beam_k

(./beam_k.m)

Function Synopsis

[kfu,kmu,kmt,kmtp] = beam_k(member,nodes);

Help text

function [kfu,kmu,kmt,kmtp] = beam_k(member,nodes);
%  Computes the stiffness tensors for a beam element.
%  Pi and Pj are the end points
%  beta is the rotation angle from y (up) or x (north)
%  A, Iss, Itt, and J are cross-sectional properties
%  E and G are material properties
 Pi = nodes(member(1),:);
 Pj = nodes(member(2),:);
 A = member(3);
 E = member(4);
 beta = member(5);
 Iss = member(6);
 Itt = member(7);
 J = member(8);
 G = member(9);

Cross-Reference Information

beam_nst       ./beam_nst.m
dot            ./dot.m
tensor         ./tensor.m

assemble_k     ./assemble_k.m
beam_installK  ./beam_installK.m

Listing of function ./beam_k.m

function [kfu,kmu,kmt,kmtp] = beam_k(member,nodes);
%function [kfu,kmu,kmt,kmtp] = beam_k(member,nodes);
%%  Computes the stiffness tensors for a beam element.
%%  Pi and Pj are the end points
%%  beta is the rotation angle from y (up) or x (north)
%%  A, Iss, Itt, and J are cross-sectional properties
%%  E and G are material properties
% Pi = nodes(member(1),:);
% Pj = nodes(member(2),:);
% A = member(3);
% E = member(4);
% beta = member(5);
% Iss = member(6);
% Itt = member(7);
% J = member(8);
% G = member(9);

%Originally by G. Miller.
%Modified by Eric Soroos to take what I want as passed parameters,
%Simply the member vector and the node list.

%Assemble the necessary quantities:
Pi = nodes(member(1),:);
Pj = nodes(member(2),:);
A = member(3);
E = member(4);
beta = member(5);
Iss = member(6);
Itt = member(7);
J = member(8);
G = member(9);

%%--compute natural directions
[n,s,t] = beam_nst(Pi,Pj,beta);

n = column(n);        %beam nst does not always return 
s = column(s);        %column vectors, so I cast them to cols.    
t = column(t);

L = dot(Pj-Pi,n);
Inertia = Iss*tensor(s,s)+Itt*tensor(t,t);
%nxIxn = cross(cross(n,Inertia)',n)';  
nxIxn = -(Iss*tensor(t,t)+Itt*tensor(s,s));
nn = tensor(n,n);

kfu = (A*E/L)*nn + 12*E*Inertia/L^3;
kmu = (6*E/L^2)*cross(n,Inertia);
kmt = (J*G/L)*nn - 4*E/L * nxIxn;
kmtp = -(J*G/L)*nn - 2*E/L * nxIxn;