Composite Beam deflections including camber
We are regularly asked questions such as:
- How do composite beam deflections work?
- Why are the design check deflections different to those in the Results View/ Load Analysis View?
- What is the “Post Composite” deflection and how is this calculated?
- How is the “Total Deflection” calculated?
- How do deflections work when camber is applied to the beam?
- Why do I need to set one Camber combination?
- Why is camber not subtracted from the Dead, Imposed and Post Composite deflections?
If you have such questions, please read on.
AnswerSee the attached Example zip files which contain:
- An example TSD file of a typical composite beam bay arrangement.
- An Excel spreadsheet showing how the various deflections including camber are calculated. You can type in your own values of camber and deflection results from TSD into this in the blue shaded boxes to see the resulting cambered deflection values for your own case.
There are two examples and zip files; one for the US AISC 360 LRFD code and one for the Eurocode UK NA. The fundamental behaviour of composite beams and the principals discussed are applicable to all design codes, differences being in detail only.
Study of the example file and spreadsheet should answer most of your questions on how the various deflection values - including the effects of camber - are calculated. Some key points are:
Fundamentals of Composite Deflection
TSD automatically carries out a highly complex and extensive set of calculations required to design composite beams and determine a reasonable estimate of their deflections following the methods outlined in various design codes and guides. For more information on this see the Help Topic Composite beam design.
- The behaviour of composite beams is complex and has a number of “stages” each of which has different stiffness characteristics:
- Pre-composite (Construction) - when the concrete slab is cast but has not set there is no composite action. Stiffness and capacity are based on the steel section properties alone.
- Post-composite - the concrete slab is fully hardened and full composite action is achieved. The stiffness and capacity are based on the composite inertia.
- This is further divided into two “sub-stages”: Short term and Long term composite.
- Fundamentally, the determination of composite deflections is a Design process, not an analytical one. Design codes and guides give various practical and semi-empirical methods to estimate the post-composite deflections, depending on multiple parameters such as; concrete grade and type, proportion of long term imposed load, steel decking form and dimensions, degree of shear connection...and many more.
- To accommodate this behaviour TSD applies a practical solution of a single global linear analysis - not some form of non-linear staged construction analysis, which would be complex and time-consuming and not necessarily any more accurate. Thus, by default*, the deflections from the analysis in the Results and Load Analysis Views are from the steel section stiffness alone with no composite action.
- (*Optionally you can set the inertia used for analysis to be the composite short or long term inertia via Analysis > Settings > Composite Steel Beams)
- The Pre-composite deflections due the beam and slab self-weight (both Wet and Dry) result from the steel beam section inertia alone. These deflections are “locked in”. The wet slab supports nothing and only sits on, loads and deflects the beam, which does not spring back up when composite action occurs.
- Post-composite deflections are calculated post-analysis, as part of the composite beam design process, which involves the calculation of the post-composite inertia (both short and long term) and a process of superposition of the various staged deflections.
- Importantly, these deflections are incremental, not absolute. They begin from the ‘locked in’ pre-composite deflection discussed above, as subsequent loads - such as Finishes, Partitions, Imposed loads etc - are added post-composite action.
- Hence the deflections of all other load cases (included in design combinations*) are assumed to occur post-composite.
- *The single exception to this is any additional load cases - such as Construction Imposed - included in the special Construction Stage Load combination (this is a special combination Class listed in the Class options) which checks that the beam is adequate for construction stage loading. Such load cases and the Construction Stage combination are NOT automatically calculated and applied and are the responsibility of the engineer to apply.
- For the Imposed (Live) load case(s) there is the additional complication of assessing both short and long term deflections. These are governed by; the % of long term set for the Imposed load case(s) (in the Loading dialog) AND the composite slab Long term elastic modulus factor (set in Slab parameters).
- The calculated short and long term composite inertias are reported in the Design details.
Deflections with Camber
Camber is NOT applied by default and must be deliberately activated by the engineer. It can be applied either automatically - as a proportion of loading deflection - or directly as a fixed value.
- Typically and by default when activated, the camber is calculated and applied automatically as a proportion (%) of the selfweight deflection, the ‘selfweight’ in question being that of the composite slab including the beam self weight - as shown in the picture below.
- The objectives of these settings are typically; to take out the pre-composite deflection so the floor is reasonably flat when additional loads - such as Finishes etc - are applied, to limit ponding of the wet concrete and to reduce the overall (Total) deflection.
- As shown below, the engineer has full control of the loading and % values to be considered.
- There can only be one, single value of camber. Thus, if it is being determined by the program for you, as a proportion of load deflection (which could include various loads and load cases), it is necessary to specify the single governing combination from which these deflections are to be taken. This combination is set by the engineer via the “Camber” check box in the Loading and Combinations Dialog.
- The calculated and applied camber is displayed in various places so you can be certain about its application (shown in the picture below via the text “C=25”*) - these are:
- The Steel Beam Design Summary Table (and the associated Report item) in the column headed "Camber".
- The Tooltip information which is displayed when you move the cursor over a beam.
- The 2D Attributes text (enabled via the Scene Content for views and included in GA drawings).
- The design summary tabular data and reports
- The header of the Design Details Summary Table.
- *Note that the units and precision of the camber value are set via Home > Model Settings > Units > Camber.
- If there is no such Camber value text, then no camber has been applied!
- Why would this be? When camber is being applied automatically - as shown in the picture above - note that there is a “Do not apply if required camber is <” minimum setting. So, when the deflection resulting from the camber settings specified by the engineer is less than this minimum - also in control of the engineer - no camber is applied.
- This can also happen if the member span length is smaller than the value set in the "Do not apply if beam length is <" minimum setting.
- Since, as discussed above, the composite beam deflections are incremental and cumulative - not absolute - camber is not subtracted from all of them.
- Each successive load case deflection takes out some amount of camber, until it is all gone. When the camber is removed, it is no longer subtracted from subsequent (incremental) deflections.
- Thus - where the objective of the camber settings is to remove the majority of the pre-composite deflection - typically none remains at the post-composite stage. Hence typically camber will not be subtracted from Dead, Live, and Post Composite deflections, since they all occur post-composite action. This is illustrated in the example spreadsheet in the “Camber Remaining” column.
US AISC 360/341 LRFD Example