L1 - California Polytechnic State University Mechanics of...

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California Polytechnic State University Mechanics of Materials II (CE207) Fall 2008 1-1 1. Review of Mechanics of Materials I (CE 204) 1.1 Class Overview This course will begin with a brief review of statics and CE 204; then, will move to devel- oping more general definitions of stress and strain in a 3D coordinate system. Plane stress, stress in pressure vessels, and strain and stress transformations will be discussed in detail. Stress transformations using the Mohr's circle will also be demonstrated. The next phase of the class will focus on bringing together equilibrium, constitution, and compatibility equations in the derivation and solution of the 4th order Bernoulli beam equation. Beam deflections due to external stimuli will be solved for using direct integration methods. The final phase of the course will focus on stability of both deformable and rigid axially loaded elements. The Euler buckling equation will be derived and solved for various end restraint conditions and general formulas for buckling will be presented within the context of the theoretical development. 1.2 Overview In this chapter, important coursework from CE 204 will be reviewed highlighting important sections that the student is responsible for knowing prior to continuation in CE 207. This course will begin by quickly deriving some basic formulas that the student should have already seen; if material covered in this chapter appears new or unfamiliar, the student is advised to use this time to become updated with the material. The review presented herein will start with the basics of drawing axial force, shear force, and bending moment diagrams. After completion of Statics and CE 204, it is expected that
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California Polytechnic State University Mechanics of Materials II (CE207) Fall 2008 1-2 every student in the class be capable of quickly constructing these diagrams without diffi- culty. Then, concepts of stress and strain within a framework of equilibrium, compatibility, and material constitution will be explained. Basic formulas relating axial force, shear force, and bending moments to local stresses will be derived and explained in detail. 1.3 Axial Force, Shear, and Bending Moment Diagrams The fundamentals of the material for this class start with the creation or axial force (P), shear force (V), and bending moment (M) diagrams. The fundamental equilibrium equa- tions governing these forces along the length from statics is given below: (1-1) In the construction of axial force, shear, or moment diagrams, the first step is always to take the free body diagram and solve for the support reactions. Then, using equations of static equilibrium ( , , and for the case of 2D), the end forces of the members can be found. 1.3.1 Construction of the Axial Force Diagram Using the beam shown in Figure 1-1, and looking at only the axial forces on the free body diagram: (1-2) Axial Force x d d Vx +, w –x = Shear Force x d d Mx = Bending Moment L wx F 1 F 2 F 3 C 1 x d d Px tx = F x ¦ 0 =F y ¦ 0 =M ¦ 0 = L F 3 F 2 R
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California Polytechnic State University Mechanics of Materials II (CE207) Fall 2008 1-3
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This note was uploaded on 11/04/2008 for the course CE 207 taught by Professor Elghandour during the Spring '06 term at Cal Poly.

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L1 - California Polytechnic State University Mechanics of...

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