Calculation of "First Yield" Capacity of the Section

To illustrate this consider the following imaginary section with two different material properties, M1(yellow) and M2 (green), that have different Young's Modulus (E) values and yield stresses (σ_y).

In all cases we use the elastic properties (area, Ixx, Iyy) and make the assumption that plane sections remain plane, ie that the distribution of strain through the section depth is linear. In the following images the distribution of strain through the section is shown, annotated with the corresponding stresses.

Please read the warnings below before using these values.

Axial case

Here the strain in the section is constant through its depth, and first yield occurs when the the weaker material M2 reaches yield at 0.0333% strain.

M1 has an E value of 210kN/mm², so at 0.0333% strain its stress is 70N/mm²

The axial force capacity of the section is then simply the sum of stress * area:

axial force = (area of M1 * 70)
            + (area of M2 * 100)

Mxx Bending case

Here the limiting strain of 0.0333% is still controlled by the outer fibre of material M2 at depth d2 from the XX axis, which reaches yield first.

However the linear strain distribution through the section means that the outer fibre of material M1 reaches about 0.0666% strain (assuming d1 = 2 x d2), so the peak stress in material M1 is about 140N/mm² .

Therefore the bending moment capacity of the section about its XX axis, Mxx, is, obtained from the standard formula M/I = stress/y giving:

Mxx = (Ixx for M1 * 140 / d1)
    + (Ixx for M2 * 100 / d2)

Myy Bending case

This is calculated using the same method as Mxx, but now the narrowness of the web means that first yield is reached at the outer fibres of material M1 at a strain of 0.119%.

The strain in the outer fibre of the web, material M2, will be about 20% of this, approximately 0.023%, giving an outer fibre stress in M2 of about 70N/mm².

Warnings about the "First Yield" calculation

1. It will be clear from the calculations above that both Young's Modulus (E) and yield stress (σ_y) must be available for every material in the section if this calculation is to be valid. These values are obtained from the material (*MAT) cards, but for some material types - especially brittle and crushable ones - either or both may not be well defined. Also it is possible for that the relevant material cards may not be present in the deck.
   
   Please see the Options panel below to see the alternatives that PRIMER uses when either of these properties are missing. Regardless of the choices you make there if any element in the section cannot extract either E or yield stress from the material card then the results will be marked as "Estimated".
   
   
   
2. This is a purely elastic calculation and, in the case of Mxx and Myy, assumes that all materials in the section behave symmetrically in tension and compression in the elastic regime, and have the same yield stress in both tension and compression. For ductile materials, eg steel, this is likely to be true; however for brittle materials (eg concrete) yield in tension may be very different to yield in compression.
   
   
   
3. It is assumed that each cut element is homogeneous with a single E value and yield stress σ_y. This will not be the case for composites, made up of layers of different materials; nor may it be a valid assumption for orthotropic materials.

Please consider the sections being cut through when you use this feature, and satisfy yourself that the calculation is valid for your model.