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Unformatted text preview: Mechanics of Solids Lecture 11 by Dr Emre Erkmen Lecturer, School of Civil and Environmental Engineering, The University of Technology Sydney Office: 2.520 Phone:9514 9769 Email: emre.erkmen@uts.edu.au Lecture hours: Tuesdays 11:0014:00, Wednesdays 15:0018:00 Office hours: Tuesdays 15:0017:00 1 Mechanics of Solids  Lecture 11 Outline Outline Shear centre External work and Strain energy 2 Mechanics of Solids  Lecture 11 Shear centre 3 Shear centre is the point through which when a force is applied it will cause a beam to bend but not twist. The location of the shear centre is dependent on the geometry of the cross section only and does not depend on the magnitude of the applied load. Mechanics of Solids  Lecture 11 Shear centre Previously, we assumed that shear force P was applied at the centroid which was on the axis of symmetry for the crosssection Centroid 4 If we do not have a symmetry axis in vertical the load applied at the centroid will cause torsion in addition to bending Axis of symmetry Mechanics of Solids  Lecture 11 Shear centre When a force P is applied to a channel section along the vertical unsymmetrical axis that passes through the centroid C of the crosssectional area, the channel bends downwards and also twist clockwise 5 Mechanics of Solids  Lecture 11 Shear centre 6 Shear center is the point through which a force can be applied which will cause a beam to bend but not twist P V Q q I = q Mechanics of Solids  Lecture 11 Shear flow in thinwalled beams 7 q = VQ I = V [d/2]((b/2) x ) t I Vtd 2I ( b 2 x ) = In horizontal flanges, flow varies linearly Mechanics of Solids  Lecture 11 Shear flow in thinwalled beams q = VQ I = Vt I ( d 2 4 y 2 ) [ db 2 + ] In vertical web(s), flow varies parabolically, 8 Mechanics of Solids  Lecture 11 Shear flow in thinwalled beams F f F f Shear centre 9 v F f F f If there is an axis of symmetry, the shear center will always lie on an the axis of symmetry of the crosssection Symmetry axis Mechanics of Solids  Lecture 11 Shear centre Determine the location of the shear center for the thinwalled channel section having the dimensions as shown. 10 Mechanics of Solids  Lecture 11 Shear centre q = VQ I Shear flow 11 Mechanics of Solids  Lecture 11 Shear flow resultants = 12 Mechanics of Solids  Lecture 11 Shear center Summing moments about point A , we require V e = F f h 13 Mechanics of Solids  Lecture 11 Procedure to determine shear centre c The direction of the shear flow is towards web above neutral axis away from web below neutral axis. c Obtain the shear flow resultant. Shear force will create a linear variation of shear flow in segments that are perpendicular to the force and a parabolic variation of shear flow in segments that are parallel to the force....
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This note was uploaded on 08/22/2011 for the course ENG 48331 taught by Professor Brown during the Three '11 term at University of Technology, Sydney.
 Three '11
 BROWN
 Environmental Engineering

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