Deflection check (concrete beam: ACI 318)
Deflection checks are divided between two deflection types: Immediate short-term deflections and long-term deflections which are resulting from creep and shrinkage of flexural members.
Two methods are given for controlling deflections:
1. By limiting span to depth ratio
For beams provision of a minimum overall thickness (min. total depth) as required by the following table satisfies the requirements of the code for members not supporting or attached to partitions or other construction likely be damaged by large deflections.
Support Conditions | Minimum thickness, h_{t} |
---|---|
Simply Supported | l_{n}/16 |
One end continuous | l_{n}/18.5 |
Both ends continuous | l_{n}/2126 |
Cantilever | l_{n}/8 |
If h ≥ h_{min}, the design passes and no further calculations are required
where
h = overall height of member
h_{min} = h_{t} * f_{y,mod}
h_{t} = minimum thickness from above table
l_{n} = clear span length
f_{y,mod} = 0.4 + f_{y} / 700 MPa (metric units)
f_{y,mod} = 0.4 + f_{y} / 100000 psi (US units)
If the deflection check fails the rigorous method below is used.
2. By calculating deflections using the rigorous method
For beams that do not meet minimum thickness requirements above, or that support or are attached to partitions or other constructions likely be damaged by large deflections, deflections are calculated by following method.
- Firstly, the beam’s cracked section moment of inertia, Icr is calculated.
- Then the cracking moment Mcr is calculated.
- The Long Term Deflection Period is read from the user specified value in Design settings. - 3 months to 5 years (default value: 5 years).
- The Time at which brittle finishes are introduced is read from the user specified value in Design settings. - 1 month to 6 month (default value: 1 month).
- For each loadcase with type = "dead", the % of load applied prior to sensitive finishes is read from the user specified value in the loadcase dialog (default value: 50%).
- For each loadcase with type = “imposed”, the % of load which is long term is read from the user specified value in the loadcase dialog (default value: 33%).
- For each span in the element the critical gravity combination is determined from the analysis. The combination reporting the max relative deflection is the one considered in the deflection check.
- The maximum deflections for the different situations below can then be determined:
- Dead load deflection (Δ_{i})_{d}
- Dead and live load deflection (Δ_{i})_{dlive}
- Live load deflection (Δ_{i})_{live}
- Sustained load deflection (Δ_{i})_{sus}
- Total load deflection(Δ_{i})_{tot}
- Deflection affecting sensitive finishes (Δ_{i})_{af}
The check passes if the calculated deflections are less than the deflection limits specified in the beam properties.