Accurate Long-Term Deflection Predictions for Concrete Structures By Jonathan Hirsch, P.E.
B entl ntley S ys tems , Inc.
SE University January 2012
www.LearnWithSEU.com www.LearnWithSEU.com
Key Objectives
How different are the results from commonly used deflection calculation techniques?
What are 4-5 key parameters that influence deflection calculations?
What is a reasonable expectation of accuracy for deflection calculations and how can they be applied in design practice?
2
Deflection Predictions in Concrete
How accurate is accurate?
Deflection prediction methods
Comparison between calculated and measured results
Design recommendations
3
What is Accurate?
Poll
4
Factors Affecting Deflections
Material Properties
Cracking and Tension Stiffening
Creep
Shrinkage
Externally restrained
Internally restrained
Load History
Redistribution of Forces 5
Tension stiffening Uncracked response
P , d a o L
3 Cracked response (no tension in concrete)
4 1
2 Assumed unloading response
0
Curvature, Ф
6
Shrinkage Warping
7
Linear Elastic Deflection Theory y f ( x) deflection y ' f ' ( x) slope y ' ' f ' ' ( x)
M EI V
y ' ' ' f ' ' ' ( x)
4
5wl
384 EI
EI w
y ' ' ' ' f ' ' ' ' ( x)
EI 8
Deflection Prediction Methods
“Deemed to Comply” rules
Deflection multipliers
Spreadsheets using load distribution factors
2-D frame programs
3-D finite element programs
9
Deemed to Comply
ACI 318 9.5.2.1
Quick and easy to apply
Very crude due to failure to explicitly consider:
Concrete properties
Cracking characteristics
Load History
Creep
Shrinkage
10
Deflection Multipliers
ACI 318 9.5.2.5
Requires good calculation of initial elastic deflections
Doesn’t explicitly consider important factors:
Shrinkage
Relationship between creep curvature and creep deflections
11
Spreadsheets Using Factors
Scanlon, A. and Suprentant, B.A., 2011, “Estimating Two Way Slab Deflections”, Concrete International,V. 33, No. 7, pp 29-34
Easy and quick to use
Conservative estimate of cracking through Ieff assumption
Good accounting of load history and material properties
Assumed factors used for load distribution Deflection multipliers for creep (and shrinkage) 12
Spreadsheets Using Factors
13
2-D Frames
Linear elastic analysis of frames I for cracking/tension stiffening, difficult to apply for column/middle strip
eff
Long-term effects using deflection multipliers
Calculate long-term curvatures and use geometrical methods to calculate deflections
Equivalent frame for 2-way slabs
Summing of strip results necessary
14
3-D Finite Element Analysis
Linear Elastic Analysis with Stiffness Modifiers
Using a number of tension stiffening models
Creep and shrinkage strains tracked and superimposed
Redistribution of loads
Rigorous analysis of internally restrained shrinkage
Treatment of externally restrained shrinkage
Nonlinear Analysis
Computationally expensive 15
3-D Finite Element Analysis
Use ageing coefficient for gradually induced strains
16
3-D Finite Element Analysis (t , t 0 )
E c (t 0 )
t
1
(t , t ) E ( ) 0
t 0
c
d ( ) d
1 (t , ) d
(t , t 0 )
1
(t , t 0 )
t 0
0.8
1.8 t 0 17
0.8
3-D Finite Element Analysis
Cross section calculations
Select material stress strain curves
Select tension stiffening model
Select creep and shrinkage models
18
3-D Finite Element Analysis
Perform a linear elastic global analysis and integrate cross section forces
Perform detailed nonlinear long-term curvature calculations on each cross section
Using the resulting axial strains and curvatures, adjust the element stiffnesses
Iterate until the solution converges
Repeat for each load history step, breaking each into instantaneous and sustained component 19
3-D Finite Element Analysis
20
Deflection Prediction Methods Calculation Method
Cracking/ Tension Stiffening
Creep Shrinkage Shrinkage – Internal – External Restraint Restraint
Load History
Load Redistribut ion
Deemed to comply Deflection Multipliers Spreadsheet with factors 2D frames Multipliers 2D frames – X-section 3D finite element
21
Deflection Calculation Comparison
Method 1 – 2D equivalent frames (ACI approach)
Method 2 – spreadsheet using factors
Method 3 – 3D finite element analysis
22
Test Slabs
University of New South Wales (Guo and Gilbert 2002)
215 West Washington Street
Aqua
23
University of New South Wales
24
University of New South Wales
25
University of New South Wales
26
215 West Washington Street
27
215 West Washington Street
28
Aqua
29
Aqua
30
Slab S6
31
Slab S6
Characteristics of this test: •No restraint due to rollers at the column base •No column cracking 3-D Element predicted deflectionsunderestimated very well – no external 2-D Finite Equivalent Frames significantly Spreadsheet •Loads near predicted cracking deflections loads very well restraint was slab modeled deflections due to under prediction of cracking •Slab cracks propagated over time 32
Slab S7
33
Slab S7
Characteristics of this test: •Same 3-D Finite slab Element load as (with S6 external shrinkage restraint •Restrained 2-D modeled) Spreadsheet Equivalent underestimated column overestimated Frames base significantly deflections, deflections, underestimated to to a reasonable a reasonable •Similar deflections degree degree finaldue slab tocrack underpattern prediction to S6 of cracking 34
Slab S4
35
Slab S4
Characteristics of this test: •Slab loading far in excess of cracking load and sustained •Restrained column base •Heavy slab cracking which propagated over time •Extensive column cracking 2-D Equivalent Frames significantly underestimated •Heavier reinforcement than S6/S7 deflections 3-D Finite Element due to under predictions prediction wereof excellent cracking Spreadsheet significantly overestimated deflections 36
Slab S5
37
Slab S5
Characteristics of this test: •Slab loading far in excess of cracking load and removed •Restrained 3-D Finite Element column predictions base (without considering external •Heavy 2-D restraint) Equivalent slab were cracking Frames overestimated which significantly propagated to a reasonable underestimated over time degree. Effects Spreadsheet overestimated deflections to a reasonable •Same deflections of external reinforcement due restraint to under to as shrinkage S4 predictionwere of cracking overestimated degree 38
Slab S3
39
Slab S3
Characteristics of this test: •Slab loading overestimated Spreadsheet similar to S6/S7 early sustained, sustained then deflections, reduced but •Restrained 2-D also 3-D Finite Equivalent overestimated Element column Frames predictions elastic base significantly and were creep underestimated reasonable, recovery, giving but elastic •Same deflections reasonable and creep reinforcement recovery final due to results under were as S4/S5 prediction overestimated of cracking 40
215 West Washington Street
41
Aqua
• •
3D finite element (method 3) underestimated short term deflections, withsignificantly improvements with 2D Spreadsheet Equivalent (method frames 2)significant significantly underestimated overestimated small offsets in time deflections
42
Performance Comparison
2D equivalent frames (method 1) significantly underestimated deflections in all cases
Spreadsheet (method 2) overestimated deflections in all cases, dependent upon the actual levels of cracking
3D finite elements (method 3) predicted most of the test slabs reasonably with external shrinkage restraint adjustment, underestimated real world slabs 43
Design Recommendations
Maintain realistic expectations
Use spreadsheet method instead of span/depth ratios
Never use full frame sections for determining cracking and effective moments of inertia
44
Design Recommendations
Be conservative with cracking
Consider load history
Consider using larger deflection multipliers for creep and shrinkage
45
Pending ACI Publication
“Practical Deflection Prediction of Concrete Slabs”
Jonathan Hirsch, Bentley Systems Inc.
Flora Calabrese, Wiss, Janney, Elstner Associates, Inc.
Eamonn Connolly, James McHugh Construction Co.
Allan Bommer, Bentley Systems, Inc.
46
