Finding spring constant and inertia

[Junkwisch]

Homework Statement

"the question is included in the attachment"

Homework Equations

F=ks, E=stress/strain=(force/area)/(change in L/L)

Second moment of inertia=I=(1/2)*base*height^3

The Attempt at a Solution

Sice F=ks

k=F/s where F=p and s= d(L) (change in L)

E=(P/A)/(strain)=> EA(Strain)=P E=Young Modulus A = Area
area of the beam is equal to base*height, let height be equal to L

Second moment of inertia=I=(1/2)*base*height^3 => base=b= (12*I)/(L^3)

Thus P=E*(strain)*L*b=(E*dL*12*I)/(L^3)

Thereby K=P/s=P/dL=(12*I*E)/(L^3)


However the suppose answer is (48*I*E)/(L^3), can anyone tell me what I did wrong?

 

[SteamKing]

I think for this problem, use the following:

F = k δ

where F is the applied load (P in this case),
k is the spring constant, and
δ is the central, transverse deflection of the beam due to the load P.

 

[Junkwisch]

Ahh, I see. Thank you so much,