L14_ PureBending- fall 10-1

L14_ PureBending- fall 10-1 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 14– Beams: Pure Bending Lecture 14 Pure Bending Structural members and loads Axial Loads (bars and cables) CHAPTERS 2 Torsional Loads (shafts and tubes) CHAPTER 3 Bending Loads (beams) CHAPTERS 4,5,6,8,9 Todays’s Objective Define pure bending Develop elastic flexure formula I My x = σ Today’s Homework Relationship between normal stress and applied moment EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 14– Beams: Pure Bending Classification of Beams Typical Beams For now, analyze only statically determinate beams Supports and reactions Roller - vertical reaction Pinned - vertical and horizontal reaction Fixed - vertical, horizontal and moment reaction
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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 14– Beams: Pure Bending Internal Forces Sign Convention M M’ M’ Hogging Sagging +ve moment Compression in top Tension in bottom -ve moment Tension in top Compression in bottom Transverse Loading : Concentrated or distributed transverse load produces internal forces equivalent to a shear force V and a bending moment M Internal forces V and M can be determined from equilibrium = = = = Px M M P V F B y 0 0 EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 4 Lecture 14– Beams: Pure Bending We will start our analysis of beams by looking at a prismatic member subjected to pure bending . Consider the beam below (which represents a barbell held overhead by a weightlifter) Within the central portion of the beam M =constant, V =0. The center section is in Pure Bending Shear force diagram 80 lb 80x12=960 lb.in Bending moment diagram Note how the beam will deform – center portion in pure bending will form a circular arc
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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 5 Lecture 14– Beams: Pure Bending Symmetric Member in Pure Bending The three equations are in terms of the normal stress, σ x . But the stress distribution is statically indeterminate, so we need to consider deformations. Consider a prismatic
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L14_ PureBending- fall 10-1 - EAS 209-Fall 2010...

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