Virtual Work - derivation of beam stiffness coefficients

[@patrikengas6479]

when you at 5:35 make that statement, how was that derived? i tried using the known curvature - moment relation to find a slope at B due to the moment "Mab" at A where i got that slope to be: θ(B) = Mab*L/2EI and using the virtual method i got the fbb' = L/3EI, and finally plugging that into the compatibility equation i got the Mba = (3/2)*Mab, so obviously this doesn't match. But then my question would be, is this a correct approach or just wrong?, and if the latter, whats the correct way?

[@ProgrammedMechanics]

follow the method at 5:07, I get \theta_B = M_{ab}*L/6EI and f_{bb} = L/3EI

[@patrikengas6479]

Okay, do you get this: "theta_B = M_{ab}*L/6EI" using the virtual moment method? does that mean that you place the unit moment in B and from there gain the moment equation m(x) and use that together with M(x) caused by the real moment Mab ?

[@patrikengas6479]

update: actually that seemed to work out trying it, i get the angle at B to be Mab*L/6EI, using the virtual moment method. only weird thing is that the relation: EI*θ = ∫M(x)dx provides a different angle. thought these should be equivalent. the M(x) i get = -(Mab/L)x + Mab, if that checks out

[@pawanacharya2915]

can you help me to find the moments ??

[@ProgrammedMechanics]

This video is just the derivation of stiffness coefficients for use in displacement based methods. You will need to use the direct stiffness or slope-deflection equations to calculate moments.