Question

4. Determine the slope and deflection at end point C of the cantilever beam shown in the figure. Use E = 200 GPa, I = 10 x 106 mm 3 kN/m 2 kN.m A B 2 m 2 m

Answer 1

Jerm- 3 kN/m X 2 KNM B MA 2m al E = 200 GPA I= 107 mme "RA х EI= 2000 kNm² Reactions [EFU =) RA 3X2 RA = 6 KN EMA right -MA + 3x2x1 - 2 = 0 MA 4 KNM By Macaulays method a El day My dn² as can Taking section X-X shown and this method be applied for discontinous loading . So, tiu extending Section X-X both sides, UDL On A X KNIM 2KNM ) MA B 2 RA € 2m

My = Rax - My Xo = 3¢ 1 + 3 (2-2)2 My = 6x – 48° - 32 Box! + 3(2-2) So, EI dy dy2 6x - 4x - 3012 +3 12-22 2 © Integrating both sides, EI dy 632-4X - 32p3 3gp +c1/+3.47 + 3 (7-2) 3 ca 2 W At il dy dx A 0 = 0 + c Cao Integrating eqh ① both sides, fly = 3x - 5y +2/+soyun

At x=0; y 20. ot (2 (2=0 Now; slope at e; from Ega ; At X=4 ; dy Oc da 3 EI/dy) dae 3 (9 – (9) - ° + (2) 2 2 ) EI OC 4 Oc 4 2000 Oc= 2x1013 rad Ans.(a) Deflection at C; from E D At x=4; y = ac =) EIDO (4)? - 269?-(4 4 8 2 2000 0,= 103 m Ansi (6)
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