Question

Using the area moment methods complete the following: E= 150 G Pa & I-65 x 100 mm [10] A. Draw the bending moment diagram by parts (Must clearly show how this was achieved) ) B. Calculate the slope at the free end of the cantilever (final answer must be degrees) A. The deflection at the free end of the cantilever (final answer must be mm) [4+3] 1531 [5+3] 80 KN 20 kN/m 2m → 2m → 2m 2m →E

Answer 1

Solution Sok 20linn = 2m x 2m x 2m x 2m {x measured from A} Bending moment calculation Section ED ME = 0 MED = -50% Mos-502 = -100 kNm sietta DB Mo = -100 KN m Mapa - 50 x – 2012-2)*(x-2) +63*72 =) MOB= -50% - 2014-2) --60 2-2) = -50x-10(2-2) io Mc = -50x4 -10 (4-2)2 = -240 kNm Mo = -50x6 -10(6-2) = -460 KNM section BA MBA = -50% - 20x4x (x-3— 87, X76 MAE -50X8 – 20x4x (8-4)=-720 kN m .. Bending moment diagram p > TALO) Tak - a - -+- 100 --460 7-720

cantilen free ) - 460-100= 360 B) slope at dea : + 2 Ap@x 100 =100 Az = 4x 100 = 400 Az = 2*100=200 Ar = 2X360 = 720 A6 $x 280x2= 260 Ay = 5 360x4 = 480 ' 1*720-460 = 260 720-460 = 240 we have slope :. From at area moment method frue end De => n OE - PA - 1 - [Area of badig monet diagram beturen] → 04-0-1 [Con+ Azt Ast Aytast he] as it is fired and therefa DA- OE = T E (1004400+ 200+ 490+4207 20)] es 10= -0.2215 radians - 100x 0.2215 = 12.750e7 Deflection at of continens Yo = ? C ,C₂,C3, cu 150X106 x 63 xlos counter clockwise dirudon Negative sign indicates free x towards end kx णला Cs, ce are centroido KX2 V VYYY x5 where *1 = 2 x 2 = 4 x2 = 2+2 = 3m * = 4 + 2 = 5m xy = 2+(2- 2-2) = 35m as = 4 + 2 = 5m 46= 4 + 2 x 2 = 16m

2 n 3 . Now moment area about point e is Alx = loox 4 - 400 kN m² Az x2 = 400X 3 = 1200 kNm? Az x3 = 200X 5 = 1000 km2 Anny = 480x 3.5 = 1680 km2 Asus = 720x $ = 3600 kam? . Ao ao = 260x16 = 4160 kNm² ... Y -Y = 1 [ Area moment of bandry manat diagram ' A EI between A and E Cabout a - CY=0 as A is fired point = YE -0 = 4 [-(4,34,+A, 4z + A3X3 +AyXy+*s *s+As Yo] ş Yerusalemine [(40€ +100+1000+ 14884 360 +41503] 3) Je=0.92307 m =-923.07 mm 4 negative sign indicates towards negative y-direction le deflection at E downwards ..