×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Eccentrically loaded beam moment distribution

Eccentrically loaded beam moment distribution

Eccentrically loaded beam moment distribution

(OP)
Hello all,

So, I am familiar with the derivation of the maximum moment and stress of an eccentrically loaded beam with pinned ends. However how does the calculation change when both ends are fixed? Is such a beam overdetermined?

Thanks for your input! :)

RE: Eccentrically loaded beam moment distribution

if fixed at both ends then the "beam" is unloaded.

how does the beam interact with the rest of the world ? You show (carefully) no contact at the ends. Say there's a shear connection at the bottom end, then this'll react the beam axial load and the beam will "cock" in the clearances and develop a lateral couple to react the offset load. If the shear attmt is inline with the load then no moment to "the rest of the world", but there'll be an internal moment in the beam.

clear as mud ?

another day in paradise, or is paradise one day closer ?

RE: Eccentrically loaded beam moment distribution

What is this beam/column doing in its application? How do you achieve this pure rotational fixity and pure lateral fixity at the same time as vertical slip?

Check out Eng-Tips Forum's Policies here:
FAQ731-376: Eng-Tips.com Forum Policies

RE: Eccentrically loaded beam moment distribution

If the ends are fully fixed, the beam does not feel the effect of the force F, i.e. the beam has no stress and no deformation.

If one end of the beam is fixed against rotation but free to move in an axial direction and the other end is fully fixed, the beam feels an axial stress of F/A but no bending.

What is the meaning of "overdetermined"?

BA

RE: Eccentrically loaded beam moment distribution

I think the OP needs to clarify the end conditions and load application. To me it appears as if there are "guides" at each end and each side of the member. Graphically, it does not look like there is any end restraint.

RE: Eccentrically loaded beam moment distribution

"overdetermined" = reduntant, indeterminate

another day in paradise, or is paradise one day closer ?

RE: Eccentrically loaded beam moment distribution

Well, a beam fixed at both ends against rotation is theoretically indeterminate in the sense that the number of reactions exceeds those determined by statics alone but in this case, it is a trivial indeterminacy because the applied moment is resisted by the fixed ends.

If both end supports permit axial translation, the beam is unstable. The beam needs one reaction to prevent translation. It can be at an end or anywhere along the beam, but it is necessary for stability.

BA

RE: Eccentrically loaded beam moment distribution

(OP)
Re-reading this after myself, I really did not do a good job at explaining the load case!
I think the following diagram explains it better.
The case is of an eccentrically loaded tension specimen with the intention of superimposing tension and bending loads.
Fixed supports are actually roller supports, as displacement is allowed in x, but is fixed in y. Under tensile loading the beam center-line (red) should then deflect toward the overall center-line. As a result, there is a bending moment in the beam. What is the distribution of this bending moment along the beam in the x direction?

RE: Eccentrically loaded beam moment distribution

ok, that's clearer !

there is some moment restraint at each end. Draw a FBD of 1/2 the specimen. In all likelihood the unsupported mid-span of the specimen will deflect towards the load line of action, reducing the off-set moment; this moment will divide itself between the ends and the mid-span.

Depending on what you're trying to test, you could put a hinge at the end of the specimen, then the specimen would be in tension and the off-set moment reacted at the ends (ie a simple tension test). If you remove the rollers, and maybe load on a single point, you'd see the ends rotate as the mid-span tries to unload moment.

another day in paradise, or is paradise one day closer ?

RE: Eccentrically loaded beam moment distribution

I guess if the two ends of the member cannot rotate, there is NO moment in the member. Hook's Law - for internal force to occur in a member, you must have a corresponding deflection.
Since 0 rotation, then 0 moment.

The F x e moment is taken "out" by the boundary condition at that point since you dis-allow rotation in the member at the end.

Check out Eng-Tips Forum's Policies here:
FAQ731-376: Eng-Tips.com Forum Policies

RE: Eccentrically loaded beam moment distribution

if the end fixity is perfectly rigid then yes, otherwise (in the real world) the two finite stiffnesses (the end fixity and the specimen) will share the moment.

another day in paradise, or is paradise one day closer ?

RE: Eccentrically loaded beam moment distribution

You should fix one end in x and leave the other end free. Otherwise you have an instability in the x direction. Then you have pure axial tension throughout the beam.

BA

RE: Eccentrically loaded beam moment distribution

I suspect that the load is applied at one end against a reaction at the other (as i think you're suggesting). I doubt he's got active loading at both ends.

another day in paradise, or is paradise one day closer ?

RE: Eccentrically loaded beam moment distribution

I suspect you are correct rb1957, but his diagram does not show that. If he were to enter his support conditions into a frame analysis program, he would get an input error.

BA

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources