What is slope diflection method, slope diflection method equation 2021

 What is slope diflection method?

Here the joint displacement ( θ , Δ ) are taken as unknown and the joints moments are derived by the force displacement rotation which is called as slope diflection method.

Note:- 

In this method axial force and shear force effects are neglected and only Bending moment effects considered.

Sign convention:-

(I) fixed end moment:- clockwise (+) , anticlockwise (-)

(ii) rotation:- same above

(iii) settlement:- 
clockwise positive when rotation is clockwise

Anticlockwise negative when rotation is anticlockwise

Slope diflection equation:-

Considering a continuous beam where A , B are the intermediate supports. The final end moments developed at A and B (Mab, Mba) will be due to the effects of

(i) effects of loading  (M̅ab)
(ii) rotation of joint A  (θa ).   (M̅ab1)
(iii) rotation of joint B (θb)  (M̅ab2)
(iv) effects of settlement of supports   (M̅ab3)

By the superposition theorem,the final end moments will be the summetion off all the effects combined.

Mab = M̅ab + M̅ab1 + M̅ab2 + M̅ab3

Mab = M̅ab + 4EIθa/L  + 2EIθb/L  + 
 (−6EIΔ/L²)

Mab = M̅ab + 2EI(2θa + θb − 3Δ/L)

Mba = M̅ba + 2EI/L(2θb + θa − 3Δ/L)


It is called slope diflection equation


  1. Bettie's law के बारे मैं जानने के लिए:- click here
  2. Three moment theorem के बारे मैं जानने के लिए:- click here
  3. Unit load method के बारे मैं जानने के लिए:- click here

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