Remathic12
New member
- Joined
- Sep 23, 2009
- Messages
- 1
I will upload my problem. I am having a problem with the notation in the integral. How do I solve the (du/dx)^2 dx part of the attached problem?
There are two cases. I am understanding Case 1 as taking the derivative of u(x) using the Product Rule or Chain rule and then plugging that into the du/dx, but then don't know how to solve the integral. Even in Case 2 where I take the derivative for each appears to be painfully obvious to me as u/5 and -u/5 and I can't even come up with the answer for those, so my problem is solving the integration and maybe incorrectly taking the derivative in case 1, where I come up with u'(x)= -10/25 + ux/25 using the chain rule and
u'(x)=(10u/25 - 2ux/25) using the product rule - I don't know if either of those is right. I've tried solving the integral with both derivatives and can't. Once the integral is solved, then the partial derivative of the potential energy has to be taken with respect to du1.
There are two values to EA, so Case 1 needs to be integrated for EA=100 (from 0 to 5) and EA=200 from 5 to 10 and added together...
Case 1 is supposed to be u1 = 1/8 and case 2 is u1 = 1/6, but I can't get either.
For problem 2, I keep coming up with w=PL^2/4EI, but it is supposed to be PL^3/4EI. Again, I think I am solving the integral incorrectly.
Any advice on either may relieve my tired mind! Thanks in advance.
There are two cases. I am understanding Case 1 as taking the derivative of u(x) using the Product Rule or Chain rule and then plugging that into the du/dx, but then don't know how to solve the integral. Even in Case 2 where I take the derivative for each appears to be painfully obvious to me as u/5 and -u/5 and I can't even come up with the answer for those, so my problem is solving the integration and maybe incorrectly taking the derivative in case 1, where I come up with u'(x)= -10/25 + ux/25 using the chain rule and
u'(x)=(10u/25 - 2ux/25) using the product rule - I don't know if either of those is right. I've tried solving the integral with both derivatives and can't. Once the integral is solved, then the partial derivative of the potential energy has to be taken with respect to du1.
There are two values to EA, so Case 1 needs to be integrated for EA=100 (from 0 to 5) and EA=200 from 5 to 10 and added together...
Case 1 is supposed to be u1 = 1/8 and case 2 is u1 = 1/6, but I can't get either.
For problem 2, I keep coming up with w=PL^2/4EI, but it is supposed to be PL^3/4EI. Again, I think I am solving the integral incorrectly.
Any advice on either may relieve my tired mind! Thanks in advance.
