Structural Theory Slope Deflection Method Reviewer

STRUCTURAL THEORY
CIVIL ENGINEERING
SLOPE DEFLECTION METHOD (SDM) - Reviewer

Reference Diagram
MAB MBA

A L B
Formula

𝑁 = 𝑁𝑒𝑎𝑟 𝑗𝑜𝑖𝑛𝑡

𝐹 = 𝐹𝑎𝑟 𝑗𝑜𝑖𝑛𝑡




Sign Convention

Moments: Deflection, δ :
Clockwise (+) Settlement (+) Position:
Initial
δ δ
Final
Counterclockwise (-) Uplift (-)
Final
δ δ
Initial


Rotation, θ : Joint Translation, R :
Clockwise (+) Final position of Right jt. lower than Left jt. (+)
L
Left jt.
Δ
Right jt.

Counterclockwise (-) Final position of Right jt. higher than Left jt. (-)

Right jt.
Δ
Left jt.
L

Note for Joint Translation:
- Δ in joint translation is the difference between the deflection of the right jt. and the deflection of the left jt.
R = Δ / L ; where Δ = δright jt. - δleft jt.

- By simply using this formula for Δ, you do not need to check the sign convention for "R" as long as you follow