Fall @BULLET 2014-2015

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Fall @BULLET 2014-2015
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  1 StaticsandStrengthof Materials MCH2011 Dr. Orhan GÖKÇÖL Department of Mechatronics EngineeringFacultof EngineeringandNatural Sciences Fall • 2014-2015 Week#12 BENDING  Membersthatareslenderandsupportloadingsthatareappliedtoperpendiculartotheirlongitidunalaxisarecalled« beams »  Ingeneral, beamsarelongandstraightbarshavinga constantcross-sectionarea.  Oftentheyareclassifiedas tohow theyaresupported. Pinsupport Roller support Fixedsupport   2 BendingDeformationof a straightmember  Whathappenswhena straightprismaticmemberis subjectedtoa bendingmoment? Notethatweassumebeamhas a cross-sectionalareathatis symmetricalwithrespecttoan axis, andthebendingmoment is appliedaboutan axisperpendiculartothisaxisof symmetry! Bottompartstostretch, top parttocompress!  3  The size and shape of the cross-section of the piece of material used  For timber, usually a rectangle  For steel, various formed sections are more efficient  For concrete, either rectangular, or often a Tee A timber and plywood I -beam  What shapes are possible in the material?  What shapes are efficient for the purpose?  Obviously, bigger is stronger, but less economicalSome hot-rolled steel sections  4  Beams are oriented one way  Depth around the X-axis is the strong way  Some lateral stiffness is also needed  Columns need to be stiff both ways (X and Y)  ‘ Stress is proportional to strain’  Parts further from the centre strain more  The outer layers receive greatest stress  5  The stresses developed resist bending  Equilibrium happens when the resistance equals the applied bending moment BendingDeformationof a straightmember  Longitidunalaxis, x, doesnot experienceanychangein length  Moment willtendtodeformthebeamsothatthislinebecomesa curvethatliesin thex-y planeof symmetry   Allcrosssectionsof thebeamremainplaneandperpendiculartothelongitidunalaxisduringthedeformation.   Anydeformationof thecrosssectionwithinitsownplanewillbe neglected,
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