CONTINUUM MECHANICS FOR ENGINEERS
TORSION OF A SHAFT BENDING OF A BEAM BY A MOMENT THIN-WALLED TUBE TENSION AND TORSION REFERENCES PROBLEMS CONTINUUM MECHANICS IF WE ACCEPT THE CONTINUUM CONCEPT OF MATTER, WE AGREE TO IGNORE (OR MORE PRECISELY, TO AVERAGE) THE DISCRETE COMPOSITION OF MATERIAL BODIES, AND TO ASSUME THAT THE SUB- STANCE OF SUCH BODIES IS DISTRIBUTED UNIFORMLY THROUGHOUT, AND COMPLETELY ?LLS THE SPACE IT OCCUPIES IN KEEPING WITH THIS CONTINUUM MODEL, WE ASSERT THAT MATTER MAY BE DIVIDED INDE?NITELY INTO SMALLER AND SMALLER PORTIONS, EACH OF WHICH RETAINS ALL OF THE PHYSICAL PROPERTIES OF THE PARENT BODY ACCORDINGLY, WE ARE ABLE TO ASCRIBE ?ELD QUANTITIES SUCH AS DENSITY AND VELOCITY TO EACH AND EVERY POINT OF THE REGION OF SPACE WHICH THE BODY OCCUPIES THE CONTINUUM MODEL FOR MATERIAL BODIES IS IMPORTANT TO ENGINEERS FOR TWO VERY GOOD REASONS ON THE SCALE BY WHICH WE CONSIDER BODIES OF STEEL, ALUMINUM, CONCRETE, ETC , THE CHARACTERISTIC DIMENSIONS ARE EXTREMELY LARGE COMPARED TO MOLECULAR DISTANCES, SO THAT THE CONTINUUM MODEL PROVIDES A VERY USEFUL AND RELIABLE REPRESENTATION ADDITIONALLY, OUR KNOWLEDGE OF THE MECHANICAL BEHAVIOR OF MATERIALS IS BASED ALMOST ENTIRELY UPON EXPERIMENTAL DATA GATHERED BY TESTS ON RELATIVELY LARGE SPECIMENS THE ANALYSIS OF THE KINEMATIC AND MECHANICAL BEHAVIOR OF MATERIALS MODELED ON THE CONTINUUM ASSUMPTION IS WHAT WE KNOW AS CONTINUUM MECHANICS THERE ARE TWO MAIN