Apis Structural Calcs


Tutorial 2 - check of L-shaped section under bi-axial bending

Before reading this tutorial, make sure you read Tutorial 1.


We need to check the capacity of the L-shaped column which is compressed and bent about both axes.

The structure is located in the UK.

Section properties:

  • Section dimensions: 500 x 500 x 200 mm
  • Reinforcement:
    • 12 No. 16mm diam. bars
    • distance from concrete surface to bar centre: 50mm
  • Steel properties:
    • characteristic yield strength (fyk): 400 N/mm2
    • class (as defined in EC2 Table 3.1): A
  • Concrete grade: C40/50

Design values of the applied forces:

  • axial force = 3000 kN
  • bending moment X = 100 kNm
  • bending moment Y = -150 kNm
  • design situation: persistent or transient
Step by step

1. Open the home page of RC Section Calculator (http://www.apiscalcs.com/rc/). Go to Data Input. Reset data if necessary.

2. Set Building code to BS-EN 1992-1-1:2004. Set Strength grade for concrete to C40/50. Set Design situation to Persistent & Transient.

3. We don't know the exact grade of the reinforcing steel, therefore we need to specify custom steel properties. First, set Grade for steel to B500B. The detailed properties displayed below were updated. Next, set Grade to Custom. Now, we just need to change the characteristic yield strength to 400 N/mm2, other values stay the same (because the steel is class B, the same as grade B500B). In the field fyk enter 400.

4. We assume the concrete cover and bar spacing are as required and they don't need to be ckecked. Therefore, set Validator type to None.

5. Now, we'll define the section shape. Set Shape type to Polygon.

6. We need to specify the coordinates of the vertices. It's going to be convenient to start from the vertex in the bottom left corner and place it at (0, 0). In the field Vertex 1 - X enter 0 and in the field Vertex 1 - Y also enter 0.

7. Subsequent vertices must be specified in the counter-clockwise order. Click Add more points to display more fields. The coordinates of the remaining vertices are: (500, 0) (500, 200) (200, 200) (200, 500) (0, 500). Enter these values in the corresponding fields.

8. You can verify the vertices' locations in the section preview on the right.

9. Now, we'll define the reinforcement. In the field Default diam. enter 16. The first reinforcing bar will be at (50, 50). In the field Single bars - 1 - X enter 50 and in the field Single bars - 1 - Y also enter 50.

10. Click Add more bars to display more fields. The coordinates of the remaining bars are:

  • (150, 50) (50, 150) (150, 150)
  • (300, 150) (450, 50) (450, 150) (50, 300)
  • (300, 50) (150, 300) (50, 450) (150, 450)

Enter these values in the corresponding fields.

11. Click show/update layout button. Look at the section preview and make sure the reinforcement layout is correct.

12. We're finished with defining the section properties. Click Submit button.

13. In the main menu go to Biaxial bending.

14. On the right there is an interaction diagram. The yellow axis is axial force, the blue axis is bending moment X and the green axis is bending moment Y.

15. To rotate the view, press the mouse button over the diagram and move the cursor.

16. To see the values of the forces corresponding to the data points in the interaction diagram, click Select data point and show forces in the Data information panel. Use the controls below (left, right, up, down) to choose the data point. The selected point is indicated by the pink line.

17. Now, we'll check the section capacity. In the field Force enter 3000, in the field Moment X enter 100 and in the field Moment Y enter -150. Click Check button.

18. The message with the check result was displayed - the capacity is sufficient. The point representing applied forces is displayed in the interaction diagram, it is indicated by the red line. Our task is finished.