Bending Stresses for Simple Shapes

Transcription

1 -6 Bendng Stesses fo Smple Sapes In bendng, te maxmum stess and amount of deflecton can be calculated n eac of te followng stuatons. Addtonal examples ae avalable n an engneeng andbook. Secton Modulus and Moment of Ineta Secton modulus and moment of neta depend on te pat s geomety and ae lsted fo seveal common pat geometes. maxmum stess at oute fbe = deflecton = foce (load) b I = b 1 b Z = 6 = dstbutve load = lengt of beam Z = secton modulus b t I = I Z = b - (b - t)(-t) 1 E = flexual modulus I = moment of neta about bendng axs I = 0.78 Z = 0.78 Smply Suppoted Beam, Cente oad Z = 8EI o I = 0.78 ( - ) o o Z = 0.78 ( - ) o

2 -7 Smply Suppoted Beam, Unfom oad 8Z = 5 8EI Fxed Suppoted Beam, Cente oad 8Z = 19EI Fxed Suppoted Beam, Unfom oad 1Z = 8EI Cantleve Beam, End oad Z = EI Cantleve Beam, Unfom oad Z = 8EI

3 -8 Fnte Element Analyss (FEA) Ovevew FEA s a metod fo smulatng component nteacton wtn a gven opeatng envonment. FEA enables te desgne to vew seveal dffeent desgn vaatons wtout dong extensve testng n te pelmnay desgn stages. FEA can also be used to pevent ovedesgnng a pat to ensue a good safety facto, and to educe te numbe of desgn teatons to eac an optmum pofle. Types of Analyss FEA allows te use to attempt many dffeent desgn altenatves based on vaous loadng condtons, ncludng extended tme of load, gtempeatue and g mostue condtons. t tese analyses, te desgne can look at pat optmzaton and examne ow seveal pat vaatons can make damatc dffeences n pat pefomance. Some of te foms of analyss ae: Stess Analyss - used to calculate elatve stess levels n components unde statc o dynamc loads, temally appled stess, etc. efomng Fnte Element Analyss USE FEA HEN Desgnng complex sapes Usng unusual loadng (.e., mpact, non-unfom) Relatve esults ae mpotant (.e., compang seveal dffeent desgns) Deflecton Analyss - used to examne ow a component wll defom unde vaous loadng condtons.

4 -9 Heat Tansfe Analyss - used to sow ow te tempeatue wll vay wtn a component fo dffeent bounday condtons and ow a component wll defom wen tee s a temal dffeental acoss te component s sufaces. ocedue Te desgne must povde te followng nput to te engnee pefomng te FEA: 1. A wefame model tat epesents te component(s) beng analyzed. Te model sould ave enoug detal to accuately potay te ctcal aeas of te component wtout attemptng to model eveytng.. Te pyscal popetes of te mateal used n te desgn of te component.. Te applcaton of loads and estants smulatng te poposed opeatng condtons to be expeenced by te component. Typcal esults fom FEA D E S I G N T I FEA esults sould be vefed by pope testng. Intepetaton of FEA esults Once te desgne as popely nput te paametes of te component(s) and te analyss as been un, t s necessay to ntepet te esults. In geneal tems, te esults fom an FEA analyss can be vey accuate. It s te esponsblty of te desgn engnee, oweve, to ealze tat FEA s smply a tool to ad n desgn.

5 -10 ofle Symmety Symmetc pofle geomety s geneally ease to extude tan nonsymmetc. Hollow pofles wt no nteo walls ae also geneally easy to extude, egadless of symmety. A symmetc pofle poduces a moe unfom tanston fom te extude to te entance of te de. Ts esults n a moe unfom flow of mateal aound te ente pofle as t exts te de. opely desgned pofles not only ncease extuson speed, tey lowe esdual stesses wtn a pat and povde balanced flow. Fo moe nfomaton on extuson efe to Secton of ts gude. Dffeent levels of symmety fo fou pofles ae llustated at left. Example A s symmetc wt no nteo walls. Ts pofle epesents te deal extuson. A ollow ppe, squae o ound, s te easest extuson. Te smple tanston fom te extude to te de entance allows fo easy contol of te mateal flow acoss te pofle. A - Easest B - Easy Example B s a non-symmetc ollow pofle wt no nteo walls. Ts pofle s moe dffcult to extude tan pofle A, but te lack of nteo walls esults n ge lne speeds and lowe esdual stesses.