Question

A cantilever beam is divided into four triangular elements, as shown in the following figure, and is subjected to a uniform shear force (the resultant is P) at the right end; the Poisson's ratio u is 0.25, and the thickness is t. Show the global stiffness matrix. an ematene Howane sienter med 1m 2m

Answer 1

Solution :- 1. Given data positson's ration M is = 0.25 thick ness ia=t 2M the Prost step is to make the free body diagrame and shows all Morrenta and force af nodes. L=2M la - 'p is the given force M2=0 since there is no external moment at right and Hence, Spr = [K] {d} for the system is

no y = / 12 GL -12 GL 16h 4h -6L Qh - 12 -6L 12 -66 6h ahl -6L ALL Boundary condition ią substituted in to edy and the corresponding row & column from above system of Equation are removed. it indicate no srotation (0,=0,0,-0) Hence the only unknow are v2go Her S-P8 = El / 12 -6L I ova 7 Loj - 23 (-6h au , l 02

here 2=2 Assume Length ah now the above solved for { we you let E = 30x106 psi (stel), 1=57in! h=144 in , p=400 lb, hence I. P-400 2. L=144 3. E=30x10" 4. I = 57.1 5. A- (Ex1']_»)x12. •C*L -12 6*2; 6. 6*2 4th 6* a*L"; GAL 12 -6XL; 8 6*2 2* L^2 =6*L 4*2V 7 -12 9.] 10. lond [D; P2;P; QJ; 11. X=A (3: End , 3: End)/ 2ond (3; End) and which gives 23-0.2324 7=-0.0024