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# Long-Term Deflection Calculation with Continuous Beam/Slab Design

In some cases, the Continuous Beam/Slab Design program gives unexpected long-term deflection values. What factors can influence the results?

Design loads, concrete cracking and reinforcement layout are major determining factors when calculating long-term deflections in beams and slabs. The Continuous Beam/Slab Design program incorporates all these parameters when calculating long-term deflections. Although the deflection behaviour of most beams and slabs are quite predictable, there are some cases where the program gives unexpected long-term deflection values.

Overview of Deflection Calculation

The Continuous Beam/Slab Design program calculates short-term (elastic) deflections using gross concrete sections. When calculating long-term deflections, however, the program considers the effects of concrete cracking, shrinkage, and creep under permanent load. All these effects are directly or indirectly related to the reinforcement in the beam or slab. The program’s online Help gives a full explanation of the calculation procedure in the Theory and Application section. In a nutshell, the program determines the level of cracking along the length of the beam, and appropriately reduces the flexural stiffness where the section is cracked. The various deflection components are then calculated using numeric integration of the curvature (M/EI) diagrams.

The Effect of Cracking

In zones where a beam is cracked, there can be a significant loss in flexural stiffness. Large creep deflections are often the result of extensive cracking in high moment zones, e.g., over supports. A quick way of identifying the zones of cracking and spotting potential problems is to review the Crack File output. It lists the gross and cracked section properties at points along the length of the beam.

The Effect of Reinforcement

Two sets of reinforcement data are used by the program: “required reinforcement” and “entered reinforcement”. By default, the program uses the “required reinforcement” to calculate cracked section properties. Once you have generated reinforcement for the beam, the program will use the “entered reinforcement” for the long-term deflection calculations. This gives you the ability to manipulate the long-term deflection by selectively adding more reinforcement. Figure 3: Reinforcement used for calculating deflection based on entered reinforcement.

Although long-term deflections are calculated at SLS, ULS loading influences the deflection calculations indirectly—the reinforcement demand is calculated at ULS, and that in turn determines the cracking strength of a beam at SLS.

Common Mistakes When Interpreting the Effect of Cracking on Long-Term Deflections

It is easy to overlook less obvious interactions between ULS loading, reinforcement and cracking in a beam, and then encounter “unexpected” long-term deflection behaviour.

Here are a few examples:

• The long-term deflection seems unrealistically high compared to the short-term deflection: Excessively large long-term deflections are usually the result of high creep. The cause of this is typically excessive cracking, especially over the supports of continuous beams. In turn, insufficient cracking strength is often due to insufficient section depth—one can often fix the problem by increasing the depth to comply with L/d ratios specified in the relevant design code. In a relatively thin slab, high deflection could be due to the neutral axis approaching the level of tension reinforcement—thicken the slab to increase stiffness and reduce deflections.
• Adding reinforcement increases deflections: The top and bottom reinforcement layout have a direct impact on shrinkage deflection. Adding more bottom reinforcement at midspan, for example, will result in additional downward shrinkage deflection (because the additional reinforcement resists shrinkage in the bottom face). The additional shrinkage deflection may exceed the other deflection components, resulting in a net increase in deflection.
• Adding reinforcement has no effect on deflection: When using the flat slab detailing modes (Column Strip or Middle Strip) to enter reinforcement, the program reverts to using “required reinforcement” for long-term deflections. This is done because deflections cannot be accurately determined for two-way spanning slabs when using the column or middle strip data in isolation. By using the “required reinforcement” instead (and ignoring your “entered reinforcement”), the program can provide a rough estimate of the average long-term deflection across the width of the slab.
• Increasing the load increases the deflection disproportionally: An increase in load may cause cracking in sections previously uncracked and increase the level of cracking in previously cracked sections. The resulting loss of stiffness leads to higher deflections in a greater proportion than the increase in load.
• Decreasing the ULS load factors increases deflection: The reinforcement demand under ULS loads will be lower for smaller ULS load factors. If using “required reinforcement” for the long-term deflection calculation, the cracking strength of the beam will generally be lower. The SLS loads remain unchanged, though resulting in higher deflection.