STUDY GUIDE for Exam II (Summer 2002) - Chapter 8 – 13 (partial)

·  You should understand what quantities the constitutive equations relate (stress and strain) and how constitutive equations are obtained. You should know the definitions of different material types like anisotropic, isotropic and isotropic. You should know the meaning of material properties like Young’s modulus, shear modulus and Poisson’s ratio and how they are obtained. You should know from memory Hooke’s law for a linear, isotropic material. You should know E and for steel and aluminum.

·  You should know typical values of Young's modulus (E) and Poisson's ratio (u) for steel and aluminum, and the relation of the shear modulus (G) to E and u.

·  You should understand the basic definitions of strain measures (extensional and shear) and how they are derived. You should know what quantities the strain equations relate (strain and displacement). You should know from memory the exx and exy equation. You should understand the difference between finite and infinitesimal strain and between tensor and engineering strain.

·  You should understand the three types of bar problems we have covered in class: bars with axial force only, circular bars with torsion loads, and beams with bending loads. You should know the four general principles (equations) used to solve any of these problems: equilibrium (COLM & COAM), constitutive (stress-strain), kinematics (strain-displacement), and boundary conditions.

·  You should understand how to solve these 3 problem types with point loads and distributed loads.

·  You should understand what an indeterminate structure is. You should understand the various types of boundary conditions in bars and the kinematic conditions needed to solve indeterminate problems.

·  You should be able to apply free-body diagrams to obtain the internal axial force (), torque (), shear (, and bending moment () equations in terms of the applied load(s) and be able to draw diagrams of each. Know how to get the same results by the integration method.

·  You should be able to apply to draw axial force diagrams (for axial bar problems) and torque diagrams (for torsion problems. You should be able to do this for concentrated loads and distributed loads.

·  You should understand boundary conditions and how they are applied in solving for internal force and torque equations (diagrams). You should understand boundary conditions and how they are applied in solving for displacement in axial bar problems and angle of twist in torsion problems.

·  You should be able to able to determine axial displacements for axial bar problems and angle of twist for torsion problems. For each of these problems you should be able to obtain the respective stress (axial stress, shear stress, etc.). You should know the relationship between internal axial force P(x) and applied distributed load ; and between internal torque and applied distributed torque .

·  You should know how to determine sectional properties for J (polar moment of inertia) and memorize J for a solid circular bar and a tube.

·  You should understand how to determine the shear and bending moment equations and diagrams – by the free-body diagram method and the integration method. You should know the relationships between applied distributed load , transverse shear and bending moment .

·  You should know how to determine the centroid and the moments of inertia for a cross-section. You know how to apply the transfer theorem for moments of inertia. You should know I and J for typical cross-sections (rectangle, solid circular shape, tube).

·  You should know how to determine axial stress for a bending problem.

·  Determination of deflection and shear stress is not on this exam.

There may be some true/false, or multiple-choice questions. There will be five or six multi-part questions.

The exam will be closed book. An equation sheet will be provided with the exam (verify contents prior to exam). The exam will be approximately 90 minutes.