Effect of Number of CFRP Layers

Figure 9 (a and b) clearly shows that bonding CFRP sheets to slender HSS members can indeed increase their axial compressive strength. For example, the predicted percentage increases in strength of specimens with one, three and five CFRP layers are 11, 25, and 40 percent for specimens with L/300 imperfection and are 12, 26, and 40 percent, respectively, for specimens with L/1000 imperfection.

Also, the percentage increases in axial stiffness are 15, 31, and 48 percent for the L/300 specimens and are 13, 29, and 45 percent, for the L/1000 specimens. These findings show that the percentage increases in axial strength and axial stiffness, for the levels of imperfections studied, are independent of the initial imperfection value. The imperfection, however, affects the absolute values of ultimate loads.

Table 1. Comparison between experimental and analytical model results

Experimental

Analytical Model

(Analytical / Experimental) ratio

Specimen I. D.

Pmax (kN)

e’

Pmax (kN)

Control

295

L/300

245

0.83

L/500

271

0.92

L/1000

297

1.01

1L-2S

355

L/300

271

0.76

L/500

301

0.85

L/1000

333

0.94

3L-2S

335

L/300

306

0.91

L/500

344

1.03

L/1000

375

1.12

5L-2S

332

L/300

344

1.04

L/500

387

1.17

L/1000

415

1.25

3L-4S

362

L/300

329

0.91

L/500

371

1.02

L/1000

415

1 .1 5

Table 2. Percentage increases in axial

strength and stiffness of retrofitted members

Imperfection value (e’)

Specimen I. D.

P

1 max

(kN.)

% Gain in strength

Axial Stiffness (kN/mm)

% Gain in stiffness

L/300

control

245

89

1L-2S

271

11

102

15

3L-2S

306

25

117

31

5L-2S

344

40

132

48

L/500

control

271

91

1L-2S

301

11

103

13

3L-2S

344

27

117

29

5L-2S

387

43

132

45

L/1000

control

297

91

1L-2S

333

12

103

13

3L-2S

375

26

117

29

5L-2S

415

40

132

45

Conclusions

A non-linear model based on the concepts of equilibrium and strain compatibility has been developed to predict the axial load capacity of slender HSS compression members retrofitted by externally bonded CFRP sheets. The model is also capable of predicting the full load versus lateral and axial displacements. The member’s initial imperfection, residual stresses, material and geometric nonlinearities are accounted for. The model was verified using experimental results and showed reasonable agreement. The effects of member’s initial imperfection and number of CFRP layers are studied. The following conclusions can be drawn, based on the simplified conservative approach followed, and the range of imperfections studied in this paper:

1. Externally bonded CFRP sheets are effective in increasing the axial strength and stiffness of slender HSS compression members.

2. For a slender member retrofitted by a given CFRP reinforcement ratio, the member’s initial imperfection has a pronounced effect on its axial strength but marginal effect on axial stiffness.

3. While initial imperfection affects the magnitude of member’s axial strength, it does not affect the percentage increase in member’s strength resulting from CFRP retrofitting, for the studied level of imperfections.

4. Ignoring residual stresses, steel plasticity, or premature delamination and crushing of CFRP in the inward side of a compression member undergoing overall buckling could highly overestimate the member’s axial strength.

Future Work

The model will be further refined to account for the effect of the variable inertia throughout the length

of the column by introducing larger number of segments.

Acknowledgement

The authors wish to acknowledge the financial support provided by the Natural Sciences and

Engineering Research Council of Canada (NSERC).

References

1. Allen, H. G. and Bulson, P. S. (1980). “Background to Buckling.” McGraw-Hill Book Company (UK) Limited. S.

2. Bjorhovde, R., and Birkemoe, P. C. (1979). “Limit States Design of HSS Columns.” Canadian Journal of Civil Engineering, 6, 275-291.

3. Canadian Standards Association, CAN/CSA-S16-01, Limit states design of steel structures, Mississauga, Ontario.

4. Chan, S. L., Kitipornchai, S. and Al-Bermani, F. G. A. (1991). “Elasto-Plastic Analysis of Box-Columns including Local Buckling Effects.” Journal of Structural Engineering. ASCE, 117(7): 1946-1962.

5. Davison, T. A., and Birkemoe, P. C. (1983) “Column Behaviour of Cold-Formed Hollow Structural Steel Shapes.” Canadian Journal of Civil Engineering, 10, 125-141.

6. Ghali, A. and Neville, A. M. (1989). “Structural analysis: A unified classical and matrix approach” Chapman and Hall, London and New York.

7. Hollaway, L. C. and Cadei, J. (2002). “Progress in the Technique of Upgrading Metallic Structures with Advanced Polymer Composites”, Progress in Structural Engineering and Materials, J. Wiley & Sons, 4(2):131-148.

8. Shaat, A., Schnerch, D., Fam, A., and Rizkalla, S. (2004) “Retrofit of steel structures using fiber-reinforced polymers (FRP): State-of-the-art.”, Transportation Research Board (TRB) Annual Meeting, Washington, D. C., USA, CD-ROM (04-4063).

9. Shaat, A. and Fam, A. (2006) “Axial Loading Tests on CFRP-Retrofitted Short and Long HSS Steel Columns.” Accepted for publication in the Canadian Journal of Civil Engineering.

10. Weng, C. C. (1984). “Cold-bending of thick steel plates at low R/t ratios.” Master’s thesis. Cornell University, at Ithaca, N. Y.

11. Weng, C. C., and Pekoz, T. (1990). “Residual Stresses in Cold-Formed Steel Members.” Journal of Structural Engineering. ASCE, 116(6): 1611-1625.

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