# Problem on stiffness matrix of beam and deflection of tapered beam

1. Aug 12, 2013

### chiraganand

1.How do i derive the stiffness matrix for a beam with nodal linkage? ie the shear force at the first node is 0 but the usual shear and moment resistance is present for the second node.

I thouth about solving the problem by just putting the first row of the stiffness matrix as 0 . Am i correct? Plee help in this

2. How do i get the deflection of a tapered beam? i have the intertia as a function of x. How do i go about the problem?
I thought of using the the the relation between EI and Moment equation and integrating it. But i a m not sure how to go further. Can someone please help me in this

2. Aug 12, 2013

### rock.freak667

Your moment equation would be

EI (d2y/dx2) = -M

where I is a function of x.

So you'd need to just do

d2y/dx2 = -M/EI

then integrate twice inputting your boundary conditions. This would depend on how your tapered beam is set up.

3. Aug 12, 2013

### SteamKing

Staff Emeritus
1. I am having trouble visualizing your beam and the nature of this 'nodal linkage'. Can you provide a picture?