Question

3) For the steel beam shown in figure, E = 200 GPa, 7 = 100 x 106 mm4, L = 5 m and w = 2 kN/m. Determine (a) the reaction force and reaction moment at A and (b) the deflection at C (30 pts) w/2 K L/2— L/2–

Answer 1

- f wl2mong B B E 2006 Amarom mp2 U2 = 2x105 th N I = 100x10 mont L=5m W=2KNIR a) find reaction forte & morment at A. we will salve it by method of superposition. above beam is equivalent to T 20 Met deflection at B ABS + DB2 + ABB 20 => 880 =-wet. 06- vue me t h eir *8*6t22 16 *SET 8 er = 7WLA 768 EP DB2 = BESI DB3= BER = 7 wit 360 76862 - wel ZEL XR13 2 SA 68

I RA + Re = x + 1 - 3 ml RAZ 3 we a & gwl 256 on we 256 RA= 103 WL 256 MA = - ( 8 9 wt xh - With + w x x ) = -1 - + ) we? me so wz?) 16 23 256 16 RA= 103 x2x5 256 S b) [RA = 4.023 kH) MAT 23 x 2x25 [MA = 4.49 KN) deflection at c. from equation of elastic curve De = - W x (4 - 4 2 +6 (4) - 24 ET TETO 8 - 47 = - + x (1 8+28) wil = 417 wil 24 X6 EI

16 X 8 EI 128GR 323 - Dez z 896L x as 6x6EI 89 x5 wat 8x6x256ta De = 17 wat - wat - 89x5 with 29x16 ER 12BET 8x6x256 67 2 0.0002441 Wh ET 2 0.0002441 X 2xlos x lavolt 1000 x 2x105 x 100x106 Dc z 0.0153 mm