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Unformatted text preview: Mechanics of Solids Lecture 7 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: Fridays 9:0012:00 Office hours: Wednesdays 10:0012:00 1 Mechanics of Solids  Lecture 7 Outline Outline Revision of the subjects covered in the exam Slope and deflection of beams 2 Mechanics of Solids  Lecture 7 Announcement Midterm Exam Autumn 2011 Wednesday, 20 th April 3 Start/End time:9:0012:10 Mechanics of Solids  Lecture 7 Formula sheet Hookes Law for axial stressstrain Hookes Law for shear stressstrain E = G = Generalized Hookes Law y x z x E E E = y x z y E E E = y x z z E E E = Deflection of a rod of span L under axial load ( ) L P x dx = Axial stress under axial load N A = Axial stress under bending moment M y I = Moment of inertia of the rectangle (about the z axis) 3 z bh I = y 4 ( ) EA x Deflection of a uniform rod of span L under uniform load PL EA = Thermal expansion of a uniform rod of span L T TL = 12 zz z Shear stress Shear flow VQ I b = VQ q I = Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (a) 5 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (a) 6 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (a) 7 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (b) 8 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (b) 9 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (b) B 10 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 1 (b) 11 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 2 12 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 2 (a) 13 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 2 (b) 14 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 2 (b) 15 Mechanics of Solids  Lecture 7 Revision of exam questionsQuestion 3 16 Mechanics of Solids  Lecture 7 Question 3 Total 12 Marks Determine the stress in the brass and the aluminium plates From equilibrium P b + P a =450 P b =450 P a 17 From compatibility P brass aluminium b a = = Mechanics of Solids  Lecture 7 Question 3 Deflection at each component can be written as 2 3 3 10 40 60 105 10 b b P = 2 3 3 10 2 10 60 70 10 a a P = rom compatibility nd equilibrium = 50 18 ( ) 3 2 2 3 3 450 10 3 10 3 10 40 60 105 10...
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