Aluminum Beams with Composite Thermal Barriers: Recent Developments in Analysis (Part 1) †
Abstract
:1. Introduction
2. Two Symmetric Concentrated Loads
2.1. Summary of Governing Equations
2.2. New Loading Type (Two Equal Concentrated Loads, Symmetrical)
3. Overhang Study Using FEA
3.1. Analyses
3.2. Comments
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
Notation | |
A | shear area of aluminum “web”; |
Ac | cross-sectional area of core; |
a1, a2 | area of Face 1 and 2, respectively; |
b | =Ac/Dc = average core width; |
c | =Gp/(EIo); |
c11, c22 | distance between face centroid and air-side surface of Faces 1 and 2, respectively; |
D | distance between centroids of facing sections; |
Dc | core depth (maximum); |
E | Young’s modulus of aluminum faces; |
Gce | effective shear modulus of installed core material; |
Gp | =IbD2Gce/(IcDc); |
I | moment of inertia of composite cross-section (no core or face shear effects) = Io + Ic; |
Ic | =a1a2D2/(a1 + a2); |
Ie | effective moment of inertia, including core shear effects; |
I’e | effective moment of inertia, including core and faces’ shear effects; |
Io | =Io1 + Io2; |
Io1, Io2 | moments of inertia of Faces 1 and 2, respectively; |
L | span length; |
M | bending moment at distance x from left support; |
V | shear at distance x from left support; |
x | coordinate, starting at the left end of the beam. |
References
- LaBelle, J. Structural Behavior of Aluminum/Elastomer Sandwich Beams. Ph.D. Thesis, University of Wisconsin-Milwaukee, Milwaukee, WI, USA, 1990. [Google Scholar]
- LaBelle, J.; Davies, M. Structural Design Method for Composite Aluminum/Elastomer Beams. In Structural Performance of Composite Thermal Barrier Framing Systems; AAMA TIR-A8-16; American Architectural Manufacturers Association (AAMA, now FGIA): Schaumburg, IL, USA, 2016; pp. 33–61. [Google Scholar]
- Hartsock, J.A.; Chong, K.P. Analysis of Sandwich Panels with Formed Faces. J. Struct. Div. 1976, 102, 803–819. [Google Scholar] [CrossRef]
- Huang, S. Investigation of Composite Façade Mullions. Ph.D. Thesis, University of Technology Sydney, Sydney, Australia, 2014. Available online: https://opus.lib.uts.edu.au/handle/10453/29258 (accessed on 21 April 2023).
- Davies, M.; (Scotland, UK). Personal communication, 2000.
- Wolf, K. TB-FEM. Engineering Software Utilizing a Special-Purpose Finite Element for Sandwich Beams (with User’s Guide). 1996; Unpublished work. [Google Scholar]
Constant | (a ≤ x ≤ L − a) | Constant | (0 ≤ x ≤ a) |
---|---|---|---|
D0 | E0 | 0 | |
D1 | E1 | ||
D2 | E2 | 0 | |
D3 | 0 | E3 | |
D4 | 0 | E4 | 0 |
Load Type | Complementary Constants * ** | |
---|---|---|
Two equal concentrated loads, symmetrical (a ≤ x ≤ L − a) | F1 | F2 |
Two equal concentrated loads, symmetrical (0 ≤ x ≤ a) | G1 | G2 |
Load Type | B | S | P* |
---|---|---|---|
Two equal concentrated loads, symmetrical; (k = a/L) |
Load Type | Max. M | M | Domain |
---|---|---|---|
Two equal concentrated loads, symmetrical (k = a/L) | Pa | Pa | a ≤ x ≤ L − a |
Px | 0 ≤ x ≤ a |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
LaBelle, J. Aluminum Beams with Composite Thermal Barriers: Recent Developments in Analysis (Part 1). Eng. Proc. 2023, 43, 33. https://doi.org/10.3390/engproc2023043033
LaBelle J. Aluminum Beams with Composite Thermal Barriers: Recent Developments in Analysis (Part 1). Engineering Proceedings. 2023; 43(1):33. https://doi.org/10.3390/engproc2023043033
Chicago/Turabian StyleLaBelle, James. 2023. "Aluminum Beams with Composite Thermal Barriers: Recent Developments in Analysis (Part 1)" Engineering Proceedings 43, no. 1: 33. https://doi.org/10.3390/engproc2023043033