This is because Diamonds shows the shadow factor k_sh multiplied by the section factor A_m/V.

Example: IPN 80 (b=42mm; h=80mm; t_w=3,9mm; t_f=5,9mm, r=3,9mm)

• The perimeter V of the cross-section equals:

     

• The area of the cross section per unit of length equals A_m

     

• The are of the bounding box of the cross-section pr unit of length equals A_m.box

     

• The shadow factor k_sh then equals (EN 1993-1-2 equ. 4.26a)

     

• The section factor A_m/V (EN 1993-1-2 Table 4.2):

     

• The result shown in the data table of Diamonds in the column ‘Section factor’ equals:

     

The choice to show the product of the shadow factor k_sh and the section factor A_m/V has several reasons:

• On the one hand, Eurocode allows the use of the shadow factor when working with nominal fire curves (EN 1993-1-2 §4.2.5.1) (which is almost always the case in Diamonds). By already including this multiplication in the ‘section factor’ column, there is no discussion for the end user that the shadow factor will be charged.
• On the other hand, there are several manufacturers of fire-resistant paints whose data is based on a k_sh x A_m/V, which makes the interpolation of the results a lot easier for the calculation core.
• Some tables also include the shadow factor like this one.

Cause

EN 1993-1-1 §6.2.6 (6) states that shear buckling for webs without intermediate stiffeners should be checked according to EN 1993-1-5 if

Diamonds shows the warning when the condition is met.

• Schematising the construction
• Determining the internal forces and moments (= global analysis)
• Checking the cross-sections (= design):
  • Strength
  • Stability 
  • Stiffness

The explanation below covers the design of steel.

In Diamonds

Strength and stability verification

The principle for verifying stainless steel is the same as for carbon steel (EN 1993-1-4 must be seen as an addition to EN 1993-1-1).

Only some parameters have a different value, or some additional formulas need to be checked in comparison to EN 1993-1-1. The table below gives an overview of the differences between carbon steel and stainless steel.

Notes:

• In Section Utility it is possible to compose custom sections from stainless steel. If you’re interested in the secant deformation, make sure the custom section is mainly composed of stainless steel. Other materials (with different material behaviour/ modulus of elasticity) will affect the stresses and thus the calculation of the secant modulus (also see section about deformations further in this article).
• It is possible to run a thermal analysis on cross-sections in stainless-steel, but it is not (yet) possible to do a steel verification of stainless steel in case of fire .
• A connection verification (PowerConnect) of elements in stainless-steel is not supported.

Deformation

Because stainless steel is a non-linear material, the modulus of elasticity depends upon the stress level in the cross-section. Therefor EN 1993-1-4 §4.2 (5) states that deflections should be calculated using the secant modulus at the stress level (SLS state).

EN 1993-1-4 uses the Ramberg-Osgood model to calculate the secant modulus. As does Diamonds.

• Diamonds will calculate the secant modulus in each mesh node as the minimum value of the secant modulus along the strong and the weak principal axis of the cross-section.
• This will result in different secant moduli along the length of the member. The secant deflection is obtained by solving an integral over the length of the member.

So, the steps to calculate the deformations in stainless steel in Diamonds are:

1. You run an elastic analysis .
   This results in a deformation calculated with the modulus of elasticity defined in EN 1993-1-4 §2.1.3 (which are included in the Diamonds material library).
   As said before, this deflection is not always accurate.
2. Either
   1. Calculate the secant deformation .
      Choose a combination. Diamonds will calculate the secant modulus using the stresses in the combination you selected. Choose the same combination as the one in which you want to verify the deformations.
      
   2. Calculate the secant deformation and redivide the internal forces .
      This option does the same as option ‘a’, but it will also redistribute the internal forces using the secant moduli.
      

Notes:

• The secant moduli are calculated based on elastic stresses, regardless of the cross-section class of the member.
• The calculated deformation for stainless steel in Diamonds is only valid when the stresses in the cross-sections (in the selected SLS state) are below the yielding strength of the used stainless-steel quality. Diamonds doesn’t literally check this condition, because it is supposed that when the steel verification is smaller than 100%, the stress requirement is also met.
• As a simplification, EN 1993-1-4 §4.2 (9) allows calculating the variation of along the member and use the minimum value throughout its length. But for stress levels above 65% of the yielding strength, this results in very high deflections. Thus this simplification is not used in Diamonds.

Regular versus thin-walled cross-sections

Eurocode makes a distinction between:

1. Regular steel cross-sections who can have the production methods: hot rolled, welded or cold formed
   These cross-sections have a thickness t >= 3mm and are designed using EN 1993-1-1.
2. Thin walled steel cross-section who have the production method: cold-formed
   These cross-sections have a thickness t < 3mm and are designed using EN 1993-1-3.

Diamonds contains a library of common thin walled cross-sections (MRP, Brause, Joris Ide, Sadef). For those sections, Diamonds will automatically apply EN 1993-1-3.

Any other type of cross-section is default calculated according to EN 1993-1-1. However, if the thickness < 3mm and the production method is defined as ‘cold formed’, you can impose Diamonds to use EN 1993-1-3 by checking this option. The parameters VzRd, VyRd and fya required for the design, need to be imposed by the user.

Effective properties

Eurocode organizes cross-sections into four classes that describe the behaviour of that cross-section.

1. Class 1 & 2 are plastic cross-sections
2. Class 3 are elastic cross-sections
3. And Class 4 are slender cross-sections.

For classes 1 to 3, it’s easy to determine the section properties required to do a design according to EN 1993. Class 4 on the other hand, requires effectieve properties to do a design according to EN 1993… which are much harder to determine.
‘Regular’ steel cross-sections can be of class 1 to 4. Thin walled cross-sections are almost always of class 4.

The table below gives an overview for which cross-sections Diamonds has these effective properties.

		Parameters for elastic analysis	Parameters for unity check (Eurocode 3)
	Cross-section procceded by	✓	✓
		✓	✓, until class 3 For class 4, you should impose the effective properties
		✓	✓
		✓	✓, until class 3 For class 4, you should impose the effective properties. Also for class 4, EN 1993-1-6: Strength and stability of shell structures applies. Diamonds does not support this part of Eurocode.
		✓	not possible [1]
		✓	not possible [2]
	(for Section Utility manual, click here)	✓	you should impose additional properties For class 4, you should also impose the effective properties.

^[1] For the cold formed cross-sections in the library, the effective properties have been provided by the manufacturers. If you select one of these cross-section shapes and change its dimensions or impose them from zero, Diamonds is not capable of recalculating these effective properties! Therefor you cannot run a unity check on these cross-sections
^[2] These cross-sections shapes are intended for concrete design.

Which commercial thin walled cross-sections are in Diamonds

The table below gives an overview of all commercial thin walled cross-sections in Diamonds:

However, you can manually verify the buckling resistance by modelling the wall as a column with height H equal to 1m and width B equal to the wall thickeness.

[NL]: Voor bepaalde staven kon de normcontrole niet uitgevoerd worden. De rekenkundige bewerking heeft geresulteerd in een overloop.

[FR]: La vérification ne pourraît pas être exécuté pour certaines barres. De objectverwijzing is niet op een exemplaar van een object ingesteld.

Cause (in general)

This error is always related to an inconsistency in the dimensions of the used cross-section(s). Resulting in cross-section classifications, imperfection factors, effective properties, … not being calculated automatically.

Example 1:

An RHS-section is used to create an elliptical cross-section. But because r0 (=25mm) equals B/2 (=50mm/2), the cross-section classification in the weak direction cannot be performed.
Solution: set B= 51mm or set r0 to 24mm.

Example 2:

Some cross-section shapes are associated with cold-formed sections, like these in the list below:

When the option ‘Automatic calculation’ is selected, Diamonds calculates the general, elastic (except T_wm) and the plastic properties of the cross-section.
But Diamonds cannot calculate the effective and design properties for these cross-section shapes. These shapes are in Diamonds because manufacturers (Joris Ide, Brausa, Sadef, …) provided us with lists of common cross-sections with their dimensions and effective properties. So although you can play around with the dimensions, Diamonds is not capable of calculating the effective properties!

So if you want to perform a steel verification on these cross-section shapes, you should:

• Check the option ‘Automatic Calculation’. This way the general, elastic and plastic properties are calculated.
• Uncheck the option ‘Automatic calculation’. This way you can adjust the value of T_wm in the tab page ‘Elastic’.
• Define all the properties in the tab page ‘Effective’.
• Define all the properties in the tab page ‘Design’.

• For Beam 1: based on the stresses, you’d expect a steel verification of 100%. But the steel verification is lower.
  This is because Diamonds shows the elastic stresses (calculated with W_el), while this section is of class 1 and thus plastic properties (W_pl > W_el) will be used in the steel verification.
• For Beam 2: based on the stresses, you’d expect a steel verification of 100%. And indeed, the steel verification is 100%.
  This is because Diamonds shows the elastic stresses and this section is of class 3 (W_el) will be used in the steel verification.
• For Beam 3: based on the stresses, you’d expect a steel verification of 100%, but the steel verification is higher.
  This is because Diamonds shows the elastic stresses (calculated with W_el), while this section is of class 4 and thus effective properties (W_eff < W_el) will be used in the steel verification.

So, it is important to do a steel verification because:

• the stresses shown in the global window in Diamonds, are stresses caused by axial force and bending around the z’ OR y’-axis.
  It neglects shear, torsion, the risk of instabilities and combinated forces (like N + V + M or N + M + M).
• Diamonds shows elastic stresses.

Note: it is not possible to show the stresses according to the Von mises criterium in Diamonds.

• What is the difference between a 1st and 2nd order calculation?
• Do I need a 1st or 2nd order calculation for my structure?
  Answer:
  • If the structure is sway → 2nd order calculation
  • If the structure is non-sway → 1st order calculation
• How do I determine if the structure is sway or non-sway?
• How does the choice ‘1st or 2nd order calculation’ affect the buckling lengths and what is the deal with imperfections?
  Global and local imperfections will increase the second order effects.
  When you let Diamonds calculate the buckling lengths (regardsless the chosen method), don’t forget to define the groups for buckling.

• Non-displaceabable nodes (syn.: non-sway buckling lengths)
• Semi-displaceabable nodes
• Displaceabable nodes (syn.: sway buckling lengths)

The prefered method depends on the sway or non-sway character of the structure and if global imperfections have been taken into account.

The diagram below gives an overview.

• The red paths are possible in Diamonds.
• Instead of non-sway buckling lengths, you may also use the semi-displaceable nodes as a conservative alternative.

(Source diagram: Krachtswerking, Grondslagen voor het berekenen en toetsen van staalconstructies voor gebouwen volgens Eurocode 0, 1 en 3, H.H. Snijder en H.M.G.M. Steenbergen, Bouwen met staal, 2011, ISBN 978-90-72830-87-6)

• are a (global) displacement of action line (of normal force) due to rotation of the bar.
• This effect is important for structures where the nodes are moving significantly under the effect of the loads.
• It results in additional moment in bars

δ – effect

• are the relative  deformation of the element in relation to the reference line between the end points. A bar doesn’t remain straight between the end points.
• This effect is important in of very slender elements.
• It results in additional deformation in bars