I have created a model using tapered composite sections to model a proposed composite bridge. I have input various load cases including expansion/contraction, settlement, shrinkage/creep, live load. I have analysed the model but some of the load effects are unexpected. I was hoping you could clarify why they are occurring. The bridge is at a skew angle of 20 degrees so I am wondering if this is the cause, or if it is an error in the way I have set up the model.
The issues are:
- Shrinkage primary is giving a sagging effect, but shrinkage
secondary is giving hogging effect. Should they not be the same?
- For the dead load case there is an unusual level of hogging
to the east pier of one beam compared to west pier of the same beam. Why is
this, I expected pretty regular distribution?
- For the uniform expansion/contraction load cases, there are hogging/sagging
moments. These were somewhat unexpected because the boundary conditions are
such that the girders are free in the x (longitudinal) direction over both
piers and the end abutment.
The model is attached for your reference.
Thank you in advance.
The answers to your questions are:
1) Shrinkage is causing the deck to shorten relative to the steel girders. This makes the bridge want to sag in one continuous curve between the two ends, thus the sagging moment under Shrinkage Primary. However, as the bridge is a continuous beam with 3 spans, the intermediate supports are resisting this global sagging by providing vertical reactions. This causes the hogging moment under Shrinkage Secondary. Please remember that Shrinkage Primary is an imaginary force, required to cause the shrinkage strain in the members, and Shrinkage Secondary is the effect of the indeterminate structure resisting the free deformation due to shrinkage primary.
2) This is caused by the skew of the supports. The transverse stiffness of the structure is attracting more loads to the closer supports to the geometric middle of the deck compared to the ones further away. This is very easy to demonstrate with a uniform slab modelled with skew and without a skew. You can see the reactions for the regular slab are symmetric and very similar, whereas the skewed one has a significant shift of the load towards the close end supports:
Additionally, there are duplicate nodes in your model where the continuity of the structure is interrupted so that the behaviour is not as expected.
3) Finally, the bending of the deck under temperature loads is a combinations of a few factors.
- the above discontinuity causes the deck not to expand uniformly as you expect.
- additionally, the edge beams have no temperature assign. Due to their eccentricity to the deck their apply bending moment to the main girders by resisting the expansion/contraction
- the skew also is trying to rotate the deck in one direction which the Dy restraints at the following support lines are resisting, leading to additional secondary effects of the deck being unable to freely deform.
If you fix the duplicate nodes, apply temperature to the edge beams as well and release the deck for Dy for all support lines but the first one you will see that the moments in the main girders are considerably smaller:
I hope this clarifies all your questions. Let us know if there is anything else.