bending energy in a beam
 

bending energy in a beam
i have a simple question which is bothering me :
if i take a clamped-clamped beam submitted to a uniformely distributed force, i can calculate its shape for a given force per unit length, as long as one stays with small deformation. because the deflection at any position along the beam is proportional to the applied charge, i can calculate a rigidity (k) for the beam as q*l/ymax
(q*l) the total force and ymax the deflection of the center of the beam. i can then calculate the energy needed to defrom the beam to reach a given deflection at its center using u=0.5*k*ymax^2
but i can also calculate the bending energy needed to reach that deformation using u=integrate[m^2/(2ei),{x,0,l}] with m the bending moment obtained from the second derivative of the deformation function.
my problem is that i do not find the same result with the two methods. with the first one i get u= 192ei*ymax/l^3 and with the second, i get u=(512/5)ei*ymax/l^3
can someone explain me why i don't get the same result?
thanks in advance.
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doh! never mind, i turned my brain on and figured this out...