Upon the completion of the course the student should be able to:
• Define the concepts of stress and strains
• Identify the Mechanical Properties of Materials and apply concepts of elasticity
• Apply Hooke’s law for plane stress and plane strain
• Determine stresses and strain in axially loaded and torsionally loaded members
• Write the equations for shear and bending moments in terms of position with respect to the beam centroid.
• Calculate the stresses in spherical and cylindrical pressure vessels and the stresses produced by combined axial, bending and torsional loads
•Calculate the deflections of statically determined beams.
• Calculate the reactions and deflections of statically indeterminate beams, using the solution of the elementary differential equation of the deflection curve, and superposition
Introduction. Review of Statics. Normal Stress and Strain. Mechanical Properties. Poison ratio. Allowable Stresses. Hooke's Law. Stresses in 3D. Torsion and Bending.
Constitutive Equations. Linear Elasticity. Axially loaded members. Statically Indetermined Structures. Thermal Effects and Misfits. Stresses on Inclined Sections. Strain Energy. Impact Loading. Dynamic Loads and Fatigue. Stress Concentration.
Torsion. Torsional Deformation on Cylindrical Bars. Torsional Formula. Non-Uniform Torsion. Stresses and Strain in Pure Shear. Statically Indetermined Torsional Members. Strain Energy in Torsion. Thin Walled tubes. .
Bending Moments and Shar Forces in Beams. Sign Convention. Relationships between Loads, Shear Forces and Bending Moments. Shear Force and Bending Moment Diagrams. Distributed Loads. Method of Superposition. Compound Beams. Curvature. Sign Convention for Curvature. Stresses and Strains due to Bending. Flexural Formula. Maximum Stresses at a Cross Section. Shear Stresses in Beams.
Analysis of Stresses and Strains. Stresses on Inclines Sections. Transformation Equations for Plane Stress. Principal Stresses and Maximum Shear Stresses. Mohr's Circle for Plane Stress. Hooke's Law for Plane Stress. Triaxial Stress. Plane Strain. Transformation Equations for Plane Strain. Principal Strains and Mohr's Circle for Plane Strain. Calculation of Stresses from Strains.
Spherical and Cylindrical Pressure Vessels. Combined Loadings. Selection of Critical Points.
Deflections of Beams. Differential equation of the deflection curve. Small angles of Rotation. Non-Prismatic Beams. Prismatic Beams. Deflections by Integration of the Bending-Moment Equation. Deflections by Integration of the Shear-Force and Load Equations. Deflections by the Method of Superposition. Deflections by the Moment-Area Method. Nonprismatic Beams. Strain Energy of Bending. Deflections by Castigliano's Theorem. Deflections produced by Impact. Temperature effects.
Statically Indeterminate Beams. Types. Analysis by Differential Equations of the Deflection Curve. Method of Superposition. Temperature Effects. Longitudinal Displacements at the Ends of a Beam.
Assessment, grades and tentative dates
Homework, attendance and exams
Final Exam
Dr. Pablo G. Caceres
Copyright © 2002 RUM-UPRM. All rights reserved.
Revised: 09/29/09.