## Using RC Design Functions – 2

In the previous post we looked at a summary of the functions in the RC Design Functions spreadsheet, and ways of using the EStress function (download file with examples).  In this post we will look in more detail at the output from EStress.

Since the last post there have been some minor changes to the EStress output, and the calculation of cracking moment including shrinkage effects has been updated to the latest version of the code, so to follow the notes below it is best to download the latest version of RC Design Functions.

The output is controlled by the arguments out1 and out2:

The “Insert Function” dialog can be displayed by clicking on the icon to the left of the Edit Bar, and selecting the function from the “User Defined” category, or enter “=Estress(” then click the Insert Function icon. Out1 selects the output column, and Out2 the output row.

Out1 = 1 returns stress values (in MPa) and Out1 = 2 returns strain and curvature (in m^-1) results: The stress and strain results are given at (controlled by the value of Out2):

1. Concrete top face
2. Top steel centroid
3. Bottom steel centroid
4. Bottom face

Note that if the concrete is in tension (negative strain) the stress displays as zero, because the analysis ignores tensile stress in the concrete.

If the Code argument is omitted, or is equal to 1 or 2, row 5 of the stress output returns the maximum allowable stress under SLS loading according to the Australian design codes, (AS 3600 and AS 5100).  If the Code value is 2, row 6 returns the maximum allowable stress under SLS dead load only, according to AS 5100 (the bridge design code).

The strains and curvature returned in column 2 are calculated assuming zero tension stress in the concrete.

Out1 = 3 or 4 returns force and moment results: The total force and moment should be equal to the input applied load values.  The force and moment in the concrete are calculated from the total section area above the neutral axis times the average concrete stress (compression face stress / 2), less the concrete force and moment over the area of the reinforcement in the compression zone (if any).

Out1 = 5 or 6 returns the depth to the neutral axis and cracking stresses and moments; and an echo of the input values respectively: The concrete design flexural tensile strength (rows 4 and 7) is based on the code provisions if f’ct is specified as -1 in the input, or the input value for any other value.

The AS 3600 cracking moment including shrinkage is based on Cl. 8.5.3.1 of the code and the input shrinkage strain:

The other code cracking moments do not allow for shrinkage.

The values in output Column 6 should be equal to the corresponding input values.  Any difference indicates that the input ranges have not been specified correctly.

Out1 = 7 returns miscellaneous intermediate results: 1, 2:  Area of tension and compression steel.
3,4:  Depth of the centroid of the tension and compression steel, measured from the compression face.
5,6: Maximum compressive load and associated bending moment.
7,8: Maximum tensile load and associated bending moment.
9:    Sign of the applied moment (tension on the bottom face positive)
10:  Ig, the second moment of area of the gross  section, including reinforcement using transformed area properties.

The maximum compressive an tensile loads are based on the specified concrete compressive strength and steel tensile strength respectively.  Note that no reduction factors are applied, and the calculated stresses and strains in output columns 1 and 2 assume elastic behaviour under all loads.

Out1 = 8 returns crack width and effective stiffness results: If the input Code value = 4 or 5 then Out1 = 8 returns just the crack width to the British code BS 5400.  The Mq/Md  ratio (Live Load/ Dead Load) is set to the input Beta value.

For a Code value of 3 (Eurocode 2) Out1 = 8 returns:

Out2
<2:   Crack width for kt = Out2-1 (kt = 0.4 for long term load, 0.6 for short term)
2:      Crack spacing
3:      Curvature with no tension stiffening
4:       Curvature to Eurocode 2, with no shrinkage
5:        Shrinkage curvature to Eurocode 2
6:        Total curvature to Eurocode 2
7:        Uncracked curvature; = 0.0 for cracked section
8:       Effective E, based on total curvature to Eurocode 2 and Ig

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