Serviceability limit state (SLS) (Composite beams: AISC 360)
Section properties (SLS)
In the calculation of the gross moment of inertia of the composite section the steel deck is ignored as is any concrete in tension. The concrete is converted into an equivalent steel section using an effective modular ratio based on the proportions of long and short term loads which are relevant to the particular calculation. Two alternative approaches are given - see p.16.1-308 in the 2005 Commentary, p.16.1-353 in the 2010 Commentary, p.16.1-381 in the 2016 Commentary, or p. 16.1-433 in the 2022 Commentary for obtaining these properties.
One (the 'traditional method') calculates the gross uncracked inertia of the transformed section, Iequiv. The other uses a given formula to determine a 'lower-bound' inertia. The simpler 'traditional method' is the approach adopted in Tekla Structural Designer.
Note: Earlier editions of the
Specification recommended an additional reduction factor of 0.75 be applied to
Iequiv, however on p.16.1-381 in the 2016 edition and p. 16.1-433 in the
2022 edition, it states that this factor could not be substantiated. Therefore, for
consistency, it is no longer applied in Tekla Structural Designer for any edition of the design code.
Tekla Structural Designer therefore calculates the deflection for the beam based on the properties as tabulated below.
| Loadcase type | Properties used |
|---|---|
| self-weight | bare beam |
| Slab Dry | bare beam |
| Dead | composite properties calculated using the modular ratio for long term loads[1] |
| Live, Roof Live | composite properties calculated using the effective modular ratio[2] appropriate to the long term load percentage for each load. |
| Wind, Snow, Earthquake | composite properties calculated using the modular ratio for short term loads |
| Total loads | these are calculated from the individual loadcase loads as detailed above. |
[1]The long term modulus is taken as the short term value divided by a factor (for shrinkage and creep), entered in the Slab properties.
nS = the short term modular ratio = Es/Ec
nL = the long term modular ratio = (Es/Ec) * kn
[2]The effective modular ratio, nE is based on the percentage of load which is considered long term. These calculations are repeated for each individual load in a loadcase. The effective modular ratio is given by,
nE = nS + ρL * (nL – nS)
ρL = the proportion of the load which is long term
The calculated Slab Dry, Live and Total load deflections (where necessary adjusted for the effect of partial interaction) are checked against the limits you specify.
Note: All the beam deflections
calculated above are “relative” deflections. For an illustration of the
difference between relative and absolute deflection see Deflection checks (AISC 360).
Stress checks (SLS)
The Commentary (Section I3.1, paragraph 2 of the 2005 version, Section I3.2, of the 2010, 2016 and 2022 versions) suggests that where deflection controls the size of the beam then either it should be ensured that the beam is elastic at serviceability loading or that the inelastic deformations are taken into account. Tekla Structural Designer adopts the former approach. This is confirmed by checking that yield in the beam and crushing in the concrete do not occur at serviceability loading i.e. a service stress check. If they are found to fail, suggesting inelasticity at serviceability loading, then a warning will appear on the deflections page and the service stress results are available to view.
Tekla Structural Designer calculates the worst stresses in the extreme fibers of the steel and the concrete at serviceability limit state for each load taking into account the proportion which is long term and that which is short term. These stresses are then summed algebraically. The partial safety factors for loads are taken as those provided by you for the service condition on the Design Combinations page. The stress checks assume that full interaction exists between the steel and the concrete at serviceability state.
Natural frequency checks (SLS)
The calculation of the natural frequency of a composite beam can be complex and is dependent upon the support conditions, the load profile and the properties of the composite section. In reality the vibration of a composite beam is never in isolation – the whole floor system (including the slabs and other adjacent beams) will vibrate in various modes and at various frequencies.
A simple (design model) approach is taken based on uniform loading and pin supports. This fairly simple calculation is provided to the designer for information only. The calculation can be too coarse particularly for long span beams and does not consider the response side of the behavior i.e. the reaction of the building occupants to any particular limiting value for the floor system under consideration. In such cases the designer will have the option to perform a Floor vibration analysis within the Tekla Structural Designer application.
Simplified approach
The natural frequency is determined from,
NF = 0.18 * √(g/ΔNF)
Where:
- ΔNF = the maximum static instantaneous deflection (in inches) that would occur under the effects of Slab Dry loading, and the proportion of dead loads and live loads specified by the user (as specified on the Natural Frequency page of the Design Wizard). It is based upon the composite inertia but not modified for the effects of partial interaction.
- g = the acceleration due to gravity (386.4 in/s2)
- Factor of increased dynamic stiffness of concrete flange (default 1.35)
This is not given in the AISC Specification but is taken from Chapter 3 of Steel Design Guide Series 11. Floor Vibrations due to Human Activity. (Ref. 3) Its formulation is derived from the first mode of vibration of a simply supported beam subject to a udl.