# Resolving line tension using vectors

I was wondering how you would go about solving the diagram I have drawn below. It is a simple representation of a body in equilibrium due to the tension of the 4 lines represented as vectors. The two forces are along the respective x and y axis.

With the forces shown one of the lines is useless however but this is necessary as the forces can change direction.

Looking at this instant simultaneous equations don't working without a lot of assumptions, I can solve part the problem with matrices or get an answer using computer software but I am interested in the process to resolve the tensions.

Any ideas?

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It's a statically indeterminate problem so it can't be solved without knowing the stiffnesses of the lines.

What do you mean by "a lot of assumptions"? Like the lines being able to support compression as well as tension?

I'm looking for a general way to solve this type of problem (that doesn't involve modeling it in software) so I can write a series of functions etc. in excel and from the data entered it can automatically solve a series of similar problems. If its possible to do?

The matrix functions in excel are limited and the Reduced row-echelon form function I used on a calculator uses a different process every time so duplicating in excel has numerous issues.

By the stiffness do you mean the young's modulus of the material, or modulus x cross section, or another?

'a lot of assumptions' meaning as the force is the -x direction there is no tension along x-axis on T3 & T4 therefore you can negate it, and visa versa in y-direction, obviously this is not the case and what I am after.

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By the stiffness do you mean the young's modulus of the material, or modulus x cross section, or another?
Young's modulus x cross sectional area.

'a lot of assumptions' meaning as the force is the -x direction there is no tension along x-axis on T3 & T4 therefore you can negate it, and visa versa in y-direction, obviously this is not the case and what I am after.
You mean you had to oversimplify it and possibly allow wrong solutions?

Have you been able to write a system of equations to describe it?

I would think it certainly requires an iterative method to detect compression and set those tensions to zero. Unless you can make more assumptions. Like are the wires prestressed before the forces are applied? Do you know in advance if any of them are slack?

The other way is to write a complete FEA solver in Excel VBA. Are you willing to include 3rd party libraries, say for equation solving? If you want I can send you a simple step-by-step tutorial (5 pages) for writing a 2D truss FEA solver. It would do exactly what you want except for diallowing compressive force. Then you could iterate through this solver to zero the stiffnesses of compressed members.

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