- #1
XaeroR35
- 5
- 0
It has been a few years since I have done beam analysis, and I really don’t remember how to solve this type of problem so I have been reading up on it. I have found similar situations but nothing that matches the problem I am having.
I have a continuous beam of 3 spans with a uniform distributed load centered in the middle span (not full width).
I believe I need to use the Equation of Three Moments to solve this with Matrices, but I am stuck.
Since my material and cross sections are the same for the beam, I believe my 3-moment equations reduce to:
(M1*La) + (2*M2*(La+Lb)) + (M3*Lb) = - (6*xa*Aa)/(La) - (6*xb*Ab)/(Lb)
(M2*Lb) + (2*M3*(Lb+Lc)) + (M4*Lc) = - (6*xb*Ab)/(Lb) - (6*xc*Ac)/(Lc)
How do I get xa, xb, xc, and Aa, Ab, Ac? I understand these to be the centroids and areas of the moment curves for each span, but I am really struggling to come up with their values.
I have a continuous beam of 3 spans with a uniform distributed load centered in the middle span (not full width).
I believe I need to use the Equation of Three Moments to solve this with Matrices, but I am stuck.
Since my material and cross sections are the same for the beam, I believe my 3-moment equations reduce to:
(M1*La) + (2*M2*(La+Lb)) + (M3*Lb) = - (6*xa*Aa)/(La) - (6*xb*Ab)/(Lb)
(M2*Lb) + (2*M3*(Lb+Lc)) + (M4*Lc) = - (6*xb*Ab)/(Lb) - (6*xc*Ac)/(Lc)
How do I get xa, xb, xc, and Aa, Ab, Ac? I understand these to be the centroids and areas of the moment curves for each span, but I am really struggling to come up with their values.