Design of Lightweight Web Core Sandwich Panels and Application

to Residential Roofs

Casey R. Briscoe April 27, 2010

Roof Panel Concept

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Conventional Construction: Panelized Construction:

Roof Panel Requirements   Structural requirements

  Long unsupported spans   Transverse distributed loads

  Thermal insulating requirements   Durability considerations

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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

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Foam Core Panel Web Core Panel

Web Core Panel Limit States

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Panel Deflection

Thermal R-Value Te

Ti

kw kc

Te

Ti

Rw Rc

Web Core Panel Limit States

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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

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  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

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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:

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  Foundation increases buckling strength significantly

Elastic Foundation Model

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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

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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

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Close web spacing

Wide web spacing

Panel designs

Shear Buckling: Application to Panels

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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

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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

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  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

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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

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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

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Shear Buckling Prototype Test

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Shear Buckling Prototype Test

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Load-Deflection Behavior: Buckling Mode:

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)

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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

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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

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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

Shear Buckling FE validation

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 χ  vs.  a/hc:  χ  vs.  p/a:

Bearing Stress Models

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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

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Flexural Web Buckling

Buckling Mode Shapes: Solutions for χ:

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  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

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Stainless steel webs

  Particularly significant with stainless steel webs   Minimum weight preferred for design

166 N/m2

88 mm

Minimum Weight Designs

Panel Depth (mm) Panel Weight (N/m2)

Carbon Steel Webs

Climate I 285 205

Climate II 379 243

Climate III ---- ----

Stainless Steel Webs

Climate I 270 204

Climate II 324 223

Climate III 398 263

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