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Dept. of Civil Engineering, KJEI’S Trinity College of Engineering and Research, Pune
Today development in the RC structure has reached a new height. Due to advancements in technology, designers can design to stand strong against natural lateral forces like wind and earthquakes. Some of the extreme human-made events or natural events damage part of the structure or can lead to the destruction of the structure. These human-made events can include bomb explosions, gas-pipe explosions, etc. The failure of a primary vertical supporting structural member-like column will force adjoining structural members to resist the load previously taken by the column. This transmission and resisting process will continue till equilibrium is attended in the structure. If equilibrium is not attended then it will end up with the collapse of the structure or major part of it. This is called 'Progressive Collapse'. Rising incidents of blast events as an act of terrorism, to harm the national important structures or to harm a large number of people have increased throughout the world. The purpose of this project was to assess the progressive collapse of RC-framed structures, according to the General Service Administration (GSA 2003) guidelines. GSA provides the procedure to perform different analyses to determine the capability of a structure against progressive collapse. In the current study, Linear Static Analysis (LSA) and Non-Linear Static Analysis (NLSA) were performed to calculate the Demand-Capacity Ratio (DCR) at critical beam sections and Plastic Hinge Formation respectively. Both analyses were performed on the model of existing structure viz. GST Bhavan located in Pune city. Model was created in SAP2000 software. The demand-capacity ratio are compared with plastic hinge formation. Comparison of linear static analysis and non-linear analysis reveals that the hinge formation starts at the location having the maximum demand capacity ratio calculated from static analysis. Also, from current scenario the middle column on the longer side has been identified as the critical column.
In this 21st century, framed RC structures are one of the most common structures built throughout the world. Due to the lack of ability to build more stories by limiting the width of the wall in load-bearing structures, framed RC structures started gaining importance. In framed structures, the gravity loads viz. dead load and live load, coming on the slab are transferred to the adjoining beams which next transfer the load on the columns then down to the foundation, and ultimately to the ground present below it. This is called ‘Gravity Load Path’. In tall structures, the loads associated with wind are greater than dead or live loads, the lateral wind load imposed on these structures is usually the governing factor in structural design. Shear walls are built within the building to resist these lateral forces. The shear walls are positioned symmetrically in the plan to avoid lateral-torsional motions. They are positioned at the perimeter of the structure or can be constructed as a shear core. Examples are encasing a lift shaft or stairwell. The way through which the lateral loads are transferred through a building to the ground is called the ‘Lateral Load Path’. The primary elements of this path include vertical and horizontal components. Vertical components are shear walls and frames while horizontal components are roofs, floors, and foundations. The lateral forces acting on roofs and floors are transferred to shear walls and then to the foundation. Shear walls transmit both lateral as well as gravity forces to the foundation, which ultimately transfers to the ground.
Historically, structural engineers have always tended to avoid designing for extremely unlikely loads and relied on built-in redundancy in traditional structural systems as well as material safety factors to cover extreme cases. The high attention given to progressive collapse analysis has materialized into explicit requirements for redundancy in building codes all over the world. As per the American Association of State Highway and Transportation Officials (AASHTO), redundancy can be defined as the capability of a structural system to carry loads after damage to or the failure of one or more of its members. There are three types of redundancy
A member is considered as a load path redundant if an alternative and sufficient load path are determined to exist. The alternative load paths must have sufficient capacity to carry the load redistributed to them from an adjacent failed member. A member is considered structurally redundant if its boundary conditions or supports are such that failure of the member merely changes the boundary or support conditions but does not result in the collapse of the superstructure. And internal redundancy is when a structural member has alternative and sufficient load paths existing within the member itself. For example, a riveted steel member connection is considered internally redundant if it has multiple plies.
Fig. 1.1 The collapse of one corner of the Ronan building (Wikipedia)
Fig. 1.2 One-third of the Murrah Federal Office damaged. (Wikipedia)
Fig. 1.3 Top view of damaged federal building. (Civil Engineering)
Past events of progressive collapse created fear in people to stay in high-rise structures. Events like the collapse of the 22-story Ronan building (Fig. 1.1) in 1968, due to a gas explosion led to the collapse of one entire corner on the 18th floor. The explosion blew the load-bearing walls, leaving four floors above it in unsupported condition and this caused the progressive collapse of the structure. This event led to having major changes in building regulations of the UK country. In 1995, there was a terrorist act of truck bomb explosion near the Murrah Federal Office Building in Oklahoma City, US (Fig.1.2). The explosion of the bomb first destroyed the column near to it. The lower floors were pushed upwards by the explosion's shockwave before the fourth and fifth floor collapsed onto the third floor, which housed a transfer beam that stretched along the length of the structure and was supporting the pillars that were above it. Due to the increased weight, the third floor and the transfer beam broke away, resulting in the structure collapsing. An aerial view of the damaged portion of the building can be seen in Fig. 1.3. Despite the fact that the structure complied with all code requirements, research conducted after the tragedy revealed that changes to the building design, such as different reinforcement detailing and the addition of some reinforcement, could have prevented the collapse without significantly increasing construction costs. Another case of progressive collapse is the failure of the World Trade Centre, US (Fig. 1.4); due to a terrorist attack in 2001. The investigation was carried out by the National Institute of Standards and Technology (NIST). The report submitted by this institute in 2005 states that the fire to be the main cause of the collapse. Perimeter columns and floors were deteriorated by the heat of the fire. Sagging of floors pulled the perimeter columns inward leading them to buckle. Impact of the airplanes with the high-speed, damaged majority of top floor portions which fell upon the lower undamaged structure. The collapse began with the drop of the upper floor on the lower floor through the height of one story which released the necessary energy to begin a progressive collapse.
Fig. 1.4 World Trade Centre, US (Los Angeles Times)
The General Service Administration (GSA) progressive collapse guideline provides a detailed methodology and performance criteria needed to assess the vulnerability of new and existing buildings to progressive collapse. For framed structures the following analysis cases should be considered (GSA 2003).
The following exterior analysis cases should be considered:
Fig. 1.5 Plan view of a typical building
Buildings that have underground parking and/or uncontrolled public ground floor areas shall use the following interior analysis case. Analyse the building for the instantaneous loss of one column that extends from the floor of the underground parking area or uncontrolled public ground floor area to the next floor (1st story). The column considered should be interior to the perimeter column lines. In the present study interior column removed condition is shown as case 4 (see Figure 1).
Fig. 1.6 Plan view of a typical building
Problem Statement
Progressive collapse occurs when local damage in a structural component initiates a chain of failures, leading to partial or total building collapse. Many reinforced concrete (RC) framed buildings, especially older ones, were not designed to resist such abnormal events—such as sudden column removal, blasts, or impacts—making them potentially vulnerable.
The General Services Administration (GSA) Guidelines offer a standardized method for evaluating building robustness under component removal scenarios. However, the progressive collapse performance of many existing RC buildings remains uncertain.
This study aims to assess the progressive collapse potential of a selected RC framed building by modeling and analyzing various column removal scenarios as per GSA Guidelines. The investigation focuses on deformation patterns, force redistribution, and demand–capacity ratios to identify structural weaknesses and evaluate the building’s ability to develop alternate load paths.
Objectives
Following are the objectives of the project
Methodology
Objectives will be accomplished by exploring various past literature available on the progressive collapse. :
Assessment of Structural Response: A comparative study among various column removal cases will lead to critical column location.
MODELLING OF AN EXISTING STRUCTURE
In this chapter, an existing structure is analyzed to study the targeted objectives. The existing structure is ‘GST Bhavan’, a RC framed structure located in Pune city. Linear Static Analysis (LSA) and Non-Linear Static Analysis (NLSA) were performed on the structure in SAP2000. Both the analysis methods are discussed in detail later in this chapter along with their step-by-step procedure to perform them in the software. Details of existing structure and modelling & designing parameters are discussed further in this chapter.
A progressive collapse analysis is performed to check the ability of structure to resist the extreme and unlikely loads coming on structure. The analysis methods used are threat independent, which means considering the removal of vertical support i.e. column was result of some short duration abnormal loading. This short duration abnormal loading can be blast load or result of car-accident or any other cause. When a RC framed structure witnesses any sudden removal of column then structure behaves dynamic, characterized by the significant material and geometric nonlinearity. Methods of analysis used to determine the possible damage to structure due to progressive collapse includes simple 2D linear procedure to complex 3D non-linear dynamic analysis.
Linear static analysis is the simplest method of analysis. In this method, intended column is removed from its location and the analysis with following load combination is carried out.
Load Combination = 2(DL+0.25LL) …(4.1)
Where,
DL = Dead load
LL = Live load
Here in static analysis, the applied gravity load is amplified by factor ‘2’ to approximately account for both nonlinear and dynamic effects. After performing analysis, Demand Capacity Ratio (DCR) at critical locations are computed. DCR is demand by capacity ratio. Demand will be obtained from analysis result with load combination given in equation 4.1 and capacity of the section of the member will be obtained from original design of structure. These DCR will be checked against their acceptance criteria given by GSA guidelines. DCR calculated from linear static analysis will help to determine the potential for progressive collapse of structure.
Non-Linear Static Analysis well known as ‘Pushover Analysis’ is used to analyze a building for lateral load. This method takes into consideration both material and geometric nonlinearity. In pushover analysis the lateral load on the building is increased step-wise until the maximum load is attained. For progressive collapse analysis, vertical pushover analysis is performed in which the amplified gravity load will be applied step-wise until the complete load attains. In software this step-wise load increment will be simulated by creating a non-linear load case. In this method, plastic hinge formation is studied. For that purpose automatic hinge properties or user-defined hinge properties can be assigned in the software. In case of automatic hinge properties, program will automatically generate hinge property at given specified location.
There are five default hinge properties available viz., Shear (V2 or V3), Axial (P), Torsion (T), Flexural Hinges i.e. Moment (M2 or M3) and Interacting Hinge (P-M2-M3). Preliminary studies indicated that collapse of the RC building under column removed case is governed by the flexural mode of failure for a beam element. For current study only moment hinges in beam were considered. SAP2000 program will use Table 10-7 of ASCE 41-17 code for default hinge properties. A graphical representation of moment-theta curve of hinge is shown in Fig. 4.1. This curve is drawn w.r.t. generalized force vs deformation curve given in FEMA 356 (Chapter 2). Moment and rotation values are normalized by dividing the actual values by scale factors. Moment values are normalized by dividing them by yield moment of respective member. Initial ascending part of curve i.e. segment AB is straight with x-coordinate zero because in this region beam will behave elastically and return to its original form without any permanent rotation. The portion before yielding is calculated by the program automatically and need not to be provided by the user. Point B is where hinge starts to yield. Point C represents the ultimate capacity of hinge after which the hinge capacity immediately drops to point D. Point D represents the residual strength of the hinge thereafter goes upto point E where total failure of hinge is reached. Approximately residual capacity is taken as 20% of ultimate capacity of hinge. Using Table 10-7 of ASCE 41-17, modelling parameters and numerical acceptance criteria for RC beams can be specified. When ‘User-Defined Hinge Properties’ option is to be used at that time this table is used or else just use ‘Automatic Hinge Properties’. Numerical Acceptance Criteria in Table 10-7 will include the limits for Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP) level.
Fig. 4.1 Moment-theta curve of a moment hinge
The results obtained from the linear static analysis are to be studied to determine the extent of distribution of the potential demands on other structural members. On removing the column form the building, there is need to check which members have exceeded their respective maximum demands. The magnitude and distribution of demands will be indicated by DCR. It is calculated as follows:
Where,
QUD = Acting force (demand) determined in a member (moment, axial force, shear)
QCE = Expected ultimate capacity (capacity) of the member (moment, axial force, shear)
In case of beam, both the demand and capacity of member will be calculated in terms of moment. DCR of structural member should be less than 2 to avoid flexure failure and less than 1 to avoid the shear failure.
Fig. 4.2 Front view of GST Bhavan
Fig. 4.3 Side view of building
The existing structure, GST Bhavan is a 6 storey RC framed structure located in Pune city. It was modelled and analyzed in SAP2000 program. Details of modelling and analysis carried out in software are discussed below.
Fig. 4.4 3D view of model in SAP2000
Fig. 4.5 Plan view of model in ETABS
Structural details of GST Bhavan are mentioned in Table 4.1 below.
|
Name of Building |
GST Bhavan |
|
Location |
Pune |
|
Storey |
G + 6 |
|
Concrete |
M25 |
|
Steel |
Fe415 as main steel Fe250 used for stirrups and ties |
|
Beam Section |
300 mm x 500 mm (all beams are of same size) |
|
Column Section |
350 mm x 600 mm (External Columns) (Fig. 4.6) 350 mm x 750 mm (Internal Columns) (Fig. 4.7) |
|
Slab Section |
125 mm Shell-thin type (all slabs) (Fig. 4.8) |
Table 4.1 Structural Details of GST Bhavan
Different loads acting on the structure are Self-weight, Dead load (DL), Super-Dead Load (SDL), Live Load (LL), Earthquake Load (EQ) and Wind Load (WL). These loads are defined as per IS 875 Part 2 (Fig. 4.9). Wall load is applied on beams, LL and Floor Finish are applied on slab elements. LL applied on the slab elements are taken as per Table 1 of IS 875 Part 2 (Business and Office Buildings). Parapet wall on terrace is of height 1.5 m. Load details for building are given in Table 4.2, 4.3, 4.4 and 4.5 below.
|
Load Type |
Magnitude |
|
Dead Load (DL) |
Self-weight of member |
|
SDL (Wall Load) Wall thickness 230 mm Wall thickness 115 mm Parapet wall 230 mm |
11.50 kN/m 5.75 kN/m 6.9 kN/m |
|
Live Load (LL) |
4.0 kN/m2 – Passage area slabs 2.0 kN/m2 – WC slabs 2.5 kN/m2 – all other slabs |
|
Floor Finish (SDL) |
7.65 kN/m2 – WC slabs 1 kN/m2 – all other slabs |
Table 4.2 Load Details for Ground to 5th floor
|
Load Type |
Magnitude |
|
DL |
Self-weight of members |
|
SDL - Parapet wall |
6.9 kN/m |
|
LL |
1.5 kN/m2 |
|
FF |
1.0 kN/m2 |
Table 4.3 Load Details for Terrace level
|
Building Location |
Pune |
|
Seismic Zone |
3 |
|
Seismic Zone Factor (Z) |
0.16 |
|
Soil Type |
Medium |
|
Importance Factor (I) |
1 |
|
Response Reduction Factor (R) |
5 |
Table 4.4 Earthquake Load Details
Time period was calculated manually using following formula mentioned in Cl. 7.6.2 (c) of IS 1893 (Part 1)-2016.
where,
T = time period (sec)
h = height of building (m)
d = base dimension of building in considered earthquake direction (m)
|
Location |
Pune |
|
Basic wind speed (Vb) |
39 m/s |
|
Terrain Category |
4 |
|
Importance Factor (I) |
1 |
|
k1 |
1 |
|
k3 |
1 |
Table 4.5 Wind Load Details
Fig. 4.6 Column positioning & orientation of 350 mm x 600 mm in ETABS
Fig. 4.7 Column positioning & orientation of 350 mm x 750 mm in ETABS
Fig. 4.8 Slab provided seen in Plan view in ETABS
Fig. 4.9 Load patterns defined in SAP2000
The building is analyzed and then designed for the load combinations as per IS 456:2000. Once model is created, define a ‘Rigid Diaphragm’ separately for all floors and assign it. Also, define a mass source as shown in Fig. 4.10 below. Mass source needs to be defined for seismic design of structure as during earthquake not 100% LL will be present. So, according to IS 1893-2016, consider 25% of LL while earthquake analysis.
Fig. 4.10 Mass source defined in SAP2000
As per GSA 2003 guidelines, different column removal cases are to be considered and separate analysis needs to be performed for these cases. For existing structure following column removal cases were studied (Fig. 4.11).
Fig. 4.11 Location of column removal cases in ETABS
Following are various procedures discussed to perform the respective actions.
Following are the steps to perform Linear Static Analysis in SAP2000 program and to calculate DCR.
To determine the expected material strength (for determining capacity), design material strength may be increased by strength increase factor (Table 4.6). Capacity of section is calculated as per IS 456-2000.
|
Material |
Strength Increase Factor |
|
Concrete |
1.25 |
|
Steel |
1.25 |
Table 4.6 Material strength increase factor
Illustration for a DCR of a beam for case 1: removal of middle column on longer side of building. Location of that column is shown in Fig. 4.12.
Fig. 4.12 Removal of middle column on longer side
Fig. 4.13 Reinforcement detailing of building
Fig. 4.14 BMD for beam corresponding to load combination = 2(DL + 0.25LL)
Beam on right side of ‘removed column’
Ast = 440 mm2 (Fig. 4.13)
fy = 1.25 x 415 MPa = 518.75 MPa
fck = 1.25 x 25 MPa = 31.25 MPa
Here, b=300, D=500, d=470 mm
xu=
MR = 0.87*fy*Ast*(d-0.42xu)
= 0.87*(1.25*415)*440*(470-0.42*58.838)
MR = 88.424 KNm = Capacity
Demand = 181.21 KNm
DCR =
Similarly, for section at left end of beam (left beam of column removed) and right section of beam (left beam of column removed)
DCRleft section = 1.405 …corresponding to Ast = 631 mm2
DCRright section = 0.885 …corresponding to Ast = 416 mm2
Following are the steps to perform Non-Linear Static Analysis in SAP2000 program and to assign plastic hinge.
(This step is required to get value of ‘Design Shear (V)’ for new load combination for every beam)
Following is the procedure to assign ‘Auto-hinge properties’ to beams in SAP2000.
Fig. 4.15 Hinge option in SAP2000
Fig. 4.16 ‘Add Hinge’ option
Fig. 4.17 Options to be selected while assigning auto-hinge property to a beam element
In order to get the PH formation in the structure, non-linear load case has to be defined. It can either be force-based case or deformation-based case. For this project as number of loads are more than 1, force-based load case was created. Following is the procedure to form a non-linear load case.
Fig. 4.18 Load Cases option in SAP2000
Fig. 4.19 Non-linear load case details
Fig. 4.20 Load application details
Fig. 4.21 Details of ‘Result Saved’ option
Fig. 4.22 Details of ‘Nonlinear Parameters’
Fig. 4.23 Deform shape option
|
PH Color |
Region of M-θ curve |
Comments |
|
Grey |
AB |
PH still not yielded |
|
Green |
BC |
PH crossed yield point |
|
Sky Blue |
CD |
PH cross ultimate-strength |
|
Pink |
DE |
PH in its residual strength |
|
Red |
After E |
Failure of PH |
Table 4.7 Defining PH State
Fig. 4.24 Deformed Shape option to view PH
Fig. 4.25 PH state in M vs θ curve
|
PH Color |
Damage Level |
|
Grey |
Immediate Occupancy (IO) |
|
Green |
Life Safety (LS) |
|
Sky Blue |
Collapse Prevention (CP) |
|
Red |
Failure |
Table 4.8 PH Damage Levels
Fig. 4.26 PH damage levels
In this chapter, procedure to perform both the analyses method are explained along with their procedure to be followed to perform them in SAP2000 program. Procedure to calculate DCR and assigning PH are also explained. Results obtained for both of them are discussed in next chapter.
RESULTS AND DISCUSSION
In this chapter, results obtained from linear and nonlinear static analysis for different column removal cases are discussed. DCR obtained from LSA and PH formed after performing NLSA are shown. Overall performance of building under different column removal scenarios were studied.
Linear Static Analysis is the simplest method of analysis, which is used in current study to determine Demand-Capacity Ratio (DCR) in every structural member. In present work, DCRs were calculated only for beams present in bay adjacent the column removal bay. Location of different column removal cases are shown in Fig. 5.1.
Case 1: Removal of middle column on longer side (Blue circle)
Case 2: Removal of middle column on shorter side (Black circle)
Case 3: Removal of corner column (Red circle)
Case 4: Removal of interior column (Yellow circle)
Frame number 239 (C239) (Fig. 5.1) was removed from its position to determine the potential of progressive collapse. DCRs obtained in X-Z plane are shown in Fig. 5.2. As per GSA (2003) guidelines, flexure DCR of right far end sections of two beams on right side of C239 has crossed flexure acceptance criteria, which means there is high possibility that these members have failed after removal of column. DCR value of far end sections from column removal location on either side are higher than that of near end sections in this case.
DCRs of beams in Y-Z plane are shown in Fig. 5.3. DCR of all the critical sections except one on the last floor had crossed the DCR flexure limit of 2. So, all beams in Y-Z plane have high possibility of being failed after removing column. DCR value of far end sections from column removal location are higher than that of near end sections in this case also.
Fig. 5.1 Location of column removal cases considered for analysis
Fig. 5.2 DCR of beam sections in X-Z plane after removing Middle Column on Longer Side C239 (case 1)
Fig. 5.3 DCR of beam sections in Y-Z plane after removing Middle Column on Longer Side C239 (case 1)
For case 2, frame number 165 (C165) (Fig. 5.1) was removed from its original position. After performing LSA, following DCR were obtained in X-Z plane (Fig. 5.4). No DCR had crossed flexure failure limit. So as per GSA (2003) guidelines, all beam members in X-Z plane are safe.
DCRs in Y-Z plane are shown in Fig. 5.5. DCR of beam sections located at far end from removed column had crossed flexure limit on 1st and 2nd floor, while ratios of all other section on remaining floors are still within acceptance limit. Beams on first two floors have high probability of being failed. It can be seen in this case too, that DCR value of far end sections from column removal location on either side are higher than that of near end sections.
Fig. 5.4 DCR of beam sections in X-Z plane after removing Middle Column on Shorter Side C165 (case 2)
Fig. 5.5 DCR of beam sections in Y-Z plane after removing Middle Column on Shorter Side C165 (case 2)
For corner column removal case, frame number 159 (C159) (Fig. 5.1) was removed from its position and LSA was performed. DCRs in X-Z plane are shown in Fig. 5.6 below. None of the beam section’s DCR had crossed the flexure limit. So, all beams in X-Z plane are safe as per GSA guideline. DCR value of far end sections from column removal location are higher than that of near end sections
Fig. 5.6 DCR of beam sections in X-Z plane after removing Corner Column C159 (case 3)
DCR in Y-Z plane is shown in Fig. 5.7 below. All the sections on right far end of the beams have crossed the flexure failure limit. There is high possibility of these all beams to be failed on removing the corner column. Similarly, for this case too, DCR value of far end sections from column removal location are higher than that of near end sections.
Fig. 5.7 DCR of beam sections in Y-Z plane after removing Corner Column C159 (case 3)
For case 4, an interior column i.e. frame number 204 (C204) was removed. DCR of beams in X-Z plane is shown in Fig. 5.5. DCR of all critical section was found to be within permissible limit specified by GSA guidelines. So, chances are that all beams in this plane are safe even after removal of column because the load has been safely re-distributed among these structural members.
Fig. 5.8 DCR of beam sections in X-Z plane after removing Interior Column C204 (case 4)
DCR of beam sections in Y-Z plane is shown in Fig. 5.6 below. No any DCR has crossed the permissible value of flexure limit. So, as per GSA guidelines, chances are that all beam members are safe even after failure of interior column. The load coming on the column has been re-distributed safely.
Fig. 5.9 DCR of beam sections in Y-Z plane after removing Interior Column C204 (case 4)
The non-linear static analysis was performed to determine the formation of hinge in the beams. Load coming on the building was increased step-wise to determine the hinge sequence corresponding to a particular displacement. Results of PH formation on removing a column is discussed for each case.
On removal of C239, middle column on longer side, NLSA was performed and PH formation pattern under non-linear load case was studied. Final state of PH formation is shown in Fig. 5.10. It can be seen that, PHs are formed only in beams adjacent to column removal bay.
In Fig. 5.11, it can be seen that as load increases, plastic hinges starts forming at various different critical sections of the beam. It can be stated that, PH initially formed in shorter length (right-side) beam and then in longer length (left-side) beam.
Fig. 5.10 Final state of PH formation for Removal of Middle Column on Longer Side
Fig. 5.11 PH formation in X-Z plane beams for Removal of Middle Column on Longer Side
PH formation in Y-Z plane can be seen in Fig. 5.12. As loading progresses, PHs are formed initially at far end of the beam from column removed location. Later formed at near end of the beam.
Fig. 5.12 PH formation in Y-Z plane beams for Removal of Middle Column on Longer Side
For case 2, C165 was removed from its location. Final state of PH formation after column removal is shown in Fig. 5.13. In this case also, PHs were formed in beams in bay orthogonal to column removal bay.
Fig. 5.13 Final state of PH formation for Removal of Middle Column on Shorter Side
PH formation for Y-Z plane are shown in Fig. 5.14. As load increases, PH starts forming initially in bottom floors beams and progresses to top floor beams. Till it reached final state, PH was formed at both critical sections of all the beams, initially forming at the far end of beam. As beam length on either side of this column are less than that in orthogonal direction, PH were formed at both the end of beam.
PH formation in X-Z plane are shown in Fig. 5.15. As loading progresses, PH starts forming from top floor beam. As beam length in this plane is more than that of Y-Z plane, PHs were formed only at the far end of the beam.
Fig. 5.14 PH formation in Y-Z plane beams for Removal of Middle Column on Shorter Side
Fig. 5.15 PH formation in X-Z plane beams for Removal of Middle Column on Shorter Side
For corner column removal case, C159 was removed and NLSA was performed. Final state of PH formation (Fig. 5.16) showed that PHs were formed only in orthogonal planes connected to column removal location.
Fig. 5.16 Final state of PH formation for Removal of Corner Column
PH formation in X-Z plane is shown in Fig. 5.17. On removal of column, PH first started at top beam and as final state of loading was reached, PHs were formed only at far end on beam as beams in X-Z plane are longer than that of orthogonal beams in Y-Z plane.
Fig. 5.17 PH formation in X-Z plane beams for Removal of Corner Column
PH formation in Y-Z plane is shown in Fig. 5.18. As load increased, PH progressed from bottom floor beams to top floor beams. In this plane, beam length was shorter than that of beams in X-Z plane. So, PHs were formed at both the end section of all the beams. First PHs were formed at far end of all beams and then started to form at near end of beams.
Fig. 5.18 PH formation in Y-Z plane beams for Removal of Corner Column
5.3.4 Case 4: Removal of Interior Column
PH final state after removing the interior column is shown in Fig. 5.19 . PHs were formed only in beams present in Y-Z plane.
Fig. 5.19 Final state of PH formation for Removal of Interior Column
No PH were formed in X-Z plane. Length of beams in X-Z plane are more than that of beams in Y-Z plane of the building. It can be assumed that, major part of extra load of the column is transferred to beams in Y-Z plane which increased moment demand thereby forming the PH in them.
PH formation in Y-Z plane is shown in Fig. 5.20. As loading was increased the PH started from bottom beams and progressed towards top beams. Once PH were formed at far end of all beams on either side, PH starts to form at near end of beams.
Fig. 5.20 PH formation in Y-Z plane beams for Removal of Interior Column
After removing particular column from its position, LSA and NLSA were performed and results obtained for each case has been discussed above. Common observations from each case for DCR and PH formation are commented in next chapter.
CONCLUSION
Past events of progressive collapse around the world lead to the formation of codes and guidelines to resist the structure and reduce the damage caused by the phenomenon. One of them is General Service Administration (GSA) 2003 guidelines. GSA provides the guidelines to reduce the potential for progressive collapse in new and existing buildings. As per these guidelines, four column removal cases were decided to study. By modelling and analyzing the structure considered by Joshi et al. in their study, validation was done in SAP2000 software.
In current study, GST Bhavan (Pune) building is considered. The building is modelled and analyzed in SAP2000 software. For this study, Demand-Capacity Ratio (DCR) from Linear Static Analysis (LSA) and Plastic Hinge formation from Non-Linear Static Analysis were determined for all four column removal cases. The results obtained from both the analysis were discussed in above chapters and the conclusions derived from them are discussed below.
1. DCR of beam sections exceeding the permissible flexure limit of 2 as per GSA 2003 guidelines are more in Y-Z plane than in X-Z plane. Number of beams exceeding the limit in Y-Z plane for case 1, case 2 and case 3 are 6 beams, 4 beams and 6 beams respectively. Almost all beams in Y-Z plane had crossed the limit which concludes that they have high possibility of being failed on removal of column.
2. While in interior column removal case, no DCR is greater than flexure limit of 2. But still DCR values of beam sections in Y-Z plane is more than that of beam sections in X-Z plane.
3. From above two statements it can be inferred that, moment-demand increases more in shorter length beam than in longer length beam on removal of column in any case.
4. 1st objective of the project has been checked. It is found that, the building designed as per IS 456-2000 is vulnerable to progressive collapse in every column removal case, as beam sections have high possibility of been failed on removal of vertical support which can further lead to failure of more structural members.
5. Also, here research gap was addressed on different spans. DCR in smaller spans is more than larger spans.
1. Plastic Hinge (PH) starts forming at location having higher DCR in all four cases studied.
2. It was observed in all 4 cases that, PHs were formed only in orthogonal planes to that of column removal location. This indicated that the column load is re-distributed among these adjacent beams which have high possibility that their elastic state has been crossed.
3. In all cases, PHs first formed at far end of beam and then at near end of beam.
4. On removal of column, PHs starts forming from lower floor beam and progresses towards upper floor beams. This indicated that load is majorly attracted by lower floor beams.
From above study it can be commented that, removal of middle column on longer side is critical in current study due to presence of structural members attached to it. More number of shorter spans beams are connected to this column bay, which resulted in forming plastic hinges in every beam in shorter span, ultimately exceeding their flexure limit of 2 as per GSA guidelines (which infers that they have very high probability of being failed on removal of column). The displacement of column removal joint was also relative more than all other cases.
So the overall results obtained and conclusions derived from them are found satisfactory and satisfy the preliminary objectives of the study.
FUTURE SCOPE
The base for progressive collapse has been made in current project by explaining the procedure to perform them step-by-step in software, illustration of some calculations, validating the past study, etc. Future scope of the project involves the more research that can be made in continuation with this as an extension of this study. Currently the RC framed structure was analyzed only statically as per GSA 2003 guidelines. Future scope of the project can involve:
1. The RC framed structure can be analyzed by ‘Dynamic Method of Analysis’, which can be more realistic and more accurate.
2. In current study, Plastic hinge formation was restricted to beams only. So in future Plastic hinges in column can be studied.
3. Advance software like ‘Perform 3D’ can be used to perform the Dynamic Analysis for better results.
4. Currently study was bound only upto analysis, further the RC framed structure can be designed to resist the progressive collapse.
REFERENCES
Chaitanya Vishnu Valekar*, S. M. Kazi, V. V. Shelar, Progressive Collapse Assessment Of Framed RC Building According To GSA Guidelines, Int. J. Sci. R. Tech., 2026, 3 (5), 851-883. https://doi.org/10.5281/zenodo.20379004
10.5281/zenodo.20379004