1. Glass Fiber-Reinforced Polymer/Steel
Hybrid Honeycomb Sandwich Concept
for Bridge Deck Applications
Final Examination
February 1, 2008
Nick Lombardi

2. Outline
 Introduction
 Hybrid Concept Parametric Studies
 Experimental Studies
 Hybrid Concept Analysis, Modeling,
and Design Methods
 Conclusions

3. INTRODUCTION:
KSCI bridge deck panel
face sheet
flute (typ.)
flat (typ.)
T-, 3-, or
out-of-plane,
direction
L-, 1-, or
longitudinal,
direction
W-, 2-, or
transverse,
direction
face sheet
flute (typ.)
flat (typ.)
T-, 3-, or
out-of-plane,
direction
L-, 1-, or
longitudinal,
direction
W-, 2-, or
transverse,
direction
W-, 2-, or
transverse,
direction
T-, 3-, or
out-of-plane,
direction
L-, 1-, or
longitudinal,
direction
flute or curve wall (typ.)
flat (typ.)
W-, 2-, or
transverse,
direction
T-, 3-, or
out-of-plane,
direction
L-, 1-, or
longitudinal,
direction
W-, 2-, or
transverse,
direction
T-, 3-, or
out-of-plane,
direction
L-, 1-, or
longitudinal,
direction
flute or curve wall (typ.)
flat (typ.)
Reinforced-sinusoidal
honeycomb core

4. KSCI core orientation on bridge
L
W
Honeycomb core
orientation
Half of Case Study Bridge
Concrete
Approach
30’- 0”50’- 0”

5. Research motivation
 Wildcat Creek Bridge rehabilitation
 AASHTO span-to-deflection ratio exceeded
EXISTING PROPOSE
D
10

6. Research motivation
 Bridge deck issues
 Uneconomical GFRP core depth
 Build up concrete approach spans
 Face sheet design and economy
CL bridge span 3-span continuous
main span (GFRP)
Approach span
(concrete)

7. Research objectives
1. To increase structural stiffness
2. To provide simplified stiffness
design procedures

8. Research tasks
 Hybrid steel-GFRP parametric studies
 Experimental studies - stiffness
 Small-scale honeycomb core
 Large-scale beams
 Analysis/Design methods
 Strip method hand calc techniques
 3D finite element analyses

9. HYBRID CONCEPT
PARAMETRIC STUDIES
 Steel plate embedded in face sheet
 Steel tube spaced within KSCI core
 Steel plate vs. steel tube
 KSCI L-dir vs. W-dir core beam study
 Steel roof deck honeycomb core
 Steel core vs. steel plate

10. Steel plate study
 Transformed
section
 Cantilever beam
model
 Plate thicknesses
 22 gage - 1/8”
bequiv
(n-1)As/2
dc tflat
tf
unit thickness P
GChSM Ac
E1 If
L
D
Exterior bridge beam

11. Steel tube studies
 ABAQUS FE
 Detailed core model
 (4) face sheet layups
 Original KSCI layup
 Highest E2 modulus
 Highest E2tf stiffness
 Highest G12tf stiffness
Clamped @ exterior
bridge beam
Load patch
L
W
L
W

12. Steel tube vs. Steel plate
1.25
3.25
5.25
7.25
9.25
11.25
13.25
0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26
Maximum deflection, in
As,in2
plate(I)
plate(II)
tube(I), s = 2ft
tube(II), s = 2ft
tube(I), s = 4ft
tube(II), s = 4ft
tube(III), s = 2ft
tube(III), s = 4ft
tube(IV), s = 4ft
tube(IV), s = 2ft
L/300

13. Face sheet stiffness/
Honeycomb core stiffness studies
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
baseline t_face E_face t_core wall E_core wall
Stiffness parameters
Midspandeflection,in
W-dir L-dir
0.845”
0.325”
0.717”
0.284”

14. Steel roof deck honeycomb core:
United Steel and Vulcraft results
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
KSCI UF1X UF2X 1.5A 3N
Honeycomb core type
Midspandeflection,in
W-dir L-dir

15. Steel roof deck honeycomb core:
Vulcraft 1.5A assembled core
L-direction steel core
W-direction steel core

16. Steel core vs. Steel plate
3ft overhang span length
1.75
2.75
3.75
4.75
5.75
6.75
7.75
8.75
9.75
10.75
0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140
Maximum deflection, in
As,in2
1.5A steel deck
steel plate
L/300

17. EXPERIMENTAL STUDY
 Specimen fabrication
 Tension coupon tests
 Honeycomb core equivalent moduli
 Large-scale beam tests

18. Specimen fabrication
 Help KSCI workers – any problems
 KSCI experience with steel core
 KSCI workers’ opinion of steel core
 Personal interest in process

19. Honeycomb core tests
 Obtain equivalent
elastic moduli
 Relevance to
sandwich theory
 In-plane
elastic moduli
 EL and EW
 Out-of-plane
elastic moduli
 ET, GLT, and GWT
l
θ
t h
b
d
L
W
c

20. L-direction equivalent modulus:
Prediction equation - theory
2
6EI
FEM = l
l
δ
 
 ÷
 δl

21. L-direction equivalent modulus:
Test setup - photos

22. L-direction equivalent modulus:
Prediction equation - experimental
2
2EI
FEM = l
l
δ
 
 ÷
 
δl

23. L-direction equivalent modulus:
Prediction equation - experimental
2
2EI W cosθ
FEM=δ =
2
l
l
l
 
 ÷
 
3
W cosθ
δ =
4EI
l
l
W
δ =
EA
h
h
( )
( )L
δ cos θ + δΔL
ε = =
L + sinθ
l h
h l
L
L
L
σ
E =
ε
σL
σL
( )( )LW = σ cos θ×bl

24. L-direction equivalent modulus:
Elastic modulus summary
EL,avg = 1,130 psi (experimental)
( ) ( )
( )
3
-4
L,theory steel steel3
h +sinθt lE = E =1.141×10 E = 3,309 psi
l cosθ
 
  
 ÷  
 
( )( )
( ) ( )( )
3
-5
L,hybrid steel steel3 2 2
t h+lsinθ
E = E =3.78×10 E = 1,096 psi
lcosθ 3l cos θ +ht
 
 
  

25. W-direction equivalent modulus:
Test setup - photos

26. W-direction equivalent modulus:
Elastic modulus summary
( )
( ) ( )( ) ( )
3
-4
W,theory steel steel
2
cosθt
E = E =2.118×10 E = 6,142 psi
l h +sinθ sin θ
l
 
  
 ÷  
  
( )
( ) ( )( ) ( )
3
-4
W,hybrid steel steel
2
cosθ1 t
E = E =1.06×10 E = 3,074 psi
2 l h +sinθ sin θ
l
 
  
 ÷  
  

27. Core L and W direction transverse shear moduli:
Theoretical KSCI and Hybrid shear moduli
GLT (ksi) GWT (ksi)
KSCI 44.2 18.4
Hybrid 498 175
HYBRID unit cell
KSCI unit cell

28. Core L-direction transverse shear moduli:
Test setup
Japanese yoke
Support beam
setup
Load plates
LVDT
(typ.)

29. Core L-direction transverse shear moduli:
Typical core shear strain distribution
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
-150 -100 -50 0 50 100 150
Shear strain, γL'T'/2 (µε)
Verticaldistancefromcenterline(in)
8,000 lb
6,000 lb
4,000 lb
2,000 lb
PARABOLIC

30. Core W-direction transverse shear moduli:
Typical core shear strain distribution
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
-150 -100 -50 0 50 100 150 200
Shear strain, γW'T'/2 (µε)
Verticaldistancefromcenterline(in)
10,000 lb
6,000 lb
8,000 lb
4,000 lb2,000 lb
LINEAR

31. Core L and W direction shear moduli:
Equivalent experimental shear moduli
Beam-1 Beam-2 Beam-3 Average Theory
GLT (ksi) -100.6 -279.1 -191.2 -190 498
GWT (ksi) 69.4 104.7 67.6 80.6 175

32. Core L and W direction shear moduli:
Face sheet thickness dependence
0.0000
0.0625
0.1250
0.1875
0.2500
0.3125
0.3750
0.4375
GLT-1 GLT-2 GLT-3 GWT-1 GWT-2 GWT-3
Shear beam specimen
Facesheetthickness,in
measured required design required-design measured-design

33. EXPERIMENTAL STUDY
 Specimen fabrication
 Tension coupon tests
 Honeycomb core equivalent moduli
 Large-scale beam tests

34. Hybrid L-direction large-scale beams:
Test setup

35. Hybrid L-direction large-scale beams:
Test setup - photos

36. Hybrid W-direction large-scale beams:
Test specimens: core orientation
span direction
"stiffener" along span
(typ.)

37. Hybrid W-direction large-scale beams:
Test setup - photos

38. HYBRID CONCEPT
ANALYSIS, MODELING, & DESIGN
 KSCI vs. Hybrid large-scale beam
equivalent modulus comparison
 Analysis methods
 Two-way vs. One-way bending
 Design example
 Demonstrate analysis/design methods

39. KSCI and Hybrid Equivalent
Experimental Flexural Modulus
( )( )
transformed transformed transformed
PL D
Mc PLD4 2σ = = =
I I 8I
Bending strains, εavg, taken from average of midspan uniaxial gages
Equivalent
Core D
Eface
Ecore
dc
bf
tf
n(bc)transformed
section
core
face
E
n =
E

40. L-direction beam σ-ε summary
Equivalent modulus comparison
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
0 500 1,000 1,500 2,000 2,500 3,000 3,500
Avg midspan strain, µε
Mc/Itransform,psi
Hybrid beam-1
2,111 ksi
Hybrid beam-2
2,051 ksi
KSCI baseline beam
1,459 ksi
Prediction
2,001 ksi

41. W-direction beam σ-ε summary
Equivalent modulus comparison
0
500
1,000
1,500
2,000
2,500
3,000
0 500 1,000 1,500 2,000 2,500
Avg midspan strain, µε
Mc/Itransform,psi
Hybrid beam-1
2,408 ksi
Hybrid beam-2
1,965 ksi
KSCI baseline beam
2,128 ksi
Hybrid Prediction
2,001 ksi
KSCI original design
1,324 ksi

42. KSCI and Hybrid Equivalent
Experimental Core τ-γ Summary
( ) transf
transf transf
transf core transf core transf core
P QVQ PQ2τ = = =
I b I b 2I b
Core shear strains, γavg, taken from average of core centerline
rosettes on each side of beam
face
core
E
n =
E
D
Equivalent
Core
Eface
Ecore
transformed
section
n(bf)
dc
tf
bc

43. L-direction beam τ-γ summary
Honeycomb core comparison
0
10
20
30
40
50
60
70
0 100 200 300 400 500
Avg max core shear strain, µε
VQtransf/Itransfbcore,psi
Hybrid beam-2
481.9 ksi Hybrid beam-1
360.9 ksi
KSCI baseline beam
141.3 ksi

44. W-direction beam τ-γ summary
Honeycomb core comparison
0
5
10
15
20
25
30
35
40
0 100 200 300 400 500
Avg max core shear strain, µε
VQtransf/Itransfbcore,psi
Hybrid beam-2
383.1 ksi
Hybrid beam-1
335.0 ksi
KSCI baseline beam
78.4 ksi

45. Analysis methods
 Detailed core finite element models
 Homogenized core finite element
models
 Hand calculation methods
 (EI)face/core + (GA)core
 (EI)face + (GA)core
 (EI)face
homogenizationhomogenization

46. Honeycomb core FE models vs.
Experimental results
1,850
1,900
1,950
2,000
2,050
2,100
2,150
2,200
L-direction W-direction
Honeycomb core span orientation
Equivalentflexuralmodulus,ksi
Detailed FE Homogenized FE Experiment (avg)
< 2% difference < 10% difference

47. Hand calculation methods vs.
Experimental results
0.0
0.5
1.0
1.5
2.0
2.5
3.0
L-direction W-direction
Honeycomb core span orientation
Normalizedstiffness,(kips/in)/in
EI_f,c+AG_c EI_f+AG_c EI_f Experiment (avg)

48. Two-way vs. One-way bending
 Effective width determination
 Based on finite element models
 Strip method vs. Finite elements
 Maximum overhang deflection analysis
 Simply supported beam with overhang
 Strip method – one-way bending
 Finite elements – two-way bending

49. Strip method vs. FE analysis
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
24 in 36 in 48 in 60 in
Overhang span length, LOH
Maximumoverhangtipdeflection,in
Strip method (EI+AG) Strip method (EI) FEA
UNCONSERVATIVE!!!

50. CONCLUSIONS:
Summary of work
 Small-scale
 Steel hexagonal honeycomb core
equivalent orthotropic elastic moduli tests
 Stiffness design equations
 Large-scale tests
 Hybrid and KSCI test beams
 KSCI vs. Hybrid equivalent flexural and
shear stiffness comparisons

51. CONCLUSIONS:
Summary of work
 Solid equivalent core modeling
 2D strip method modeling
 3D FE modeling

52. CONCLUSIONS:
Main conclusions/results
 Replacement of KSCI GFRP core with
steel core
 Elastic characterization of steel
honeycomb core
 Steel core significantly reduces shear
deformations
 Overall increase in stiffness relative to
KSCI GFRP core

53. CONCLUSIONS:
Main conclusions/results
 Maintain light-weight honeycomb core
 17.6 pcf (hybrid) vs. 14.2 pcf (KSCI)
 2D strip method
 Conservative: One-way bending
 Unconservative: Two-way bending
 3D FE modeling necessary
 Two-way bending – shorter overhangs

54. Future work
 Address manufacturing techniques
 Mechanize steel core construction
 Improve face sheet-to-honeycomb
core interface connection
 Strength characterization of new
hybrid GFRP-steel sandwich bridge
deck
 Experimentally and theoretically

55. QUESTIONS???

56. INTRODUCTION:
KSCI core unit cell/face sheet layup
(1) 3oz/ft2 ChSM ply
(7) biaxial plies
(2) 3oz/ft2 ChSM plies
(bonding layer to honeycomb)
(1) 3oz/ft2 ChSM ply
(7) biaxial plies
(2) 3oz/ft2 ChSM plies
(bonding layer to honeycomb)
b
h
h
s
t
t t/2
x
y

57. INTRODUCTION:
KSCI core orientation on bridge
stringer centerline (typ.)
steel tube
(typ.)
honeycomb core
orientation

58. Face sheet stiffness/
Honeycomb core stiffness studies
L-direction core beam
W-direction core beam

59. Tension coupon tests
 Constituent elastic moduli
 Five different samples
 Vulcraft steel decking
 3 oz/ft2
chopped strand mat
 Face sheet layup
 Biaxial plies
 Face sheet with embedded strain gage

60. Core W-direction transverse shear moduli:
Test setup
Japanese yoke
LVDT
(typ.)
Support beam
setup
Load plates

61. Effective width calculation
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Node across width
S11,ksi
S11node,max
( )
,max
11
11
trib node
eff
node
S b
b
S
Σ ×
=

62. Effective width:
Varying overhang spans
y = -0.0275x
2
+ 3.4865x - 24.287
0
10
20
30
40
50
60
70
80
90
100
18 24 30 36 42 48 54 60 66
Overhang span length, LOH (in)
Effectivewidth,beff(in)
beff = -0.0275LOH
2
+ 3.4865LOH - 24.287

63. Design example:
Strip method
 Wildcat Creek Bridge: Lafayette, IN
 Bridge widening
 Stringer spacing same
 5’-7”
 Overhang increased
 2’-9” to 3’-2”: strip method conservative
 Design GFRP-steel hybrid decking for
stiffness using AASHTO specs

64. Design example:
Overhang span design
Model as simply supported beam with an overhang:
P P
L x
a b y
10"
P
(kips)
Ef
(ksi)
tf
(in)
a
(in)
b
(in)
y
(in)
x
(in)
L
(in)
21 2,001 0.625 23 44 38 28 67

65. Design example:
Overhang span design
2
= -0.0275 + 3.4865 - 24.287 = 68.5 ineffb y y
( )
( )
23
2
2.787 21.41 0.625
6 2
eff f c feff f
f c
b t d tb t
I d
+
= + = + +
Compute effective width, beff:
Compute face sheet moment of inertia and equivalent core area in
terms of the core depth design variable, dc:
68.5c eff c cA b d d= =

66. Design example:
Overhang span design
4
2,770 infI =
( )
( )
( )
( )
2
300 6 3
overhang
f f
y Paby Px
L a L x
EI L EI
∆ = = + + +
( )
2
2,770 2.787 21.41 0.625cd= + +
The deflection at the overhang tip due to applied loads is set equal
to the AASHTO recommended span-deflection ratio:
Substitute all defined variables and solve for If:
Set required If equal to expression for If in terms of dc and solve:
10.75 incd ≥

67. Design example:
Stringer span design
Model as simply supported beam between stringers:
P
L
Use all previously
defined variables from
overhang design.
Equivalent L-dir core
shear modulus:
GLT = Gc = 498 ksi

68. Design example:
Stringer span design
( ) ( )
3
6
800 48 5 4
stringer
f c
L PL PL
EI AG
 
∆ = = +  ÷
 
3 2
1.793 1.976 65.16 0.1379 0c c cd d d+ − − =
The midspan deflection (bending and shear) due to applied loads is
set equal to the AASHTO recommended span-deflection ratio:
Substitute all known variables and expressions, and solve for the
design core depth, dc:
5.5 incd ≥
Therefore the overhang design governs and the minimum core
depth must be 10.75in to satisfy AASHTO span-deflection limits.

69. Design example verification:
Homogenized core FE model
-5
L 1 steelE = E = 3.802×10 E
-4
W 2 steelE = E = 1.059×10 E
-2
T 3 steelE = E = 2.432×10 E
-2
LT 13 steelG = G = 4.465×10 G
-2
WT 23 steelG = G = 1.567×10 G
-6
LW 12G = G = 10 ksi (assumed)
LW 12 steelν = ν = 2.447 ν
-3
LT 13 steelν = ν = 1.564×10 ν
-3
WT 23 steelν = ν = 4.355×10 ν
E1
(ksi)
E2
(ksi)
E3
(ksi)
G12
(ksi)
G13
(ksi)
G23
(ksi)
ν12
ν13
(x10-4
)
ν23
(x10-3
)
1.10 3.07 705 10-6
498 175 0.59 4.69 1.31

70. Design example verification:
Homogenized core FE model
L 38 in
= = 0.127 in
300 300
∆FEM = 0.085 in OK