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Member End Moment by Slope-Deflection

Mediumslope-deflectionend-moment
A prismatic member AB has EI = 20,000 kN·m² and L = 4 m, with no member loads and no chord rotation. Its end rotations are θA = 0 and θB = +0.002 rad, clockwise positive. Using the slope-deflection equation MAB = (2EI/L)(2θA + θB), find the moment at end A.
  1. A+40.0 kN·m
  2. B+20.0 kN·m
  3. C+10.0 kN·m
  4. D−20.0 kN·m
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Answer: B. +20.0 kN·m

Stiffness factor 2EI/L = 2(20,000)/4 = 10,000 kN·m. Rotation term for end A: 2θA + θB = 0 + 0.002 = 0.002 rad. MAB = 10,000(0.002) = +20.0 kN·m. Wrong: 40 kN·m is MBA, which uses the near/far coefficients the other way round (2θB + θA); 10 kN·m uses EI/L instead of 2EI/L; −20 flips the sign convention.
kN·m
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