Question

4G . 9:18 ... Lecture 08 Machine Design ME... X Example 1 for the following bean find the equation of singing in the Find deflection at the free end Mar Compare results using the cross section below cas 800 200 40 Example 1 Calculate feliness of beam El Material Gray cast iron AS 10 (a) 1 -213333.33 mm (6) I-125600 mm (c) 1978400 y-har=4008 Example 1 -

Answer 1

800 0.6 E1200 200 300 500 As, units are not mentioned in question 0.6 N/mM wniform distributed load is ay ume Point load is 800 N and Moment is 1200 N-m and distarces 200, S00 ane taken in mm and materialgiven a Grey Calt Iron E = 100 Gfa 100X 10 fa wing Macaudey'smethod 12.00/-800 8-0:3)/-0-a-0 Py E1 on Integrating 12.00-800 (4-0-3)03 (-03) Again Inteyrating 1200/-400 (-03) - 01 (a-03)4 +G+C2 EIY at &=0.5 m y-0 0 = 600x05-40o (o5-031 05-03)'+ osG tc 3 - -148.933 at -0.5M 12.c0KO 5-800y Co5-0af - a9 (05-0.3)+C C -583.9992

0.5Ct C2 --148.933 OSX(-583.9992) +C2=-148.933 C 143.0666 Hence the elastic equation is 1200 x-00(-03) -a-03-583.92 1+143.0666 EIy 11 To find deflection at the free end, put -O EI 1200o-583.992X0 t 143 0666 143.0666 E1 143.0666 100X10 I -II 143.0666 X10 Squane For reutan Cross section I 213333 33 mmt ET = 21333.3 Nm 43.0666 X 16 213333.33 X1O12 0.0067 m 6.706 mm for circulan cross section I= 125600 mm1 EI= 12560 NM 143.0666 X 10 1256 00 X1012 0.01139 m 1.39 mm I = 1378400 mm7 EI= 137840 Nm For channel section 143.0666 X1011 = \ 12 1378400 X10 =0.001037 m 037 mm