Procedure 4 Large Structures Construction Stage Analysis)
4.5.4 Four Step stay cable geometry adaptation
This step is the same as the calculation of the “final state system” (described above):
% The final system must be active for the calculation (no construction stages!)
% Internal subdivision of the Cable elements must be specified as the defi- nition of the new cables nodes are based on this subdivision.
% All loads must be defined in one single (final) loading case.
(alternatively, as defined in detail in Step 4, different loading cases, com- plying with the sequence of load application, can be defined and calcu- lated by selecting
# Accumulate Permanent Load in the " RECALC box)
These conditions are needed for the design of the cables, the girder and the pylon.
Apart from the cross-section design, the most important result from this design process is the determination of the stressing forces of the cables.
The following options are provided in RM2000 to supply these initial forces:
"LOADS AND CONSTR. SCHEDULE #LOADS !LSET:
# Stressing % Cable / external tendon stressing FCAB
# Initial Stress % Uniform temperature load T
# Initial Stress % Initial normal force FX0
# Initial Stress % Stress free element length LX0
# Actions on Element End % Element end displacements VGA We recommend that the initial forces are applied either as “Initial normal force” FX0 or as “Stress free element length” LX0 which are equivalent.
The “Initial normal forces” FX0 should be defined as unit loads for each cable in the design calculation (using ADDCON)
N.B. The initial nominal “unit loading” to the cable (First Loading Case) consists of two load sets, the first set being the normal “stressing force” (FXO) and the second set being a transverse load (the self weight).Since in a non-linear calculation it is not possible to vary the stressing force “FXO” and maintain equilibrium with the self weight part of the load, a Second Loading Case must be defined that contains the normal “stressing force” –FXO - on its own. This second loading case is then set up as the variable load and is operated on and modified by ADDCON.
Every newly activated cable therefore must have 3 load sets acting on them in this cal- culation: an initial force FX0 plus a transverse load forming the first Loading Case and a second Loading Case with the “initial force” defined on its own and having the vari- able factor (factor updated by ADDCON).
Note: Generally a non-linear ADDCON calculation can be accelerated by using better starting conditions. These “good” starting values can be found by first running ADDCON with lin- ear cables!
Summary of Step 1:
- Design of the structure using ADDCON on the “Final State System”.
- A single “Final state LC” containing all dead loads and the initial cables forces (the first calculated Loading Case after activation of a non-linear cable must contain one initial force - LX0 or FX0 - and at least one transverse force - e.g.
cable self-weight)
- To run ADDCON, more LSet’s and LC’s with initial cables forces have to be defined. – each of them corresponding to the cable stressing procedure.
- All LC’s must be accumulated in LC1000.
- Use “Accumulate Permanent Load” for calculation.
- Generally it is helpful to use an increment of 10 for cable-numbering.
Note: TDV has special macro tools for simplifying the input of large numbers of LSet’s and LC’s.
Step 2: “Modification of the stay cable geometry” (first intermediate step) The cable geometry is modified to the (un-deformed) basic system in this step.
All system nodes must be rigidly supported. - The user should select “step2-nodesupp”
to define the “high” spring constants for simulating a rigid support. (see chapter 4.5.1) The deformation of the subdivided cable is found, by the program, including the dis- placement at every subdivision point by calculating using this new system and using the loads, defined in Step 1.
These points define the node coordinates of the new cable elements, specified in Step 3.
N.B. The primary node support conditions must be restored before proceeding to the next step (The user should select “step2-undosupp” to restore the old constraints)
Summary of Step 2:
- Calculation at the undeformed system. (needed to find the “undeformed” posi- tion of the cable subdivision points.)
- All nodes of the primary structure must be rigidly supported for this calculation.
- The original node support conditions must be restored after the calculation.
Note: TDV has special macro tools for steps 2 and 3.
Step 3: “Input of the new cable elements” (second intermediate step)
The full cable lengths in step 1 are replaced by the shorter cable elements from the step 2 cable geometry calculation in this step.
Define the new cable nodes first.
The new node coordinates for these cables comes from the displaced subdivision point of the cables in step 2. - The user can recalculate the coordinates of the displaced subdi- vision point of the cables from the known coordinates of the undeformed cable subdivi- sion points.
Note: Nodes between cables need to have rigid conditions in rotation - these nodes, therefore, must be rigidly constrained against rotations (DOF 4,5,6) -. (see chapter 4.5.1)
The new cables can now be defined and activated between these nodes with the same parameters as the old cables.
The initial forces, defined in Step 1 for the single cable have to be recalculated to one initial load - “stress free element length” LX0 - being subdivided according to the cable subdivision and be given as unit loads to the new cable elements.
The old cables must be deactivated or deleted before proceeding to the next step.
The cables are now ready for the non-linear calculation in the construction stage sequence (step 4).
Summary of Step 3:
- The position of the subdivision points of the cables are recalculated from the re- sult of Step 2 (LC 1000) calculation.
- The nodes of the new cable elements are defined - The new (shorter) cables are between these nodes
- The new “subcables” have the same cross section and material properties as the original full length cable.
- The cable from Step 1 is deactivated and the new cables are activated in the con- struction stages.
Note: TDV has special macro tools for steps 2 and 3.
Step 4: “Construction stage sequence”
The construction stages can be calculated now that the system geometry is defined.
The first loading case calculated on any cable after its activation in this construction schedule must contain the initial cable force. This loading case must also contain at least one vertical load on the cable (generally the cable self-weight).
It must be repeated, because of its importance, that the “Stress free element length” LX0 of a cable is input as a load but is to be understood as a characteristic of the cable.
Note: Initial internal forces do not give a contribution to the load vector in the system of equa- tions. They are only superimposed on the analysis results as they might affect the element stiffness matrices in the case of a geometrically non-linear or in a stability analysis.
Because the “cable stiffness” is load-dependent it is of particular importance that the load sequence must be in the correct order!
To take into account this stiffness change due to changing load select:
# Accumulate stiffness (SumLC) in the " RECALC box
In this case all loads have to be accumulated into one defined load case. (default:
SumLC=1000) The load management. (see chapter 6.6) can be used advantageously for this.
If the design conditions for the Construction Stage Sequence and the Final State System are as defined in step 1, then the same ADDCON input can be used for this step
(step 4).
N.B a creep and shrinkage calculation it is not compatible with a selection of:
4.5.4.1 Proposed procedure to use non-linear cable elements in construction stage sequence:
Step 1:
Final State System
- final state system
- cables with subdivision points - all loads in one final state LC
- LSet’s with initial force and selfweight of the cables
- LSet’s with the additional initial force for all cables
DESIGN
of the structure
recalc
ADDCON
restore original nodesupports
- use “Accumulate Permanent Load”
- ADDCON converged faster, if the addcon first is calculated with linear cables and after that with nonlinear cables
Step 2: support all nodes
recalc - same LSet’s and LC’s as in Step 1
- results for a defined SumLC
- recalculate the position of the cable subdivision points from the result in SumLC of Step 2 - these are nodecoordinates of the new cables - deactivate the old cable
- transfer all initial forces, defined in Step 1, to a “stress free elementlength” of the old cable - this length divided through the number of the new cables gives the initial force of the new cables
input the “new”
cablegeometrie
Input of the
Construction Stages
- activate the cables in the construction stages - the first calculation on a new activated cable has to contend the initial force and the self- weight of the cable
final forces meet design criteria ?
Design OK ?
no .
yes
Step 3:
define the LSet’s and LC’s for the
new cables
Step 4:
Constr. Stage Sequence
recalc
ADDCON - use “Accumulate stiffness (SumLC)”
in the recalc-box
no .
yes