Element rotation means the angle caused according to the lateral deformation of the element.
However, the deformation by analysis includes the rotation value due to the deformation of the adjacent constraint as shown below.
Therefore, the element rotation can be calculated by removing the rotation by constrained deformation from the total rotation.
Hinge rotation means the curvature caused by the bending moment. It is usually considered where large moment occurs, and the hinges usually occur at the ends of the elements. Hinge rotation is calculated from the relationship between bending moment and stiffness of the element as shown on the right.
Example Model
** Note.
There is a slight difference in the midas Gen because the rotation by shear deformation is also removed.
Location |
Lateral Displacement |
Rotation by Constraint |
|
Element No |
Node No |
Dx (mm) |
Ry (rad) |
1 |
1 |
0.000 (Dxi) |
0 |
2 |
50.000 (Dxj) |
0.001760 |
|
2 |
2 |
50.000 (Dxi) |
0.001760 |
9 |
56.287 (Dxj) |
0.000902 |
Location |
Element Rotation (rad) *(Dxi-Dxj)/Length - Ry |
|
Element No |
Node No |
|
1 |
1 |
(50-0)/3500 – 0 = 0.0142857 |
2 |
(50-0)/3500 – 0.001760 = 0.0125257 |
|
2 |
2 |
(56-50)/3500 – 0.001760 = 0.0000363 |
9 |
(56-50)/3500 – 0.000902 = 0.0008943 |
Location |
Moment at 50th step (Mu) |
Yielding Moment (My) |
Hinge Rotation (rad) |
|||||
Element No |
Node No |
|||||||
Initial Stiffness (Ki) |
Stiffness after yielding (0.1*Ki) |
Elastic (θe) |
Plastic (θp) |
Total (θt = θe+θp) |
||||
1 |
1 |
239.3 |
235 |
25160 |
2516 |
0.009340 |
0.001709 |
0.011049 |
2 |
238.7 |
235 |
25160 |
2516 |
0.009340 |
0.001471 |
0.010811 |
|
2 |
2 |
50.6 |
235 |
25160 |
2516 |
0.002011 |
0 |
0.002011 |
9 |
158.4 |
235 |
25160 |
2516 |
0.006296 |
0 |
0.006296 |
Check ‘Structural Performance Level and Damage’ as per EC8-3 A.3.
Check ‘Analysis Result’ & ‘Acceptance Criteria’ as per FEMA 356.