What are Element Rotation and Hinge Rotation?

April 25, 2022
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What are Element Rotation and Hinge Rotation?

 

 

 

 

What is Element Rotation?


 
Element Rotation Model
Figure 1. Element Rotation Model

 

 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.



Calculation of Element RotationFigure 2. Calculation of Element Rotation 
 
 
  
 
 
 
 

 

What is Hinge Rotation?


 
Hinge Rotation Model
Figure 3. Hinge Rotation Model
 

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.

 

 
Calculation of Hinge RotationFigure 4. Calculation of Hinge Rotation

 

 

 

 

 

How to Calculate Element Rotation & Hinge Rotation in midas Gen


Example Model

 
Hinge Properties of Column
Figure 5. Hinge Properties of Column
 
 
 
 
Pushover Analysis Result
 
Figure 6. Pushover Analysis Result
 
 
 

 

 

 

How to Calculate Element Rotation

 

 Displacements at 50th Step  
 
 Figure 7. Displacements at 50th Step
 
 
 

 

 

Calculation of Element Rotation

 

** 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

 
 
 

 

 

 

How to Calculate Hinge Rotation

 
 
Moment at 50th StepFigure 8. Moment at 50th Step
 

 

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

 

  • Elastic Hinge Rotation (θe) = Min(Mu, My) / Ki
  • Plastic Hinge Rotation (θp) = Max(0, Mu – My) / 0.1*Ki
  • Total Hinge Rotation = θe + θp
 
 
Figure 9. Element 1 & 2 Model
 

 

 

 

 

 Where are Element Rotation and Hinge Rotation Used?


 

Element Rotation - Eurocode 8-3 A.3.

 
Check 'Safety Verification' as per EC8-3 A.3. 

 

 Limit State of Near Collapse
 
Figure 10. Limit State of Near Collapse
 
 
* Element rotation (= chord rotation) < chord rotation Capacity (θum)
 
 
 
 
 

Element Rotation - FEMA 356 C1.5.1

 

Check ‘Structural Performance Level and Damage’ as per EC8-3 A.3.

 
Structural Performance Levels and DamageFigure 11. Structural Performance Levels and Damage
 

 

 

 

 

 

Hinge Rotation - FEMA 356 C1.5.1

 

Check ‘Analysis Result’ & ‘Acceptance Criteria’ as per FEMA 356.

 
Hinge Rotation Analysis ModelFigure 12. Hinge Rotation Analysis Model
 

 

 
Modeling Parameters and Acceptance Criteria for Nonlinear Procedures
Figure 13. Modeling Parameters and Acceptance Criteria for Nonlinear Procedures

 

 

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Author Information
Yeong-il Seo | Principal Structural Engineer

Young-il has over 13+ years of experience in building design, especially high-rise buildings with column reduction analysis, plant structures, pushover analysis, health monitoring, and vibration control projects. Since 2016, he is planning and providing technical supports for midas building products such as midas Gen, nGen, and Design+.

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