# sign of moment in buckling of column

Can someone explain why the M is assigned to be anticlockwise here ?

When i assign it as clockwise , i will get -P(δ -v) , which is different from the author ... If i do so , then , all the sign will be different Can i do so ? Why ?

or the second example here , i can understand that M = -Pv , since M+Pv = 0 at either end when it's in equlibrium.

P/s : I know the the sign convention of the bending moment of beam is positive when the beam upwards as shown ...

For the first example , i gt M+P(∂-v) = 0 , so M = - P(∂-v) . I am not sure whether is my concept correct or not .

Simple. The bending moment caused by $P\delta$ is clockwise, so the bending moment reaction must be counter-clockwise to resist it. The bending equilibrium equation should be
$$\begin{gather} \sum M_{support} = M + (-P\delta) = 0 \\ \therefore M = P\delta \end{gather}$$