RAM Concept’s load history deflection calculations are complex due to the many non-linear behaviors that are considered (see Load History Deflection Calculations for more information). When unexpected results are obtained, it can be difficult to verify the calculation or even isolate the effect of the different behaviors (creep, shrinkage, cracking, etc).
The Load History Deflection Analysis Results Tables were added in RAM Concept Version 8 Update 2 to give the user more access to the data used to calculate the load history deflections. These tables include both information that is directly used by RAM Concept to calculate the load history deflections and information that is not used directly but is useful for better understand the relative importance of different behaviors. A separate table is available for each load history step. Each table includes information for all sections, both span sections and design sections, included in the model.
This article defines the information included in the table and provides insight on how the information might be used.
Definition of Tabulated Items
Fa/Fcr– The ratio of the calculated axial stress at the extreme fiber of the section over the cracking stress (normally the modulus of rupture). A separate ratio is tabulated for both the top and bottom of the section. The calculated axial stress is the result of applied loads and induced strains, including the shrinkage restraint %. A section is considered cracked when this ratio is greater than or equal to 1.
Fa/Fcr (unrestr.)– The Fa/Fcr ratio above but with the effect of the shrinkage restraint % removed. A ratio is tabulated for both the top and bottom of the section. These ratios are not used directly in the load history calculations. They are intended to be compared with Fa/Fcr ratios, which include the effect of the shrinkage restraint %, to better understand the influence of external restraint to shrinkage on the load history deflection calculations.
Modulus of Rupture– The calculated modulus of rupture, which is normally the cracking stress of section. The tabulated value includes adjustments to account for reduced concrete strength at early ages (less than 28 days). Refer to the RAM Concept Manual for more information on this adjustment.
Max Fa/Fc Ratio – The maximum ratio of the calculated axial concrete compressive stress in the section over the concrete compressive strength. A ratio is tabulated for both the top and bottom of the section. This ratio may be used to identify sections with high compressive stress that may be subject to non-linear creep behavior (see AS 3600-2018 3.1.8.3 and Eurocode 2-2004 3.1.4(2)). Non-linear creep behavior is not accounted for in RAM Concept’s load history deflection calculations.
Max Fs/Fy Ratio – The maximum ratio of the calculated tensile stress in the reinforcement over the yield stress of the reinforcement. A separate ratio is tabulated for the extreme top and bottom reinforcement. The reinforcement is yielding when this ratio is greater than 1. A ratio much larger than 1 indicates excessive yielding, which could lead to significant element stiffness reduction and possible local instability.
Incr. Creep Coefficient– The incremental creep coefficient (creep strain/elastic strain) over the duration of a given load history step based upon a loading applied at the initial load application time. This coefficient excludes the creep effects from any previous load history step. The coefficient includes adjustments to account for time of loading for creep models that calculate creep based on the modulus of elasticity (Ec) at the time of loading instead of the 28-day Ec (refer to the RAM Concept Manual for details).
***. Creep Coefficient– The cumulative creep coefficient (creep strain/elastic strain) over the total age of a given load history step based upon a loading applied at the initial load application time. This coefficient includes the creep effects from all previous load history steps. The coefficient includes adjustments to account for time of loading for creep models that calculate creep based on the modulus of elasticity (Ec) at the time of loading instead of the 28-day Ec (refer to the RAM Concept Manual for details).
Incr. Shrink. Strain - The incremental shrinkage strain over the duration of a given load history step. This strain excludes the shrinkage from any previous load history step.
***. Shrink Strain - The cumulative shrinkage strain occurring up to the end of a given load history step. This strain includes the shrinkage from all previous load history steps.
Gross Curvature – The calculated curvature using gross section properties caused by externally applied loads and post-tensioning only.
Uncr. Trans. Curvature– The calculated curvature including the effects of creep and internal restraint to shrinkage on the uncracked transformed concrete section.
Cracked Curvature - The calculated curvature including the effects of creep and internal restraint to shrinkage on the cracked transformed concrete section.
Mean Curvature– The average curvature interpolated between the uncracked transformed curvature and the cracked curvature using the tension stiffening model. This curvature includes the effects of external restraint to shrinkage. The element stiffness reduction is determined by the ratio of the mean curvature to the gross curvature.
Uncr. Shrink Warp.– The calculated curvature due to only internal restraint to shrinkage (shrinkage warping) on the uncracked transformed section. This ratio can be compared with the uncracked transformed curvature to better understand the influence of internal restraint to shrinkage on the load history deflection calculations.
Cracked Shrink. Warp. - The calculated curvature due to only internal restraint to shrinkage (shrinkage warping) on the cracked transformed section. This ratio can be compared with the cracked transformed curvature to better understand the influence of internal restraint to shrinkage on the load history deflection calculations.
Mean Shrink. Warp.– The average curvature due to only internal restraint to shrinkage (shrinkage warping) interpolated between the uncracked transformed and cracked shrinkage warping curvatures. This ratio can be compared with the mean curvature to better understand the influence of internal restraint to shrinkage on the load history deflection calculations.