How is Moment Redistribution Performed?

Objective

1) What is the Delta Value?

2) What is the relationship between x_u, Delta Value, and moment Redistribution?

Parameters

1. Getting Started

Open an analyzed project

1. Click the red box icon and ‘Open (Ctrl+O)’ to open an analyzed project.
2. The image shows a 3D frame analyzed in nGen as a reference.

2. Member Parameters

Define the Moment Redistribution Factor for concrete

1. Select [Design > Member Parameter].
2. Select RC Member.
3. Select the members in the model for which Member Parameters is to be set up.
4. Input [Moment Redistribution Factor (𝛿) ].
5. Click [Apply].

3. Eurocode Provisions

Eurocode 2

Define Moment Redistribution Factor based on Eurocode 2 for RC structure.

                                                                                                                                                                                                                                                                            - Clause 5.5 of Eurocode 2: -
Linear Elastic Analysis with Limited Redistribution: -
Sub-clause 4: In continuous beams or slabs which: b) have the ratio of lengths to adjacent spans in the range of 0.5 to 2, redistribution of bending moments may be carried out without explicit check on the rotation capacity, provided that:-

 𝛿   ≥ k₁ + k₂x_u/d          for  f_ck ≤ 50 MP_a

 𝛿   ≥ k₃ + k₄x_u/d        for  f_ck > 50 MP_a             

Where,
𝛿 : ratio of the redistributed moment to the elastic bending moment.
x_u : depth of the neutral axis at the ultimate limit state after moment redistribution.
d : effective depth of the section

- Moment redistribution

If the hinge is created in the negative moment region in the continuous beams or slabs, the deflection would be caused and the moment would be redistributed. Thus, the negative moment will be decreased and the positive moment will be increased.

This takes into account the plastic behavior of concrete.

The depth of neutral axis (xu) increases with reinforcement. Thus if xu is increased, it leads to increase in delta values .
Thus, if (𝛿) is big, it implies that a lesser portion of moment was redistributed.
Thereby, if a lot of reinforcement is provided to the section, it increases the xu values, leading to less moment redistribution and vice-versa.
This delta (𝛿) obtained can be input in Moment Redistributed Factor in Midas nGen.

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