Graphical Analysis - A Text Book in Graphic Statics (1921) Book

Text extracted from opening pages of book: GRAPHICAL ANALYSIS A TEXT BOOK ON GRAPHIC STATICS BY WILLIAM S. WOLFE, M. S. Head of Structural Department, Smith, Hinchman & Gryllx. Formerly Instructor in Architectural Engineering, University of Illinois. Associate Member American Society of Civil Engineers* Associate Member Society of Naval Architects and Marine Engineers FIRST EDITION PROPERTY OF WSTITUW OF TMMLOG1 McGRAW-HILL BOOK COMPANY, INC. NEW YORK: 370 SEVENTH AVENUE LONDON: 6 & 8 BOUVERIE ST., E. C. 4 1921 PREFACE THIS book has been developed from notes and blue prints prepared by the writer and used in his classes at the University of Illinois. Certain additional material has been added, a part of which has been briefly presented in a number of articles con tributed by the writer to the technical press. The notes referred to above were modeled after a set prepared by Dr. N. C. Ricker, several years before, to whom the writer is greatly indebted. Many additional problems might have been added and the discussion greatly extended. This is especially true of Chapters IV and VII to X inclusive. However, it has been thought best to keep the book to smaller proportions, and the writer believes that a thorough mastery of the constructions and solutions here presented will give the student an excellent grasp of the subject. The object has been to deal with the analysis of stresses rather than with design or the computation of loads. Nevertheless it has seemed desirable to give some attention to the determination of loads, and Chapter IX has been devoted almost exclusively to design. Material and ideas have, of course, been drawn from many sources. The writer is especially indebted to Prof. C. R. Clark for assist ance in connection with the early part of the work and to Prof. L. H. Provine for encouragement and constructive criticism. w. s. w. DETROIT, MICH. October, 1921. TABLE OF CONTENTS PAGE PREFACE v NOTATION xiii CHAPTER I GENERAL METHODS ART. 1 . Introduction 1 2. Definitions 2 3. Graphical Construction and Measurement of an Angle 3 4. Representation of Forces . . , . 4 5. Composition of Forces 6 6. Resolution of Forces 8 7. Concurrent-Coplanar Forces, Conditions for Equilibrium 10 8. Unknowns 11 9. Non-Concurrent Coplanar Forces . . . . . . 13 10. Funicular or Equilibrium Polygon . . 14 11 Resultant a Couple . . 18 12 Non-Concurrent Coplanar Forces, Conditions for Equilibrium 19 13 Parallel Forces 19 14. Resultant of a Number of Parallel Forces .... 21 15 Reactions for a Beam ... 23 16 Reactions for a Beam with a Distributed Load .... 25 17. Reactions for a Beam with Inclined Loads . ... 26 18. Reactions for a Truss, Vertical Loads 27 19. Reactions for a Truss with Vertical and Inclined Loads .... 27 20 Horizontal Component Divided Equally between the Two Reactions 31 21. Reactions of a Rafter Supported on Purlins 32 22. Stresses in the Members of a Frame 33 23. Stresses in a Bicycle Frame .... 35 24. Passing a Funicular Polygon through Three Given Points 37 CHAPTER II CENTROIDS 25. Centroid of a Broken Line 40 26. Centroid of an Arc 42 27. Centroid of a Curve 44 28. Centroids of Areas 45 viii TABLE OF CONTENTS ART. PAGE 29. Ccntroid of a Triangle 45 30. Centroid of a Quadrilateral 46 31. Centroid of a Trapezoid 47 32. Given the Centroid, Area and Distance between the Two Parallel Sides of a Trapezoid to Find the Lengths of the Parallel Sides 48 33. Centroid of a Sector 49 34. Centroid of a Circular Segment 50 35. Centroids of Irregular Areas 51 36. Centroids of Volumes 53 37. Centroid of a Triangular Pyramid 53 38. Complex Volumes which can be Divided into a Number of Regular Volumes 54 39. Irregular Volumes, Division into Slices 57 40. Centroid Located by the Use of Sections and Area Curves 59 41. Stress Volumes 61 CHAPTER III MOMENTS 42. First Moment of a Force about a Point 64 43. First Moment of a Number of Forces about a Point 65 44. First Moment of an Area about a Given Axis 67 45. Moment Diagram for a Beam 68 46. SRead More