1. Sean Dalton www.itsligo.ie/staff/sdalton Chapter 3 Slope and deflection of beams

2. Deflectiony Slopedy dx Bending EI d 2 y Moment dx 2 Shear EI d 3 y Force dx 3 LoadEI d 4 y dx 4

3. Direct integration method Slope and deflection of beams by direct integration method - Cantilever beam with concentrated load - Cantilever beam with uniformly distributed load

4. Example A uniform cantilever is 4m long and carries a concentrated load of 40 kN at a point 3m from the support. Determine the vertical deflection at the free end of the cantilever if EI = 65 MN/m 2 How would this value change if the same load were applied but uniformly distributed over the portion of the cantilever up to 3m from the support? [8.31mm, 3mm]

5. Macauleys Method For the beam shown determine the deflection at its mid point. E = 208 GN/m 2, I = 82 x l0 -6 m 4 [38.4mm]

6. Macauleys Method Determine the slope and deflection under the 50 kN load for the beam shown. Find also the position and magnitude of the maximum deflection. E = 200GN/m 2, I = 83 x l0 -6 m 4 [0.00265 rads, 19mm] [2.67m, -19.4mm]

7. Macauleys Method Determine the deflection at a point 1m from the left hand end of the beam loaded as shown using Macauleys method. EI = 0.65 MNm 2 [-5.34 mm]