Beam and Floor Vibration Checks - Dynamic Modular Ratio and SCI AD 433
The SCI have published AD 433 (Advisory Desk note) providing advice on the choice of elastic modulus of concrete when undertaking the vibration analysis of a composite floor. The article can be downloaded from the New Steel Construction website here.
In the context of Tekla Structural Designer, this elastic modulus of concrete discussed by the AD is embodied in the dynamic modular ratio (also termed short term modular ratio) which is used in two design checks:
- Individual composite beam Vibration Checks.
- The SCI P354 Floor Vibration Check.
The dynamic modular ratio is Es/Ecm_d where;
- Es is the steel elastic modulus (210 GPa for the Eurocode)
- Ecm_d the dynamic concrete elastic modulus, which in TSD is taken as the value from Table 3.1 of EN 1992-1 for the specific concrete grade of the composite slab, increased for dynamic effects.
The dynamic modular ratio value used in checks (both individual beam and Floor Vibration) is controlled by the beam property setting labelled “Factor for increased dynamic stiffness of the concrete flange”* (see picture below). The factor is applied to the concrete modulus ‘static’ value from Table 3.1 of EN 1992-1, the default being 1.1 thus increasing it by 10% (following common practice in place for a number of years).
- (*Note that prior to the 2020 SP1 release the Floor Vibration check always used a fixed value of 1.100)
SCI P354 gives a fixed value of the dynamic concrete elastic modulus as 38.0 GPa and 22.0 GPa for Normal and Lightweight concrete respectively (regardless of concrete grade). SCI AD 433 advises “When using references 2 and 3, the stated values for dynamic modulus should not be enhanced by 10%”. Should the engineer wish to comply with this advice and NOT vary the dynamic concrete elastic modulus and hence modular ratio with the concrete grade, the factor discussed above can be set to a value that will yield the fixed value in the SCI advice - see below for a worked example.
E.g. for Grade C25/30 concrete, to set Ecm_d = 38.0 GPa, set the TSD factor = 1.226 which is calculated as follows:
The resulting modular ratio used in the Vibration checks is reported in the design details as the Short term modular ratio shown below.