# Shigleys Indeterminate Beam Derivation

## Homework Statement

Folks,

I am having difficulty deriving the moment expressions for a rigidly supported beam fixed at either ends and subjected to a point load. I have two attachments, one for the expressions given in Shigleys and the other for my attempted derivation.

The problem is that I want to derive the left hand fixing moment $M_1$ and $M_{ab}$ as in Shigleys. However, I believe my attempts are not leading to these expressions.

Is anyone good at these indeterminate derivations?

Thanks
Bugatti79

In attachments

## The Attempt at a Solution

In attachments
NOte that I have posted this in the math help forum http://www.mathhelpforum.com/math-help/f9/shigleys-indeterminate-beam-derivation-189693.html"

I will inform both post of any updates on a daily basis.

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## Answers and Replies

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
It seems your work is OK as far as it goes. Remember, the slope and deflection of the beam are both zero at the right end of the beam as well.

Hi Steamking,

Thanks for your reply.
$EI \frac{dy}{dx}=M_1 x+\frac{F(x-a)^2}{2}-\frac{R_1 x^2}{2}+c1$

$EIy=\frac{M_1 x^2}{2}+\frac{F(x-a)^3}{6}-\frac{R_1 x^3}{6}+c1 x+c2$

applying the BC's gives c1 and c2 both =0.

Yes, I get 2 equations and 2 unknowns as below...eliminating R1 to find M1

$\frac{1}{6} M_1 x^2 =-\frac{F(x-a)^3}{6}+\frac{F(x-a)^2 x}{6}$

I dont see how this leads to M1 in shigleys because it also has a b term in it. Also, I am curious how to derive $M_{ab}$...........

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
You have determined M1 in terms of F and x. You should be able to substitute for M1 in the slope equation and evaluate it at x = L. Knowing the value of the slope should allow you to solve for R1.

Dear Steam King,

I have obtained both M1 and Mab! Thanks

bugatti79