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MECHMAT 14: BEAMS IV – YOUTUBE PLAYLIST
Session 14.1 Beams IV – Single and Double Shear (Very Short Beams)
This video describes single and double shear scenarios, which can be visualized as an average shear stress acting on a cross section of a very short beam.
I made a mistake on the slide right before Question 1. The equation for the average shear stress in double shear should be P/(2A) instead of P/(4A). The notes for Session 14 have been corrected.
Session 14:Q1 Average Shear Stress vs Maximum Bending Stress in Single Shear
For a rectangular profile with a base b and height h under single shear, at what length L will the average shear stress be half the maximum bending stress?
Session 14:Q2 Average Shear Stress vs Maximum Bending Stress in Double Shear
For a rectangular profile with a base b and height h under double shear, at what length L will the average shear stress be half the maximum bending stress?
Session 14.2 Beams IV – Transverse Shear Stress (The Shear Formula)
This video describes the relationship internal shear force (derivative of bending moment), average shear stress, and transverse shear stress.
Session 14:Q3 Maximum Bending Stress in a Cantilevered Beam
For a beam with a rectangular profile with a base b and thickness/height h, what is the transverse shear stress at the neutral axis along the beam where the internal shear force is V? Hint: Q = bh2/8 at the neutral axis.
Session 14.3 Beams IV – First Moment of Area and Transverse Shear Stress
This video describes how to calculate the first moment of area for rectangular, circular, and hollow cross sections for use in determining the transverse shear stress at a specified location along a beam.
Session 14:Q4 Transverse Shear Stress in a Section of an Overhanging Beam
A beam has a distributed force applied to its overhang as shown. If the square has a side length of 10 mm and the point of analysis is a distance y above the neutral axis with a distance d from the right end of the beam, what is the transverse shear stress at this location in units of MPa? Hint: Take a look at 2015 Exam 2.
Mechanics of Materials – Session 14: Beam Bending IV
In-class problem-solving in small groups working to solve problems involving shear stresses along a beam.
Date: June 15, 2023
Date: March 7, 2023
Notes
Session 14: MechMat – Beams IV – Instructional Slides
Fa 2023 In-class and Office Hours Notes
Su2023 In-class and Office Hours Notes
Sp2023 MechMat In-class Notes Starting from Session 9
Session 14: MechMat- Beams IV – Colab IPython
Additional Video Content
Single Shear and Double Shear
This video by purdueMET describes applications where single shear and double shear are relevant.
Watch all 6:15.
Understanding Shear Stresses in a Beam
This video provides an excellent description of the internal stresses in a beam. For this session, focus on the second portion of the video discussing shear stresses.
Watch from 6:06 to 14:31 to understand shear force-shear stress relationships in a beam.
What is Transverse Shear Stress?
Jeff Hanson describes transverse shear stress. Near the end of the video, he also provides an explanation for how the transverse shear stress relates to the direction of shear force at a slice in the beam.
Watch all 15:58.
What is the First Moment of Area Q?
Jeff Hanson describes how to calculate the first moment of area, which is necessary for calculating transverse shear stress.
Watch all 18:02.
Online Text
5. Transverse Shear in Beams – TU Delft OCW
First moment of area – Wikipedia
4.2: Stresses in Beams – Engineering LibreTexts
Structural Analysis and Design | SkyCiv Engineering
For complementary information, see our YouTube Channel and the Wikibook.
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