Moment is not continuous

Question:

Hi,
In the attached model, the right member is a tapered member.
This is a simple beam and the load is at the center.
But the moment is not continuous.
Please check why is that.
Thanks.


Answer:

Hello,
Greetings.

Thanks for reaching us.
Let me explain this with help of example in which I took beam where half of beam is given with section detail as 1x1m rectangle and rest half with 0.5x0.5m rectangle and is simply supported. A 100 kN point load in applied in vertical (gravity) direction. Angle of beam with horizontal is 5 deg as shown below.
4 similar beams were created where centre-centre, centre-top, left-centre and left-top offset was used for beam section definition.


Now, the structure is analysed and results for bending moment My for 100 kN point load is observed as shown below. 


When centre top section is provided, the section will create the rigid link joining the centre top offset point and centre line. 
Now, due to this, beam acts as portal frame and bending moment generated at centroidal axis is displayed at the reference offset line. 
As the beam is inclined with horizontal, the axial force in beam is produced due to vertical load as shown below. This axial force is create additional moment due to offset with respect to the centroidal axis.
When centre-centre is given, moment is 100 kNm. When centre top offset is provided, axial force in left part beam is 4.4 kN and offset distance is (1/2) m, thus additional moment is 4.4 * 0.5 = 2.2 kNm. Net moment is 102.2 kNm. Similarly, for right part offset is (0.5/2) m and moment is 100- (4.4*0.25) = 98.9 kNm.



For more on section offset, click here. The model file has been attached for further review.

Creation date: 6/4/2021 3:31 PM      Updated: 6/4/2021 3:31 PM
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DataImage83.png
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DataImage80.png
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DataImage53.png
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check.mcb
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DataImage71.png
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temp.mcb
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