Description: Discussion of AutoPIPE Advanced Non- Linear Analysis Engine Product: AutoPIPE Version number: V8i (v9.2) Submitted by: MU Revison : 0.

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1 Description: Discussion of AutoPIPE Advanced Non- Linear Analysis Engine Product: AutoPIPE Version number: V8i (v9.2) Submitted by: MU Revison : 0.0 Table of Contents Table of Contents... 1 Non-Linear Friction... 2 Reference: TREATMENT OF SUPPORT FRICTION IN PIPE STRESS ANALYSIS (1989). 3 Reference: IMPROVED ITERATION STRATEGY FOR NONLINEAR STRUCTURES... 6 Load Sequencing... 7 Nonlinear Solution Load Case Sequence... 7 Total vs. Incremental Loading... 7

2 Non-Linear Friction A simplified explanation is below Imagine friction "building up" on the piping after thermal load. It hasn't broken friction or closed a support gap yet, but it's building up to that point of doing so. Wind or seismic just gives it that little push to break friction and or close the gaps, but it does require that extra push to make it happen. Therefore, the boundary conditions change, but only AFTER the wind load hits, so boundary conditions are different between the thermal and wind load analysis. This is only captured using a Non-Linear incremental approach and not Total Loads approach. Note: It is not uncommon in fact and stated by many building design codes like UBC and IBC that friction should not be considered for occasional type loads like Seismic. This is only possible using an incremental load case analysis engine like AutoPIPE when other non-linear conditions like support gaps needs to be considered.

Friction is calculated as friction factor x bearing force. The vertical or lateral support bearing force (hence friction) changes for each different load case applied by the piping on the support.

3 Friction is calculated as friction factor x bearing force. The vertical or lateral support bearing force (hence friction) changes for each different load case applied by the piping on the support. Of course the lateral bearing force is also dependent on the support gap which is changing by load case. The Total Load approach like with Caesar does not understand the boundary conditions and bearing force (hence friction) are changing by load case. It assumes constant boundary conditions from one Total load vector to another e.g. GR+T1+P1+E1 compared to GR+T1+P1 which is incorrect. Reference: TREATMENT OF SUPPORT FRICTION IN PIPE STRESS ANALYSIS (1989) By Liang-Chuan Peng Pang Engineering The author has stated in a couple of highlighted sections it is preferable to perform incremental analysis such as in AutoPIPE, to ensure no extreme load is overlooked the complication of the support stop and the friction has to be adjusted. Most pipe stress programs like Caesar use an old total load approach as described in ref 5.

4 AutoPIPE is one of the few programs capable of performing an incremental analysis

5 AutoPIPE has option to disable friction during earthquake since incremental analysis is performed. Total Load methods cannot evaluate this condition

Reference: IMPROVED ITERATION STRATEGY FOR NONLINEAR STRUCTURES (1981) By GRAHAM POWELL AND JEFFREY SIMONS Department of Civil Engineering Division of Structural Engineering

6 Reference: IMPROVED ITERATION STRATEGY FOR NONLINEAR STRUCTURES (1981) By GRAHAM POWELL AND JEFFREY SIMONS Department of Civil Engineering Division of Structural Engineering and Structural Mechanics, University of California AutoPIPE is based on advanced displacement increment method developed and published from the University of California (Berkeley)

7 Load Sequencing Nonlinear Solution Load Case Sequence For a linear analysis, the results for each load case are obtained all at once. However, for a nonlinear analysis the results are obtained sequentially. There are two reasons for this. First, the analysis of a nonlinear system requires iteration (successive trials), and different load cases will usually require different numbers of iterations. Second, (and more important) the result for any AutoPIPE load case will generally depend on the initial state for that case. For example, the result for a thermal expansion load will generally depend on the state of the system after gravity load is applied (e.g. which gaps are open and which are closed). The solution for the gravity case must thus be obtained first, and used as the initial state for the thermal expansion case. For a nonlinear analysis, the user has the option of selecting a default load sequence or of specifying a user defined sequence. It is important to note that in an AutoPIPE analysis, each load case is an increment of load, not a total load. To illustrate the difference, consider two alternative procedures for obtaining thermal expansion effects. If analyses are performed for total loads, the steps are: 1. analyze for gravity; 2. analyze for gravity plus thermal; then 3. subtract Step 1 from Step 2 to get thermal. If analyses are performed for load increments, the steps are: 1. analyze for gravity; then 2. analyze for thermal, specifying gravity as the initial state. AutoPIPE uses the second of these procedures. Thus, to obtain the results for gravity plus thermal, a load combination must be defined in using the commands in the Result menu. Total vs. Incremental Loading A load case (e.g. gravity, thermal, wind, etc.) represents an increment of load, not a total load (except for gravity). Hence, pipe forces, displacements, support forces, etc. calculated for a load case represent the increments produced by that case regardless of the type of static analysis performed (linear, or nonlinear). In particular, the results for a thermal case define the changes in the forces and displacements due to thermal expansion, not the total effects due to combined gravity and thermal. In order to obtain total load effects, combinations must be defined which include the load cases that have been used to hold the specific loads of interest. "Superposition" of load cases is a commonly accepted principle for a static linear analysis. However, it is not so straight forward for a nonlinear analysis.

8 Linear: Perform linear analyses. Initial states are not needed. All gaps are assumed to be closed and friction is ignored for occasional load cases. Linear soil properties are used, and yielding of soil is not taken into account.

Lab M5: Hooke s Law and the Simple Harmonic Oscillator

M5.1 Lab M5: Hooke s Law and the Simple Harmonic Oscillator Most springs obey Hooke s Law, which states that the force exerted by the spring is proportional to the extension or compression of the spring