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# How does program calculate member deflections?

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## How does program calculate member deflections?

(OP)
I don't have RISA3D, but how do typical 2D or 3D frame analyzers determine member deflections (displacement), at every 1/50 member length or what?

I know they calculate each node displacement and rotation by the basic stiffness or flexibility matrices, but does it then use slope-deflection to calculate slope and displacement along each member, at every 1/50 of L?

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.

### RE: How does program calculate member deflections?

Nodal deflections are calculated, of course, based on the stiffness matrix solution.

Member deflections between nodes are based on standard beam theory considering loading and member stiffness and such... the same way the shear and moment diagrams are derived.

Standard Beam theory does not inherently account for shear deformation whereas the FEM solution does(based on your solution settings). So, we use any joints along the length of the member as known deflections when solving the deflection equations. That way, we are guaranteed to wind up at correct deflection at each node along the length of the beam.

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