The ultimate collapse load (P) in terms of plastic moment

The ultimate collapse load (P) in terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with P acting as its mid-span as shown in the figure, would be

By principle of virtual work
- M_P θ - M_P θ - M_P θ + P.(L/2)θ = 0
- M_P θ + P.(L/2)θ = 0

P =	6M_P
	L

P =	2M_P
	L

P =	4M_P
	L

P =	8M_P
	L