A-10 (3D Frame with Rigid Diaphragms) |
  
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A-10 (3D Frame with Rigid Diaphragms) |
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Objective
To verify the behavior of the rigid diaphragms in 3D Frame
Problem Description
A two-story building is subjected two nodal loads in global X direction at the two story level nodes. The X-bay and Z-bay distances are both 18 ft. The story height is 12 ft.
Material properties: E = 3155.92 ksi, ν = 0.15
All Sections: rectangular 12x12 in.
Iyy = Izz = 1728 in4; J = 2920.32 in4 ;
Az = 144 in2; Ax = Ay = 120 in2
Loads: two 20 kips nodal loads in global X direction as shown.
Finite Element Model
Model type: 3D Frame, with rigid diaphragms defined at two story levels.
Diaphragm stiffness factor: default value (=10000)
Results
The displacements and support reactions given by ENERCALC 3D with and without rigid diaphragm actions are shown below.
Displacements:
Node |
Dx (in) |
Dy (in) |
Dz (in) |
Dox |
Doy |
Doz |
Diaphragm actions considered |
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5 |
1.01E+00 |
4.95E-03 |
6.70E-01 |
1.01E-03 |
6.20E-03 |
-2.01E-03 |
6 |
1.01E+00 |
-4.95E-03 |
-6.70E-01 |
-1.01E-03 |
6.20E-03 |
-2.01E-03 |
11 |
2.35E+00 |
4.95E-03 |
6.70E-01 |
1.01E-03 |
6.20E-03 |
-4.03E-03 |
12 |
2.35E+00 |
-4.95E-03 |
-6.70E-01 |
-1.01E-03 |
6.20E-03 |
-4.03E-03 |
Diaphragm actions ignored |
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5 |
8.36E-01 |
4.17E-03 |
5.03E-01 |
8.31E-04 |
5.99E-03 |
-1.81E-03 |
6 |
8.36E-01 |
-4.17E-03 |
-5.03E-01 |
-8.31E-04 |
5.97E-03 |
-1.81E-03 |
11 |
2.53E+00 |
5.72E-03 |
5.03E-01 |
8.31E-04 |
5.99E-03 |
-4.23E-03 |
12 |
2.52E+00 |
-5.72E-03 |
-5.03E-01 |
-8.31E-04 |
5.97E-03 |
-4.24E-03 |
Reactions:
Node |
Rx (kip) |
Ry (kip) |
Rz (kip) |
Rox |
Roy |
Roz |
Diaphragm actions considered |
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1 |
-5.42E+00 |
-1.15E+01 |
-4.58E+00 |
-3.37E+01 |
-7.63E+00 |
4.30E+01 |
2 |
-5.42E+00 |
1.15E+01 |
4.58E+00 |
3.37E+01 |
-7.63E+00 |
4.30E+01 |
7 |
-1.46E+01 |
-1.15E+01 |
-4.58E+00 |
-3.37E+01 |
-7.63E+00 |
1.10E+02 |
8 |
-1.46E+01 |
1.15E+01 |
4.58E+00 |
3.37E+01 |
-7.63E+00 |
1.10E+02 |
Diaphragm actions ignored |
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1 |
-3.96E+00 |
-9.55E+00 |
-3.12E+00 |
-2.34E+01 |
-7.55E+00 |
3.26E+01 |
2 |
-3.96E+00 |
9.55E+00 |
3.12E+00 |
2.34E+01 |
-7.52E+00 |
3.26E+01 |
7 |
-1.61E+01 |
-1.34E+01 |
-3.12E+00 |
-2.34E+01 |
-7.55E+00 |
1.21E+02 |
8 |
-1.60E+01 |
1.34E+01 |
3.12E+00 |
2.34E+01 |
-7.52E+00 |
1.21E+02 |
Comments
The diaphragm actions are noticeable in this example. Although the model is subjected to unsymmetrical loads, the nodal rotations about global Y axis are the same for nodes on the diaphragms. This means that the diaphragm stiffness factor, which happens to be the default value 10000, is appropriate for this example. The program is also capable of handle slanting diaphragms. For example, you may rotate the model about Z axis by (-30) degrees. Adjust the local angles for horizontal members as well as the nodal forces accordingly. The Dx for the Node 5, 6, 11 and 12 given by the program are 8.769e-001, 8.720e-001, 2.037e+000 and 2.032e+000 in. The correctness can be verified as the following:
Dx @ node 5: 1.01cos30 + 0.00495sin30 = 0.877
