Chapter 13 - Strain Transformations

Announcements

If you have two final exams scheduled for the same time period or three final exams on the same day, you must visit the Registrar's office as soon as possible. You will be given a letter to deliver to the instructor that is to reschedule your final.  It is not determined by your instructors.

Objectives

Course objective:  To understand the concept of strain as a second order tensor.

Learning objectives:

  • Apply strain transformation equations and Mohr's circle to the following calculations.
  • Calculate normal and shear strains for inclined planes (or rotated elements) (0.99).
  • Calculate principal orientation and principal strains (1.13).
  • Calculate maximum-shear orientation, maximum-shear strain, and average strains (1.13).
  • Draw (or identify correct) strain-element diagram for the following calculations (1.20).
  • Calculate absolute-maximum-shear strain.
  • Acquire information from a given Mohr's circle (1.18).
    • normal and shear strains, principal strains, maximum shear strain, average strains, absolute maximum shear strain, orientation angles
  • Draw Mohr's circle based on normal and shear strains and then acquire remaining information.
    • center point, radius, principal strains, maximum shear strain, average strains, absolute maximum shear strain, orientation angles
  • Recognize the difference between plane stress and plane strain.
  • Derive information from strain-gage readings.
    • normal and shear strains (0.85)
    • maximum shear strain (1.15)
    • principal orientation (0.78)
  • Convert between stresses and strains based on Hooke's Law (1.14).
  • Calculate changes in dimension for vessels, plates, and rods.
    • length (1.08)
    • thickness (0.96)

The values in orange represent quiz performance.  One represents average.  Values greater than one represent easier topics.  Values less than one represent harder topics.

Concepts  (19 minutes)

1. plane strain video notes
2. generalized hooke's law video notes
3. theories of failure video notes
4. algebra help for strain gages
    - solving for multiple variables in multiple equations

Demos  (4 minutes)

1. strain gages video
2. strain indicator video

Quiz Prep

1. The quiz will be multiple choice as usual.  Instead of asking you to draw pictures of stress elements, you will be asked to identify the correct picture from a group of five.
2.  You will need to know how to both read and draw Mohr's circles in order the answer the questions related to them.

Problems  (119 minutes)

assigned 3e 2e & 1e aids WP format
equations   13.001+ 13.001 video solution TENU
yes 13.002+ 13.002 strategy solution GO
  13.003+ 13.003 -- -- TENU
  13.004+ 13.004 -- -- --
  -- 13.005 -- -- --
  -- 13.006 -- -- --
    yes   13.005   --   --   --   TENU  
        13.006   --   --   --   GO  
  13.007* 13.007 video solution --
  13.008* 13.008 -- -- --
  13.009* 13.009 strategy solution --
  13.010* 13.010 -- -- --
  -- 13.011 strategy solution --
  -- 13.012 -- -- --
        13.011*   --   --   --   --  
        13.012*   --   --   --   --  
  13.013* 13.013 video solution --
  13.014* 13.014 -- -- --
  13.015* 13.015 -- -- --
yes 13.016* 13.016 video solution TENU
  13.017* 13.017 -- -- TENU
  13.018* 13.018 strategy solution --
yes 13.019* 13.019 -- -- TENU
  13.020* 13.020 -- -- --
  13.021* 13.021 -- -- --
  13.022* 13.022 -- -- --
mohr's
circle
yes 13.023* 13.023 strategy solution TENU
  13.024* 13.024 -- -- --
  13.025* 13.025 video solution --
  13.026* 13.026 -- -- --
yes 13.027* 13.027 strategy solution TENU
  13.028* 13.028 -- -- --
  13.029* 13.029 -- -- --
  13.030* 13.030 -- -- --
  13.031* 13.031 strategy solution --
  13.032* 13.032 video solution --
yes 13.033* 13.033 -- -- TENU
  13.034* 13.034 -- -- --
  13.035* 13.035 -- -- --
  13.036* 13.036 -- -- --
  13.037* 13.037 video solution --
  13.038* 13.038 -- -- --
strain
gages
  13.039* 13.039 strategy solution --
yes 13.040* 13.040 -- solution TENU
yes 13.041* 13.041 video solution GO
  13.042* 13.042 strategy solution TENU
  13.043* 13.043 -- -- GO
  13.044* 13.044 -- -- TENU
  13.045* 13.045 strategy solution --
yes 13.046* 13.046 video solution TENU
  13.047* 13.047 -- -- --
  13.048* 13.048 -- -- TENU
hooke's
law
yes 13.049* 13.049 strategy solution TENU
  -- 13.050 video solution --
        13.050   --   --   --   TENU  
  13.051* 13.051 -- -- TENU
yes 13.052* 13.052 strategy solution TENU
  13.053* 13.053 -- -- TENU
  13.054* 13.054 -- -- --
        13.055   --   --   --   TENU  
        13.056   --   --   --   GO  
  13.057* 13.055 -- -- TENU
  13.058* 13.056 -- solution --
  -- 13.057 strategy solution GO B137
yes -- 13.058 video solution TENU B131
        13.059   --   --   --   GO  
        13.060   --   --   --   TENU  
        13.061   --   --   --   TENU  
  -- 13.059 -- -- --
  -- 13.060 -- -- TENU B132
  -- 13.061 -- -- --
yes -- 13.062 video solution TENU B133
        13.062   --   --   --   TENU  
  13.063* 13.063 -- -- --
  13.064* 13.064 -- -- --
  13.065* 13.065 -- -- --
  13.066* 13.066 -- -- --
  13.067+ 13.067 -- -- TENU
  -- 13.068 -- -- GO B138
        13.068   --   --   --   --  
  13.069+ 13.069 -- -- --
  -- 13.070 strategy solution TENU B134
        13.070   --   --   --   --  
  13.071+ 13.071 video solution --
  -- 13.072 -- solution TENU B135
        13.072   --   --   --   --  
yes 13.073+ 13.073 video solution GO
  -- 13.074 -- solution TENU B136
        13.074   --   --   --   --  
  13.075+ 13.075 -- -- --
  13.076+ 13.076 strategy solution --
  13.077* 13.077 -- -- TENU
  13.078* 13.078 -- solution GO

* numbers were changed between the second and third editions
+ problem statement changed between second and third editions

props

 

 

 

Problems 12.46 in the second edition and 12.69 part c will not be on the quiz.