Strength of Materials · T3 · Problem 4
Three-moment equation
Problem statement
Using the three-moment method, analyze the continuous beam ABCDE (A pinned; B, C, D and E rollers) with support settlements A: 6, B: 7, C: 8, D: 4 and E: 3 mm. E = 200 GPa, section b = 30 × h = 80 cm. Loads: W₁ = 30 + W/10 kN/m on AB, P = 300 + W kN at the midpoint of BC, Q = 350 + W kN at the midpoint of CD and W₂ = 40 + W/10 kN/m on DE; L₁ = 7 + X/10, L₂ = 7.5 + Y/10, L₃ = 6 + Z/10, L₄ = 8 + Z/10 (m).
a) Three-moment equations and MB, MC, MD.
b) Reactions by superposition.
c) Shear and moment diagrams.
* W, X, Y, Z = last 4 digits of the student code (N0000WXYZ).
Concepts: continuous beam, support settlements, Clapeyron's theorem, superposition, shear and moment diagrams
