Spring, 2019 ME 323 Mechanics of Materials Lecture 18 Review for Exam 1 Reading assignment: HW1-HW5 News: Ready for the exam? Instructor: Prof. Marcial Gonzalez
Announcements Exam 1 - Wednesday February 20 th, 8:00-10:00 p.m., room FRNY G140 (please arrive 15 minutes before the exam and bring a picture ID) - Formula sheet will be provided and it is already uploaded to the blog. - Those of you who require extra accommodation please come to ME2053 and bring your accommodation letter and picture ID. (please arrive 15 minutes before the exam, e.g., 6:45 p.m.). - Lecture this Wednesday at 11:30 a.m. your Friday is free!!!! 2
Review Summary of topics - State of stress vs. state of strain (generalized Hooke s law) - Bolted and pinned joints. Factor of safety. - Axial deformations (statically indeterminate problems) - Thermal loads - Torsional deformations (statically indeterminate problems) - Truss structures (statically indeterminate problems) - Shear force and bending moments in (determinate) beams - Lectures 1 14 (stresses in beams is NOT included) 3
Equation sheet for Exam 1 B A 4
Equation sheet for Exam 1 B A 5
Shear stress and strain Direct shear: Bolted joint & Pinned joint Average shear stress: Average shear stress: 6
Axial deformation Axial deformation (summary) - Geometry of the solid body: straight, slender member with cross section that is either constant or that changes slowly along the length of the member. - Kinematic assumptions: cross sections, which are plane and are perpendicular to the axis before deformation, remain plane and remain perpendicular to the axis after deformation. In addition, cross sections do not rotate about the axis. Strain: Elongation: - Material behavior: isotropic linear elastic material; small deformations. Homogeneous: - Equilibrium: Homogeneous: Homogeneous, constant cross section, no body forces, thermal load: Homogeneous, loaded with body forces: 7
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Cross sections, which are plane and are perpendicular to the axis before deformation, remain plane and perpendicular after deformation. Radial lines remain straight and radial as the cross section rotates about the axis Shear strain Total angle of rotation - Material behavior: isotropic linear elastic material; small deformations. Homogeneous: - Equilibrium: (torque-twist equation) max = r 0 L max = Tr 0 I p Homogeneous: Homogeneous, constant cross section: 8
Equilibrium of beams Equilibrium relationships (summary) - Sign convention! These are all positive external loads and couples = = Note: become familiar with sign convention for external loads and for internal reactions. 9
Review problems Axial deformations statically indeterminate structures 1) Free body diagram 2) Equilibrium equations 3) Force-displacement behavior 4) Compatibility conditions 5) Solve for unknowns Problem 10) Compatibility conditions Problem 9) Compatibility conditions For a small angle of rotation and member AD rigid: 10
Review problems Indeterminate trusses (ToDo: ) statically indeterminate structures 1) Free body diagram 2) Equilibrium equations 3) Force-displacement behavior 4) Compatibility conditions 5) Solve for unknowns Problems 12-13) Compatibility conditions with B fixed (angle measured at D from x-axis to the member counterclockwise) with C fixed with D fixed 11
Review problems Torsional deformations Example 16 Determine the maximum shear stress in the steel and the maximum shear stress in the aluminum. Example 17 Determine the strain energy density. Determine the total rotation at D. Determine the state of stress at given points. Example 18 Select dimensions that fulfill design constrains 12
Review problems Conceptual examples (40 short questions!!) - Start working on the lecture book! https://www.purdue.edu/freeform/me323/lecture-notes/430-section/ 13
Review session Exam 1 Best of luck in the exam! Examples for today: 1- Indeterminate axial loads 2- Indeterminate trusses 3- Indeterminate torsional loads 4- Shear force and bending moment diagrams 14