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E, Ih

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COLLEGE OF

ENGINEERING Department of Civil & Geological Engineering

CE 463.3 Advanced Structural Analysis

Lab 6 SAP2000 Geometric Nonlinearity and P- effect

March 27th, 2013

T.A: Ouafi Saha Professor: M. Boulfiza 1. P- Effect http://www.youtube.com/watch?v=B6ZPNb-XIBQ This example will illustrate how to use SAP2000 to include geometric nonlinearity in a static analysis. In this case, the deformation due to an applied static vertical load will include second order effects caused by the eccentricity of the axial load. E= 200 GPa h = 3 m = 10 cm P = 100 kN Default Section i. General Definitions Choose (kN, m, C) as principal units and a grid system X(0, 0.1), Y(0), Z(0, 3) ii. Material and Section Definition Define Material (MAT) having Self-Weight = 0, E = 200 GPa and v = 0.3 Dont define frame section, just draw the model, and then change the default section material to MAT iii. Drawing the Model Draw a frame from point p1(0,0,0) to p2(0,0,3) and finish it in point p3(0.1,0,3) iv. Boundary Displacement Conditions Assign fixed restraints to the base. v. Loading Condition Assign a concentrated load under the DEAD load case to joint p3 equal to -100 kN in the Global Z axis. There are two main methods to include P-Delta effects in Sap2000, we will use only one in this example

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Menu Define > Load Cases

vi. Analyse the System Select XZ plane frame in the analysis option to reduce the problem size, then Run the analysis. vii. Display Output Open a second display window to see the linear and non linear results on the same screen. (Small triangle at the top left of the main graphic interface window, see red circle below)

Difference in the Horizontal (U1) Displacement between Linear and non Nonlinear analysis

Select nonlinear type

Select P-Delta

Add the Dead

Choose a name for the load case

Choose Static load case

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10.0

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ltotal

Flexural Moment (M3-3), Constant in the column for the classical linear analysis and

varying according to the deformation shape for the nonlinear analysis. Note that those values are obtained using a scale of 10 times the actual vertical loading condition. 2. Geometric non-linearity http://www.youtube.com/watch?v=K9dDpBQbUsk The second example will illustrate how to include large deflections in a static nonlinear analysis for a typical case of geometric instability. Material E= 200 GPa, v = 0.3, = 0 kg/m3 Section A = 4000 mm4 P = 10 kN ltotal = 4 m Run the analysis twice one with 1 = 10 cm and the other with 2 = 5 cm. For simplicity assume all the nodes to be articulated (truss structure). To solve this example follow the same steps as usual, the only difference is the definition of the static nonlinear analysis case, named here NL. You may need to specify the moment releases of the members.

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Run the analysis twice, the first run with 1 = 10 cm.

For 1 = 10 cm, there is no inflection (members in compression)

For the second run with 2 = 5 cm, it is better to do a database editing instead of redrawing the whole structure from scratch again. Go to Menu Edit > Interactive Database Editing Select Model Definition > Connectivity Data > Joints Coordinates > Table: Joint Coordinates Then change the Z coordinate of the appropriate node from 0.1 to 0.05

Static Nonlinear

P-Delta + Large displacements

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PyPx

For 2 = 5 cm, the nonlinear analysis leads to an inflected beam (members in tension) whereas the

linear analysis still shows a compression in the members. As you can see from these two runs, we ended up with two completely different results for the linear and the nonlinear analysis. Additional Example - Repeat example 1 for the column loaded with vertical and lateral forces. Try different values of Py and see what happens when the vertical load gets close to the critical value Pcr (Euler critical load for the first mode).