Question

4. Consider the 2D truss system shown below which contains only pinned connections. The length of each member is 1 = 1.5 m, their cross-sectional areas are A = 1 cm', and their Young's moduli are E = 69 GPa. The applied force, P = 500 N, and the angles a = 30° and B = 60°. Determine the displacement of each node, the stress in each member, the strain in each member, and the reaction forces.

Answer 1

CA A 'xiy eXz 4. 0= 30° }= 600 P= 5000 E = 69 Gpa A= 1cm² = IXIÓ“m? la 1,5 m sor": F = 69 G Pa je 69x10' N/m? ie (9 xloʻkn/m2 Co-adinates o coch node: *4= 0,0 Cat nade D X297 [1.3, 0.75] at node a X2 43= [2.6; o] 'at node 3 X444: [1.3, 2.25 at node 4. Carch table: Telement I L Istort nado Xi Yi ... end node , Xi Y I 115 X,CI)| 00 XC 3) 1.3 10.75 11.5 2 | 1-3 0.75 L 31.3 2.25 schned with 1-3 075 3 2. 60 CamScanner

elemen rement ins (Nj-Xi), m= Chi-Gi), e . 0.8667 0.5 0.75116 Ima 0.25 i lim 0.43335 0.8667 | -0-5. - 0.75116 0.25 -0.4 3335 Elemental stress matix for element ! [klo = Are Im l-le in I mm? Ám -m21; AE, 10*x Oqxd 1.5 Elm -mal im m² ie 4.68100 50.75116 0:435 -0.75116 -0.43335 C-43335 0.25 -0-49335 -0.25 |-0-75116 - 043335 0.75116 0:4335 1-C.43135 -0.25 0:44335 0-25 7 X 4.6X10 19.93,-34.5 -19.93 11.5 -19.93 -11. 5 -19.93 34.5 19.93 -11.5 119.93 11.5 1. x 105 T3-4.5 19.93 -34.5 L-19.93 for eleret a 4 [K] =(AE) TO oool OO mooloo ! CS Scanned wito CamScanner

E [K]- Laves 42 AS e E for element 3 0.75116 -C-43351-0-75116 0:43335 +0.43335 0.25 10.43335 : -0.25 192 F075116 0:43335 0.75116 0:4333 5 [0:43335 6.25 -0.43335 0.25 183 . X2 q xo' 4 - | 34.5 -19.93 -34.5 19.93 | X2 . |--19.93 11.5 19.93 -11.5 142 x 105 - 34.5 19.93 34.5 -19.93 143 CS Scanned wit993 -11.5 -19.93 11.5 ] Jo CamScanner TTT77 h

. . Kalbad - 34.5.19931-34.5*419:43. olololo Ty 119.93 111.5 119.93.-11.5. Oo o To 14 134.5-19936910 -34.519.93 lo lo -9.93-115 69 19.93 -11. 5 0 -45 192 100 TRANS 19.93 34.51-1993 o o 0 0 19.931-11.5 -19.93 | 11. 5 0 lö lolololololo Cs Scanned with o 0 -46o CS Scanned vath olo o o 45 lei CamSchmer! 54.5

Since. F- [K]: [c] Exi 53 Sincle' 42 F५० Exy - Vivi, Uz Vz, UVA zo. - U₂ V2 = ? Fy= Pcos B = 250 N T J Fag = Psin B = 433 N Simplified ca ? Cdisploemens] 105 x 69 U₂= Pros B= 250 Uz = 30x10 cm 105x69 We = 433 Y = (3x17m ! : • Recchons + Fxz - 34.5x15V2 -19.93 xid? V2 = -250 N Fyrs - 19.9x13 U2 - 11:5X105 V, 3, -144N Fra - 34.5x16°0+19.9381 65 V2 = 1.35.N Fuga 19.93x6+U2 -11.5*16* V2 = -0.7 N Felpa o. FYA? -46X165 V2 = -289-8 N Scanned with CamScanner

☆ Shers; Cola Ernem de m] 10.7 0.8007.- 0.8067 0 SSN V21 [-] = 2.854 xíc? Nm 2. - Set Cover 05 c2c 0877 Ea- Episu say | set • • I: | S 4r > > = - 2.898 xl 69 Noma (-1; [s-]: m -m Im -0.8007 +0.5 +0.8667 -0.51 - 69x10 1.5 > ON VNN » 13.74 N/m² Scanned with CamScanner

1 .&, Strain : fim ] ro Vz : -0.8007 -0.5 0.8167 05 355 V2 , DIXG4 = '3 tur 4-r]73 - Ez = 42X166 > C3 6:45-a donna > Scanned with CamScanner