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MECHMAT 18: Plane Stress II: Principal Normal Stresses & In-Plane, Max Shear Stress – YOUTUBE PLAYLIST
Session 18.1 Plane Stress II – In-plane Principal Stresses
Question 18.1
If an element has σx= 50 MPa, σy= -10 MPa, and τxy=10 MPa, what are in-plane principal stresses and what is the associated angle of rotation θp?
Session 18.2 Plane Stress II – In-plane Max Shear Stress
Question 18.2
If an element has σx=100 MPa, σy= -100 MPa, and τxy= 0 MPa, what is the maximum in-plane shear stress and what is the associated angle of rotation θS?
Session 18.3 Plane Stress II – Calculating Max/Min In-plane Principal Stresses
Question 18.3
For the element shown on the surface of this circular beam/shaft fixed to a wall with radius c, axial force P, and torque Tapp, what is the larger of the two in-plane principal stresses?
Session 18.4 Plane Stress II – Calculating In-plane Max Shear Stress
In the video, there is a typo with an extra x for one of the equations for tau_max. The latter instructional slides have this correction.
Question 18.4
For the element shown on the surface of this circular shaft/beam fixed to a wall with radius c, axial force P, and torque Tapp, what is the maximum in-plane shear stress?
Live Session 18: Plane Stress II – In-class Session
In-class problem-solving in small groups working on problems involving plane stresses, normal principal stresses, and in-plane max shear stresses.
Date: November 7, 2023
Date: June 22, 2023
Date: March 28, 2023
Notes
Session 18: MechMat – Plane Stress II – Instructional Slides
Fa 2023 In-class and Office Hours Notes
Su2023 In-class and Office Hours Notes
Sp2023 Session 18: MechMat – Plane Stress II – Instructional Slides
Sp2023 MechMat In-class Notes Starting from Session 9
Session 18: MechMat- Plane Stress II – Colab IPython
Additional Video Content
Understanding Stress Transformation
This video by the Efficient Engineer does an excellent job describing the use of the stress-transformation equations and how rotating an element affects depicted state of stress.
Watch from 2:12 to 3:33.
Principal Stresses Explained Using an Experiment (No Math)
This video by Solid Mechanics Classroom shows an interpretation of principal stresses experimentally by drawing a square and a square rotated by 45 degrees under pure shear.
Watch all 3:19.
Stress Transformation Example for Principal Stresses
This video by structurefree shows how to use equations to calculate principal stresses given a state of stress.
Watch all 7:20.
Stress Transformation Example for Principal Stresses
This video by structurefree shows how to use equations to calculate max in-plane shear stress given a state of stress.
Watch all 3:45.
Online Text
3.3: Tensor Transformations – Engineering LibreTexts
Plane Shear Stress – an overview | ScienceDirect Topics
1.10 Principal Stresses and Maximum in-plane Shear Stress | Advanced Mechanics of Materials and Applied Elasticity: Analysis of Stress | InformIT
Plane stress – Wikipedia
For complementary information, see our YouTube Channel and the Wikibook.
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