Question

Problem 1. Establish the loading and moment functions for the beam using singularity functions. W max = 2 kN/m L WR = 1 kN/m TIITT - - >X 4 m- 4 m Problem 2. Take E=150 GPa and I=65x109 mm .Determine the maximum deflection of the beam. Use singularity functions. 2.20kN 800 N k am *2m ***227

Answer 1

Free body diagram 2 kN/m IKN/m 4m AB C 4m Step 1 - Calculation of Reactions VA B. Skyzo VA + V₂ = 1 nefox 4m + 1 x 4m x 2 kilom → VA + VB = 8 EMA=0 + Vex(4+ 4) = 1x 4x(1+4) +(4x4x2)x({ x4) p = 4.33 KN VA = 8 - VB [From equation ] = 3.67 KN

(Wxx) Loading at section x-X - 2 kN/m x x 4 m. Wax = 3 kN/m. Shear equation ( Vxx) xxx = + VA - 11x xm x 2 kn/on Vex = 367 - att X x m XX Moment equation (Max) Mxx = V x x - (3 x x x 2 ) x 2 4

Equations for span Be zkolm X 2 kN/m X rkN/m 1 Consider a section x-x in span Bl at a distance & from B. Shear Equation (Vxx) Vxx = – VB + 1 kN/m x x m. [Vxx = – 4.33 + x Moment equation (Max) Mxx = VB XX - I kn/on x xm x x