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# QUICK ESTIMATE FOR SWAY DEFLECTION IN A MULTISTOREY STEEL MOMENT FRAME

## QUICK ESTIMATE FOR SWAY DEFLECTION IN A MULTISTOREY STEEL MOMENT FRAME

(OP)
I'm preparing for the IStructE Chartered member examination in January. I'm looking for a very "quick and dirty" way of estimating the sway deflection under wind load in a steel building moment frame. Typical building bay width is 6 to 8 m and storey height 3 to 4 m. Could be any number of bays or storeys.

Been googling this all day but no success. Needs to be a 2 minute back of envelope calculation.

Thanks.

### RE: QUICK ESTIMATE FOR SWAY DEFLECTION IN A MULTISTOREY STEEL MOMENT FRAME

Here is what I did when I took the Illinois SE examination (many years ago!).

Assume joints do not rotate. Assume point of inflection is always at mid-height of story. Then, the deflection of each half story height is equal to the deflection of a fixed end cantilever: VL^3/3EI, where V is the story shear and I is the summation of I for the story.

DaveAtkins

### RE: QUICK ESTIMATE FOR SWAY DEFLECTION IN A MULTISTOREY STEEL MOMENT FRAME

(OP)
Great idea, The beams will magnify the displacement though. I will model a typical frame on computer, assuming equal stiffness of members for comparison. That will give me an idea of the magnification factor. I'll report back. Thanks.

### RE: QUICK ESTIMATE FOR SWAY DEFLECTION IN A MULTISTOREY STEEL MOMENT FRAME

(OP)
OK using Dave Atkins method above I checked it against an SFRAME analysis model. A two storey frame with three bays. Bay width 6m and storey height 3m.

Assuming beams and columns of equal stiffness rotation at beam-column joints will magnify Column displacements By a factor of 2.25 approx. using this I will develop a table of factors to amplify column sway displacement for various ratios of beam and column stiffness.

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