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Design of Lightweight Web Core Sandwich Panels and Application
to Residential Roofs
Casey R. Briscoe April 27, 2010
Roof Panel Requirements Structural requirements
Long unsupported spans Transverse distributed loads
Thermal insulating requirements Durability considerations
3
Limits of Foam Core Panel Design Minimum panel depth vs. panel length:
Foam core panels limited to short spans Webs allow the design of longer panels with reduced depth
4
Foam Core Panel Web Core Panel
Web Core Panel Limit States
6
Face Sheet Buckling
Web Shear Buckling
Web Flexural Buckling
Panel Deflection
Thermal R-Value Core Shear Failure Bearing Stress Failure
Buckling of the Face Sheet into the Webs
Te
Ti
kw kc
Te
Ti
Rw Rc
Web Shear Buckling
7
Model as plate on Pasternak foundation
Analysis in three steps 1. Plate buckling model 2. Foundation model 3. Application to panels
q
x
y x
Panel Loading:
Buckled Web:
a b
y x
b
a
Plate Buckling Model Minimum potential energy
Assume deflection function
Obtain set of equations of the form
Solve for χ
8
fP fW
x
z
Plate:
Foundation:
x
y a
b ss
ss ss ss
τ
Plate Buckling Model Solutions Buckling Mode Shapes: Solutions for χ:
9
Foundation increases buckling strength significantly
Elastic Foundation Model
10
Panel Cross Section
Symmetry
Web p
b p/2
b
Foam dissipates the deformation caused by web buckling:
Shallow foundation (closely-spaced webs)
Deep foundation (widely-spaced webs)
Symmetry (fixed base)
Elastic Foundation Model
11
Infinitely deep foundation Exponential decay
Determine foundation constants using energy methods
Applicable for deep foundations
Validated using FEA
Model valid for
Elastic Foundation Model: Range of Applicability
12
Close web spacing
Wide web spacing
Panel designs
Shear Buckling: Application to Panels
13
Finite Element Model:
Symmetry
x z
y
p
a/2
q (uniform over entire surface)
Uy = 0 on x = 0
Buckling load Buckling coefficient , compare to
Shear Buckling FE Results
14
Buckling Coefficients: Buckling Mode Shapes:
Face sheets provide rotational restraint Buckling strength predictions conservative (10–20%) Reasonable agreement for design
Web Core Roof Panel Design Loads and R-value
requirement climate dependent
Three representative cases Designs determined by a
subset of limit states Web shear buckling Face sheet buckling Panel Deflection Thermal performance
15
Example: Load 1576 N/m2 R-value 5.3 m2-K/W Assume 2.0 mm face sheets and 1.2 m web spacing
Feasible designs shaded
Minimum depth design Depth to meet structural requirements: 176 mm Depth to meet structural and thermal requirements: 282 mm Using stainless steel webs: 190 mm
Effect of Limit States on Design
16
Limits of Foam Core Panel Design Minimum panel depth vs. panel length:
Webs allow the design of longer panels with reduced depth Thermal requirement important for design
17
Foam Core Panel Web Core Panel
Conclusions Structural and thermal requirements must be considered
for roof panel design Use webs to reduce the impact of foam creep on performance Thin, widely-spaced webs to minimize impact on thermal
insulating performance
Foam has a major impact on local failure modes Modeled successfully as an elastic foundation Order of magnitude increase in local buckling strength
Web core panels are a viable design option for roofs
18
Bearing Stress Failure Plastic failure mechanism
Web crippling Core crushing Assume effects independent
Factors affecting strength include: Load/geometric imperfections Stress concentrations/residual
stresses Support location (end vs.
interior)
22
θ hD hD
c LD
Yield line
Plastic Hinge
Bearing Strength Models
Yield line mechanism solution Strength contributions:
Based on unified empirical web crippling equation
Simplified core crushing term
23
Mechanism Solution: Modified AISI Equation:
Web crippling strength
Foam failure Foam failure
Web crippling strength
Models predict ≈80% of strength is from foam crushing
≈0
Bearing Strength Validation
24
Prototype Test Results: Model Comparison:
Core crushing strength insensitive to web imperfections Reduced variability in strength compared to webs with no foam May allow smaller safety factors compared to current practice
Roberts model and data
UMN model and data
Bearing Stress Models
26
Analytical vs. Semi-Empirical: Contribution from Foam:
Analytical web crippling strength prediction higher than semi-empirical Semi-empirical model predicts larger contribution from core crushing Both models predict ≈80% of strength is from core crushing
Design Comparison Compare designs based on
material cost Stainless steel webs Two-layer (carbon steel webs) Truss core panels
Web core panels lighter weight and comparable or lower panel depth than truss core
Truss core panels allow lowest cost 60–90% of web core material
cost is due to foam Truss core panels use almost
50% less foam than web core
27
Flexural Web Buckling
Buckling Mode Shapes: Solutions for χ:
28
Model core as elastic foundation (same as shear buckling) Determine χ using minimum potential energy Shear buckling strength always lower than flexural buckling strength
Tradeoff between Depth and Weight
29
Stainless steel webs
Particularly significant with stainless steel webs Minimum weight preferred for design
166 N/m2
88 mm