Algorithm for Fortran Structural Analysis

[JohnNichols]

@mecej4 and @jimdempseyatthecove

I was looking at amending one of the structural programs to include prestressed cables.  

The challenge is the cable is stretched first, so I have an axial problem that is solvable 

Pa = K * da

I know Pa and I know K so we have da

But can I then load Pa and da into 

Load + Pa = Stiffness * (Defln + da) 

in the correct entry points for the full 3d matrix

invert the stiffness matrix and solve for deflection or am I missing something in the math

Thanks 

John

[jimdempseyatthecove]

Can you define your symbology?

Is Pa pascals (force/area)

Is P pascals and a area (thus Pa = force)

I assume K is the spring constant (or is it).

so what is da? change in area? or change in length?

Do a dimensional analysis (make sure the resulting units on both sides of = are the same).

Jim Dempsey.

[JohnNichols]

Jim:

Thanks.  I will do a sketch of the problem, at the moment I am just trying to get the visual picture of the math right in my head, setting it out for you gives me a starting point.  The current method for design dates from the 1970's for prestressed planks, it is quite simple, but I am trying to model failing beams, and it is not as simple as modelling a degrading Young's Modulus which applies to most.   I have the change in measured frequency now I need a Fortran program that can model that event, which is part concrete failure and part bar slippage or breaking from strike loads of unknown size.  

It can only be programmed in Fortran or C++ as I need the mkl inverters.  

And I know Fortran and dislike the C language. 

John

[jimdempseyatthecove]

From my little understanding of your work, I presume you are talking about concrete bridges (or concrete something or other).

In this domain, prestressed, refers to embedded wire(s) or cable(s) tensioned during curing (end points may be capped).

In a general sense, you are not provided with the cross-sectional area, Young's Modulus or strain, of the wire(s)/cable(s), just a tensioning amount.

I think from what you are given, you need to determine the above properties, then from these, determine what is suitable for input to the code you have. Internally, for computational efficiencies, you would want to reduce the external properties to:

Undeformed Length

Strain (Deformed Length - Undeformed Length)

Spring Constant

(optionally Spring Damping constant)

(optionally thermal coefficient (concrete and wires), temperature, absorption properties, heat transfer properties)

(optionally shear point between wire and concrete interface)

(and a few others)

Then let these produce the tension.

During modling, as you apply external load, you compute the force vectors and determine how it affects the strain. Not quite as simple as this as you are likely modeling a dynamic system, the bridge has inertia, which gets in the way of external force transitioning to strain over time.

Sounds like a fun project.

It would be handy to have a well written, and easy to follow, a reference document (thesis?) on this subject.

Jim Dempsey