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**Unformatted text preview: **Mechanics of Solids Review Lecture by Dr Emre Erkmen Lecturer, School of Civil and Environmental Engineering, The University of Technology Sydney Office: 2.520 Phone:9514 9769 Email: [email protected] Lecture hours: Tuesdays 11:00-14:00, Wednesdays 15:00-18:00 Office hours: Tuesdays 15:00-17:00 Mechanics of Solids - Lecture 13 For forces on a particle to be in equilibrium, the net force must be equal to zero ∑ F = 0 Forces on a particle In contrast to the forces on a particle, the forces on a rigid-body are not usually concurrent and may cause rotation of the body (due to the moments created by the forces). For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point i must be equal to zero. ∑ F = 0 and ∑ M i = 0 Forces on a rigid body Mechanics of Solids - Lecture 13 Consider the Moment of Inertia about each of the four axes. About which axis will the Moment of Inertia be the smallest number? A) Axis 1 d 3 d 2 4 3 2 A • C Axis B) Axis 2 C) Axis 3 D) Axis 4 E) Can not tell. d 1 1 Mechanics of Solids - Lecture 13 Given: Internal shear force 1. Determine the location of the neutral axis and calculate the ___________________________ of the entire cross section bout the neutral axis Calculate: Shear stress : using the shear formula moment of inertia about the neutral axis 2. Pass an imaginary horizontal section through the point where the shear stress is to be determined. Measure the width of the area at this section 3. Calculate the ___________________ for the area laying either above or below the section first moment of area Mechanics of Solids - Lecture 13 1) For a beam subjected to bending moment, which of the following statement is incorrect? A) Plane section remains plane C) The length of the longitudinal axis remains unchanged B) Cross section remains perpendicular D) In-plane distortion of cross section is not negligible 2) Which of the following statements is incorrect for bending of a straight member? A) Bending stress is proportional to the C) bending stress is not a function bending moment of the location B) Bending stress is inversely proportional D) None to the moment of inertia of the section Mechanics of Solids - Lecture 13 1) The stress distributions at different cross sections are different (see figure below). However, at locations sufficiently far away from the support and the applied load, the stress distribution becomes uniform. This is due to A) Principle of superposition C) Poisson’s effect B) Inelastic property D) Saint Venant’s Principle Mechanics of Solids - Lecture 13 The principle of superposition is valid provided that a) The loading is linearly related to the stress or displacement b) The loading does not significantly change the original geometry of the member c) The Poisson’s ratio v ≤ 0.45 d) Young’s Modulus is small A) a, b and c C) a and b only B) a, b and d D) All Mechanics of Solids - Lecture 13 A) mm B) N/m C) micron D) no unit What is the unit of strain? Mechanics of Solids - Lecture 13...

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