Diving board problem Name The deflection of a cantilevered beam subject to a poi

Question

Diving board problem Name The deflection of a cantilevered beam subject to a point load at the end is: y=deflection L=length of beam 3m E-modulus of elasticity 15 GPa (convert to Pa) l=moment of inertia 2160 cm4 (convert to m) b= 30 cm (convert to m) h= 6 cm (convert to m) y = PL 3/( 3EI ) P is the force at the end of the beam (890N). The moment of inertia (E) is bh3 /3 If your 200 lb (890N)engineering professor stood perfectly still at the end of a cantilevered diving board with the dimensions given above, how much would it be deflected? (if it came to a steady state and stopped moving up and down before he fell off) If an engineer snuck into the natatoruim (place where the pool is) and stole the diving board to use in constructing a tree house in his back yard; and intended to use the diving board as the main structural member where it had to support a very significant vertical load (the keg, maybe), what would the maximum deflection be under the load depicted below? (board is pinned at both ends) uniform load w = 25/m point load at center of 50 kg 1 degree 2 degree 3 degree 4 degree It doesn't matter; an engineer would not steal a diving board.

Explanation / Answer

DATA
L= length=3m
E=15GPa=15 x109 Pa
I=2160cm^4=2.16 x10^-5 m4

b=30cm=.30m
h=6cm=.06m
y=deflection =?

solution
as by formula
y=PL^3/(3EI)
as force at the end by professor =890N
using all these value in above formula
y=890x(3)3/(3x15 x109 x2.16 x10-5)
=.33375 m
for centre loaded beam use the formula
y=PL^3/(48EI)
using all value answer comes in meter convert it in inches and
answer is 1''
so option a in true

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