MT-1620 al.2002 Unit 18 Other lssues In Buckling/structural Instability Readings. Rivello 143,14.5,146,14.7( (read these at least, others at your leisure") Ch.15.Ch.16 Timoshenko Theory of Elastic Stability Jones Mechanics of Composite Materials. Ch. 5 Paul A Lagace, Ph. D Professor of aeronautics Astronautics and Engineering Systems Paul A Lagace @2001
MIT - 16.20 Fall, 2002 Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your “leisure”) Ch. 15, Ch. 16 Theory of Elastic Stability Mechanics of Composite Materials, Ch. 5 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems Paul A. Lagace © 2001
MT-1620 al.2002 Have dealt, thus far, with perfect columns, loading eccentricities, and beam-columns. There are, however, many more issues in buckling/(static) structural instability, most of which will try to touch on a) Buckling versus Fracture Have looked at columns that are long enough such that they buckle However, it is possible that the material compressive ultimate stress may be reached before the static instability occurs Consider short/'squat column(saw in Unified) Figure 18.1 Representation of short column under compressive load Paul A Lagace @2001 Unit 18-2
MIT - 16.20 Fall, 2002 Have dealt, thus far, with perfect columns, loading eccentricities, and beam-columns. There are, however, many more issues in buckling/(static) structural instability, most of which will try to touch on. (a) Buckling versus Fracture Have looked at columns that are long enough such that they buckle. However, it is possible that the material compressive ultimate stress may be reached before the static instability occurs. Consider short/”squat” column (saw in Unified) Figure 18.1 Representation of short column under compressive load Paul A. Lagace © 2001 Unit 18 - 2
MT-1620 al.2002 丁 If o=compressive ultimate before P=Par, then failure occurs by material failure in compression squashing Using the slenderness ratio" previously defined E Where. define a column by its slenderness ratio and can plot the behavior and failure mode of various columns Paul A Lagace @2001 Unit 18-3
MIT - 16.20 Fall, 2002 P σ = A If σ = σcompressive ultimate before P = Pcr, then failure occurs by material failure in compression “squashing” Using the “slenderness ratio” previously defined: P π2 cr E σ cr = = ′ ρ 2 A (l ) where: l l′ = c “define” a column by its slenderness ratio and can plot the behavior and “failure mode” of various columns… Paul A. Lagace © 2001 Unit 18 - 3
MT-1620 al.2002 Figure 18.2 Summary plot showing general behavior of columns based on stress level versus slenderness ratio Euler curve ED-compressive yield actual I Transition behavior Regions of values depend on E and o What happens in the transition region? Paul A Lagace @2001 Unit 18-4
σ MIT - 16.20 Fall, 2002 Figure 18.2 Summary plot showing general behavior of columns based on stress level versus slenderness ratio actual behavior Euler curve compressive yield Regions of values depend on E and σcu What happens in the transition region? Paul A. Lagace © 2001 Unit 18 - 4
MT-1620 al.2002 (b Progressive Yielding Figure 108.3 Typical stress-strain plot for a ductile metal (in compression e As the column is loaded there is some deflection due to slight mperfections this means the highest load is at the outer part of the beam-column Paul A Lagace @2001 Unit 18-5
MIT - 16.20 Fall, 2002 (b) Progressive Yielding Figure 18.3 Typical stress-strain plot for a ductile metal (in compression) As the column is loaded, there is some deflection due to slight imperfections. This means the highest load is at the outer part of the beam-column. Paul A. Lagace © 2001 Unit 18 - 5