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UNIVERSITY OF ILLINOIS ENGINEERING EXPERIMENT STATION BULLETIN No. 80 JUNE, 1915 WIND STRESSES IN THE STEEL FRAMES OF OFFICE BUILDINGS. BY W. M. WILSON, ASSISTANT PROFESSOR OF STRUCTURAL ENGINEERING, AND G. A. MANEY, FORMERLY RESEARCH FELLOW IN DEPART- MENT OF THEORETICAL AND APPLIED MECHANICS.* CONTENTS. Page I. INTRODUCTION ... ............ . ........... . . 5 1. P relim inary .................................... 5 2. Acknowledgment ........... ................... 5 II. PRESENT METHODS OF CALCULATING WIND STRESSES IN OFFICE BUILDINGS .... ...................... 5 3. Classification of Methods......................... 5 4. Approximate Methods .......................... 6 5. Exact M ethods ................... ............ . 7 III. OUTLINE OF THE PROPOSED ANALYSIS ................... 8 6. Outline of the Method........................... 8 IV. ASSUMPTIONS UPON WHICH THE ANALYSIS Is BASED ..... 9 7. Statement of Assumptions ....................... 9 V. FUNDAMENTAL EQUATION .......... ................. .. 10 8. Fundamental Proposition ....................... 10 9. Proof of the Proposition......................... 10 10. Derivation of Fundamental Equation.............. 11 VI. DERIVATION OF GENERAL EQUATIONS. ................... 14 11. N otation ...................................... 14 12. Derivation of Equations ......................... 15 *While the bulletin is the result of the joint efforts of the two writers, certain parts are so distinctly the work of one that it seems desirable to make a statement relative to the part which should be credited to each. The method of making the analysis involving the use of the slope-deflection equations should be credited to G. A. Maney. The con- ception of the bulletin as a whole, the method of presenting the results, and the authorship of the text should be credited to W. M. Wilson. The numerical calculations of Tables 11 to 22, inclusive, were made by both writers.-The Editor.

ILLINOIS ENGINEERING EXPERIMENT STATION 21. Elimination of the Unknown Quantities in the Equations Used to Determine the Slopes and the Deflections in the Bottom Story of the Symmetrical Three-Span Twenty-Story Bent Shown in Fig. 5 by a Modification of the Slope-Deflection M ethod ............. ....................................... . ..... ...... . 77 22. Determination of the Changes in the Slopes and the Ratio of the Deflection to Story Height in the Bottom Story of the Symmetrical Three-Span Twenty- Story Bent Shown in Fig. 5 by a Modification of the Slope-Deflection Method.... 78 23. Comparison of the Approximate Methods with the Slope-Deflection Method When Applied to the Symmetrical Three-Span Twenty-Story Bent Shown in Fig. 5..... 79 24. Comparison of the Approximate Methods with the Slope-Deflection Method When Applied to the Symmetrical Three-Span Twenty-Story Bent Shown in Fig. 5..... 80 25. Comparison of the Approximate Methods with the Slope-Deflection Method When Applied to the Symmetrical Three-Span Twenty-Story Bent Shown in Fig. 13.... 81 26. Comparison of the Approximate Methods with the Slope-Deflection Method When Applied to the Symmetrical Three-Span Twenty-Story Bent Shown in Fig. 13..... 82 27. Effect of the Proportion of a Bent Upon the Accuracy of Method I................ 85 28. Effect of the Proportions of a Bent Upon the Accuracy of Method I. All Girders Proportional to the Bending M oments ........................ . .............. 84 29. Effect of the Proportions of a Bent Upon the Accuracy of Method II............... 85 30. Effect of the Proportions of a Bent Upon the Accuracy of Method III .............. 86 31. Effect of the Proportions of a Bent Upon the Accuracy of Method IV .............. 87 32. Log of the Test of Celluloid M odel No. 4 ................. ...... .. ............... 88 LIST OF FIGURES. 1. Proof of Fundamental Equation ................ . ............. .. ................ 11 2. Derivation of Fundamental Equation ............................ ............... 18 M 3. - D iagram .................................................................. 13 El 4. Bottom Five Stories of a Symmetrical Three-Span Bent .......................... 15 5. Symmetrical Three-Span Bent, Twenty Stories High................... ............ 20 6. Approximate Moment at the Top and Bottom of Column A. (Insert) .............. 26 7. Approximate Moment at the Top and Bottom of Column B. (Insert) ............... 6 8. Approximate Moment at the Ends of Girder b. (Insert).......................... 26 9. Moments Acting at Points A8 and B8 of a Symmetrical Three-Span Bent ............ 9 10. Diagram Showing Change in the Moment at the Top and the Bottom of Column A of a Symmetrical Three-Span Bent Due to a Change of K of the Other Members 80 11. Diagram Showing Change in the Moment at the Top and the Bottom of Column B of a Symmetrical Three-Span Bent Due to a Change of K of the Other Members 31 12. Diagram Showing Change in the Moment at the End of Girder b of a Symmetrical Three-Span Bent Due to a Change in K of the Others Members................ 32 13. Symmetrical Three-Span Bent Twenty Stories High with Long Span at the Center.. 88 14. Celluloid M odel ..................... .................... .................. ... . 41 15. Diagram of Results of the Tests of Celluloid Model ............................... 43