3D Effects of several beams joined at an acute angle with one another
The most likely 3D effect is one where the beam design forces generated are not always what you are expecting form a traditional 2D analysis.
This sort of effect could happen in many different ways and becomes more likely as the structural arrangement becomes more complicated and irregular.
We can demonstrate this effect with very simple model, with several floor beams joined a an acute angle (less than 90%) with one another, as shown below.
This model contains:
- 5 beams with size of 250 mm x 500 mm
- 4 columns with the size of 400 mm x 400 mm
- 2 slabs with the thickness of 120 mm.
The loading, shear & moment diagrams for the diagonal beam 1B5 are as shown below:
As both ends of the beam are fixed joint (supported by columns), hence it is expected to see approximately symmetrical hogging moment at both ends.
However, the moment diagram of the beam 1B3 is significantly different compared to1B5, although it is supported by the same columns at both ends.
The loading, shear, and moment diagram for the beam of 1B3 are shown below:
The loads are slightly offset due to the triangular area of slab being supported, but the bending moment diagram shows a sagging moment at the left end support and a hogging moment at the right end support. This result is unexpected as the bending moment diagram is not symmetrical.
The explanation relates to the diagonal beam across the floor. When the structure is assessed in the building analysis post processor > Analytical Model, the analytical wire frame with bending moment due to ultimate load case is as shown below.
Note that rigid zone (Reduced by 25%) was turned on, hence automatic rigid links (dark blue lines) were automatically created in the analysis to simulate the rigidity of the beam column joint. As a result, the moments are interpolated and shown at the end of the rigid zone, which is approximately at the face of the column & soffit of the beam.
The reason rigid zone is applied in this example is to accentuate the stiffness of the joint, so that this 3D behaviour can be better illustrated.
To better visualize the deflection, the animated deflection is as shown below.
The heavily loaded diagonal beam is causing a big hogging moment into the supporting columns and the joint is clearly rotating. This rotation cannot happen without some effects on the other connected beams, especially members that are connected less than 90 degrees (perpendicular).
In this case, the diagonal beam is forcing a rotation of joint clockwise at the column, i.e. left support of beam 1B3. This effectively means there is an externally applied clockwise moment at the left support of 1B3, which cancels out or negates any internal hogging moment.
As a conclusion, the design moments of 1B3 is correct in the context of 3D analysis. If the same model is analysed in other general 3D analysis program (e.g. SAP), the result will be the same.
Innumerable examples of this nature could be developed. The point is that if the design forces in a member seems wrong you cannot assume that the analysis is wrong. You need to review the results carefully and in particular look at the nature of deflections of all connected members to the common joint, as the deflection is a reflection of the internal forces in the member.
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