.

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All the corner nodes of the top floor are in orange colour representing their occurrence beyond CP level.

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All the central columns in X direction are in dark blue in colour implying occurrence in IO-LS zone.

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And the remaining nodes in the top floor are light blue in colour implying their occurrence in LS-CP zone.

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All the nodes in first floor are belonging to IO-LS zone.

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All the central nodes in X direction of second floor are in LS-CP zone and remaining all nodes in IO-LS zone.

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And the node represented in pink colour in the ground level implies its

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Occurrence below the IO zone.

Fig.6: Nodes Corresponding to Different Zones for Case 2 Case 3: Single Floored Asymmetric Plan Building on Sloping Ground •

A sloped structure is developed with a ground slope of 30 degrees.

•

Four bays in both X and Y directions with bay size of 4.2m and 3.6m respectively are developed with similar column sizes in Y direction the size of the columns vary with respect to each bay in X direction.

•

Connecting beams are provided for columns of second third and fourth bays in X direction with a height difference of 3m from ground level downwards.

•

Above the ground level a single story is considered with slab load and the total dead load of the structure is considered.

•

Nonlinear static analysis is carried out to the structure and deformed shape is obtained.

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Failure nodes are shown in the below fig 7.

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The bottom nodes of the shortest side are represented in red colour implying the severity level beyond the CP zone because short column effect arises over there.

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Pushover Analysis of Unsymmetrical Framed Structures on Sloping Ground

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The two nodes above the red coloured nodes are in orange colour which implies their occurrence beyond CP zone but are less severe than the red coloured ones.

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All the nodes in the top floor coloured in either dark blue or light blue, hence belonging to zones IO-LS or LS-CP respectively.

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All the nodes in the first floor except the orange coloured ones are in dark blue and pink in colour implying their occurrence either in IO-LS or below IO zones respectively.

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In the ground floor level nodes are belonging to IO-LS,LS-CP and below IO levels represented in dark blue, light blue and pink colours respectively

.

Fig.7: Nodes Corresponding to Different Zones for Case 3

COMPARISION OF PUSHOVER CURVES Pushover or nonlinear static analysis is carried out for all the cases considered in the thesis and finally pushover curves are obtained.

Pushover curves are obtained with Displacement on X-axis and Base reaction on Y -axis.

Depending on the pushover curves comparisions are carried out between: •

Symmetric 3 floor building and Asymmetric 3 floor building.

•

Asymmetrical 1 floor building and asymmetric sloped building.

Comparision 1 In the First comparision we compare the pushover values obtained from the graph between Symmetric 3 floor building and asymmetric 3 floor building as shown in table 1.

1.

The maximum displacement that the symmetric 1 floor building can withstand up to the elastic limit is 120x10-3m and the base reaction for this displacement is 3.16 x103KN.

2.

The maximum displacement that the symmetric sloped 1 floor building can withstand up to the elastic limit is 220x10-3m and the base reaction for this displacement is 1.85 x103KN.

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N. Jitendra Babu, K.V.G.D Balaji & S.S.S.V Gopalaraju

Table 1 Structure

Displacement

Base Shear

Symmetric 3 floor building

120x10-3m

3.16 x103KN

Asymmetric 3 floor building

220x10-3m

1.85 x103KN

In the above comparison the base shear resisted by the symmetric 3 floored building for a maximum displacement of 120x10-3m is 3.16 x103KN and for the asymmetric building with 3 floors the base shear and the maximum displacement values have reduced to 1.85x103KN and 220x10-3m respectively.

A symmetric 3 floored structure can resist 1.31x103KN more base shear than that of a asymmetric 3 floored structure upto elastic limit and also displacement is 100x10-3m larger for asymmetric building to that of symmetric building.

As the asymmetry of the structure increases the resistance value of base shear and also the maximum displacement before the elastic limit failure reduces as shown in the above case

Comparison 2 In the second comparison we compare the pushover values obtained from the graph between Asymmetric 1 floor building and asymmetric building on sloped ground shown in table 2.

Table 2 Structure Asymmetric 1 floor building Asymmetric building on sloped ground

1.

Base Shear

129x10-3m

3.14 x103KN

104x10-3m

2.77 x103KN

The maximum displacement that the Asymmetric 1 floor building can withstand up to the elastic limit is 129x103

2.

Displacement

m and the base reaction for this displacement is 3.14 x103KN.

The maximum displacement that the Asymmetric sloped 1 floor building can withstand up to the elastic limit is 104x10-3m and the base reaction for this displacement is 2.77 x103KN.

Pushover Analysis of Unsymmetrical Framed Structures on Sloping Ground

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In the above comparison the base shear resisted by the Asymmetric 1 floored building for a maximum displacement of 129x10-3m is 3.14 x103KN and for the asymmetric building with 3 floors the base shear and the maximum displacement values have reduced to 2.77x103KN and 104x10-3m respectively.

The above comparison indicates that as the asymmetry of the structure increases the structure becomes less effective.

CONCLUSIONS 1.

A symmetric 3 floored structure can resist 70% more base shear than that of a asymmetric 3 floored structure upto elastic limit.

2.

The base shear resisted by the Asymmetric 1 floored building on sloping ground for a maximum displacement upto failure limit is 24% more than that of the base shear resisted by asymmetric building on plain Ground.

3.

The structure with vertical irregularity is more critical than a structure with plan irregularity.

REFERENCES 1.

Kazem shakeri(2012),”An adaptive modal pushover procedure for asymmetric-plan buildings”, Engineering Structures 36 (2012), pg 160-172.

2.

ATC-40 : Seismic Evaluation and Retrofit of Concrete Buildings.

3.

Chatpan Chintanapakde (2004), “Seismic Response of Vertically Irregular Frames: Response History and Modal Pushover Analyses”, Journal of ASCE 0733-9445(2004)130:8-1177.

4.

FEMA-356: Prestandard and Commentary For The Seismic Rehabilitation of The Buildings.

5.

Emrah erduran(2008), “Assessment of current nonlinear static procedures on the estimation of torsional effects in low-rise frame buildings”, Engineering Structures 30 (2008) 2548-2558.