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
circleyes 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
gages13.039* 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
lawyes 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
Problems 12.46 in the second edition and 12.69 part c will not be on the quiz.