Question

Question 1 (CLOI, 10 marks) a) Figure I shows a triangular element with respective node numbers and coordinates. If the modulus elasticity, E = 30 x 10 N/mm and Poisson ratio, v0.3. determine the element equation of the triangular element. (10 marks) 3 (18,9) 2 (5.7) b) Assume the triangular element has thickness of 25mm and fixed supported along node 1 to node 2. If a tension force of 200 N is applied on node 3. determine the nodal displacement and element stresses. (10 marks)

Answer 1

solution Element equation of the triangular elements. E = 80x 100 lmm2 CC > 3418,9) )=0.3 poission's ratio t = 250 mm F2.200N Nodal coordinate table i Hodal nos long 1 x2 72 21 = 15 21. A = -40.5mm² displacement matrix strain . Tave o que o 93 0 7 ZA lo rio r2 or Iiri g. 12 % 3 % z. کہ

a,.="/2-73= -2 92 =43-4,=9 V = 41-42 = 7 = x3-32 zxgx3 = -18 3=r;-r2c 1-2 o q 0 -70 -lo 13 o 18 os [ 13 -2 -18 a 5.-7 constitutive matrix ( 30x16 [ 0.3 20.3 1 o 0 (1-0:37 10o.1-09 [0] - 32.96X1of Li 6.3 07 1 ó 0 0-35 D) - 32.5X 16.3 Lo stiffness matopx - (k] = [BJT [o] [BJACE 1o 13 2. 190 -18 0 -18 q -705 To 5-7 ri 0:3 07 a lazi * 32.967 10 10.3 1 0 LO O 0:35 F-2 o 900 - 70 X-BO 13 -18 0 SX (-40.5) <25 13 -2 -18 a 5-7

S 2. 0. 6 NOV 2.7 ooooo ai X- too.9 5.4 -18 -2.1 XC-40:5)x25 E24060 3.9 13 5:08X10 1.9 2. 5.418 -7-21 stressl- -] - P][B][u ) F4, (3) IN212) Paz 39 9 -5.4 -71.5 n113) -5.08x10 F06 13 2-7 -18 -2ils 42 (2) Loo 0 0 0 olis 41 =3 =3, 42=2102=2 (2) cassumie : uz=3 i V3 = 2 osoooo go 3.9 130 19:27 0 15.4 -1. 8 0 5:08 X10 -7 -2.1