Question

Finite element problems

For the bar elements shown in Figure P3–16, the global displacement have been deter- mined to be up = 0.5 in., V = 0.0, uy = 0.25 in., and V2 = 0.75 in. Determine the local x' displacements at each end of the bars. Let E = 12 x 106 psi, A = 0.5 in?, and L = 60 in. for each element. 45° 30° (a) (b) - Figure P3–16

Answer 1

Given data! l, 2 0.5 in; V, 0. Cu in liga 025 in; V = 0.76 in E=12x8gb Pri Azos na La both 2 ។ Love 745' 30 Solution : The local displacement, sui u, $ o . - ( vi aq 0 O С s V U, a la global displacement at end 1 kend 2 along x asis vespt. V, V₂ Globul displacement at end f. & end a alung yaris respt. a) To determine load clisplacements at both the ends Caladate the value of (os angle made by bas element with X-ascis) Cacos Bo c and S, (=coso C-B3 Cosu = 0.866 109

0.5 0 0 S = sin o= Son Bos Substitute C -0.866 and S = 0.5 in equ 0 1.866 0.5 015 0 K' 0 6.866 0.5 Ph. 0.25 0.95 0.86605.5 L(0,866 * 0, as) +(0.5*0.45) 10.433 01592 0.433 ihlx at end 2 (0.592 Cosuery] ih is Local displacement at end 1 = (0.433 in C = woso a -0.5 b) Determine lord in displacement at both ends, cos (630) - 0.866 sasnio a Sin (30) Substitute S=2015 and a = 0.866 in En uil 10.866 -0.5 -0.5 Ma' 0.75 0 0 O 0.866 0. 0.25 10N

6.836 uil 876 * 25 ) 0.8064 0.24) -0.5 80.75) o a Ligy Loistes 0.433 -0.1585 periode at and 1 is Local displacement and end 0.433 in q is -0.1585 h Answers g Local x' displacement at end 1 and at end a is 10.592 ih i 60.433 h 8) Local x' displacement at end is 0.433 in and end of is (0.1585 in Please upvote