Precast Diaphragm Analysis: A Comparative Study between Beam ...

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Research Article May 2016 Special Issue on International Conference on Advances in Engineering (ICAE) -2016 Conference Held at Hotel Magaji Orchid, Sheshadripuram, Bengaluru, India. © 2016, IJERMT All Rights Reserved Page | 132 International Journal of Emerging Research in Management &Technology ISSN: 2278-9359 (Volume-5, Issue-5) Precast Diaphragm Analysis: A Comparative Study between Beam Analogy and Stress Analysis Using FEM Based Software (ETABS) 1 Arjun M V, 2 Tanuja M R, 3 Rachitha V J 1 Structural Engineer, General Manager, Precast Division, TRC Engineering Pvt Ltd, Bangalore, India 2 Assistant Professor, Civil Engineering Department, ACSCE, Bangalore, India 3 M.Tech Student, Structural Engineering Department, ACSCE, Bangalore, India Abstract- Precast building structures are typically analyzed and designed on the assumption that floor serve as semi- rigid diaphragm spanning between vertical lateral resisting elements. Usually diaphragms are laterally supported by shear walls. Seismic forces are transferred from the diaphragm to the shear walls. If diaphragm deflection and the deflection of the vertical lateral load resisting elements are of the same order of magnitude, then the diaphragm cannot reasonably be assumed as either rigid or flexible such a diaphragm is classified as semi-rigid. Semi-rigid diaphragm analysis plays vital role in determining the maximum bending moment and shear force transferred to each wall by the diaphragm. In this paper we have studied the comparison between the beam analogy and stress analysis on semi-rigid diaphragm using FEM based software ETABS. Keywords- Diaphragm, Semi-rigid diaphragm, Equivalent static method, Shear walls, Beam analogy, Stress analysis I. INTRODUCTION The concept of precast construction includes those buildings, where the majority of structural components are standardized and produced in plants in a location away from the building, and then transported to the site for assembly. These components are manufactured by industrial methods based on mass production in order to build a large number of buildings in a short time at low cost. Cost effective, proven technologies ensuring the highest standards and uniformity in quality are the need of the hour; a need that is now effectively met by Prestressed and Precast Technology. Concrete cast at a location other than in its final position, usually under plant-controlled conditions is called precast concrete. Diaphragms are horizontal elements that distribute seismic forces to vertical lateral force resisting elements. They also provide lateral support for walls and parapets. Diaphragm forces are derived from the self weight of the diaphragm and the weight of the elements and components that depend on the diaphragm for lateral support. Any roof, floor, or ceiling can participate in the distribution of lateral forces to vertical elements up to the limit of its strength. In order to function as a diaphragm, horizontal elements must be interconnected to transfer shear, with connections that have some degree of stiffness. Beam Analogy: The shear walls making up the components of other lateral-force-resisting systems are the supports for this beam. As in a beam, tension and compression are induced in the chord or flanges of the analogous beam. The shear in the diaphragm is resisted by the web of the analogous beam. Diaphragm Stress Analysis: The Lateral forces are transferred to the Shear walls through Diaphragms. To analyses this, the same is modeled as a Semi-Rigid Diaphragm in ETABS which is essentially a FEM Software. The Diaphragm is divided into various finite elements and upon the applied Lateral forces, these elements are subjected to an in-plane bending stress and the same is combined using matrix analysis to arrive at the Diaphragm forces. ETABS calculates the forces in the Diaphragm considering the Shear wall as Rigid supports. The results can thus be seen accordingly. The phenomenon in calculating the forces is as follows As we know the Bending Theory equation is: M/I = f/y = E/R ETABS calculates the bending stress “f” and the corresponding Bending Moment in the diaphragm. II. OBJECTIVE OF THIS PAPER The objective of this paper is to compare the diaphragm force obtain from beam analogy method and Stress analysis using FEM based software ETABS. III. MODELING ETABS is a sophisticated, yet easy to use, special purpose analysis and design program developed specifically for building systems. It offers the widest assortment of analysis and design tools available for the structural engineer working on building structures. The E-TABS software is used to develop 3D model and to carry out the analysis. The G+4 floors are carried out for moment resisting frame situated in seismic design category: B. The Precast parking garage diaphragm is analysed with vertical lateral resisting elements and with different types of walls. The lateral loads and horizontal force is to be applied on the diaphragm structure are based on the American (US) standards.

Transcript of Precast Diaphragm Analysis: A Comparative Study between Beam ...

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Research Article

May 2016

Special Issue on International Conference on Advances in Engineering (ICAE) -2016

Conference Held at Hotel Magaji Orchid, Sheshadripuram, Bengaluru, India.

© 2016, IJERMT All Rights Reserved Page | 132

International Journal of

Emerging Research in Management &Technology

ISSN: 2278-9359 (Volume-5, Issue-5)

Precast Diaphragm Analysis: A Comparative Study between Beam

Analogy and Stress Analysis Using FEM Based Software (ETABS) 1Arjun M V,

2Tanuja M R,

3Rachitha V J

1 Structural Engineer, General Manager, Precast Division, TRC Engineering Pvt Ltd, Bangalore, India

2 Assistant Professor, Civil Engineering Department, ACSCE, Bangalore, India

3 M.Tech Student, Structural Engineering Department, ACSCE, Bangalore, India

Abstract- Precast building structures are typically analyzed and designed on the assumption that floor serve as semi-

rigid diaphragm spanning between vertical lateral resisting elements. Usually diaphragms are laterally supported by

shear walls. Seismic forces are transferred from the diaphragm to the shear walls. If diaphragm deflection and the

deflection of the vertical lateral load resisting elements are of the same order of magnitude, then the diaphragm

cannot reasonably be assumed as either rigid or flexible such a diaphragm is classified as semi-rigid. Semi-rigid

diaphragm analysis plays vital role in determining the maximum bending moment and shear force transferred to

each wall by the diaphragm. In this paper we have studied the comparison between the beam analogy and stress

analysis on semi-rigid diaphragm using FEM based software ETABS.

Keywords- Diaphragm, Semi-rigid diaphragm, Equivalent static method, Shear walls, Beam analogy, Stress analysis

I. INTRODUCTION The concept of precast construction includes those buildings, where the majority of structural components are

standardized and produced in plants in a location away from the building, and then transported to the site for assembly.

These components are manufactured by industrial methods based on mass production in order to build a large

number of buildings in a short time at low cost. Cost effective, proven technologies ensuring the highest standards and

uniformity in quality are the need of the hour; a need that is now effectively met by Prestressed and Precast

Technology. Concrete cast at a location other than in its final position, usually under plant-controlled

conditions is called precast concrete.

Diaphragms are horizontal elements that distribute seismic forces to vertical lateral force resisting elements. They also

provide lateral support for walls and parapets. Diaphragm forces are derived from the self weight of the diaphragm and

the weight of the elements and components that depend on the diaphragm for lateral support. Any roof, floor, or ceiling

can participate in the distribution of lateral forces to vertical elements up to the limit of its strength. In order to function

as a diaphragm, horizontal elements must be interconnected to transfer shear, with connections that have some degree of

stiffness.

Beam Analogy: The shear walls making up the components of other lateral-force-resisting systems are the supports

for this beam. As in a beam, tension and compression are induced in the chord or flanges of the analogous beam. The

shear in the diaphragm is resisted by the web of the analogous beam.

Diaphragm Stress Analysis: The Lateral forces are transferred to the Shear walls through Diaphragms. To analyses

this, the same is modeled as a Semi-Rigid Diaphragm in ETABS which is essentially a FEM Software. The Diaphragm

is divided into various finite elements and upon the applied Lateral forces, these elements are subjected to an in-plane

bending stress and the same is combined using matrix analysis to arrive at the Diaphragm forces. ETABS

calculates the forces in the Diaphragm considering the Shear wall as Rigid supports. The results can thus be seen

accordingly.

The phenomenon in calculating the forces is as follows

As we know the Bending Theory equation is: M/I = f/y = E/R

ETABS calculates the bending stress “f” and the corresponding Bending Moment in the diaphragm.

II. OBJECTIVE OF THIS PAPER

The objective of this paper is to compare the diaphragm force obtain from beam analogy method and Stress analysis

using FEM based software ETABS.

III. MODELING

ETABS is a sophisticated, yet easy to use, special purpose analysis and design program developed specifically for

building systems. It offers the widest assortment of analysis and design tools available for the structural engineer

working on building structures. The E-TABS software is used to develop 3D model and to carry out the analysis. The

G+4 floors are carried out for moment resisting frame situated in seismic design category: B. The Precast parking garage

diaphragm is analysed with vertical lateral resisting elements and with different types of walls. The lateral loads and

horizontal force is to be applied on the diaphragm structure are based on the American (US) standards.

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ISSN: 2278-9359 (Volume-5, Issue-5)

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3.1 Data of the modelled structure considered for the study

3.1.1 Structure:

Parking Garage: G+4 storey of Diaphragm design

Storey Height: 10.00 ft

3.1.2 Codes Standards: The following codes and standards, and all referenced standards therein, shall apply to the design construction and

quality control of all work performed on the project. Use the latest editions unless noted otherwise. Safety and

construction means and method are the sole responsibility of the contractor.

a. 2005 State Building Code, State of Connecticut

b. International Building Code, 2003 and American Concrete Institute (ACI 318-05)

c. Precast and Prestressed Concrete (PCI) 7TH Edition Design Handbook d. PCI Clues:

4.8.1 – Simple Diaphragm Design – Horizontal Beam Analogy

4.8.2 – Rigid and Flexible Diaphragms

4.8.3 – Diaphragm Design Forces

4.8.4 – Diaphragm Detailing Considerations

4.8.5 – Methods of Diaphragm Design

e. “Minimum Design Load for Buildings and Other Structures”, American Society of Civil Engineers.

f. “Manual of Steel Construction – Load and Resistance Factor Design”, Second Edition, 1994, American Institute of

Steel Construction.

3.1.3 Design Data:

1. Floor Dead Load:

Weight of structure

5PSF super imposed dead load

2. Floor Live Load:

AREA UNIFORM LOAD CONCENTRATED LOAD LL REDUCIBLE

Parking Areas 40 psf 3,000 Ibs No

Stairs & Lobbies 100 psf 300 Ibs No

Vehicular Barriers 6,000 Ibs No

Handrails 50 psf 200 Ibs No

3. Roof Snow Loads:

Ground snow load, Pg = 30 psf

Flat roof snow load, Pf = 30 psf

Snow exposure factor, Ce = 1.0

Snow load important Factors, Is = 1.0

Thermal factor, Ct = 1.2

Stockpiled snow area = 150 psf

4. Wind Load:

Basic wind speed V = 95 MPH

Wind important factors, Iw = 1.0

Wind exposure: B

Internal pressure coefficient, Gcpi = +/-.55

Wind directionality factor Kd = 0.85

Topographic factor, Kzt = 1.0

5. Earthquake Design Data:

Seismic use group: 1

Seismic important factors, IE = 1.0

Mapped spectral response coefficients: Ss = .239 Sl = 0.064

Site class: D

Seismic design category: B

Spectral response coefficients Sds = 0.255 Sdl = 0.102

Basic seismic-force-resisting system: Ordinary Reinforced Concrete Shear Walls

Response modification factor, R = 4

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Deflection amplification factor, Cd = 2.5

Over strength factor, Wo = 2.5

Design base shear, Vb = 1,081 k

Fig.1 Plan

3.2 Analysis of diaphragms: The analysis of diaphragms is performed using Microsoft excel spreadsheet involving the following steps,

1. Listing of story shears obtained from output results of ETABS.

2. Diaphragm analysis in East-West and North-South directions.

3. Preparing chord reinforcement.

Fig.2 3D View of Diaphragm

3.2.1 Listing of story shears obtained from output results of ETABS In this step, the output results of ETABS are studied to get the story shears at different floor levels in both

North-South and East-West directions and the same is listed in the format as shown below,

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3.2.2 Beam analogy Diaphragm Analysis:

a) Diaphragm Analysis in the North-South direction: Critical Case Shear is @ Roof: Worst case shear loads occur @ Roof = 357.9 Kips

Total load @ worst case story Eu (Kips/ft) = 317.9Kips/127.00’

= 2.82 Kips/ft

Worst Case Mu = 5685.47 Kips-ft

Where,

1. Diaphragm #1 is analyses based on taking support @ Lite wall @ grid B.

2. Total Earthquake Force is distributed on X-direction.

3. Based on bending moment, steel (Tu/Cu) is provided.

Diaphragm #1

Fig.3 Chord force in N-S Direction

Fig.4 Moment and Shear diagram.

b) Diaphragm Analysis in the East-West Direction: Critical Case Shear is @ Roof: Worst case shear loads occur @ Roof = 357.9 Kips

Total load @ worst case story Eu (Kips/ft) = 317.9Kips/256.83’

= 1.39 Kips/ft

Worst Case Mu = 8740.00 Kips-ft

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Where,

4. Diaphragm #1 is analyses based on taking support @ Shear wall @ grid 2 & 9.

5. Total Earthquake Force is distributed on Y-direction.

6. Based on bending moment, steel (Tu/Cu) is provided.

Fig.5 Chord force in E-W Direction.

Fig.6 Moment and Shear diagram.

3.2.3 Diaphragm Stress Analysis:

a) Diaphragm Analysis in the North-South direction:

Where maximum chord force is expected, draw or define a section cut as shown in figure 7:

Critical Case Shear is @ Roof:

Worst case shear loads occur @ Roof = 357.9 Kips

Total load @ worst case story Eu (Kips/ft) = 317.9Kips/127.00’

= 2.82 Kips/ft

Worst Case Mu = 5400.14 Kips-ft

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Moment about the Z-axis represent in-plane moments as shown in section figure 8:

b) Diaphragm Analysis in the East-West direction:

Where maximum chord force is expected, draw or define a section cut as shown in figure 9:

Critical Case Shear is @ Roof:

Worst case shear loads occur @ Roof = 357.9 Kips

Total load @ worst case story Eu (Kips/ft) = 317.9Kips/256.83’

= 1.39 Kips/ft

Here, we can increase 100 percentage of total load per feet of multiplied 1.05 factors. Worst Case Mu

= 8740.00 Kips-ft

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Moment about the Z-axis represent in-plane moments as shown in section figure 10:

For shear and collector forces located at the connection between the diaphragm and a shear wall, draw or define a

section cut next to the support which follows the wall direction, as shown in figure 11:

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The shear/collector force, which is presented as shown in figure 12:

IV. RESULT AND DISCUSSION In this study, an attempt has been made to understand the comparison between the diaphragm beam analogy and stress

analysis based on chord forces. We are using the finite element method based software ETABS for knowing the base

shear in each level. Then we are analyzing the each level according to beam analogy method and stress analysis based.

Here, we are showing only critical section of shear at roof level remaining diaphragm levels are similar in the beam

analogy and stress analysis method.

Diaphragms results at all the levels of Beam Analogy method tabulated below:

Storeys

Lite walls Shear walls

Moments

(Kip-ft)

Shear forces

(Kips)

Moments

(Kip-ft)

Shear forces

(Kips) Roof 5685.47 179.07 8740.0 160.78

Level-3 4556.44 143.51 7040.0 129.55

Level-2 3044.35 95.89 4720.0 86.75

Level-1 1512.09 47.62 2330.0 42.79

Diaphragms results at all the levels of Stress Analysis method tabulated below:

Storeys

Lite walls Shear walls

Moments

(Kip-ft)

Shear forces

(Kips)

Moments

(Kip-ft)

Shear forces

(Kips)

Roof 5400.14 174.84 8794.75 159.02

Level-3 4333.70 142.38 6813.00 127.74

Level-2 2892.47 93.62 4588.60 85.05

Level-1 1430.62 46.5 2402.57 42.34

Percentage of the diaphragms according to Beam Analogy Stress Analysis Methods:

Storeys

Percentage of Lite Walls according to

Beam Analogy and Stress Analysis

Percentage of Shear Walls according to

Beam Analogy and Stress Analysis

Total percentage of

moments (Kip- ft)

Total percentage of

shear forces (Kips)

Total percentage of

moments (Kip- ft)

Total percentage of

shear forces (Kips)

Roof 5.28 2.42 0.63 0.007

Level-3 5.14 0.79 3.22 0.046

Level-2 5.25 2.42 2.78 0.036

Level-1 5.69 2.41 3.11 0.019

The above diaphragms beam analogy and stress analysis’s tables are comparing we got the results are vary with an

acceptable range of 2% to 6% of moments and 0.1% to 2% of shear force. Hence, the diaphragm moment values

between the beam analogy method and stress analysis from ETABS closely match each other.

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V. CONCLUSION Design of diaphragm structures has been always a challenging task for engineers with all the uncertainties, inevitable &

numerous risks involved in it. The design must also satisfy all the necessary boundary conditions of its design aspect &

simultaneously, therefore diaphragms design must be economically feasible.

The diaphragm results vary with an acceptable range and also closely match each other. Hence it can be concluded that

given a precast semi-rigid diaphragm structures of the analysis would be either simplified as a beam analogy or carried

out using a finite element method program based on stress analysis.

REFERENCES [1] Precast/Prestressed Concrete Institution. (2010). “PCI design handbook: precast and prestressed concrete.”

Seventh Edition, Chicago IL.

[2] ACI Committee 318 (2005). Building Code Requirements for Structural Concrete and Commentary,

American Concrete Institute, Farminton Hills, MI.

[3] Cao, L. (2006). “Effective Design of Precast Concrete Diaphragm Connections Subjected to In-Plane

Demands”, Ph.D dissertation, Lehigh University, Bethlehem, PA

[4] IBC (2006). International Building Code, 2006 Edition. International Code Council, Inc., Falls Church, VA.

[5] ASCE/SEI 7-05, Minimum Design Loads for Buildings and Other Structures, 2005 with Supplement 1.

American Society of Civil Engineers, Reston, VA.

[6] Fleischman, R. B., and Farrow, K. T. (2001) “Dynamic Response of Perimeter Lateral-System

Structures with Flexible Diaphragms”, Journal of Earthquake Engineering & Structural Dynamics, V.30,

No. 5, May, pp. 745-763.

[7] Iverson, J.K., Hawkins, N.M. (1994). “Performance of Precast/Prestressed Concrete Building

Structures during Northridge Earthquake.” PCI Journal, 39 (2), 38-55.

[8] Ghosh, S. K., Hawkins, Neil M., "Proposed Revisions to 1997 NEHRP Recommended Provisions for Seismic

Regulations for Precast Concrete Structures: Part 1-Introduction," PCI Journal, Vol. 45, No. 3, May-June 2000.