A fixed end beam is subjected to a load, W at 1/ 3rd span

A fixed end beam is subjected to a load, W at 1/ 3rd span from the left support as shown in the figure. The collapse load of the beam is

Plastic hinges = 3

α =	θ
	2

⇒ θ = 2α

θ =	∆
	L/3

⇒ ∆ = θ	L
	3

= 2α	L
	3

2M_Pθ + 2M_Pθ + 2M_Pα + M_Pα = W∆