Deformations in stainless steel

Because stainless steel is a non-linear material, the modulus of elasticity depends upon the stress level in the cross-section. There for 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.

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 material library).
   As said before, this deflection is not always accurate.
2. Either
   • 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.
     
   • 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 E_s,ser 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.