Short Notes: Displacement Method of Analysis (Slope Deflection Method) | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


 
 
DISPLACEMENT METHOD OF ANALYSIS (SLOPE DEFLECTION METHOD) S 
Definition: Slope deflection method is a classical method which is very useful in analysis of 
indeterminate structure like continuous beams and plane frames. In this method the unknown loads 
are written in terms of the displacement by using the load-displacement relations, then these 
equations are solved for the displacements using the joint equilibrium conditions. After computation 
of displacements, loads are computed using load displacement relations. 
Important Results: 
(i) Angular Displacement at A: 
 
The load displacement relations are 
?? ????
=
4????
?? ?? ?? 
?? ????
=
2????
?? ?? ?? 
(ii) Angular Displacement at B: 
 
?? ????
=
2????
?? ?? ?? 
?? ????
=
4????
?? ?? ?? 
(iii) Relative linear displacement, d: 
 
?? ????
= ?? ????
= -
6??????
?? 2
 
Sign Convention: 
(i) Clockwise moment is taken as positive. 
(ii) If d gives clockwise rotation to member, it is considered as positive. 
 
 
Page 2


 
 
DISPLACEMENT METHOD OF ANALYSIS (SLOPE DEFLECTION METHOD) S 
Definition: Slope deflection method is a classical method which is very useful in analysis of 
indeterminate structure like continuous beams and plane frames. In this method the unknown loads 
are written in terms of the displacement by using the load-displacement relations, then these 
equations are solved for the displacements using the joint equilibrium conditions. After computation 
of displacements, loads are computed using load displacement relations. 
Important Results: 
(i) Angular Displacement at A: 
 
The load displacement relations are 
?? ????
=
4????
?? ?? ?? 
?? ????
=
2????
?? ?? ?? 
(ii) Angular Displacement at B: 
 
?? ????
=
2????
?? ?? ?? 
?? ????
=
4????
?? ?? ?? 
(iii) Relative linear displacement, d: 
 
?? ????
= ?? ????
= -
6??????
?? 2
 
Sign Convention: 
(i) Clockwise moment is taken as positive. 
(ii) If d gives clockwise rotation to member, it is considered as positive. 
 
 
 
 
FIXED END MOMENTS FOR SOME STANDARD CASES 
Beam Fixed End Moments 
 
MA = MB = 
Pl
8
 
 
 
==
22
AB
Pb a Pa b
MM
LL
 
 
==
22
AB
wL wL
MM
12 12
 
 
==
22
AB
wL wL
MM
20 30
 
 
??
==
AB
22
6EI 6EI
MM
LL
 
 
==
22
AB
5wL 5wL
MM
96 96
 
 
?? ?? =
3???? ?
?? 2
, MB = 0 
 
Slope Deflection Equations: 
?? ????
= ?? ?????? +
4????
?? ?? ?? +
2????
?? ?? ?? -
6??????
?? 2
 
? ?? ????
= ?? ?????? +
2????
?? (2?? ?? + ?? ?? -
3?? ?? ) 
And, 
?? ????
= ?? ??????
+
2????
?? ?? ?? +
4????
?? ?? ?? -
6??????
?? 2
 
? ?? ????
= ?? ??????
+
2????
?? (?? ?? + 2?? ?? -
3?? ?? )