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
Engineering and Comp Sci Homework Help
Calculating Deflection and Stress in a Tapered Cantilever Beam
Reply to thread
Message
[QUOTE="SteamKing, post: 5076146, member: 301881"] There probably won't be a simple deflection formula. Since the moment of inertia of the beam varies with length, deflections will probably best be calculated using the double integration method: [itex]θ(x) = \int^x_0 \frac{M(x)}{EI(x)} dx + C_1[/itex] [itex]δ(x) = \int^x_0 θ(x) dx + C_2[/itex] where: θ(x) - slope of the beam δ(x) - deflection of the beam I(x) - moment of inertia of the beam, as a function of the length E - Young's modulus for the beam material C[SUB]1[/SUB] and C[SUB]2[/SUB] - constants of integration; determined by applying the boundary conditions at the fixed end, i.e. θ(0) = δ(0) = 0. Even if you can determine the moment of inertia I(x) as a function of x, you probably won't get simple functions for M(x)/I(x) to integrate. You may have to use a numerical integration method to obtain θ and δ. The shear force and bending moment diagrams are calculated based on the loading of the beam only. The taper does not come into play. The regular formulas for bending stress and shear stress still apply ... you do have to calculate the section properties of the beam at the location where you want to determine the stresses. Unlike a prismatic beam, if you change the location of where the stresses are calculated, you must re-calculate the section properties at that new location. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Engineering and Comp Sci Homework Help
Calculating Deflection and Stress in a Tapered Cantilever Beam
Back
Top