Materials Mechanics 　　　　　　　　Beam Bending

Materials Mechanics
Beam Bending

　　　　

Materials Mechanics
Beam Bending

Author　Takashi Sasaya

English Translation by Toshihiko Chimura

Publishing Office　Greenwich Meridian

TEL/FAX +81-467-77-7742

mail meridiangreenwich@gmail.com

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This book explains in a manner as simple as possible the detailed　　　　　　　　　

calculation methodology for the deflection and stress of the basic 25　　　　 　　

kinds of beam for which the reader is likely to encounter beam bending issues.


The theory of curved beam is also explained in this book, specializing in the　

thin-walled beam.This book focuses on ark beam, which is the simplest shape,

and Archimedes curved beam as an extension of the ark beam.　　　　　　　　　　


The gnuplot sample program also contained in this book provides actual　　　　

examples for your reference, anticipating leverage to the fullest for　　　　 　　

drawing the deflection curve.　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

　

「Beam Bending」

Contents

1.Beam Bending

　1.1 Shearing force & bending
　　　　moment of beam

　1.2 Bending stress of beam

　1.3 Geometric moment of inertia

　1.4 Deflection of beam

2. Stress & Deflection of Beam

　2.1 Cantilever beam receiving the
　　　　concentrated load at end

　2.2 Cantilever beam receiving the
　　　 concentrated load at arbitrary
　　　 position

　2.3 Cantilever beam receiving the
　　　　uniformly distributed load

　2.4 Cantilever beam receiving the
　　　　uniformly distributed load at
　　　　arbitrary position

　2.5 Cantilever beam receiving the triangular distributed load

　2.6 Cantilever beam receiving the triangular distributed load at arbitrary
　　　　position

　2.7 Cantilever beam receiving the inverted triangular distributed load

　2.8 Cantilever beam receiving the inverted triangular distributed load
　　　　at arbitrary position

　2.9 Cantilever beam receiving the moment at end

　2.10 Cantilever beam receiving the moment at arbitrary position

　2.11 Simply supported beam receiving the concentrated load at arbitrary
　　　　position

　2.12 Simply supported beam receiving the uniformly distributed load

　2.13 Simply supported beam receiving the triangular distributed load

　2.14 Simply supported beam receiving the moment at one end

　2.15 Simply supported beam receiving the moment at both ends

　2.16 Simply supported beam receiving the moment at arbitrary position

　2.17 Statically indeterminate beam receiving the concentrated load
　　　　 at arbitrary position

　2.18 Statically indeterminate beam receiving the uniformly distributed load

　2.19 Statically indeterminate beam receiving the triangular distributed load

　2.20 Statically indeterminate beam receiving the moment at one end

　2.21 Statically indeterminate beam receiving the moment at arbitrary position

　2.22 Both ends fixed beam receiving the concentrated load at arbitrary position

　2.23 Both ends fixed beam receiving the uniformly distributed load

　2.24 Both ends fixed beam receiving the triangular distributed load

　2.25 Both ends fixed beam receiving the moment at arbitrary position

3. Thin-walled Curved Beam

　3.1 Stress of thin-walled curved beam

　3.2 Deflection of thin-walled curved beam

　3.3 Deflection of arc beam

　3.4 Stress of arc beam receiving the load at end

　3.5 Deflection of Archimedes curved beam

4. Sample Program of gnuplot

　4.1 Deflection of cantilever beam receiving the concentrated load at arbitrary position

　4.2 Deflection of cantilever beam receiving the uniformly distributed load at arbitrary
　　　　position

　4.3 Deflection of cantilever beam receiving the triangular distributed load at arbitrary
　　　　position

　4.4 Deflection of cantilever beam receiving the inverted triangular distributed load at
　　　　arbitrary position

　4.5 Deflection of cantilever beam receiving the moment at arbitrary position

　4.6 Deflection of simply supported beam receiving the concentrated load at arbitrary
　　　　position

　4.7 Deflection of simply supported beam receiving the uniformly distributed load

　4.8 Deflection of simply supported beam receiving the triangular distributed load

　4.9 Deflection of simply supported beam receiving the moment at both ends

　4.10 Deflection of simply supported beam receiving the moment at arbitrary position

　4.11 Deflection of statically indeterminate beam receiving the concentrated load at
　　　　　arbitrary position

　4.12 Deflection of statically indeterminate beam receiving the uniformly distributed
　　　　　load

　4.13 Deflection of statically indeterminate beam receiving the triangular distributed
　　　　　load

　4.14 Deflection of statically indeterminate beam receiving the momentat arbitrary
　　　　　position

　4.15 Deflection of both ends fixed beam receiving the concentrated load at arbitrary
　　　　　position

　4.16 Deflection of both ends fixed beam receiving the uniformly distributed load

　4.17 Deflection of both ends fixed beam receiving the triangular distributed load

　4.18 Deflection of both ends fixed beam receiving the moment at arbitrary position

　4.19 Deflection of arc beam receiving the load at end

　4.20 Deflection of Archimedes curved beam receiving the load at outer end

　4.21 Deflection of Archimedes curved beam receiving the load at inner end

5. Appendix

　5.1 Multiplication formula

　5.2 Integral formula of trigonometric function