Slope Deflection Method - Frame with Support Settlement Example

[@ednaacosta9490]

When to use the modified slope deflection equation?

[@notSavant]

In a beam problem I had with singularity functions, one of the compatibility equations was that the Moment of a support is zero... does that mean the sum of the moments is zero or that there's no moment in the reaction??

[@AFMathandEngineering]

Hey man, thanks for your questions. It depends on what kind of support you're talking about. If the support in question resists rotation, there will be a moment developed at that support, assuming some load is acting on the beam. However, if you have a support that doesn't resist rotation, e.g. pin or roller connection, the sum of moments at that support must equal zero.

[@AFMathandEngineering]

Just a hint: It helps to think about it in terms of restraint against rotation or movement. If a support prevents a member or whatever it's attached to from moving, the support itself must be resisting that movement and that internal force will be developed there.

[@notSavant]

Shouldn't it be wL^2/8 for the FEMcd? From the tables I have, wL^2/12 is when there are moments on both sides like both ends are fixed ie.

[@AFMathandEngineering]

wL^2/8 is the equation for the maximum moment of a simply supported beam at midspan. wL^2/12 is the formula for a beam in which both ends have fixed supports, and is the value of the moment at the supports. Hope that helps!

[@billyjanssen5823]

@@AFMathandEngineering wl^2/8 is FEM_cd where joint C is fixed and joint D is a pin or roller. Also if Joint D is a pin or roller, there is no fixed end moment so FEM_cd would not equal -FEM_dc.

[@AFMathandEngineering]

@@billyjanssen5823 reread his post, I was clarifying to him why we don't use wl^2/8. It doesn't matter if there isn't any fixed end moment in the actual beam, assuming the ends are fixed and finding the moment is a technique used in a number of structural analysis techniques.

[@wilsonteh1467]

@@AFMathandEngineering so when im finding FEM for any question, i just have to assume both ends are fixed eventhough there is a roller support in the question?

[@AFMathandEngineering]

@@wilsonteh1467 Yes

[@niruda638]

If the Frame is sway but the question say "Neglect the axial deformation " then how to solve the problem (Can I consider as non-sway Frame ?)

[@AFMathandEngineering]

It sounds like they want you to ignore p-delta (second order) effects on the frame with that note. Does the question say sway? If it states sway I dont think you can assume non sway.

[@AFMathandEngineering]

Or perhaps they're referring to slenderness of the members (buckling) that you can ignore. Sorry I'd need to see the question!

[@zikas-dev]

2020