Moving load analysis resulting in negative bending moment at pin support at abutment
For the moving load analysis, I am getting different values for the maximum negative bending moment based on different support conditions.
Attached you see models of a two-span bridge with deck element modeled as plate element. Image 1 shows a model with the pin-roller-roller boundary condition, and Image 2 shows a model with the roller-pin-roller condition. As shown in Image 1-1 the negative moment at the left support due to truck loading is -7 kNm to -6 kNm. The negative moment at the left support due to truck loading on Image 2-1 is -384 kNm to -535 kNm.
The connection between the support is formed using elastic rigid link.
Please advise why I am getting different results.
1. This is happening for the live load, but the difference is negligible for the self-weight. The rotations (RY) and displacements (DX) at the end of the each girders are different for the vehicle loads, while those are similar for the self weight. These different rotations and displacements between girders are restrained by each other because the girders are connected by the plate elements.
2. The location of support is at the bottom of the girder, not at the centroid of the section. The support and the girder is connected with Elastic Rigid Link.
3. Under this condition (point 1 and 2 above), the negative moment can occur at the support.
4. Why we get larger negative moment at the left end of the girder when the left end is the pinned support compared to the roller support? In order to find the reason, I tried to make a model below which is simple but satisfies the above conditions. Pinned support at the left and roller support at the right.
- Bending moments due to self-weight. The moments are zero at either ends as expected. The moment results are the same after switching pinned support and roller support.
- Bending moments due to one wheel load.
A concentrated load at the 1/4 point of the girder. Negative moment at the pinned support: -226, at the roller support: -2
A concentrated load at the center of the girder. Negative moment at the pinned support: -258, at the roller support: -4
A concentrated load at the 3/4 point of the girder. Negative moment at the pinned support: -161, at the roller support: -3
As you see, we get larger negative moment at the pinned support than roller support for all three cases above. Even the moments are not symmetric when the concentrated load is applied at the center of the girder. We can see that the degree of the restraint of rotation is higher at the pinned support than roller support, and the rotational restraint can only occur when the load is applied locally on the bridge.
|Image 1 roller-pin-roller .JPG|
|Image 1-1 roller-pin-roller.JPG|
|Image 2 pin-roller-roller.JPG|
|Image 2-1 pin-roller-roller.JPG|