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

by chiraganand
Tags: beam, deflection, matrix, stiffness, tapered
 P: 56 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
HW Helper
P: 6,202
 Quote by chiraganand 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

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.
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,474 1. I am having trouble visualizing your beam and the nature of this 'nodal linkage'. Can you provide a picture?

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