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FIGURES (Continued)
20. Theoretical and Experimental Curves for 7075-T6 Aluminum Alloy
Tension Members 34
21. Theoretical and Experimental Curves for 4340 Alloy Steel Tension
Members 34
22. Theoretical and Experimental Curves for Annealed Type 304 Stain-
less Steel Tension Members 35
23. Theoretical and Experimental Curves for 7075-T6 Aluminum Alloy
Tension Members 35
24. Time-Deflection Diagrams for Sustained and Alternating Eccentric
Tensile Loading 36
25. Theoretical and Experimental Curves for Angle-Section Tension
Members Bent About Maximum and Minimum Axes of Inertia 37
26. Theoretical and Experimental Curves for 2024-T4 Aluminum Alloy
Columns Having Slenderness Ratios of 46 39
27. Theoretical and Experimental Curves for SAE 1020 Steel Columns
Having Slenderness Ratios of 60 39
28. Theoretical and Experimental Curves for SAE 1020 Steel Columns
Having Slenderness Ratios of 60 40
29. Theoretical and Experimental Curves for a 2024-T4 Aluminum Alloy
Column Having a Slenderness Ratio of 49 40
30. Theoretical and Experimental Curves for 7075-T6 Aluminum Alloy
Columns 41
31. Theoretical and Experimental Curves for Annealed Type 304 Stain-
less Steel 42
32. Stress Distributions at Various Positions on the Straight Line Portion
of the Interaction Curve 47
TABLES
1. Data for Eccentrically-Loaded Tension Members 22
2. Data for Eccentrically-Loaded Columns 23

ell + E,2 Eel + Ee2 kh a This is the curvature for the member corresponding to point A at the end of the straight line portion of the interaction curve (see Fig. 32b). For any point B on the straight line the stress on the tension side of the member is given by D-B and is less than ae2. The resulting stress distribution for the same depth of yielding is UDBFTH. This distribution is represented by the same rectangular distribution and two triangular distributions FTJ and FBC. The moment arms m and n remain constant and, hence, the following expressions can be written: 1 F1B = 2 AiaiKa F2B = 2 Ao MB = F1Bm + F2Bn = (mAiiK + nA MB = CEe The curvature corresponding to point B is given by the geometry of deformation as (see Eq. 31) 1 E E 7RB kh a Comparison of the radii of curvature corresponding to points A and B shows that 1 e 1 Eel + Ee2 RA But it has been shown that MB and el + Ee2 = MA/C Therefore, 1 1 BM RB RA MA) Since the radius of curvature and the deflection are proportional, the deflection corresponding to any point B on the straight line portion of the in- teraction curve is given by the following relation: '1B 5 M- MA VII. REFERENCES 1. Shanley, F. R., and Ryder, E. I., "Stress Ratios," Aviation, June 1937. 2. Harvout, R. E., "Allowable Shear from Combined Bend- ing and Torsion in Round, Elliptical, and Streamlined Tubes and Allowable Normal Stress from Bending in Thin-walled Tubes," Air Corps Information Circular 669, Washington, U.S. Government Printing Office, 1932. 3. Onat, E. T., and Prager, W., "Influence of Axial Forces on Collapse Loads of Frames," First Midwestern Conference for Fluid and Solid Mechanics, Engineer- ing Experiment Station, University of Illinois, April 1953. 4. Tuckerman, L. B., Petrenko, S. N., and Johnson, C. D., "Strength of Tubing Under Combined Axial and Transverse Loading," NACA Technical Note 307, Washington, Bureau of Standards, June 1936. 5. Munse, W. H., and Cox, H. L., "The Static Strength of Rivets Subjected to Combined Tension and Shear," University of Illinois Engineering Experiment Station, Bulletin Series No. 437, 1956. 6. Ketter, R. L., Beedle, L. S., and Johnston, B. G., "Col- umn Strength Under Combined Bending and Thrust," Welding Journal Research Supplement, December 1952. 7. Shanley, F. R., "Strength Analysis of Eccentrically- Loaded Columns," Department of Engineering, Uni- versity of California, Report 54-57, May 1954. 8. Ketter, R. C., "Stability of Beam-Columns Above the Elastic Limit," Proceedings ASCE, Vol. 81, No. 692, October 1955. 9. Jordan, W. D., "The Inelastic Behavior of Eccentrically- Loaded Columns," Unpublished Ph.D. Thesis, Uni- versity of Illinois, 1952. 10. Clark, M. E., Corten, 11. T., and Sidebottom, 0. M., "Inelastic Behavior of Ductile Members Under Dead Loading," University of Illinois Engineering Experi- ment Station, Bulletin Series No. 426, 1954. 11. Morkovin, D., and Sidebottom, 0. M., "The Effect of Non-uniform Distribution of Stress on the Yield Strength of Steel," University of Illinois Engineering Experiment Station, Bulletin Series No. 372, 1947. 12. Brush, D. 0., and Sidebottom, 0. M., "Axial Tension and Bending Interaction Curves for Members Loaded Inelastically," Transactions ASME, Vol. 75, No. 1, pp. 63-72, January 1953. 13. Maeda, Y., Van Lierde, P., Sidebottom, 0. M., and Clark, M. E., "The Effects of Inelastic Action on the Resistance to Various Types of Loads of Ductile Members Made from Various Classes of Metals, Part VI. A Digital Computer Analysis of Bending Moment- Axial Load Interaction Curves," Wright Air Develop- ment Center Technical Report 55-330. 14. Clark, M. E., and Sidebottom, 0. M., "An Inexpensive Constant-Load Testing Machine," ASTM Bulletin No. 203, January 1955. 15. Costello, G. A., "The Influence of the Stress-Strain Diagram Representation on the Critical Load of Ec- centrically-Loaded Members," Unpublished Master's Thesis, University of Illinois, 1956. 16. Manjoine, M. J., "Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel," Jour- nal of Applied Mechanics, Vol. II, No. 4, December 1944.

ell + E,2 Eel + Ee2 kh a This is the curvature for the member corresponding to point A at the end of the straight line portion of the interaction curve (see Fig. 32b). For any point B on the straight line the stress on the tension side of the member is given by D-B and is less than ae2. The resulting stress distribution for the same depth of yielding is UDBFTH. This distribution is represented by the same rectangular distribution and two triangular distributions FTJ and FBC. The moment arms m and n remain constant and, hence, the following expressions can be written: 1 F1B = 2 AiaiKa F2B = 2 Ao MB = F1Bm + F2Bn = (mAiiK + nA MB = CEe The curvature corresponding to point B is given by the geometry of deformation as (see Eq. 31) 1 E E 7RB kh a Comparison of the radii of curvature corresponding to points A and B shows that 1 e 1 Eel + Ee2 RA But it has been shown that MB and el + Ee2 = MA/C Therefore, 1 1 BM RB RA MA) Since the radius of curvature and the deflection are proportional, the deflection corresponding to any point B on the straight line portion of the in- teraction curve is given by the following relation: '1B 5 M- MA VII. REFERENCES 1. Shanley, F. R., and Ryder, E. I., "Stress Ratios," Aviation, June 1937. 2. Harvout, R. E., "Allowable Shear from Combined Bend- ing and Torsion in Round, Elliptical, and Streamlined Tubes and Allowable Normal Stress from Bending in Thin-walled Tubes," Air Corps Information Circular 669, Washington, U.S. Government Printing Office, 1932. 3. Onat, E. T., and Prager, W., "Influence of Axial Forces on Collapse Loads of Frames," First Midwestern Conference for Fluid and Solid Mechanics, Engineer- ing Experiment Station, University of Illinois, April 1953. 4. Tuckerman, L. B., Petrenko, S. N., and Johnson, C. D., "Strength of Tubing Under Combined Axial and Transverse Loading," NACA Technical Note 307, Washington, Bureau of Standards, June 1936. 5. Munse, W. H., and Cox, H. L., "The Static Strength of Rivets Subjected to Combined Tension and Shear," University of Illinois Engineering Experiment Station, Bulletin Series No. 437, 1956. 6. Ketter, R. L., Beedle, L. S., and Johnston, B. G., "Col- umn Strength Under Combined Bending and Thrust," Welding Journal Research Supplement, December 1952. 7. Shanley, F. R., "Strength Analysis of Eccentrically- Loaded Columns," Department of Engineering, Uni- versity of California, Report 54-57, May 1954. 8. Ketter, R. C., "Stability of Beam-Columns Above the Elastic Limit," Proceedings ASCE, Vol. 81, No. 692, October 1955. 9. Jordan, W. D., "The Inelastic Behavior of Eccentrically- Loaded Columns," Unpublished Ph.D. Thesis, Uni- versity of Illinois, 1952. 10. Clark, M. E., Corten, 11. T., and Sidebottom, 0. M., "Inelastic Behavior of Ductile Members Under Dead Loading," University of Illinois Engineering Experi- ment Station, Bulletin Series No. 426, 1954. 11. Morkovin, D., and Sidebottom, 0. M., "The Effect of Non-uniform Distribution of Stress on the Yield Strength of Steel," University of Illinois Engineering Experiment Station, Bulletin Series No. 372, 1947. 12. Brush, D. 0., and Sidebottom, 0. M., "Axial Tension and Bending Interaction Curves for Members Loaded Inelastically," Transactions ASME, Vol. 75, No. 1, pp. 63-72, January 1953. 13. Maeda, Y., Van Lierde, P., Sidebottom, 0. M., and Clark, M. E., "The Effects of Inelastic Action on the Resistance to Various Types of Loads of Ductile Members Made from Various Classes of Metals, Part VI. A Digital Computer Analysis of Bending Moment- Axial Load Interaction Curves," Wright Air Develop- ment Center Technical Report 55-330. 14. Clark, M. E., and Sidebottom, 0. M., "An Inexpensive Constant-Load Testing Machine," ASTM Bulletin No. 203, January 1955. 15. Costello, G. A., "The Influence of the Stress-Strain Diagram Representation on the Critical Load of Ec- centrically-Loaded Members," Unpublished Master's Thesis, University of Illinois, 1956. 16. Manjoine, M. J., "Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel," Jour- nal of Applied Mechanics, Vol. II, No. 4, December 1944.