Estimate stiffness/drift in a steel moment frame

[adamewood]

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?

 

[JAE]

Once you have a moment diagram for the frame you can use the Moment Area method to get the deflection at the top. Just add up the moment areas up one column and you have it.

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[HouseBoy]

Would the equation for deflection of a cantilever with a point load at the end be accurate enough?
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...

 

[ukbridge]

IIRC theres a method described in Iain MacLeods book "Modern Structural Analysis" that treats the moment frame as an equivelant cantilever based on the number of bays - you can then calculate dx based on PL3/48EI using the value of EI you work out using the method.

 

[adamewood]

Because you are putting the inflection point at around 0.5 to 0.6 the height (assuming all EI are equal), the deflection would be less than 1/3 PL^3/EI... so moment area method does make sense.

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?

 

[DaveAtkins]

I had this exact question when I took, the SE exam (many years ago). I divided the column into two cantilevers--one from the base up to an inflection point at mid height, the other from the top of the frame down to the inflection point. Assuming V is the horizontal shear at the top of the portal frame and H is the height of the frame, then V/2 is the shear in each column (since there are two columns in a portal frame). The deflection of the frame will be [(2)(V/2)(H/2)^3]/[(3)(E)(I)].

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

 

[ukbridge]

I think I can now remember the method.

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).

 

[BUGGAR]

Kleinlogel

 

[gte447f]

From April 1993 Modern Steel Construction, Steel Interchange, for fully fixed 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.