GeoStudio | PLAXIS - Asymmetric moment-axial force interaction for elastoplastic plates and embedded beams

Application	PLAXIS 2D
Version	PLAXIS 2D 2024.2
Date created	30 December 2024
Date modified	30 December 2024
Original author	Felipe Fonseca - Technical Writer Geotechnical Analysis

With the release of PLAXIS 2024.2 a new capability is added to consider the asymmetric interaction between bending moments and axial forces in elastoplastic plates and embedded beams materials.

1- Symmetric moment-axial force interaction (already available in previous versions of PLAXIS 2D)

In symmetric combinations of bending moments (M) and axial forces (N), failure occurs under identical states of compressive (N<0) and tensile forces (N>0), this represented, in PLAXIS 2D as |N_p,1,tens| = |N_p,1,comp|. Therefore:

Maximum available bending moment |M_p| when axial forces are zero (i.e., |N_p,1,tens| = |N_p,1,comp| = 0).,
Maximum axial force in the material when bending moments are zero.

Figure 1 displays the ultimate combinations of symmetric Mp-Np interactions for which plasticity will occur. Notice that force combinations inside the diamond correspond to purely elastic deformations.

Figure 1: Interaction of maximum bending moment and axial force in plates and embedded beam materials

Remarks:

If anisotropy is considered in PLAXIS 2D plates, different axial forces can be assigned per local axis i.e. |N_p,1,tens) |= |N_p,1,comp) |≠|N_p,2,tens|= |N_p,2,comp>|. Notice that the axial forces in the second local axis |N_p,2)| are not part of the interaction diagram and behave independently of the ones acting in the primary axis.
The convention used for the material strength parameters for plates and elastoplastic embedded beams was updated in PLAXIS 2024.2 for extra clarity and consistency with the new parameters for asymmetric moment-axial force interaction behaviour.

2- Asymmetric bending moment-axial force interaction (Available from PLAXIS 2D 2024.2)

In asymmetric bending moments and axial force interactions (as it can be for materials such as concrete) failure might be reached under different compressive and tensile states, where |N_p,1,tens|≠ |N_p,1,comp| . In this circumstance. Therefore, the maximum bending moment allowed is no longer reached when axial forces are zero. Instead, the maximum bending capacity is found at a certain axial force N_1,|Mp|.

In asymmetric conditions, elastic deformations occur when the combination of forces fall inside the region described in the expression below and Figure 2:

Figure 2: Asymmetric interaction of maximum bending moment and axial force in plates and embedded beam materials

Note:

The PLAXIS 2D implementation of both symmetric and asymmetric bending moment-axial force interaction for plates and embedded beams uses an idealized “diamond” diagram to separate elastic from plastic deformation.

In the PLAXIS 2D interface, the material strength parameters of elastoplastic plates under non-isotropic conditions can be visualized as in Figure 3:

Figure 3: Material strength parameters for elastoplastic plates.

where:

Parameter	Description	Units
	Maximum bending moment (without any acting normal force) of the plate material.	[KNm/m]
	Maximum tensile axial force along plate's first local axis (without any acting bending moment) of the plate material.	[KN/m]
	Maximum tensile axial force along plate's second local axis of the plate material. Note that the axial force in the second local axis direction does not take part in the interaction diagram shown in figure 3.	[KN/m]
	Maximum compressive axial force along plate's first local axis (without any acting bending moment) of the plate material.	[KN/m]
	Maximum compressive axial force along plate's second local axis of the plate material. Note that the axial force in the second local axis direction does not take part in the interaction diagram.	[KN/m]
	Axial force N1 for which the maximum bending moment \|Mp \| can be obtained. The value can be either positive (tension) or negative (compression).	[KN/m]

The moment-axial force interaction for elastoplastic embedded beams follows similar principles to those of plates in terms of their material strength parameters. However, since embedded beams are one-dimensional structural elements with only a single main axis, isotropy is not applicable. The strength parameters for these structural required by PLAXIS 2D are displayed below:

Parameter	Description	Units
	Maximum bending moment (without any acting normal force) of the embedded beam material.	[KNm/m]
	Maximum tensile axial force (without any acting bending moment) of the embedded beam material.	[KN/m]
	Maximum compressive axial force (without any acting bending moment) of the embedded beam material.	[KN/m]
	Axial force N for which the maximum bending moment \|Mp\| can be obtained. The value can be either positive (tension) or negative (compression).	[KN/m]