## Lesson 21. SOLVING NUMERICAL

 Module 4. Beams and bending moments Lesson 21SOLVING NUMERICAL 21.1 Problem A beam made of cast iron having a section of 50 mm external diameter and 25 mm internal diameter is supported at two points 4 m apart. The beam carries a concentrated load of 100 N at its centre. Find the maximum bending stress induced in the beam. Fig. 21.1 Bending stress Solution: Given that Outer diameter of cross-section D0 = 50 mm Inner diameter of cross-section Di = 25 mm Length of spam ‘L’ = 4 m Load applied W = 100 N For a simply supported beam with point load at center For AC Mx = RA.X = W/2 x When x = 0, MA = 0 At x = L/2 MC = W/2.L/2 = WL/4 By symmetry MB = Maximum bending moment occurs at center and its value is WL/4 From bending equation σ/y = M/I, where s is bending or flexure stress M is bending moment , I is moment of inertia, y is the distance of point from neutral axis. σ = M.y/I = M(D0/2) / π/64 [D04 – D14] σ = (100 × 100) × (50/2) / π/64 ((504 – (25)4)) σ = 8.692 N/mm2