The previous post on this topic presented a spreadsheet performing elastic analysis of composite reinforced or prestressed composite beams, available for download from: Composite Design Functions-GS.zip. This post will look in more detail at how the spreadsheet works, and a preview of changes that will be presented in future versions.
The basis of the spreadsheet is the CompForceMom User Defined Function (UDF):
|=CompForceMom(DNACurveA, Conc, Reo)|
The three inputs for this function are:
- DNACurveA, a 2×2 range containing the calculated neutral axis depth and curvature of the Stage 1 beam under self weight and weight of the wet in-situ concrete for Stage 2 in column 1, and the estimated neutral axis depth and curvature of the composite beam under the incremental Stage 2 loading (i.e. live load plus any additional dead load applied to the composite beam after curing of the second stage concrete).
- Conc – a six column range with details of the composite section concrete, listed from top to bottom
- Reo – a six column range with details of the composite section reinforcement, listed from top to bottom, with the reinforcement depth of the Stage 1 beam measured from the top of the beam.
- The Stage 2 concrete (shaded light grey) must be a single rectangular layer with one or two layers of reinforcement.
- The Stage 1 concrete (shaded darker grey) may have any number of trapezoidal layers, specified as a continuous layer or with a central trapezoidal void.
- The elastic modulus for the Stage 2 concrete (Ec) and reinforcement (Es) must be specified in the top row. All other layers may be specified, or will be taken as equal to the row above.
Based on the specified neutral axis positions and section curvatures the CompForceMom function calculates the strains and stresses in each layer of concrete and steel (assuming concrete takes no tension), and hence the total axial force and bending moment for both Stage 1 and Stage 2 (composite section).
The Stage 1 neutral axis depth and curvature are calculated by the spreadsheet (using the Elastic UDF), but in general the Stage 2 values (input by the user) will not result in load values matching the specified combined loads on the section:
Note that the “combined moment” is the sum of the Stage 1 and Stage 2 applied moments, plus the moment due to the axial load about the the top face of the Stage 1 beam.
The Stage 2 neutral axis depth and curvature may now be adjusted by clicking the “Find NA and Curvature” button, which calls the SeekDNA routine. SeekDNA simply calls the Excel GoalSeek function to adjust first the Neutral Axis depth to match the input and calculated axial loads, then the curvature to match the input and calculated bending moments. This is repeated until both axial load and bending moment match within the specified tolerance.
Having found the final neutral axis depth and curvature the “ElasticCompGS” UDF is used to return details of stresses, strains, forces and moments on the section:
Proposed future developments of this spreadsheet are:
- Replace the Goalseek routine with the QuadBrent UDF, allowing the entire analysis to be encapsulated in a single UDF, for better performance and flexibility.
- Allow specified tension stresses in the concrete.
- Allow for specified differential strains between Stage 1 and Stage 2 concrete, and within each beam.
- Allow non-rectangular Stage 2 concrete slabs.
Any other requests? Please post a comment!