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.
DNACurve input (B11:C12); Stage 1 values are calculated, Stage 2 are use input
Concrete data range (A21:F27); top row is Stage 2 (in-situ) concrete
Reinforcement input range (I21:N25); Top 2 rows are for Stage 2 concrete
CompForceMom Function Results
Note that:
- 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:
Calculated Force and Moment (B45, B46) do not match the specified values (B8, C8)
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.
After iterative solution of NA Depth and Curvature; calculated force and moments match input values
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:
Display results using ElasticCompGS
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!
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Hi Doug,
I’m just about to start playing with the next version of your composite beam spreadsheet (VBA version) – have only read the website so far so not sure if these requests are already in the spreadsheet or easy to do:
– Ability to handle steel beam with concrete slab. I think in principal it would just need the beam section not to crack (ie handle tension stresses)?
– Redistribution of stresses and increase in curvature due to (differential) creep.
Cheers, Stephen
(only 5 years late…)
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Thanks for comments Stephen,
I haven’t done much with this spreadsheet since 2012, but your suggestions would certainly make it more useful.
I was working on adding a maximum concrete tensile stress (rather than zero), but that’s not finished. It would be easier to add a steel option, with no limit on tensile stress, so I’ll have a look at that.
As a work-around, I had a look at applying a concentric axial load at the centroid of the stage 1 beam, to keep everything in compression, but for some reason that seems to cause problems, especially if I specify no reinforcement (set all bar numbers to zero).
Adding provision for differential creep, shrinkage and temperature should be fairly easy, and I’ll do that when I have time. That won’t be for at least a couple of weeks, but I hope less than 5 years.
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