Question 928763
Assume a steel beam with {{{E=30x10^6}}}{{{psi}}}.
Assume a 6" square beam, 60" long.
So then {{{w=0.283*6*6=10.2}}}{{{lb/in}}}
{{{I=b^4/12=6^4/12=108}}}{{{in^4}}}
{{{L=60}}}{{{in}}}
The equation becomes,
{{{48(30x10^6)y=10.2(2x^4-5(60)x^3+3(60)^2x^2)}}}
{{{y=(6.94x10^(-10))(2x^4-300x^3+10800x^2)}}}
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There is a problem with your equation. 
The deflection should be negative, going downwards.
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*[illustration beam.JPG]