The number of slope deflection equations available for a two span continuous beam:

Question

Question

This question was previously asked in

OSSC JE (Civil) 2015 Official Paper

Answer 1

Explanation:

Let a two-span continuous beam, shown in the figure below:

F1 Engineering Mrunal 20.02.2023 D16

Slope deflection equations

For span AB:

\(M_{AB}=Mf_{AB}+{2EI\over L_1}(2θ _A+θ _B-{3Δ\over L_1})\)

Where Mf_AB = Fixed end moment at A for span AB

θ_A = Slope at A

θB = Slope at B

Δ = Settlement of support.

\(M_{BA}=Mf_{BA}+{2EI\over L_1}(2θ _B+θ _A-{3Δ\over L_1})\)

For span BC:

\(M_{BC}=Mf_{BC}+{2EI\over L_2}(2θ _B+θ _C-{3Δ\over L_2})\)

\(M_{CB}=Mf_{CB}+{2EI\over L_2}(2θ _C+θ _B-{3Δ\over L_2})\)

There will be 4 Nos. of slope deflection equations, for a two-span continuous beam.