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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 8, 2024
Date: June 20, 2024
Date: November 7, 2023
Date: June 22, 2023
Date: March 28, 2023
Notes
Fa 2024 Session 18: MechMat – Plane Stress II – Instructional Slides
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
Select Assignment Questions
Session 18 – Question 1
Using Trial-and-Error Method with Colab (Python) Script to Transform and Find Max In-plane Shear Stress on a Material Element
Using an Analytical Expression to Calculate the Max In-Plane Principal Stresses for an Axially Loaded and Twisted Shaft
Using an Analytical Expression to Calculate the Max In-Plane Shear Stress for an Axially Loaded and Twisted Shaft
Additional Video Content
Understanding Stress Transformations
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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