Consider a cantilever beam as shown in the figure with length and the left end fixed to a wall. Derive the deflection of the beam along under a single downward force on the right, and assume that the moment of inertia is constant along. (Show complete derivation instead of the final function ) Now consider that the beam has two connected parts, with the part on the left (of length ) having a moment of inertia , and the part on the right . Derive the deflection again. Ignore stress concentration. Further, consider that the cross-sections for the two parts are both circular, and the total volume of the beam is constant. What should and be for the beam to have minimal maximum deflection?
Consider a cantilever beam as shown in the figure with length and the left end fixed to a wall.
-
Derive the deflection of the beam along under a single downward force on the right, and assume that the moment of inertia is constant along. (Show complete derivation instead of the final function )
-
Now consider that the beam has two connected parts, with the part on the left (of length ) having a moment of inertia , and the part on the right . Derive the deflection again. Ignore stress concentration.
-
Further, consider that the cross-sections for the two parts are both circular, and the total volume of the beam is constant. What should and be for the beam to have minimal maximum deflection?
![ㅋ
Length = l
F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbb5604a-0a4b-46ed-92e3-55159cd22786%2F005ea389-ef06-444c-b9e1-aba6726f1677%2Fxw5lw49_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Structural Analysis](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781337630931/9781337630931_smallCoverImage.jpg)
![Structural Analysis (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134610672/9780134610672_smallCoverImage.gif)
![Principles of Foundation Engineering (MindTap Cou…](https://www.bartleby.com/isbn_cover_images/9781337705028/9781337705028_smallCoverImage.gif)
![Structural Analysis](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781337630931/9781337630931_smallCoverImage.jpg)
![Structural Analysis (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134610672/9780134610672_smallCoverImage.gif)
![Principles of Foundation Engineering (MindTap Cou…](https://www.bartleby.com/isbn_cover_images/9781337705028/9781337705028_smallCoverImage.gif)
![Fundamentals of Structural Analysis](https://www.bartleby.com/isbn_cover_images/9780073398006/9780073398006_smallCoverImage.gif)
![Sustainable Energy](https://www.bartleby.com/isbn_cover_images/9781337551663/9781337551663_smallCoverImage.gif)
![Traffic and Highway Engineering](https://www.bartleby.com/isbn_cover_images/9781305156241/9781305156241_smallCoverImage.jpg)