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RPI - ENGR 2090 - Engineering Dynamics Exam 1 - Study Guide

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RPI - ENGR 2090 - Engineering Dynamics Exam 1 - Study Guide

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background image Topic=Yellow  Subtopic=Green  Engineering Dynamics Study Guide Exam 1   Brief Review of Statics    Types of Support  1 unknown    -force with known line of action     - eg.; rollers, rockers, frictionless surfaces   2 unknowns    -force of unknown direction    -eg.; pins, hinges, rough surfaces   3 unknowns    -unknown forces and moment    -eg.; fixed support    Types of Loading  Forces: Distributed, point  Moments: bending, torsional     The Tools  Free Body Diagrams (FBD)  Equations of Equilibrium  -  F=0 M=0  Stress  Types of Stress  Normal Stress  -  Perpendicular to plane  Tensile Stress (+)  Compressive Stress (-) 
background image Shearing Stress  -  Transverse (parallel to the sectioning plane)  -  Eg.; bolts, pins, rivets  Bearing Stress  Stress  Internal Stress  -  There are six independent components to internal stress  Stress on an oblique plane  -  Normal Component 𝐹𝐹 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃  -  Tangential Component 𝑉𝑉 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 
-  Area 𝐴𝐴
𝜃𝜃 = 𝐴𝐴 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛ℎ𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃   Max Stress Directions  -  Normal stress is max when 𝑃𝑃 is 0  -  Tangential is max when 𝑃𝑃 is 45 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑐𝑐   Factor of Safety  𝑈𝑈𝑈𝑈𝑡𝑡𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑 𝑆𝑆𝑡𝑡𝑑𝑑𝑑𝑑𝑐𝑐𝑐𝑐 𝐴𝐴𝑈𝑈𝑈𝑈𝑐𝑐𝐴𝐴𝑖𝑖𝐴𝐴𝑈𝑈𝑑𝑑 𝑆𝑆𝑡𝑡𝑑𝑑𝑑𝑑𝑐𝑐𝑐𝑐    Stress and Strain  -  Normal Stress 𝜎𝜎 = 𝑃𝑃
  -  Normal Strain (elongation) 𝜖𝜖 = 𝛿𝛿
  Stress/Strain Graph  -  Area = Strength  -  𝜎𝜎 𝑢𝑢 = 𝑢𝑢𝑢𝑢𝑢𝑢𝑃𝑃𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑃𝑃𝑢𝑢𝑠𝑠𝑢𝑢𝑃𝑃𝑠𝑠𝑢𝑢ℎ  -  𝜎𝜎 𝑦𝑦 = 𝑦𝑦𝑃𝑃𝑢𝑢𝑢𝑢𝑦𝑦 𝑃𝑃𝑢𝑢𝑠𝑠𝑢𝑢𝑃𝑃𝑠𝑠𝑢𝑢ℎ    Statically Indeterminate Problems  -  Structures for which internal forces and reactions cannot be determined from statics alone are  said to be statically indeterminate   -  A structure will be statically indeterminate whenever it is held by more supports than are  required to maintain its equilibrium   Thermal Stress  -  𝛿𝛿 𝑇𝑇 = 𝛼𝛼(𝛥𝛥𝛥𝛥)𝐿𝐿  -  𝛼𝛼= thermal expansion coefficient  
background image -  A temperature change results in a change of length or thermal strain. There is no stress  associated with the thermal strain unless the elongation is restrained by the supports.  Side Notes  -  Normal stress is perpendicular to plane  -  Shear is tangential to plane   -  Shear can’t take place in one plane only   -  Shear stresses on perpendicular faces are equal in magnitude and opposite in rotation  orientations   -  The state of stress at a point in the body is defined by all the stress vectors which constitute a  second-order tensor   Poisson’s Ratio  -  𝑉𝑉 =  − 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑠𝑠𝑢𝑢𝑢𝑢 𝑃𝑃𝑢𝑢𝑠𝑠𝑢𝑢𝑃𝑃𝑃𝑃/ 𝑢𝑢𝑎𝑎𝑃𝑃𝑢𝑢𝑢𝑢 𝑃𝑃𝑢𝑢𝑠𝑠𝑢𝑢𝑃𝑃𝑃𝑃     Hooke’s Law  -  𝜎𝜎 = 𝐸𝐸𝜖𝜖 𝑃𝑃𝑃𝑃 𝑃𝑃𝑃𝑃𝑢𝑢𝑦𝑦 𝑢𝑢𝑠𝑠𝑦𝑦𝑢𝑢 𝑓𝑓𝑃𝑃𝑠𝑠 𝑢𝑢𝑃𝑃𝑃𝑃 − 𝑢𝑢𝑎𝑎𝑃𝑃𝑢𝑢𝑢𝑢 𝑃𝑃𝑢𝑢𝑃𝑃𝑢𝑢  Bulk Modulus  -  K represents s bulk modulus   -  G is the shear modulus   Saint Venant’s Principal   -  Stress distribution may be assumed independent of the mode of load application except in  the immediate vicinity   Stress Concentration Factor  -  𝑘𝑘 = 𝜎𝜎
  Torsion   -  Circular shafts in torsion  -  Torsion causes shear in longitude and latitude surfaces   -  C represents radius of shaft  -  L represents length of shaft   -  𝛾𝛾 = 𝑃𝑃ℎ𝑢𝑢𝑢𝑢𝑠𝑠 𝑃𝑃𝑢𝑢𝑠𝑠𝑢𝑢𝑃𝑃𝑃𝑃  -  Torque = sum of moments about axis   

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School: Rensselaer Polytechnic Institute
Department: OTHER
Professor: John Drazan
Term: Fall 2017
Tags: Engineering and dynamics
Name: Engineering Dynamics Exam 1
Description: These notes cover exam 1 of Engineering Dynamics.
Uploaded: 02/26/2018
7 Pages 51 Views 40 Unlocks
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