Register to reply

Non-standard Beam Bending Question - Parallel to Neutral Axis

by TerryTate
Tags: axis, beam, bending, neutral, nonstandard, parallel
Share this thread:
Jun12-12, 10:16 AM
P: 3
Hi there, first post on these forums. I have a seemingly simply question about beam bending.

We (mechanical engineers) are all very familiar with the standard beam bending scenario. The beams are always shown being loaded perpendicular to the neutral axis, regardless of the type of support. My question is, what is the method of solving a beam loaded parallel to the neutral axis? (See attachment)

The image depicts a beam being pulled by a rope, lets say. The interesting part of it is that as the beam deflects, the moment arm of the load begins to grow with respect to the support.

Any suggestions as to how to solve such a thing without resorting to computer modeling? I'm really just looking for the beginnings of an approach so that I can work it out for myself, but I'm on the fence as to where to begin.

Any thoughts appreciated!
Attached Thumbnails
Phys.Org News Partner Engineering news on
Researchers use 3D printers to create custom medical implants
For secure software: X-rays instead of passport control
Razor-sharp TV pictures
Jan31-13, 12:04 PM
P: 3
Bump, because why not! Still interested in an approach.
Jan31-13, 03:23 PM
Sci Advisor
HW Helper
PF Gold
P: 6,474
IMO, you won't be able to do the calculation in one step. An iterative approach will be called for, whether by hand or by computer. One method to research is called the 'P-delta' method, which is used a lot for columns loaded eccentrically.

Obviously, if you want to do a few iterations by hand, replace the tension on the eyebolt with an equivalent axial load and end moment at the free end. Calculate deflections using regular beam methods. Use resulting deflection to recalculate the end moment. Check deflections to see how much of an increase results. Rinse and repeat until the change in deflection becomes small enough to ignore.

Jan31-13, 05:58 PM
Sci Advisor
HW Helper
P: 7,115
Non-standard Beam Bending Question - Parallel to Neutral Axis

You can formulate a linearized model that can be solved "in one step". The effect of the load acting about a new position is the same as an extra stiffness term, which can be negative or destabilizing, unlike the stiffness due to the material properties.

This extra term is called the "load stiffness", or sometimes a "follower force". Google will find the math details for you.

This linearized formulation is often a good enough approximation, if the final displacements of the structure are small. Otherwise, as SteamKing said, you have to do an iterative numerical solution.

Register to reply

Related Discussions
Beam bending-neutral axis General Physics 4
Neutral axis in a composite beam Mechanical Engineering 1
Establishing Neutral Axis & Second Moment on a T bar beam Engineering, Comp Sci, & Technology Homework 25
Finding Neutral Axis & Second Moment on a T-beam Introductory Physics Homework 9
Neutral axis in a beam-proof Classical Physics 0