Pushover Analysis

Figure 1 – Definition of a plastic hinge

Each plastic hinge has its unique ID that contains some information regarding the hinge position and its type. For example, the meaning of the “PLH-L112-1 C” ID is:

•   “PLH” – plastic hinge;
•   “L112” – the plastic hinge is positioned on linear element 112;
•   “1” – the plastic hinge is positioned at extremity 1;
•   “C” – the element is a column.

The software will detect whether the element is a column (vertical element), or if it is a beam (horizontal or inclined element) and will assign by default the appropriate hinge type.

The Eccentricity represents the position of the plastic hinge along the local X-axis of the element with respect to the corresponding extremity. The value of Clipping of forces is defined according to the Eccentricity. It is set on the corresponding planes with respect to the directions on which the plastic hinges are enabled. This is performed in order to consider the internal forces diagrams up to the location of the plastic hinges.

The properties of the plastic hinge can be defined by opening the Plastic hinge definition dialog from the   “ ” icon.

Plastic hinge definition dialog – Auto defined

By default, when enabling a plastic hinge, the Definition is set to “Auto defined”, the Code is set with respect to the norms used for the model and the Type is set according to the type of the element. The dialog is shown in Figure 2.

Figure 7 – Pushover load case family – properties

Overview of the Pushover Load case family properties panel:

1. Load Type – There are two load types available - both FEMA 356 and EC 8-3 require that the Pushover analysis is performed with two different load distributions. For each load type, up to four load cases can be defined. Also, each load type can have its own load distribution pattern and its own manner of load application.
2. Control – Shows how the load is incremented.
3. State – The generation of load cases for the given Load Type can be enabled/disabled.
4. Distribution – The load distribution on the height of the structure can be selected from the dropdown menu, or from the Pushover Loads Distribution dialog, accessible via the “ ” icon. The dialog is shown in Figure 8.

Figure 9 – Pushover load case – properties

Overview of the Pushover Load case properties panel:

1. Direction – Displays the direction of the load case. The property is inherited from the load case family.
2. Point of application – Displays the type of loads that are applied to the structure. The property is inherited from the load case family.
3. Load eccentricity – The use of eccentricity for the generation of Pushover loads can be enabled/disabled. For punctual loads – the loads are applied with the corresponding eccentricity from the center of mass of each floor. For surface loads – the loads are redistributed in order to account for the eccentricity.[1]
4. On X-direction – The direction of the eccentricity (+/- Y) – applicable for the Pushover load cases on the X direction can be defined.
5. On Y direction – The direction of the eccentricity (+/- X) – applicable for the Pushover load cases on the Y direction can be defined.

Note: The Pushover load cases on the X direction have an eccentricity on the Y direction, while the Pushover load cases on the Y direction have an eccentricity on the X direction. Eccentricities are not combined.

6. Percentage of distance on the X direction – The magnitude of the eccentricity as a percentage of the dimension of each floor’s envelope on the global X-axis of the structure can be defined. The eccentricity is calculated for each level.
7. Percentage of distance on the Y direction – The magnitude of the eccentricity as a percentage of the dimension of each floor’s envelope on the global Y-axis of the structure can be defined. The eccentricity is calculated for each level.

Note: For the mode shape distribution of the Pushover Loads, the eccentricities are inherited from the Modal Analysis

8. Distribution – Displays the pattern for the distribution of loads on the height of the structure. The property is inherited from the load case family.
9. Mode no. – The eigen mode used for the distribution of loads on the height of the structure can be selected. Available when the mode shape distribution is used.[1]
10. Maximum total lateral load – It refers to the sum of the applied lateral loads at the last step of analysis (total load that is distributed on the structure) for a given Pushover load case. This load can be calculated as follows:
    • Percentage of the total gravity loads – the load is computed as the sum of all gravitational loads (loads on the Z direction) from all load cases, except the Pushover load cases. The loads from these load cases are unfactored;
    • Seism base shear force on X – the load is computed as the sum of actions on supports of the seismic load case on the X-direction;
    • Seism base shear force on Y – the load is computed as the sum of actions on supports of the seismic load case on the Y direction;
    • Imposed Value – the value of the load is manually defined.
11. Value (%) – The maximum total lateral load is factored by the percentage that is defined here.
12. Value (as force) – Available when the Imposed Value option is selected. The value of the maximum total lateral load can be defined here.
13. Control type – It can be defined as the node used for the generation of the Pushover curve (load-displacement curve). There are two options:
    • Max displacement – The maximum displacement at each step of the Pushover Analysis it is used for the generation of the load-displacement curve;
    • Master node – A node can be defined for which the displacement is read at each step of the Pushover Analysis. This displacement is used for the generation of the load-displacement curve.
14. Node – It can be defined as the mesh node ID of the Master node to be used for the generation of the load-displacement curve.
15. Direction – The direction on which the displacement to be read can be defined. There are two options: X and Y.
16. Max displacement – A maximum displacement for the node defined at the Control type can be defined. The Pushover Analysis is stopped when this displacement is reached.[8]

[1] This feature is not yet available or with a limited scope in the release 2021 of Advance Design.

[7] This feature is not yet available or with a limited scope in the release 2021 of Advance Design.

[8] This feature is not yet available or with a limited scope in the release 2021 of Advance Design.

Figure 10 – Automatic generation of the Pushover Loads

Having defined the properties of the Pushover load cases, the Pushover Loads can be generated by using the Automatic generation of loads command, shown in Figure 10.

Pushover loads

The loads for each Pushover load case are generated in accordance with the settings defined in the Pushover load case family and the Pushover load cases properties panels.

Note: The magnitudes of the generated Pushover loads are computed during the Pushover Analysis.

Figure 12 – Pushover Analysis – definition

Figure 14 – Launch Pushover Calculation – Model tab

Figure 15 – Launch Pushover Calculation – Results tab

Depending on the material and the type of Plastic Hinges, there are certain results that need to be available, in order to be calculated. Thus, in some cases, it is mandatory to perform the RC calculation or the Steel calculation.

Requirements for the calculation of the Plastic Hinges on steel elements

•   If the Definition set to Auto Defined and the Cross-section class is set to auto class – the Steel calculation needs to be run (cross-section class is required for the computation of the plastic hinge). This is exemplified in Figure 16.

Figure 16 - Auto-defined plastic hinge + auto cross-section class

•   If the Definition is set to Auto Defined and the Cross-section class is imposed – the Steel calculation is not necessary.
•   If the Definition is set to User Defined and the Yield Bending Moment and Yield Rotation are imposed, as shown in Figure 17, – the Steel calculation is not necessary, even if the Cross-section class is set to auto class.

Figure 17 - User Defined plastic hinge + auto cross-section class

•    If the Definition is set to User Defined and the Yield Bending Moment and Yield Rotation are set to be computed by the software – the Steel calculation needs to be run.
•    If the Definition is set to Auto Defined and the Plastic Hinge is defined along the X direction – the Steel calculation needs to be run ( is required for the computation of the plastic hinge). This is exemplified in Figure 18.
•    If the Plastic Hinge is defined along the X direction and the Yield Axial Force is custom-defined – the Steel calculation is not necessary.

Figure 18 - Auto defined - DOF on local X enabled

Note: Currently, on Advance Design 2021 only I-shaped cross-sections (W, IPE, HEA, etc.) can be used for the Auto defined Plastic Hinges.

Requirements for the calculation of the Plastic Hinges on reinforced concrete elements

•   If the Definition is set to Auto Defined, the RC calculation needs are run with the Detailed rebar definition on beams and columns enabled from the Calculation Settings. The real reinforcement is required for the computation of the Yield Bending Moments, Yield Rotations, and the Limit states/Acceptance criteria.

Figure 20 – Pushover FEM results

Figure 21 - Pushover FEM results – reports

Plastic Hinge results

Once the Pushover Analysis is completed, the Yield Bending Moment and Yield Rotation are available on the Plastic hinge definition dialog, Figure 22. Also, the Normalized setting can now be unchecked – in this manner the effective value of the hinge properties and limit states/acceptance criteria will be shown, they will no longer be displayed as a ratio.

Figure 22 - Plastic hinge definition dialog - Normalized unchecked

In addition to this, the elastic releases that are defined, in accordance with the plastic hinge law, during the pushover analysis can be reviewed, as shown in Figure 23.

Figure 23 – Plastic Hinge – Elastic Release

Note: The elastic releases defined in accordance with the Plastic Hinge law are defined at the location of the Plastic Hinge (e.g. eccentricity of 0.05m).

Note: On the elastic domain (until the Yield Bending Moment is reached) the elastic releases are defined with a close to infinite stiffness. Hence, it does not alter the behavior of the element on the elastic range.

Pushover Graphical results

The Plastic Hinge status for each hinge can be displayed graphically on the structure for each step of the Pushover Analysis. These results are accessible from the ribbon, under the Pushover Analysis results, as shown in Figure 24. The rotation of the plastic hinges is compared with the limit states/acceptance criteria and the plastic hinge symbol is colored accordingly. The meaning of the Plastic Hinge statuses is explained in Table 1 for FEMA 356 and in Table 2 for EC 8-3 plastic hinges.

Figure 24 – Plastic Hinge status

Note: If for a plastic hinge multiple DOF are enabled, the most detrimental hinge status is considered.

Table 1 – FEMA 356 Plastic Hinges – Acceptance Criteria

Table 2 – Eurocode 8-3 Plastic Hinges – Limit States

Pushover Results curves

The Pushover curve (Load-displacement curve) is accessible from the ribbon, by using the Pushover results curves. A load-displacement curve is available for each Pushover Load Case.

The curve is obtained by plotting the displacement against the total applied load for each step of the analysis. The displacement of the node selected in the Pushover Load Case properties is used.

Figure 25 – Pushover curve

Using the scroll bar below the graph, it can be browsed through the curve. For each point on the curve, it is shown the step number, the total applied lateral load, and the displacement of the master node.

Pushover Reports

Once the Pushover Analysis has been performed, several reports can be generated from the Report Generator, Figure 26.

Figure 26 – Report Generator

•   Flexural plastic hinges status by load step

The table is shown in Figure 27. It displays the rotation, the bending moment, and the status of the flexural plastic hinges (hinges enabled around the local Y and around the local Z-axis) for each step of the Pushover Analysis.

Figure 27 – Report - Flexural plastic hinges status

Overview of the report:

1. Load case id – name – Displays the ID and the name of the Pushover Load Case.
2. Load step – Displays the load step of the analysis.
3. Plastic Hinge – displays the ID of the Plastic Hinge.
4. Ry – Displays the rotation of the plastic hinge around the local Y-axis.

Note: Since the stiffness of the plastic hinge on the elastic range is close to infinite, the rotation of the plastic hinge is close to zero at yielding.

5. My – Displays the bending moment at the location of the plastic hinge.
6. Ry_pl – Displays the rotation at yielding of the element’s cross-section around the local Y-axis, at the location of the plastic hinge.

Note: This rotation is used for the calculation of the limit states/acceptance criteria thresholds.

7. My_pl – Displays the yield bending moment of the element’s cross-section around the local Y-axis, at the location of the plastic hinge.
8. Status – Displays the status of the plastic hinge in accordance with Table 1 and Table 2.

The same information is provided for the Z Direction.

•   Axial plastic hinges status by load step

The table is shown in Figure 28. It displays the axial deformation, the axial force, and the status of the axial plastic hinges (hinges enabled on the local X-axis) for each step of the Pushover Analysis.

Figure 28 – Report – Axial plastic hinges status

Overview of the report:

1. Load case id – name – Displays the ID and the name of the Pushover Load Case.
2. Load step – Displays the load step of the analysis.
3. Plastic Hinge – displays the ID of the Plastic Hinge.
4. ΔDx – Displays the axial deformation of the plastic hinge.

Note: Since the stiffness of the plastic hinge on the elastic range is close to infinite, the axial deformation of the plastic hinge is close to zero at yielding.

5. N – Displays the axial force at the location of the plastic hinge. Tension for positive values, compression for negative values.
6. Δt_pl – Displays the axial deformation at yielding, at the location of the plastic hinge, when the element is subjected to tension.

Note: This axial deformation is used for the calculation of the limit states/acceptance criteria thresholds when the element is in tension.

7. Nt_pl – Displays the yield bending moment of the element’s cross-section around the local Y-axis, at the location of the plastic hinge.
8. Δc_pl – Displays the axial deformation when the buckling critical load is applied, at the location of the plastic hinge.

Note: This axial deformation is used for the calculation of the limit states/acceptance criteria thresholds when the element is in compression.

9. Nc_pl – Displays the buckling critical load of the element at the location of the plastic hinge.
10. Status – Displays the status of the plastic hinge.

•   Overstrength ratio (α_u/α₁)

The table is shown in Figure 29, displaying the overstrength factor for each calculated Pushover Load Case. Many seismic codes permit a reduction in design loads, taking advantage of the fact that the structures possess significant reserve strength.