Active Learning

Bending: Loading Configurations

BIOE 3200 - Fall 2015

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Learning objectives:Identify internal shear forces and bending moments for different loading configurationsDraw FBD and determine reaction forces and moments on a rigid bodyApply method of sections (including FBD of each section) to determine internal shear forces (V) and bending moments (Mz) during bending, and compare these for different loading configurationsSketch shear force and bending moment diagramsBIOE 3200 - Fall 2015

Torsion testing; define torsional strength, torsional stiffness, torsional rigidity, torsional load capacity or torsional limit, torsional energy absorbed

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Bending: Different loading configurations result in bending of rigid bodiesBIOE 3200 - Fall 2015

Three point bendingFour point bendingCantilever bendingDistributed load

Simply supported beams: 3-point bending, 4-point bending, distributed loadsBIOE 3200 - Fall 2015

Sign convention (same as in Humphrey and Delange, p. 204): positive shear is down on rt side of cut, up on left side of cut; positive moment is ccw on right side of cut, cw on left side of cutMethod of sections: make cuts at changes in load or support, geometry, or material propertiesInternal shear force is constant within each section; jumps at point of concentrated loadMoments are linear, with peak at PL/4 and slope of V within each section; no discontinuity unless there is a concentrated moment applied 4

Cantilevered Beam: Single point load, multiple point loads, distributed load BIOE 3200 - Fall 2015

From http://www.roymech.co.uk/Useful_Tables/Beams/Shear_Bending.html

Cantilever beam the mode for loading of an Atomic Force Microscope tip; also typical or orthodontics and prosthetics5

Comparing bending moments in different loading configurationsPure bending

Cantilever

3-point bending

4-point bendingBIOE 3200 - Fall 2015