# Factors that affect rigorous slab deflection estimates

Many input parameters have an impact on the rigorous deflection estimates. These include:

- Level of Restraint
- Concrete properties
- Stiffness adjustments
- Allowance for shrinkage effects
- Event sequence parameters
- and even the assumed analysis properties of connected columns and walls

Some of the key factors are described below, these vary depend on the regional code being worked to.

# Quasi-permanent load factors (EC2)

_{2}(Psi

_{2}) factor is applied to the imposed load which varies based on the use of the structure. These are dealt with when defining the imposed loadcase.

# Beta coefficient (EC2)

Beta relates to the duration of the load and tension stiffening effects.

- For loads with a short duration, and for cyclic loads, Beta should be set to 1.0.
- For loads with a long duration, Beta should be set to 0.5.

Since these phenomena are irreversible, it is not recommended that Events have a value of Beta greater than that set for any previous Event and a warning will be issued if you do this.

However, there are circumstances where you may wish to have a value of Beta=0.5 in the earlier events, and Beta=1.0 in a later Event. For example, TR58 suggests that Beta=1.0 be used for the variable part of imposed load (if you wish to consider that at all).

In this case the analysis will permit you to enter these values. However, because the reduction in tension stiffening is carried forward and is irreversible in the analysis, caution is advised.

To explain this issue more fully, the impact of choosing Beta=1.0 at a later event, for different extents of cracking, is explored below.

Consider 3 possible configurations of a model, where:

- There are many elements that are uncracked at the end of earlier events. For a later event where the duration is short (which implies you should set Beta=1), setting Beta=0.5 could lead to an overestimation of incremental cracking, and subsequently overestimation of deflection.
- There are many elements that are cracked in an earlier event, for which you have chosen Beta=0.5. For a later event where the duration is short (which implies you should set Beta=1), if cracking increases in that Event, setting Beta=1.0 could lead to an underestimate of incremental cracking, and subsequently an underestimate of deflection for this later event.
- The majority of cracking occurs in an earlier event, for which Beta=0.5, if cracking does not increase in a later Event, the value of Beta in that later Event will have minimal impact on deflection. To ascertain whether the cracking increases, you may run separate analyses, with values of Beta=0.5 & 1.0, and compare the results.

In summary, it is prudent to consider whether cracking is likely to increase in later events for which you wish to set Beta=1.0.

However, it is likely that you will observe minimal difference between the total deflection estimates, and that other assumed values will be of much greater significance.

It is straightforward to run the analysis with different values of Beta to determine whether this is the case.

# Restraint type (EC2)

**Restraint type**, which is located under the Deflection parameters heading in the slab item Properties Window is used for specifying the degree of restraint resisting shrinkage.

- The default of 100% corresponds to high restraint and is conservative.
- The range of input is 50%-100%
- 50% corresponds to low restraint and is not conservative.

_{ct}) as follows:

**For Restraint Type = 100% (High) -**the tensile strengthwhich is the strength adjusted for the concrete age at time of loading (for each load event)**f_ct = f_ctm(t)**per EC2 cl 3.1.2 (9). This is the minimum value of**t****f_ct**(at any given age).**For Restraint Type = 50% (Low) -**following Cl 7.4.3(4), we refer to cl 3.1.8(1) for flexural tensile strength and set- again adjusted for the concrete age per EC2 cl 3.1.2 (9). This is the maximum value of*f_ct = f_ctm,fl*(at any given age)*f_ct***For 50% < Restraint Type < 100%**- we linearly interpolate between these max/min values.- Note you can verify the value of
calculated and used by the program for the current input for each load event - the value is reported in cursor tooltip for any selected element when viewing the "Extent of cracking" Results as shown in the picture below.*f_ct*

- Note you can verify the value of

The value to adopt is a matter of judgment - for guidance on this refer to EC2 cl 7.4.3(4) and TR58.

# Restraint constant (ACI)

For US customary units, restraint constant values from ACI 435 are:

- For situations with significant restraint - 4.0
- For insignificant restraint - 7.5

The default is conservatively set to 4.0.

The allowable input range is between 1 and 10 and is a user specified value by the engineer.

The restraint constant is used to
determine the Modulus of Rupture, f_{r} = “restraint constant” x λ x
√(f_{c}’)

Where:

f_{c}’ = specified compressive
strength (psi)

λ = 1.0 (for normal weight concrete)

# Concrete Properties (Eurocode)

The elastic deformation of concrete
largely depends on its composition (especially the aggregates). For C35/45 concrete,
Eurocode 1992-1-1:2004 Table 3.1 provides a modulus of elasticity, E of 34GPa (34000
N/mm^{2}) as a mid range value using quartzite aggregate. For different
aggregates this can range between -30% and +20%.

What is the correct E value for your concrete?

If you know the value, you should set
up a new material grade and assign it to the elements in the model. It may, however,
be easier when assessing the impact, to use the stiffness adjustment option, for
details of which see the **Stiffness Adjustments** section below.

# Concrete Properties (ACI)

What is the correct E value for your concrete?

If you know the value, you should set
up a new material grade and assign it to the elements in the model. It may, however,
be easier when assessing the impact, to use the stiffness adjustment option, for
details of which see the **Stiffness Adjustments** section below.

# Stiffness Adjustments

The relative stiffness of the interconnecting elements will play a role in the force distribution and hence the deflection results.

For existing models the values can be reviewed
and amended by clicking **Settings > Modification Factors** on the Slab
Deflection ribbon. These are user defined values with assumed defaults.

As mentioned in the above **Concrete
Properties (Eurocode)** and **Concrete Properties (ACI) **sections, an
alternative to assessing the impact of a different grade could be to alter the
Modification Factors specified for flat slab E and G values. i.e. Concrete material
property of slab = 34000 N/mm2. What impact would using a value of 32000
N/mm^{2} make? Flat slab stiffness adjustment = 32000/34000 = 0.9412

# Shrinkage

Shrinkage is the strain in hardened concrete that can occur due to moisture loss.

Shrinkage is taken into consideration by making an overall adjustment to the total deflection. This approach is in line with many other software products.

The adjustment is specified in the
**Slab Deflection Settings** dialog.

We recommend an allowance with an upper limit of 30%. The default is set as 0.25 (25%).