## Estimate stiffness/drift in a steel moment frame

## Estimate stiffness/drift in a steel moment frame

(OP)

Is there a quick way to estimate lateral deflection in a moment frame? Like say you have a portal frame fixed at the base and at all connections, dummy lateral load at the top, find the deflection within 30 seconds (without a computer - Im studying for the SE).

I get estimating the inflection point to get shear/moment, but then what? Is there a way to get to deflection by just using FEMs of the beam and columns? Or is moment area method and integration the only way to go?

I get estimating the inflection point to get shear/moment, but then what? Is there a way to get to deflection by just using FEMs of the beam and columns? Or is moment area method and integration the only way to go?

## RE: Estimate stiffness/drift in a steel moment frame

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## RE: Estimate stiffness/drift in a steel moment frame

PL^3/3EI

Guess one would need to be careful about that is L and what is I but it seems like a quick and dirty start.

Would depend on if the frame is fixed base or not I suppose...

## RE: Estimate stiffness/drift in a steel moment frame

## RE: Estimate stiffness/drift in a steel moment frame

I guess maybe the question is how do you estimate the inflection point if you have a different length and EI for the columns and beams? Like is it possible to take a ratio of column rigidity to beam rigidity to estimate the inflection point, then do moment area method to get deflection? Or is 0.5 to 0.6 height nearly always OK to use?

## RE: Estimate stiffness/drift in a steel moment frame

This is somewhat inaccurate, of course, because it assumes the connection at the top of the portal frame, between beam and column, does not rotate. But it is in the ball park.

DaveAtkins

## RE: Estimate stiffness/drift in a steel moment frame

Basically work out the inertia of the column group (i.e. Sum of Ah2 where A is the column area, and h is the distance from the column group centroid to the centre of the column.)

Using PL^3/3EI for the bending deflection, and WL/AG for the shear deflection I imagine that will give you a reasonable estimate of the frame sway

(N.B. just checked on a 4 bay frame - factor of 10 out so maybe not).

## RE: Estimate stiffness/drift in a steel moment frame

## RE: Estimate stiffness/drift in a steel moment frame

delta = (P*h^3)/(12*E*Icol)*(3*K+2)/(6*K+1)

where:

K = (Ibm/Icol)*(h/L)

P = lateral load on frame

h = height of frame

L = length of frame

E = modulus of elasticity

Icol = moment of inertia of column

Ibm - moment of inertia of beam

There is a similar equation with the same terms arranged differently in an August 2008 Structure Magazine article titled "Optimum Beam-to-Column Stiffness Ratio of Portal Frames Under Lateral Loads". I assume the two equations give same or similar results, but I have not evaluated both side by side.

Both articles also have an equation for pinned base moment frames.