Chapter 12 - Stress Transformations

Objectives Course objectives: To understand the concept of stress as a second order tensor. To learn how to calculate the principal stresses, and how they are related to the failure of various materials. Learning objectives: Apply plane-stress transformation equations and Mohr's circle to the following calculations. Draw (or identify correct) stress-element diagram for the following calculations. Calculate normal and shear stress for inclined planes (or rotated elements) (1.08). Calculate principal orientation and principal stresses (1.02). Calculate maximum-shear orientation, maximum-shear stress, and average stresses (1.17). Calculate absolute-maximum-shear stress (1.11). Acquire information from a given Mohr's circle (1.17). normal and shear stresses, principal stresses, maximum shear stress, average stresses, absolute maximum shear stress, orientation angles Draw Mohr's circle based on normal and shear stresses and then acquire information from the circle (1.25). center point and radius for Mohr's circle, principal stresses, maximum shear stress, average stresses, absolute maximum shear stress, orientation angles 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  (26 minutes) 1. state of stress at a point video notes 2. plane stress transformations video notes 3. hibbeler's stress-visualizer software video 4. principal stresses and maximum shear stresses video notes 5. mohr's circle video notes

Problems  (121 minutes) assigned 3e 2e 1e aids WP format   stress element   yes   12.001   12.001   --   --   --   TENU           12.002   12.002   --   --   --   TENU           12.003   12.003   --   --   --   --           12.004   12.004   --   --   --   GO           12.005   12.005   --   --   --   --           12.006   12.006   --   --   --   GO           12.007   12.007   --   --   --   --           12.008   12.008   --   --   --   TENU           12.009   12.009   --   --   --   --           12.010   12.010   --   --   --   TENU           12.011   12.011   --   --   --   --       yes   12.012   12.012   --   --   --   GO           12.013   12.013   --   --   --   --           12.014   12.014   --   --   --   TENU           12.015   12.015   --   --   --   TENU           12.016   12.016   --   --   --   TENU   equilibrium   12.017* 12.017 12.001 -- -- TENU   12.018* 12.018 12.002 -- -- TENU   12.019* 12.019 12.003 video solution --   12.020* 12.020 12.004 -- -- --   12.021* 12.021 12.005 -- -- --   12.022* 12.022 12.006 -- -- TENU   12.023* 12.023 12.007 -- -- TENU   12.024* 12.024 12.008 -- -- TENU equations yes 12.025* 12.025 12.009 strategy solution TENU   12.026* 12.026 12.010 -- -- TENU   12.027* 12.027 12.011 -- -- --   12.028* 12.028 12.012 -- -- TENU   12.029* 12.029 12.013 strategy solution --   12.030* 12.030 12.014 strategy solution TENU   12.031* 12.031 12.015 video solution --   12.032* 12.032 12.016 -- -- --   12.033* 12.033 12.017 -- -- TENU yes 12.034* 12.034 12.018 video solution TENU   12.035* 12.035 12.019 strategy solution TENU   12.036* 12.036 12.020 -- -- --   12.037* 12.037 12.021 -- -- TENU   12.038* 12.038 12.022 -- -- TENU   12.039* 12.039 12.023 video solution -- yes 12.040* 12.040 12.024 strategy solution TENU principals and max shear yes 12.041* 12.041 12.025 video solution TENU yes 12.042* 12.042 12.026 video solution TENU yes 12.043* 12.043 12.027 video solution TENU   12.044* 12.044 12.028 -- -- TENU   12.045* 12.045 12.029 strategy solution --   12.046* 12.046 12.030 strategy solution --   12.047* 12.047 12.031 strategy solution --   12.048* 12.048 12.032 strategy solution --   12.049* 12.049 12.033 -- -- GO   12.050* 12.050 12.034 -- -- TENU   12.051* 12.051 12.035 -- -- TENU   12.052* 12.052 12.036 -- -- TENU   12.053* 12.053 12.037 -- -- --   12.054* 12.054 12.038 -- -- --   12.055* 12.055 12.039 -- -- --   12.056* 12.056 12.040 -- solution --   12.057 12.057 12.041 -- -- --   12.058 12.058 12.042 -- solution TENU   12.059 12.059 12.043 -- -- GO   12.060 12.060 12.044 -- solution TENU   12.061 12.061 12.045 -- -- TENU   12.062 12.062 12.046 strategy solution -- mohr's circle   12.063 12.063 12.047 video solution --   12.064 12.064 12.048 strategy solution --   12.065 12.065 12.049 -- -- --   12.066 12.066 12.050 -- -- --   12.067 12.067 12.051 video solution --   12.068 12.068 12.052 strategy solution -- yes 12.069* 12.069 12.053 -- -- TENU yes 12.070* 12.070 12.054 -- -- TENU   12.071* 12.071 12.055 -- -- TENU   12.072* 12.072 12.056 -- -- TENU   12.073* 12.073 12.057 strategy solution --   12.074* 12.074 12.058 -- -- --   12.075* 12.075 12.059 -- -- --   12.076* 12.076 12.060 strategy solution --   12.077* 12.077 12.061 -- -- --   12.078* 12.078 12.062 -- -- --   12.079* 12.079 12.063 -- -- --   12.080* 12.080 12.064 -- -- -- yes 12.081* 12.081 12.065 video solution GO   12.082* 12.082 12.066 video solution GO     12.083* 12.083 12.067 video solution GO   12.084* 12.084 12.068 video solution GO yes 12.085* 12.085 12.069 strategy solution GO   12.086* 12.086 12.070 -- -- GO   12.087* 12.087 12.071 -- -- GO   12.088* 12.088 12.072 -- -- GO   12.089* 12.089 12.073 video solution TENU   12.090* 12.090 12.074 -- -- GO general stress state   12.091 12.091 12.075 -- -- TENU   12.092 12.092 12.076 -- solution GO   12.093 12.093 12.077 -- -- --   12.094 12.094 12.078 -- solution --   12.095 12.095 12.079 -- -- --   12.096 12.096 12.080 -- -- TENU   12.097 12.097 12.081 -- -- --   12.098 12.098 12.082 -- -- --   12.099 12.099 12.083 -- -- -- * numbers changed between first and second editions props

 

 

 

2. The tau on 12.2 in the second edition should be +1478 psi.

3. The tau on 12.14 in the second edition should be +3.69 MPa.