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MECHMAT 13: BEAMS III – YOUTUBE PLAYLIST
Session 13.1 Beams III – Radius of Curvature and Longitudinal Strain
This video describes the general local deformation of a beam subjected to a bending moment, the relationship between radius of curvature and longitudinal strain, the effect of Poisson’s ratio on normal strains orthogonal to the longitudinal axis.
Session 13:Q1 Longitudinal Strain for a Given Radius of Curvature
If the radius of curvature for a bending beam is 𝜌 and the specified location is a distance 𝑦 above the neutral axis, what is the longitudinal strain along the beam at the specified location in percent? If the Poisson’s ratio for the material is 𝜈, what is the corresponding strain in the vertical direction at the specified location in microstrain?
Session 13.2 Beams III – Bending Moment and Bending Stress (Flexure Formula)
This video describes the relationship between bending moments and bending stresses, along with brief introductions of the 1st and 2nd moments of area.
Session 13:Q2 Maximum Bending Stress in a Cantilevered Beam
For a beam with length L, height h, and second moment of area I loaded with force P as shown in the diagram, what is the maximum bending stress in the beam in units of MPa?
Session 13.3 Beams III – Second Moment of Area and Bending Stresses
This video describes how to calculate the second moment of area for rectangular and circular cross sections, use the parallel axis theorem to calculate the second moment of area for complex chapes, and calculate bending stresses at a given location with a specified cross-sectional profile.
Session 13:Q3 Bending 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 bending stress at this location in units of MPa? Hint: Take a look at 2015 Exam 2.
Notes
Su 2023 Session 13: MechMat – Beams III – 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 13: MechMat- Beams II – Colab IPython
Mechanics of Materials – Live Sessions 13: Beam Bending III
In-class problem-solving in small groups working to solve problems involving radius of curvature-strain in a beam, along with the flexure formula: internal bending moments and bending/normal stresses along a beam.
Date: October 19, 2023
Date: June 14, 2023
Date: March 3, 2023
Additional Video Content
Understanding Shear Force and Bending Moment Diagrams
This video provides an excellent description of the internal stresses in a beam. For this session, focus on the first part of the video discussing bending stresses associated with internal moments.
Watch first 6:32 to understand bending moment-bending stress relationships.
Understanding the Area Moment of Inertia
This video provides an excellent description of how the area of moment of inertia provides resistance to bending. It also details the math necessary to perform the appropriate integrals about designated axes and directions, the parallel axis theorem, and adding and subtracting shapes to form composite shapes.
Watch up to 7:30 to cover the relevant material in this session.
Online Text
lec18.pdf | Mechanics & Materials I | Mechanical Engineering | MIT OpenCourseWare
lec19.pdf | Mechanics & Materials I | Mechanical Engineering | MIT OpenCourseWare
4.2: Stresses in Beams – Engineering LibreTexts
The Ultimate Guide to Shear and Moment Diagrams | DegreeTutors.com
Structural Analysis and Design | SkyCiv Engineering
For complementary information, see our YouTube Channel and the Wikibook.
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