A-08 (A Simple Suspension Bridge) |
  
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A-08 (A Simple Suspension Bridge) |
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Objective
To verify the behavior of the beam element with moment releases
Problem Description
A suspension bridge consists of a 60m long beam fixed on both ends and two 25m long truss members which suspend the beam as shown below.
Lengths: shown in parentheses
Material properties: E = 200 kN/mm2, ν = 0.3
Beam Section: Ix = Iy = J= 0.1 m4, Az = 1.0955 m2
Truss Section: Ix = Iy = J= 2e-6 m4, Az = 0.005 m2
Uniform load on beam: -10 kN/m
Finite Element Model
5 beam elements (moment release at truss ends connecting the beam)
Model type: 2D Frame (shear deformation ignored)
Results
The displacements and internal forces given by ENERCALC 3D are compared with the reference [Ref 1].
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ENERCALC 3D |
Ref 1 |
Displacement Dy @ N2 (m) |
-3.970e-003 |
79400/(EI) = -3.97e-3 |
Rotation Doz @ N2 (rad) |
-2.540e-004 |
5080/(EI) = -2.540e-004 |
Maximum (+) Moment in Beam (kN-m) |
674.755 |
675 |
Maximum (-) Moment in Beam (kN-m) |
-682.840 |
682 |
Shear at Beam Ends (kN) |
42.88 |
42.8 |
Shear at Beam Third Point (kN) |
100 |
100 |
Maximum Axial Force in Trusses (kN) |
95.2 |
95.2 |
Comments
The results given by ENERCALC 3D are very close to the referenced values. Since the model contains both truss and beam members, we used 2D Frame model type and applied moment releases to beam elements for truss members.
The reference gives the relationship of section properties as (EA)truss = (EI)beam/(20m). The properties used in the problem were selected based on this assumption. The beam section area is much greater than the truss section area. Therefore, the axial deformation in the beam is practically ignored.
The moment, shear, and axial force diagrams are shown below for illustration purposes.
Major Moment Diagram (Mz) |
Shear Diagram (Vy) |
Axial Force Diagram (Vx)
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Reference
[1]. Long & Bao, “Structural Mechanics”, pp279, People’s Educational Publishing House, China, 1983.
