this tutorial will show you how to use the SAFE program to perform a cracked section analysis SAFE’s automated procedure determines cracked bending moments and curvatures for every element and then uses an iterative process to determine flexural stiffness modifiers here are the general steps for each element initial forces are calculated based on elastic properties and the reinforcing is determined either by the program based on the elastic forces or as input by the user cracked bending moments and then interpolation coefficients are computed based on the applied and cracked moments curvatures for the uncracked and fully cracked state are determined and then used to obtain the curvature for the applied moment a ratio of curvatures is then used to compute a flexural stiffness modifier which the program uses to adjust the bending properties using the modified stiffnesses displacements are then calculated the program will iterate through this process until the change in the maximum displacement is small the moment curvature transition between uncracked and fully cracked is shown in this graph SAFE offers two options when calculating cracked deflections one for immediate deflections and one for long-term deflections we will demonstrate both options but we’ll start by calculating immediate deflections of course both are based on service loads our model will be a simple two bay by two bay flat slab which we will load with three load patterns dead superimposed dead and live we start by defining our load patterns in addition to the dead and live we will add a pattern called sdead for superimposed dead load make sure that the self weight multiplier is set to 1 for the dead load pattern next we will assign the loads select the slab and assign a surface load using the sdead pattern with a magnitude of 20 pounds per square foot repeat the selection and add a surface load of 80 pounds per square foot for the live pattern now we will define our load cases in addition to the three default linear static cases which are needed to calculate reinforcing we will add a case called immediate all loads with the type of nonlinear cracked because we are calculating the immediate deflection we will apply all three load patterns with scale factors of one in this nonlinear load case note that when working with nonlinear load cases results may not be superimposable like they are with linear static load cases next we will define a load combination for displaying the elastic deflections we will call the combination elastic we are now about ready to run the analysis before we do however we will set the options for the cracking analysis here we can specify the source of the reinforcement for calculating the cracked inertias which can be user specified calculated by the program from the analysis or quickly input by the user we will use the program calculated values we can also adjust the minimum reinforcing ratios as well as the modulus of rupture with these values set we are ready to run the analysis this may take some time as the program runs multiple iterations we will switch the display to show the deformed shape for the elastic combination note that the maximum deflection is approximately 0.249 inches in the down direction next we will switch to the immediate cracked section case the deflection has increased to approximately 0.862 inches remember these values for comparison later with the long term cracked deflection next we will ask SAFE to determine the long term cracked deflection we start by unlocking the models so that we can set up the additional load cases needed to include creep and shrinkage the first load case will be dead plus sdead plus 0.25 live with creep and shrinkage this long-term case uses only sustained loads and we are assuming only twenty-five percent of the live load is sustained however this case is missing the deflection component from the 75 percent of the live load that is not sustained this is the part of the live load that contributes to an immediate deflection to isolate that live load deflection we will use two load cases dead plus sdead plus live- dead plus sdead plus 0.25 live neither of these cases will use creep or shrinkage we will call the case with creep and shrinkage long-term sustained and it will have a type of nonlinear long-term cracked in this case we apply dead and sdead with factors of one and the live load pattern with a factor of 0.25 the next case needed was previously defined as immediate all loads the last case we will add will be called immediate sustained and it will have a type of nonlinear cracked no creep or shrinkage in this case and again the dead and sdead will be applied with factors of one while the live load pattern will have a factor of 0.25 next we will define a load combination to combine these three load cases we will call this combination long term we will add the long-term sustained and immediate all those cases together but we’ll subtract the immediate sustained case the last two cases provide the live load immediate deflection for the non sustained component we can now run the analysis for the long term cracked section calculation again this may take some time due to the iterations switching the display to the long term deflection combination we see that the maximum deflection in the down direction is now approximately 1.439 inches compared to 0.862 from the immediate cracked analysis and 0.249 for the elastic analysis this concludes this tutorial on cracked section analysis