## Member Sizing

Member Sizing Process: The process involving member sizing includes calculations based on structural steel tables and assume equations standard in the field. The following link is a set of 3 tables with all member sizes, maximum moments, shear stresses, deflections and other useful information :

Member Size Tables:

Below, we have documented our member sizing process step by step.

The first step was to determine the live and dead loads within the building. These are summarized as follows:

- Dead Loads

* Steel Framing: 10 psf

* 6″ Concrete Deck: 72 psf

* Interstitial: 10 psf

* Ceiling: 5 psf

-Live Loads

* Office Live Load – 1st floor: 100 psf

* Office Live Load – subsequent floors: 80 psf

* Snow Load: 30 psf

-Total First Floor Load: 197 psf or 0.197 ksf

-Total Subsequent Floor Load: 177 psf or 0.177 ksf

-Total Roof Load: 127 psf or 0.127ksf

These figures were taken from the IBC 2009. The following map shows, for example, how we deduced the snow load for our building.

The wind loads acting on the ASCE National Headquarters are first defined by the basic wind speed map provided in the IBC 2009.

The following map shows that the design wind speed for our area is 90 mph. The effects of wind loads on our building are included in the stress diagram section of this website. Wind loads were not, however, used to size the members as we were not asked to design bracing or shear walls.

The second step for our member sizing was to decide how many types of beams and columns to design.

1. Columns: For ease of construction and reasons of aesthetics, the columns on each floor will be identical. All columns are therefore sized based on first floor loading as this is the worst case scenario. Furthermore, on each floor, there will be 3 sizes of columns, each carrying loads from a different tributary area: 2 types of facade columns and one type of interior column. For simplicity of construction, corner columns have been overdesigned as facade columns.

2. Beams: Different beam sizes were required for the first floor, the roof . Beam sizes on floors 2 through to 5 are identical. Furthermore, on each floor, 3 different beam sizes may be found according to their length (20 ft, 25ft and 40 ft) and tributary width.

3. Shear connections were designed for each beam.

The third step was calculating the maximum moments, shear stresses and axial loads on the members and sizing them according to the AISC.

Sample Calculations:

In order to size beam B1-A and its shear connection, the following steps were taken:

* Calculate w = load per square ft x tributary width= 0.197 x 5 = 0.985 k/ft

* Calculate the maximum moment M= wl2/8 = (0.985 x 202)/8 = 49.25 k.ft

* Read from the AISC ASD Curves ,the most efficient beam size for this moment is W10 x 30

* Check allowable deflection for this beam using the following table present in IBC 2009

For our building, we assumed this beam will be supporting a non plaster ceiling. Therefore the allowable deflection is l/240 = 20 x 12″/240 = 1 in

* calculate actual deflection = (5wl4)/384EI= (5 x 0.985 x 204 x 123)/ 384 x 29000 x 170) = 0.719 in.

* Actual deflection is lower than allowable deflection so the beam size is safe and serviceable.

* Calculate the maximum shear V= wl/2= 0.985 x 20/2 = 9.85 k.

* Read from AISC the shear connection that will withstand 9.85 k: A325, SC class A, t=1/4″ has an allowable stress of up to 21.3 k

In order to size column C1, the following steps were taken:

* Calculate axial load = (first floor load + 4 x 2nd floor load + roof load) x tributary area = (0.197 + 4 x 0.177 + 0.127) x 20 x 20 = 1.032 x 400 = 412.8 k

* Reading from AISC, the most efficient column size is W14 x 74