Help with Timoshenko theory of elastic stability

[ChooChoo]

In trying to continue my education past my Bachelor's, I'm using my lunch time at work to sharpen the saw, so to speak. I acquired a copy of Timoshenko's Theory of Elastic Stability and am currently working through Chapter 1 in an attempt to expand my knowledge base. I have noticed that in the text, the authors often skip through a small mountain of math to give either the intermediate or final answer. If you are naturally gifted or have someone teaching this to you, I don't suppose that's too bad; however, that is not the boat I've caught.

Specifically, my question is on Ch. 1, page 5. At the top of the page, the authors are solving for the undetermined coefficents in the differential equation by noting that the left and right sides of beam under the load 'Q' have common slopes and deflections. No problem there, but i am getting tripped up on the math. First, I assume that the second equation is the derivative of the first relationship with respect to 'c'. Now, if I do that, I don't understand how the -Qc(l-c)/Pl term becomes +Q(l-c)/Pl in the second equation. I'm also struggling with the solution for parameter 'D'.

Could somebody point this hapless soul in the right direction? I have run around this thing so many times that I've lost the capability of novel thought. All help is appreciated.

Thanks.

 

[ChooChoo]

OK, I kept plugging and got parameters B & D - something to be said for good bookkeeping. But I still get tripped up with the relationship at the top of pg. 5; I still don't see how the -Qc(l-c)/Pl in eq. 1 becomes +Q(l-c)/Pl in eq. 2.

 

[ChooChoo]

Never mind, I figured it out. Sorry to bother everybody.

 

[austim]

ChooChoo - Well Done. I'm glad to see your persistence rewarded