IJSRD - International Journal for Scientific Research & Development| Vol. 4, Issue 05, 2016 | ISSN (online): 2321-0613
Second Order or P-Delta Effects in Tall Structures Chetan Pramod Gull1 Vinod I. Hosur2 1 P.G. Student 2Assistant Professor 1,2 Department of Civil Engineering 1,2 KLS Gogte Institute of Technology Belgaum, Karnataka, India Abstract— Tall building structures are in practice now a days. Due to the frequent earthquakes happening around the world, these buildings need to be designed Earthquake resistant. The second order effect or P-delta effect has to be included in the analysis since the deflections are generally large for tall building structures. The objective of the current work is to study is to the influence of second order or P-Delta effect in the structural behaviour of tall building structures. Alternative lateral load resisting systems i.e. OMRF (Ordinary moment resisting system), SMRF (Special moment resisting system), Shear wall system and Bracing system for the tall building structures are considered. For this purpose 5, 10, 15 and 20 story structures are modelled and analysed using ETABS software and using the Indian Standard Codes for analysis and design namely, IS 1893:2002, IS 456:2000. The buildings modelled are with floor area of (20m x 20m) with 4 bays of 5m span along both directions. Key words: Second Order Effect, P-Delta Effect, SMRF, OMRF, Bracing System, Shear Wall System
the structure that is equal to the total vertical load (P), times the lateral displacement (Δ).
Fig. 2: P- “Little” Delta (P-δ) Effect P- “Little” delta (P-δ) effect has reference to the effects of the axial in an individual members of the structure, subjected to a deflection (curvature) between its endpoints due to buckling of member. For example, column load (P), due to gravity load, wind load or seismic forces act on a column, that has curvature induced in it by buckling which depends on the type of the beam-column connection. Moments are induced in member equal to the axial load (P), times the member deflection (δ).
I. INTRODUCTION Definition: “ When the horizontal loading acts on a building causing it to deflect, the resulting eccentricity of the gravity loading from the inclined axes of structure’s vertical members causes the lateral displacements of the structure and the moment in the member to increase. This secondorder effect is termed as the P-Delta effect”. P- Delta effect is the non-linear (Second order) effect that occurs in every structure, where the elements are subjected to axial loads. D-delta effect is the genuine effect that is associated with the Magnitude of the applied axial Load (P) and the lateral displacement (Delta). II. TYPES OF P-DELTA EFFECTS
P- “BIG” Delta (P-Δ) effect: Structural Instability Effect. P- “Little” Delta (P-δ) effect: Member Instability Effect.
Fig. 1: P- “BIG” delta (P- Δ) effect P- “BIG” delta (P- Δ) effect has references to the effects of vertical load acting on the laterally displaced structures. For Example, Seismic force or wind force (V), Causes a horizontal displacement (Δ), of the structure, while the gravity load (P), simultaneously act vertically on this displaced structure. Due to this moments are introduced into
III. METHODS OF Ρ-DELTA ANALYSIS OF BUILDING STRUCTURES
Amplification Factor Method Iterative Method Iterative Gravity Load Method Negative Property Fictitious Member Method Moment Amplification Factor Method IV. LITERATURE REVIEW
Regina Gaiotti and Bryan Stafford Smith (1989) inferred that, the demand for the high rise slender and lighter buildings has led the structures possibly more likely to be effected by the p-delta effect. Several methods estimating second order effects have been compared in terms of their accuracy, effectiveness and ease of calculation. The main factor that differentiate these different method of p-delta analysis are the ease of use or calculation, accuracy, time taken for the analysis and whether they fit for the hand calculation or the computer calculation only and whether they can be applied to all type of structures or only specific type of structure. The American institute of steel construction, load and resistance factor design (AISC-LFRD), indicates that the P-delta or the second order effect should be accounted in the design of structural frames. To consider this second order or p-delta effect for the design requirements, the AISC-LFRD provided the approximate method, based on first order analysis with Moment Amplification Factor (Sheng-Jin Chen and Wu-ChyuanWang, 1999).
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Second Order or P-Delta Effects in Tall Structures (IJSRD/Vol. 4/Issue 05/2016/421)
V. PROBLEM DEFINITION AND MODELING A 5, 10, 15 and 20 story building of symmetric plan dimensions of 20m x 20m, bay spacing of 5m along each direction and story height of 3m is considered. The properties of material are as shown below. 1) Properties of Concrete Grade of Concrete M25 Elasticity Modulus 25000MPa Poisson’s Ratio 0.2 2) Properties of Reinforcement Steel Grade of Steel Fe415 Modulus of Elasticity 210000MPa Density of Concrete 25kN/m3 Poisson’s Ratio 0.3 3) Properties of Masonry Density of brick wall including plaster 20kN/m3 Poisson’s Ratio 0.2 The Loads on Structure and Dimensions of structural elements: 4) Loads on Structure Live load on Roof and Floor 3kN/m2 Roof/Floor finish 1.5kN/m2 Brick wall on External Beams 230mm (13.8 KN/m) Brick wall on Internal Beams 150mm thick (9 KN/m) Parapet wall on Roof 150mm thick (3 KN/m) Slab Thickness 150mm thick Shear wall Thickness 230mm Beam size 300mm x 475mm Bracing size 300mm x 350mm Story height 3m Damping 5% 5) Seismic Parameters (IS 1893): Zone V Soil Type 1(Hard Soil) Importance factor (I) 1 Building System with Response Reduction Factor SMRF (R=5) OMRF (R=3) 6) Column Dimensions (shorter dimension in X-direction) a) 5 Story Model 375 x 450 mm (All Columns) b) 10 Story Model 450 x 650mm (Story 1 to Story 5) 450 x 450mm (Story 6 to Story 10) c) 15 Story Model 600 x 800mm (Story 1 to Story 5) 450 x 650mm (Story 6 to Story 10) 450 x 450mm (Story 11 to Story 15) d) 20 Story Model 750 x 950mm (Story 1 to Story 5) 600 x 800mm (Story 6 to Story 10) 450 x 650mm (Story 11 to Story 15) 450 x 450mm (Story 16 to Story 20) e) OMRF and SMRF Models 5 Storey OMRF and SMRF Model: The 5 Storey OMRF model 3D view and plan view are shown in Fig 4.1 and 4.2 respectively.
Fig. 3: 3D View of 5 Storey Model
Fig. 4: Plan View of 5 Storey. Similarly, the frames for 10, 15 and 20 story have been modelled. Similar 4 models for Special moment resisting frame (SMRF) system for 5, 10, 15 and 20 story models have also been considered. 7) Shear Wall System 5 story Shear wall System: The 3D view of the 5 Storey Shear wall model are shown in figure 4.3
Fig. 5: 3D view of 5 Storey Shear wall System In the shear wall system the central column along the periphery of the frame were replaced by the shear wall. The width of shear wall is taken as 5m and thickness as 230mm. Similar shear walled frames for 10, 15 and 20 story have been modelled. 8) Bracing System 5 story Bracing System: The 3D view of the 5 Storey Bracing model are shown in figure 5.4.
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Second Order or P-Delta Effects in Tall Structures (IJSRD/Vol. 4/Issue 05/2016/421)
Similar Bracing system frames for 10, 15 and 20 story have been modelled. VI. RESULTS AND DISCUSSIONS: The different building models of 5 story, 10 Story, 15 story and 20 story were modelled in the ETABS software. In the models different lateral load resisting properties like special moment resisting frames (SMRF), Shear wall system and Bracings were introduced in the model, to study their Second order or P-delta effects, with the increase in height of the structure. The lateral loads, dead load and live load are considered for the design of structure as per the Indian standard code of practice for Seismic Zone V. Fig. 6: 3D View of 5 Storey Bracing system. In the bracing system, the bracing were assigned in The comparison of displacements for different second and third bays along the periphery of the frame. The heights of the structure with and without P-delta effect is as X-type of bracing have been assigned to the all 4 models. shown in table-1 below. Displacement of Top and Middle story of Building Displacement Without P-Delta Displacement With P-Delta Average % Model Story X Direction Y Direction X Direction Y Direction Increase in Displacements 5th Story 55.60 48.30 57.30 49.70 2.98 % 5 Story OMRF Model 3rd Story 38.70 33.30 40.20 34.40 3.59 % 5th Story 33.40 29.00 34.30 29.70 2.55 % 5 Story SMRF Model 3rd Story 23.20 20.00 24.00 20.60 3.22 % 5th Story 11.00 10.50 11.10 10.60 0.93 % 5 Story Shear wall Model 3rd Story 5.70 5.50 5.70 5.50 0.00 % 5 Story Bracing Model
5th Story
10.50
10.20
10.50
10.30
0.49 %
3rd Story
6.30
6.10
6.30
6.20
0.82 %
10 Story OMRF Model
10th Story
112.20
102.60
118.00
107.40
4.92 %
5th Story
64.00
54.40
68.10
57.60
6.14 %
10 Story SMRF Model
10th Story
67.30
61.60
70.30
64.00
4.18 %
5th Story
46.90
41.10
49.30
43.10
4.99 %
10 Story Shear wall Model
10th Story
41.20
40.00
41.70
40.50
1.23 %
5th Story
23.10
22.20
23.50
22.50
1.54 %
10th Story 28.10 27.60 28.30 27.80 0.72 % 10 Story Bracing Model 5th Story 16.00 15.60 16.10 15.70 0.63 % 15th Story 178.80 165.00 189.50 176.20 6.39 % 15 Story OMRF Model 8th Story 106.90 95.80 114.80 104.00 7.97 % 15th Story 107.30 99.00 113.10 104.70 5.58 % 15 Story SMRF Model 8th Story 64.10 57.50 68.40 61.50 6.83 % 15th Story 81.90 78.50 83.70 80.40 2.31 % 15 Story Shear wall Model 8th Story 41.10 39.10 42.10 40.10 2.50 % 15th Story 55.60 54.50 56.40 55.20 1.36 % 15 Story Bracing Model 8th Story 26.10 25.40 26.40 25.70 1.17 % 20th Story 250.20 233.90 274.30 255.20 9.37 % 20 Story OMRF Model 10th Story 133.70 124.60 150.20 139.20 12.03 % 20th Story 150.10 140.30 162.20 150.90 7.81 % 20 Story SMRF Model 10th Story 80.20 74.70 88.40 81.90 9.93 % 20th Story 127.80 122.90 132.40 127.20 3.55 % 20 Story Shear wall Model 10th Story 60.10 58.00 62.60 60.30 4.06 % 20th Story 88.60 86.80 90.40 88.50 2.00 % 20 Story Bracing Model 10th Story 37.10 36.30 37.90 37.00 2.04 % Table 1: comparison of displacements for different heights of the structure with and without P-delta effect is as shown in table-1 below. The second order effect in all the 5 story models effect indicating the second order effects need to be around 0 to 3%, which increases to 2 to 12% in all the 20 considered for tall structures. story models. Therefore 5 story models are least affected It is observed that OMRF being very less stiff while the 20 story models are most affected by second order structures, is more effected due to P-delta effect as there is
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Second Order or P-Delta Effects in Tall Structures (IJSRD/Vol. 4/Issue 05/2016/421)
maximum 9.37% & 12.03% increase in displacements in 20 story frame in 20th & 10th story respectively, but for SMRF there only 7.81% and 9.93% increase in displacement in 20th & 10th story respectively, for 20 story frame, and still lesser displacements were observed in shear wall and bracing systems. Both the shear wall system and bracing systems being very stiff structures, are least affected by the p-delta effect. There is only 2 to 4% increase in displacement in these two systems, but whereas both OMRF and SMRF system show 9 to 12% increase in displacement. This is observed due to bracing and shear wall system are very stiff and therefore have very less lateral displacements. The design base shear of the structure is not significantly affected by the second order effects in the structures. VII. CONCLUSIONS The structural performance of buildings with OMRF, SMRF, Shear Wall System and Bracing System and for different heights, 5, 10, 15 and 20 stories is studied with specific objective of the influence of second order or PDelta effect. The buildings are modelled and analysed using standard ETABS software. On the bases of results of analysis, the following conclusions are drawn: 1) The second order or P-delta effect in the structure increases with the increase in height of the structure. The second order effect is observed to be more in the mid height of the structure rather at the top. 2) P-Delta effects have to be included in analysis of tall buildings. P-Delta Effect is prominent in tall structures (15 Story and above), and not significant in short buildings (Less than 10 story). 3) The P-Delta effect is prominent in structural systems having very less lateral stiffness such as, OMRF and SMRF structures, but it has less effect in structural systems having very high lateral stiffness such as on shear wall system and bracing system. In general, as the lateral stiffness of structure increases, the P-Delta effect decreases. REFERENCES [1] Bryan Stafford Smith and Alex Coull, “Tall Building Structural Analysis and Design”, Wiley India Pvt.ltd. [2] Allen Adams, “Second-Order Analysis”, Chief Structural Engineer, RAM/Bentley Systems, Inc. [3] Regina Gaiotti and Bryan Stafford Smith, (1989) “PDelta Analysis of Building Structures”, ASCE, J.Struct.Eng. 115(4): 755-770. [4] Sheng-Jin Chen and Wu-Chyuan Wang, (1999) “Moment Amplification Factor for P-Delta Effect of Steel Beam-Column”, ASCE, J.Struct.Eng. 125(2): 219223. [5] David Brown, (2002) “Multi-Story Frame Design”, New Steel Construction, Vol. 10, No.6, Nov/Dec 2002. [6] Dr. Vinod Hosur, “Earthquake Resistance Design of Building Structures”, Wiley India Pvt.ltd.
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