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Problem on stiffness matrix of beam and deflection of tapered beam

by chiraganand
Tags: beam, deflection, matrix, stiffness, tapered
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chiraganand
#1
Aug12-13, 09:09 AM
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
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rock.freak667
#2
Aug12-13, 05:16 PM
HW Helper
P: 6,208
Quote Quote by chiraganand View Post
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
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.
SteamKing
#3
Aug12-13, 07:12 PM
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Sci Advisor
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Thanks
PF Gold
P: 6,272
1. I am having trouble visualizing your beam and the nature of this 'nodal linkage'. Can you provide a picture?


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