Skip to main content
Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

IntMath forum | Applications of Integration

Catenary Equation [Pending...]

My question

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

http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf

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

X

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

Re: Catenary Equation

Nevermind! I ended up being able to solve it

X

Nevermind! I ended up being able to solve it

Re: Catenary Equation

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

X

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

Reply

You need to be logged in to reply.

Related Applications of Integration questions

Applications of Integration lessons on IntMath

top

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.