![Quasielastic Method
Schapery (1965)
Vinogradov (1987)
Kang (2001)
Remove Eccentricity from Kang’s Analysis
λ tn
δ = Ai (3) ψ (t ) = (4)
1− λ β
λ [1 +ψ (t )]
δ (t ) = Ai (5)
1 − λ [1 +ψ (t )]](https://image.slidesharecdn.com/ebennettpresentation-12552016777207-phpapp02/85/Thesis-Presentation-11-320.jpg)
![Findley’s Power Law
1
10 PG-90-R
ε (t ) = ε 0 + mt n (6)
0.1
1
d (mm)
m
d (in)
0.01
n
δ (t ) = δ 0 + mt n
0.1
(7)
0.001
0.01
0.0001
1 10 100 1000 10000
Time (hours)
log[δ (t ) − δ 0 ] = log(m ) + n log(t ) (8)](https://image.slidesharecdn.com/ebennettpresentation-12552016777207-phpapp02/85/Thesis-Presentation-14-320.jpg)
Thesis Presentation
- 1. Influence of Creep on the Stability of Pultruded E-Glass / Polyester Composite Columns at Elevated Service Temperatures By: Evan A. Bennett Advisor: David W. Scott, Ph. D.
- 2. FRP in Civil Engineering FRP Components in Civil Engineering No Reliable Design Criteria Long-Term Behavior Elevated Temperatures Goals of the Current Work Expand on Previous Creep Studies on FRP Components Develop Semi-empirical Predictive Equations for Lateral Creep Displacement Better Understanding of Long-Term Behavior Examine Impact of Elevated Temperatures
- 3. Short-Term Properties Test Specimens 4 Pultruded 4 x 4 x ¼” Square Tubes 6 ft Length 4 Extren Series 500 1/4 Isophthalic Polyester Resin E-Glass Rovings and CSM
- 4. Buckling Loads π 2 EL I C PE PE = Pe = 1 + (ns PE Ag GLT ) 2 (1) (2) Leff Short-Term Critical Load Approximations Approximation Current Study Butz Euler Modified Euler (Experimental) (Experimental) (Equation 1) (Equation 2) Pcr 50.5 46.6 53.5 49.9 (kips)
- 5. Testing Apparatus Top Plate Knife Edge Typical Creep Frame (Room Temp. Tests) L eff = 75 in 1-1/2" Threaded Rod 1-1/2" Hexagonal Nut Middle Plate 20 x 20 x 1" Steel Spring Plate Bottom Plate Hydraulic Jack Load Cell FRONT VIEW
- 8. Manufacturers Recommendations From Strongwell Corporation Extren Design Manual (2002) F.O.S. = 3
- 9. Long-Term Testing Creep Test Matrix Temperature Duration Specimen l (P/Pcr) (°F) (hours) PG-33-R 0.33 73 1000 PG-33-E 0.33 150 1000 PG-67-R 0.67 73 1000 PG-67-E 0.67 150 1000 PG-90-R 0.90 73 1000 PG-90-E 0.90 150 1000
- 10. Long-Term Results Midheight Lateral Deflection of All Specimens 0.14 PG-33-R PG-33-E PG-67-R 0.12 3 PG-67-E PG-90-R PG-90-E 0.10 2 0.08 d (mm) d (in) 0.06 1 0.04 0.02 0 0.00 0 200 400 600 800 1000 1200 Time (hours)
- 11. Quasielastic Method Schapery (1965) Vinogradov (1987) Kang (2001) Remove Eccentricity from Kang’s Analysis λ tn δ = Ai (3) ψ (t ) = (4) 1− λ β λ [1 +ψ (t )] δ (t ) = Ai (5) 1 − λ [1 +ψ (t )]
- 12. Determination of Quasielastic Parameters 3.0 Room Temperature 0.12 Specimens 2.5 0.10 PG-33-R PG-67-R PG-90-R 2.0 0.08 PG-33-R Prediction PG-67-R Prediction d (mm) d (in) PG-90-R Prediction 1.5 0.06 1.0 0.04 0.5 0.02 0.0 0.00 0 200 400 600 800 1000 1200 Time (hours)
- 13. Determination of Quasielastic Parameters 0.14 Elevated Temperature Specimens 0.12 3 0.10 2 0.08 d (mm) PG-33-E d (in) PG-67-E PG-90-E PG-33-E Prediction 0.06 PG-67-E Prediction PG-90-E Prediction 1 0.04 0.02 0 0.00 0 200 400 600 800 1000 1200 Time (hours)
- 14. Findley’s Power Law 1 10 PG-90-R ε (t ) = ε 0 + mt n (6) 0.1 1 d (mm) m d (in) 0.01 n δ (t ) = δ 0 + mt n 0.1 (7) 0.001 0.01 0.0001 1 10 100 1000 10000 Time (hours) log[δ (t ) − δ 0 ] = log(m ) + n log(t ) (8)
- 15. Inclusion of Temperature Effects in Predictive Model Findley et al. (1956) ⎛σ ⎞ ⎛σ ⎞ ε (t ) = ε '0 sinh⎜ ⎜σ ⎟ + m' t n sinh⎜ ⎟ ⎜σ ⎟ ⎟ (9) ⎝ ε ⎠ ⎝ m⎠ Applied to Lateral Deflection ⎛ λ ⎞ δ (t ) − δ 0 = m' t sinh⎜ ⎟ n ⎜λ ⎟ (10) ⎝ m⎠ Including Temperature ⎛ λ ⎞ δ (t ,τ ) − δ 0 = τm' t sinh⎜ ⎟ (11) T n ⎜λ ⎟ τ = (12) ⎝ m⎠ TR
- 16. Findley Predictions of Lateral Creep 0.14 Room Temperature Specimens 3 0.12 PG-33-R PG-67-R 0.10 PG-90-R PG-33-R Prediction PG-67-R Prediction d (mm) d (in) 2 0.08 PG-90-R Prediction 0.06 1 0.04 0.02 0 0.00 0 200 400 600 800 1000 1200 Time (hours)
- 17. Findley Predictions of Lateral Creep 0.14 Elevated Temperature Specimens 0.12 3 0.10 PG-33-E PG-67-E PG-90-E 2 PG-33-E Prediction 0.08 d (mm) d (in) PG-67-E Prediction PG-90-E Prediction 0.06 1 0.04 0.02 0 0.00 0 200 400 600 800 1000 1200 Time (hours)
- 18. Extended Predictions of Lateral Creep Deflection Predicted Lateral Deflection (in) Specimen 1000 1 Year 5 Years 10 Years 25 Years Hours PG-33-R 0.004 0.007 0.010 0.012 0.015 PG-33-E 0.008 0.014 0.021 0.025 0.031 PG-67-R 0.013 0.022 0.032 0.038 0.048 PG-67-E 0.026 0.045 0.066 0.078 0.098 PG-90-R 0.027 0.046 0.068 0.080 0.100 *PG-90-E 0.127 -7.694 -0.288 -0.219 -0.174 *Predicted using Quasielastic Creep Parameters
- 19. Post-Creep Buckling Tests d (in) Recovery 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 60 1 Week (168 Hours) 250 PG-33-E Permanent Modulus 50 Reduction 200 π 2 EL I C 40 PE = Load (kips) 50 Load (kN) 2 150 Leff 40 30 d (mm) 30 100 Specimen Failure 20 Slope = 227 kN (50.9 kips) 20 10 50 0 10 0.00 0.05 0.10 0.15 0.20 0.25 d/P (mm/kN) 0 0 0 10 20 30 40 d (mm)
- 20. Specimen Failure
- 21. Post-Creep Buckling Test Results Experimental Buckling Loads Pexp Pexp /PE Pexp /PST Specimen (kips) (%) (%) PG-33-R 50.5 94.4 99.9 PG-33-E 50.9 95.3 100.8 PG-67-R 50.5 94.4 99.9 PG-67-E 34.1 63.7 67.5 PG-90-R 59.2 110.7 117.2 PG-90-E 32.5 60.7 64.4 PE (kips) 53.5 PST (kips) 50.5
- 22. Conclusions Quasielastic Method Effective with Bending Power Law Model Effective without Bending Transition Point Between l = 0.67 and l = 0.90 Sustained Loads and Elevated Temperatures Reduce Modulus F.S. = 3 Appears Reasonable