MechMat: Beams VI – Superposition, Indeterminacy, and Springs

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MECHMAT 25: Beams VI – Superposition, Indeterminacy, and Springs – YOUTUBE PLAYLIST

Session 25.1 Beams VI – Superposition

Session 25.1 Beams VI – Superposition
My reasoning for Session 25 Question 1 and the solution posted for the class are flawed. While the approach is reasonable, the exact solution is incorrect.
Note about issue with Session 25 Question 1 added on April 18, 2024.

Session 25.2 Beams VI – Indeterminacy

Session 25.2 Beams VI – Indeterminacy
In Example 25.4, the expression for \delta_M should be \delta_M=-\delta_M_1+\delta_M_2. The updated slides from Su2023 have the negative in the correct spot.

Session 25.3 Beams VI – Beams as Springs

Session 25.3: Beams VI – Beams as Springs
My reasoning for Session 25 Question 4 and the solution posted for the class are flawed. Question 4 has been adjusted in the fall of 2024 to be a reasonable example of how to think about a beam working in parallel with a given spring.
Note about issue with Session 25 Question 4 added on April 18, 2024.

Notes

Fa2024 Session 25: MechMat – Beams VI – Superposition, Indeterminacy, and Springs – Instructional Slides
Su2024 Session 25: MechMat – Beams VI – Superposition, Indeterminacy, and Springs – Instructional Slides
Fa2023 Session 25: MechMat – Beams VI – Superposition, Indeterminacy, and Springs – Instructional Slides
Fa 2023 In-class and Office Hours Notes
Su2023 Session 25: MechMat – Beams VI – Superposition, Indeterminacy, and Springs – Instructional Slides
Su2023 In-class and Office Hours Notes
Sp2023 Session 25: MechMat – Beams VI – Superposition, Indeterminacy, and Springs – Instructional Slides
MechMat In-class Notes Starting from Session 9

Online Text

Euler–Bernoulli beam theory – Wikipedia
Beams – Wikiversity
Roark’s Formulas for Stress and Strain – Wikipedia
List of finite element software packages – Wikipedia

Live MechMat Session

Mechanics of Materials – Session 25: Beams VI – Superposition, Indeterminacy, and Springs
In-class problem-solving in small groups working on problems involving deflection of determinate and indeterminate beams with techniques of superposition, integrations, and treatment of beams as springs.

Fa 2024 MechMat Session 25: Beams VI – Superposition, Determinacy, and Effective Springs
Date: December 10, 2024

Live MechMat Session 25: Office Hours and Beams VI – In-class Session (Mechanics of Materials)
Date: July 3, 2024

Live MechMat Session 25: Beams VI – In-class Session (Mechanics of Materials)
Date: December 7, 2023

MechMat Session 25+: Beams VI – In-class Session (Mechanics of Materials)
Date: July 5, 2023

MechMat Session 25: Beams VI – In-class Session (Mechanics of Materials)
Date: April 28, 2023

Select Assignment Questions

Session 25 – Question 2
Derive the elastic curve/displacement along an indeterminate beam constrained between two walls with an applied distributed force

Session 25 – Question 3
Using Superposition of Pre-determined Solutions/Table Entries to Determine Displacement Halfway along a Beam Constrained between Walls

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