The ACI code controls differential deflections occurring after attachment of nonstructural elements. ACI specifies two deflection limit states:

1. Immediate live load deflection
2. Long-term deflections due to sustained loads plus immediate live load deflection

Note that there are no specified limits for total deflection, however most engineers decide to apply practical limits.

Immediate Live Load Deflection

The sustained load plus live load deflection is typically calculated as follows:

1. Calculate the deflection due to dead load and live load using an effective moment of inertia based on the applied dead and live load.

2. Calculate the deflection due to dead load using an effective moment of inertia based on the applied dead load only.

3. Calculate the immediate live load deflection as the deflection from Step 1 less the deflection from Step 2

Sustained Load plus Immediate Live Load Deflection

The sustained load plus live load deflection is typically calculated as follows:

1. Calculate a final long-term deflection based on the applied dead load and a sustained live load (if applicable). The effective moment of inertia used to calculate this deflection is based on the total load (dead load plus any sustained live load). The multiplier based on the load duration is calculated from ACI Eq 9-11 and used to approximate the long-term deflections due to creep and shrinkage.

2. Calculate an initial long-term deflection. This would represent the deflection at the point at which nonstructural elements are attached. Typically, this deflection considers dead load only (self-weight plus any other dead load that may be in place before nonstructural elements are attached). Again, the deflection is calculated using an effective moment of inertia based on the applied dead load and a time dependent multiplier based on the duration of these loads.

3. Calculate the sustained load plus live load deflection as the deflection from Step 1 less the deflection from Step 2 plus the immediate live load deflection discussed in the previous section.

RAM Concept Load History Calculations and ACI Deflection Limits

The RAM Concept load history calculations include several powerful features that facilitate the differential deflection checks specified by ACI:

1. Finite Element Analysis. The long-term deflections are based on a finite element analysis, so stiffness, cracking, and long-term effects are considered in two directions simultaneously. Hand calculations or programs using strip based methods only consider cracking and long-term effects in a single direction at a time.
2. Load History Steps. Each step can be defined with any load combination and duration. Virtually any loading sequence can be defined and used to predict long-term deflections.
3. Cracking and Redistribution of Forces. RAM Concept predicts the amount of cracking in each cross section and modifies the stiffness of the elements at each load step. Once a cross section is determined to be cracked, it is assumed cracked for all future iterations and load history steps. This ensures that the deflections are calculated with the correct element stiffness. It also accounts for redistribution of forces from highly cracked areas to areas that are less cracked.
4. Shrinkage Restraint Percentage. Stiff column and walls supports restrain shrinkage deflection, which leads to cracking. The shrinkage restraint percentage is a simple way to account for this cracking. Click on the following for more information on the shrinkage restraint percentage: RAM Concept Load History Calc Options
5. Difference Plot Controls. A deflection plot can be created that displays the difference in deflection between any two deflection plans, including deflection plans on the Load History Deflection Layer. See Example Section on this web page for more information.

RAM Concept Load History Steps

The default load history steps are shown in the screen capture below. While these load steps may apply to many structures that are modeled in the program, the loading sequences can vary project to project and customization of the default load history steps may be required.

When customizing the load history steps, think about the following:

• At what duration will nonstructural elements be attached to the structure?

• What loads will act before and after the nonstructural elements are in place.

• Is a portion of the live load a sustained load that will act over a long duration and contribute to creep?
  

Example

Consider the following structure:

• Forms removed after 3 days

• Before nonstructural elements are attached, the structure is loaded with:

  • Structure Self-Weight
  • 20 psf Construction Live Load (assume a 30-day duration)

• After nonstructural elements are attached, the structure is loaded with:

  • Structure Self-Weight
  • 10 psf superimposed dead load
  • 40 psf reducible live load (33% of this load is to be considered as a sustained load)

The following load history steps could be used to check the ACI deflection limits:

The “Construction Loads” step references the Initial Service LC shown below. A 20 psf surface load would be modeled for the Temporary Construction Loading to account for the construction loads.

The “Nonstructural Element Attachment” step references the All Dead LC (or Dead + Balanced) shown below and a 0 day duration. This step is intended to be used for the base deflections used to determine the differential deflections due to immediate live load and sustained load plus immediate live load. If the structure is post-tensioned then the combination used in this step should also include the Balanced Load, assuming the PT is stressed at this point. 

The “Sustained Loads” step references the Sustained Service LC shown below. The default load factors for this combination use 0.5 for the transient live loads. These have been changed to 0.33 to match the assumed 33% sustained live load. The 5000 day duration ensures that the maximum long-term effects are incorporated in the analysis.

Both the “Immediate Live Load” and “Sustained + Immediate Live Load” steps reference Service LC: D+L shown below. This combination includes all dead load and live load. The duration is set to 0 days since immediate live load deflection is being checked.

The ACI immediate live load deflection can be found by creating a new plot on Layers – Load History Deflections – Immediate Live Load and using the Difference Plot Controls to subtract the deflections for the Nonstructural Element Attachment step. To do this, follow the steps below:

Step 1:  Click on Layers - New Plan.

Step 2:  In the Create New Plan dialog that appears, enter a plan name and choose the layer from which the base deflections will be subtracted from. Click OK to Create the Plan.

Step 3:  The Visible Objects dialog will appear. Click OK to close it; no changes are needed.

Step 4:  A plan showing the meshed slab with no information will be the active plan on screen. To plot the differential deflections on this plan, open the Plot Settings dialog by clicking on View - Plot.

Step 5:  In the Plot Setting dialog, select the base deflection layer for "Diff Layer" and choose to plot vertical slab deflections as shown below. Click OK to plot the information.

Step 6:  The new plot will show the deflections from the Default Plot Layer less the deflections from the Diff Layer. In this case, the plotted deflections would represent the load history deflections at the end of the "Immediate Live Load" step less the deflections at the end of the "Nonstructural Element Attachment Step." These deflections would represent the immediate live load deflection.

A similar procedure would be used to find the differential deflection due to sustained loads plus immediate live load. In Step 2, the layer selected would be “Sustained + Immediate Live Load.” The remaining steps are identical. At the end of the process, the plotted deflections would represent the load history deflections at the end of the “Sustained + Immediate Live Load” step less the deflections at the end of the “Nonstructural Element Attachment Step.” These deflections would represent the sustained plus immediate live load deflections.

See Also

RAM Concept Load History Calc Options [TN]