web shear buckling bearing strength · • box beams tested at the civil engineering structures lab...

Casey Briscoe, Susan Mantell, Jane Davidson Department of Mechanical Engineering, University of Minnesota

Prototype Testing

•  Box beams tested at the Civil Engineering Structures Lab

•  Experimental validation of the interaction between structure and foam

•  Web shear buckling •  Bearing failure

Prototypes

•  Four-point bending test •  Examined shear buckling and postbuckling

behavior of the webs •  Good agreement between predicted and

observed buckling strength

Shear Buckling Test •  Shear buckling failure mode:

•  Core shear failure mode:

•  Bearing failure mode:

Bearing Failure Test

•  Three-point bending test (end one-flange loading condition)

•  Good agreement between model and results •  AISI demonstrates superposition of web

and foam strength •  Analytical model works with

•  Up to 3 day erection time requiring skilled labor

•  Loose fill insulation has gaps and thermal bridges

•  On-site construction waste

•  Off-site manufacture and ½ day field installation

•  Open attic space •  Reduced construction waste •  Possible energy savings up to 35%

A Better Performing Roof The objective of this study is to develop a one-piece modular roof panel system that is manufactured in a continuous process and provides a more energy efficient building envelope.

Panel Concepts

Truss Core Panel Web Core Panel

Two panel concepts were investigated:

•  Metal structural component •  Insulating component fully

separated from structural •  Insulation is attached to

interior or exterior surface

•  Structural and thermal components are integrated

•  Can partially separate the insulating component to use less foam

Sponsored By: U.S. Department of Energy

Face Sheet Buckling

Panel Deflection

Web Shear Buckling

Web Core Failure Modes

Core Shear Failure

Bearing Failure •  Balance between structural and thermal requirements

•  Foam core material used in novel way to strengthen sheet metal components

•  New structural models developed

•  Snow/wind (live) loads •  Self weight (dead) loads •  Sustained/cyclic loading

•  Insulating R-Value •  Thermal bridging due to webs •  Temperatures up to 80°C at

exterior surface

Roof Panel Requirements Structural Thermal

Integration between Structural and Thermal Functions

Web Core Panels

Bearing Strength

•  Plastic collapse mechanism (Roberts and Newark, 1997):

Analytical Model Semi-Empirical Model (AISI)

•  Bearing failure involves deformation/crushing of foam

•  Foam strength superimposed with web strength

•  Factor FC accounts for variability in bearing test data

•  Based on unified web crippling model used in prescriptive steel design codes (AISI)

•  Factors CR, Cc, and Ch are functions of web geometry and construction

•  Effect of foam crushing strength accounted for using superposition

•  Matches current design practice

Panel Designs •  Failure mode map (feasible

designs shaded):

•  Most designs limited by thermal requirement and shear buckling

•  Can separate design process into two steps: •  Design web geometry

(thermal/shear buckling) •  Design face sheets

(deflection/face buckling)

•  Minimum weight designs developed •  Four panel types compared:

•  Truss core panels •  Web core panels with carbon steel

webs •  Web core panels with stainless

steel webs •  Web core panels with exterior foam

layer (separated) •  Southern US: low loads and R-value •  Northern US: high loads and R-value

Southern US: q = 1576 N/m2, R = 5.3 m2-K/W Depth (mm) Weight (N/m2)

Truss Core 272 265 (Carbon) Web Core 284 205 (SS) Web Core 275 206 Separated Web Core 280 203

Northern US: q = 3537 N/m2, R = 6.8 m2-K/W Depth (mm) Weight (N/m2)

Truss Core 359 354 (Carbon) Web Core ---- ---- (SS) Web Core 400 283 Separated Web Core 400 407

Web Shear Buckling Plate on Pasternak Elastic Foundation

Buckling Solutions

Foundation Modeling

•  Relate the foundation constants KW and KP to foundation material properties

•  Model validated using finite element analysis

•  Pasternak model applicable to deep foundations with high shear stiffness

Application to Panels

•  Buckling mode shapes:

•  Buckling coefficient vs. web spacing:

•  Wider web spacing increases the effect of the face sheets

•  Plate buckling model •  Foam modeled as a Pasternak foundation

•  Buckling coefficient χ determined analytically using energy methods

•  Finite element model:

•  Buckling coefficient vs. web slenderness:

•  Analytical model under-predicts buckling strength by 11–21%

•  Face sheets provide added rotational resistance to webs

•  Buckling coefficient: •  Buckling mode shapes: