SOLUTION: One end of a cantilever beam of length 𝐿 is built into a wall, while the other end is simply supported. If the beam weighs 𝑤 lb. per unit length, its deflection &#

Algebra ->  Volume -> SOLUTION: One end of a cantilever beam of length 𝐿 is built into a wall, while the other end is simply supported. If the beam weighs 𝑤 lb. per unit length, its deflection &#      Log On


   

Question 928763: One end of a cantilever beam of length 𝐿 is built into a wall, while the other end is simply supported. If the beam weighs 𝑤 lb. per
unit length, its deflection 𝑦 at a distance 𝑥 from the built-in end satisfies the equation
48𝐸𝐼𝑦 = 𝑤(2𝑥4 − 5𝐿𝑥3 + 3𝐿2𝑥2) ,
where 𝐸 and 𝐼 are constants which depend on the material of the beam and the shape of its cross section. Sketch the graph of the
deflection with all details and discuss it. Where does the maximum deflection occur?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Assume a steel beam with E=30x10%5E6psi.
Assume a 6" square beam, 60" long.
So then w=0.283%2A6%2A6=10.2lb%2Fin
I=b%5E4%2F12=6%5E4%2F12=108in%5E4
L=60in
The equation becomes,
48%2830x10%5E6%29y=10.2%282x%5E4-5%2860%29x%5E3%2B3%2860%29%5E2x%5E2%29
y=%286.94x10%5E%28-10%29%29%282x%5E4-300x%5E3%2B10800x%5E2%29
.
.
.
There is a problem with your equation.
The deflection should be negative, going downwards.
.
.
.