Catenary Equation [Pending...]

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I understand that a bridges main cable can be modelled using the parent catenary function, y = a cosh(x/a), where cosh(x)=(e^x+e^-x)/2. However, I was confused on how to obtain the parameter 'a'. I've read online that 'a' is a constant to do with horizontal tension? I also understand that 'a', essentially changes the overall wideness of the curve if I'm correct. 

Can someone please help me to understood how to solve for a?

Relevant page

<a href="http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf">http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf</a>

What I've done so far

∫_0^x▒〖√(1+(dy/dt)^2 )  dt=1016.5〗

Secondly, I will consider the equation which describes the height of the towers:

y(x)=206.4

After integrating the first equation and substituting the expression for y from the rationale into the second equations, my two main equations become:


a sinh⁡〖(x/a)=1016.5〗
And 
a cosh⁡(x/a)=206.4+a

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Nevermind! I ended up being able to solve it

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Log-lin models where the dependent variable is logarithmic, but the explanatory variables can be either logarithmic or linear.

X

For the first equation involving the integral, you need to solve it numerically because it's not a simple algebraic equation. You can use numerical methods or software to perform the integration and find the value of 'a' that satisfies both equations.

Once you have the value of 'a', you can substitute it back into the second equation to get the specific form of the catenary that models the bridge cable. Keep in mind that finding a closed-form solution for 'a' may not be possible, and numerical methods might be the most practical approach.

X

hello, if you know the desired horizontal tension in the cable, you can set up an equation using the tension, the span length, and the catenary equation. The horizontal tension can be determined based on structural requirements or load considerations. By solving the equation for 'a', you can obtain the parameter value.