Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Advanced Physics Homework Help
Elastic energy of a bent steel rod
Reply to thread
Message
[QUOTE="cedricyu803, post: 4493107, member: 423695"] [h2]Homework Statement [/h2] [Math. for Physicists, M. Stone Problem 1.4] Assume that a rod of length L is only slightly bent into the yz plane and lies close to the z axis, show that the elastic energy can be approximated as [tex]U[y]= \int_{0}^{L} \frac{1}{2}YI(y'')^2 dz[/tex] [h2]Homework Equations[/h2] It is given that the elastic energy per unit length of a bent rod , [tex]u=\frac{1}{2}YI/R^{2}[/tex] R is the radius of curvature due to the bending, Y is the Young's modulus of the steel and I is the moment of inertia of the rod's cross section about an axis through its centroid and perpendicular to the plane in which the rod is bent. [h2]The Attempt at a Solution[/h2] I don't quite get the picture. Does it mean that each infinitesimal piece is a segment of a circle R with a different center? Or should I consider the whole bent rod as a segment of a circle of radius R? But still the infinitesimal rod length should be [tex]\sqrt{1+(y')^2} dz[/tex], so how can I get [tex]y''^2 [/tex]? Thank you very much! [h2]The Attempt at a Solution[/h2] [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Elastic energy of a bent steel rod
Back
Top