Moment Frame Napkin Calculations

This Dynamo script computes the maximum permissible beam spans for a rectangular moment frame system. These computations are based on material and section properties of the structural elements.

Based on user-defined mass element, beam section, column section, and area load, the script assembles a structural moment frame with the maximum span.

It provides owners/architects a preliminary estimate of how bulky, costly, and sustainable (embodied CO2) the frame structure will be.

How to use the tool

Download the Moment_Frame_Napkin_Calculations bundle zip folder, extract its contents.

1. Place a mass element in Revit. Assign it mass floors.
2. Open Dynamo Player and locate Moment_Frame_Napkin_Calculations.
1. Ensure that Moment_Frame_Napkin_Calculations.Dependencies folder is accessible.
3. Define the inputs for the script:
• Click on Mass Element with mass floors (from Step 1).
• Press ESC key to deselect the element in the Revit Workspace because the Mass Modify interface may obstruct the Dynamo script.
• Uniformly distributed area load (pounds per square foot)
• Structural Beam
• Type (any Structural Framing Family loaded in the Revit Project, includes material)
• Cost per cubic foot
• Embodied Carbon Factor (ECF): ratio of embodied CO2 weight to beam weight
• Structural Column Type
• Type (any Structural Column Family loaded in the Revit Project, includes material)
• Cost per cubic foot
• Embodied Carbon Factor (ECF): ratio of embodied CO2 weight to beam weight
4. Click the Run/Play button.
5. Scroll down to see the output metrics, look at Revit workspace to see the elements.

Computations

Beam capacity

Based on the yield moment (yield stress * strong axis plastic section modulus), determine the maximum (square) span dictated by the beams (bending capacity). The beam spans will determine how much bending moment the beam will undergo, which cannot exceed the beam’s capacity:

$M_{max}=w L_y L_x^2/8=wL^3/8$

$M_y=F_y S_{strong}$

$L_{max}=(8 F_y S_{strong} / w)^{1/3}$

Column capacity

Based on the interstory height and the column section area, determine the maximum (square span) dictated by the columns (compression capacity). The beam spans will determine how much compression the column will undergo, which cannot exceed the column’s capacity:

$P_{critical}=A*f(F_y,F_e)$ [critical stress]

$F_e=(\pi r/kL)^2E$ [buckling stress]

$P=wL_xL_y=wL^2$

$L_{max}=(P_{critical}/(w N_{floors}))^{1/2}$

Frame design

Use the smaller of the beam-/column-driven maximum spans (Lmax) to draw the structural grid (X and Y spacing). The Z spacing is provided by the mass floor elevations.

Results

Moment frame assembly:

Based on the computed structural grid,

For this proof of concept, the column orientation is unidirectional throughout the structure. There is a strong and weak direction.

Gross metrics of the structural system:

• Gross volume of the structural elements
• Ratio of structural element volume to total mass volume
• Total cost
• Weight of structural moment frame (pounds)
• Embodied CO2 from structural moment frame (pounds)
• Column moment capacity check (true if stronger than beams, false if weaker (problem!))

Video Example

(No sound, just walking through the steps)