See how this Cantilever Design Problem was Solved

I came across an Instagram post on the design of reinforced concrete cantilever beams that forms part of a modern residential dwelling. According to the author of the post, the cantilever beam is about 5 m long.


Cantilevers are beams that are rigidly fixed at one end, and freely supported at the other end. By implication, they are very susceptible to excessive deflection and vibration.

The architectural rendering of the structure in question is shown in Figures 1 and 2.

Figure 1: A 3D render of the proposed building
Figure 2: Another 3D render of the proposed building

As can be seen from the images above, the architectural rendering depicts a contemporary building with a cantilever projection at the front. To solve the problem, the design engineer, decided to introduce a diagonal/slanted reinforced concrete column, which would act as tension members to support the cantilever beam. The structural modelling of the scheme adopted by the structural engineer is shown in Figures 3 to 5.

Figure 3: Structural scheme of the building
Figure 4: Typical analytical model of the building on a design software
Figure 5: Another view of the structural scheme

By all indications, the design has been completed and the contractor has gone to the site. The construction images of the models are shown in Figures 5 – 7.

Figure 5: Picture of the building under construction
Figure 6: Another picture of the building under construction
Figure 7: Another picture of the building under construction

As can be seen in Figure 7, the reinforced concrete diagonal columns were cast monolithically with the frame of the structure. Then bricks were used to cover the openings to create a plain wall that matches the architectural requirements.


Why did the Model Succeed?

The model adopted by the structural engineer succeeded because there are full walls without openings where the inclined columns can be hidden without any implications. Because there are no openings (doors, windows, or curtain walling) on the first bay of the first floor, the inclined columns can be introduced without affecting the architectural concept of the building.

If there had been need for openings in those walls, the adopted structural scheme would not have been an ideal solution. Therefore the ingenuity of the design engineer is appreciated.

How Efficient is the Model?

To check the structural efficiency of the model, let us carry out a comparative assessment of a cantilever beam with and without diagonal columns on Staad Pro software. The 3D rendering of the model without diagonal columns is shown in Figure 8.

Figure 8: 3D rendering of the test model without diagonal columns

For simplicity, all the first floor beams were loaded with a uniformly distributed load of 25 kN/m as shown below. Furthermore, a uniformly distributed load of 10 kN/m was applied to the roof beams.

Figure 9: Typical loading and dimensions of the model

The analysis comparison is going to check the effect of introducing a diagonal column on the deflection, bending, and shear force on the structure.

Figure 10: 3D rendering of the test model with diagonal columns

Analysis Results: Without diagonal column

Figure 11: Deflection profile of the structure (without diagonal columns)

As can be seen above, without the presence of the diagonal columns, the maximum deflection at the free end of the cantilever was 35.261 mm.


Figure 12: Bending moment diagram of the structure (without diagonal columns)

Without the presence of the diagonal column, the maximum cantilever moment was 372.701 kNm. However, the column sitting on top of the cantilever beam appeared to be tension, assisting in supporting the cantilever beams and sending the load to the roof beams.

Figure 13: Shear force diagram of the structure (without diagonal columns)

A maximum shear force value of 158.518 kN was observed at the fixed end of the cantilever without diagonal columns.

Figure 14: Axial force diagram of the structure (without diagonal columns)

The axial force diagram confirms that the column sitting on top of the cantilever beam is in axial tension, as well as the roof beams.

Analysis Result: With Diagonal column

Figure 15: Deflection profile of the structure (with diagonal columns)

As can be seen in Figure 15, when diagonal columns were introduced, the maximum deflection at the free end of the cantilever reduced to 23.301 mm.

Figure 16: Bending moment diagram of the structure (with diagonal columns)

With the presence of the diagonal column, the maximum cantilever moment was 219.221 kNm (see Figure 16). However, the column sitting on top of the cantilever beam reversed to be a compression column, thereby transferring its loads to the cantilever beams.

Figure 17: Shear force diagram of the structure (with diagonal columns)

With the presence of diagonal columns, the shear force at the fixed end of the cantilever is reduced to 106.244 kN as shown in Figure 17.

Figure 18: Axial force diagram of the structure (with diagonal columns)

Axial force diagram in Figure 18 shows that the diagonal column is in axial tension.

A table of comparison has been prepared below to show the effect of diagonal tension column support on the deflection behaviour of long span cantilever beams.

Without diagonal ColumnWith diagonal columnPercentage decrease
Deflection (mm)35.261 mm23.301 mm33.91%
Bending moment (kNm)372.701 kNm219.221 kNm41.18%
Shear force (kN)158.518 kN 106.244 kN32.97%

It can therefore be seen that the diagonal tension columns were effective in reducing the deflection, bending moment, and shear force on the cantilever beams. Where architectural specifications permit, cantilever beams and slabs can be supported using diagonal tension members for more structural efficiency.

Source of images:
Instagram @engnivaldo
Architects: @curvoarquitetos

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