Tendon Profile Parabolic and CircularProfile

[SPRstructur]

Dear all

can you help me to construct the tendon profile (Parabolic and Circle)?

Thank in advance

[terryhendicott]

Hi,

Here is the parabolic answer.

It is a Mathcad 15 file as I do not have full Prime 9 only express and programming is not available in express.

You can convert the file to Prime 9 full with the converter.

The circle shapes can be approached in a similar manner.

[SPRstructur]

Thank Sir.

[terryhendicott]

Hi,

At present I do not have Prime 9.

You will need to use the xmcd converter to get Prime 9.

Here is an update with a very subtle change in the solve blocks

Cheers

Terry

[SPRstructur]

can we construct without input angle ?Sir

[terryhendicott]

Hi

Equation of a parabola is:   a*x^2 + b*x + c so three unknowns need three equations to solve for a, b, and c.

One equation at each end of the parabola using x and y coordinates leaves another equation.

Slope at either end is the missing equation.

So it is simple to solve using the given angles as you can solve each segment in turn..

You can create a large matrix solving for seven a, b, and c parameters of each segment needing 21 total unknowns in a 21 x 21 matrix

End points of the seven segments gives 14 equations.

Equating Slopes or derivative of the parabolas at intermediate points gives another 6 equations .  

It is possible to create a number of equations equating the slope at each matching end of the segments without knowledge of the actual slope at these intermediate points. but you still need the end slopes then solve the whole matrix of equations for the twenty one unknowns.

If you want this demonstrated it will take a day to work it up.

Cheers

Terry

[terryhendicott]

Hi,

Here is the matrix method.

It can be done in Prime Express

Gives slightly different parabolas.

Cheers

Terry

[terryhendicott]

Hi,

Have added some text to explain the matrix method

[SPRstructur]

hi Sir

thank you for you help. your sheet really worked with my problem but I feel its complexity to input in large matrix . picture below show user input then get result and be able to apply any problems. this what I want to solve any problem

thank you Terry

[SPRstructur]

Thank you

[SPRstructur]

hi @terryhendicott  and all

This problem is same as I posted in this community.

its general idea of my problem

1. first pic is tendon profile. I think we can do it as functions then 

2. Second picture show we apply tendon per span.

3. Purpose: plot the tendon profile (X, Y) and use in future purpose

Thank you in advance

[SPRstructur]

Typical Tendon Profile per spanAssign or Apply Tendon Profile to any span and Example

[terryhendicott]

Hi,

For completeness here is the circular profiles,

Again a Mathcad 15 file you will need to convert to Prime 9.

The seven steps could easily be put into a program with a 7x7 matrix input of values to the seven calls of circ_m() function.

To eliminate input for the intermediate slopes you cannot use a 21x21 matrix method like the parabolic curves.

You would need to create a 21 equation solve block.

Cheers

Terry

[vnamboodheri]

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