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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.
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 133
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
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 134
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,
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 135
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
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 136
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
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 137
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
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 138
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:
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 139
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.
Arjun et al., International Journal of Emerging Research in Management &Technology
ISSN: 2278-9359 (Volume-5, Issue-5)
© 2016, IJERMT All Rights Reserved Page | 140
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.