Question

Q3. A rod is under distributed and concentrated forces as shown in Figure 2. The overall length is Im, the cross-section area is 0.01m²: 40 = 1000N Concentrated forces, F4 = 500N and F5 = 10000, are applied to nodes 4 and 5, respectively. Giving the Young's modules of 2 x 1011 Pa. Please calculate the displacement on node 2, node 3, node 4 and node 5 and stress on elements 1, 2, 3 and 4 using the finite element equation ([k]{u}={f}) Node Displacement, m Element Stress, Pa q= 1000N/ m -- F 4 = 500NFs = 1000N ------- -- -- | C = 0,25 sto lo lote la Figure 2: Rod under distributed and concentrated forces Page 2 of 2

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Answer 1

& Answer: Node Displacement cm) 2:34xö7 4.378x109 6254107 7.5x167 element 3 1 stoess, pa 2x105 175x105 115x105 I 1X105 Now, Shese secti 1,2,3,4 stess for each section 1,2,3,4 por seelon 4-s, elemend to 300

1000 Cup = 109px for section 3-4, element -> 1500 1800 = 1500 TOT 5150000 63215x10589 for setron 2-3, element @ 1900 1950

len OSS in element @ stress es variable, for design point of view, we should take maximum shess, means worst condition for safe design. so, max@ - So Omare . 175000 Comer@ - 1:75*10% pa for sectoon 1-2, element o 260011750 semel aalys to elemendid so, man mano - Pintar = 2000 501

m 200000 omano = 2xlopa - 83-4 = PL AE - = 1500* .25 01X 2x104 - 375 2000000000 (83-4 = 1875x106) =) Surs a PL AE = 1000X.25 0.1*2x104 a 250 20000cco'o [54.5 = 1.25x107

30, Total deformation at Ss = &n3+ Soz-ut Sus 879 Ss +375 + 2 250 AE. AE AE ISOO Sasa ho AE we know that AEA 0.01x2x10" substite en At place Ssa 1500 0.0172210" Ss 1500 2000000000 Ssa 7.5x107m iSs = 0.00075 mm

Deformation at © Sua Sir3 + 83-4 .8875 + 375 AE AE - 1250 1250 0:01X2X10" 1250 2000000000 = 6.25x10th [84 = 6:25*10" him S3= S1-3 1875 0.01x2 Rio" * 4.375 kio?m a) 832 4.375xco Ymm

Deformation of node -82284-28 AE 0.25 121 (2000 - 1000x) de AE DOROG 20 OS 822 he (20002 -100924oes SOO- 31.25 001XLXO Sz 3 o'cl rexion [ 500 - 31.25] 822 2.34167m S2 = 2:34x104mm Aved ® Goven dato overall length a l= im cooss-section area (A)2 0.01 m2 load intensity q= 0ood 11 m

. f4 s soon 3 FSI (OOON E lyong's modelos) = 2xoºpa 1% =000/m Fuz soon Juany of 1000N LA d= 0.25m desplacemend at node Elsa Slezt & lz 37 83-4+ Syris 8.5 = 81-3+ - + 84- Sinza Podsi - (2000 -1000D )dx AE. 81-33 te (2000-40002 ) de 0.01%2x109 1 2000 - 10000

00020 - O'olX2 - ਸਫ਼ਾ Czoor - Boot | Just another licno - Seoxoas] Simsa mer O - SOX0:25 DO1X2X10 87 AE 8143= 875 d1-32 0:0larxioli (1-3= 875 2000000000 fis3 = 4.375 +10 m [5.30 4.375 700 mm