Question

5. For the one-dimensional problem shown below, calculate: a. The global stiffness matrix before the application of boundary conditions. b. The reduced stiffness matrix after the application of boundary conditions. c. Solve for displacements d. Find strains e. Find stresses K1 = 4000 N/mm K2 = 8000 N/mm K3 = 6000 N/mm F = 1200 N L1 = L3 = 50 mm, L2 = 100 mm, A1 = A2 = A3 = 4 mm2 SWASTA 888888888888

Answer 1

Col Given data, kiuooo N(mm k ooo (mm k3 Gooo almm F 200N LiL350mm, L2= l00 Mm A1 Az A3 4mm Element stffness 'matrices- 2 1k y000 Soo0 Cooo a) Glebel ctiffness matiix before the of beundary conditons- applicabTon C uooo -4o00 -800o -6 000 4000 -6000 go00 S00o 42 C looo -6 8 uz -9 5 1

Þ) Reduced stffness matrix after the application of boundary cendttions Note u,u3- o, eliminating corresponding rows and columns 1 and u we qet the aeduced System matrf . tooo |-8. solve for displacenen3 Equil brfum euations are given by -S q000 u4tSuy2 Su2t8u4 = (-2 -8x y 0.2mm o.hmm 42- d) stiains 24 x io mm|mm 5x (0mm Imm 3 2-4x1o mm Imm

e stresses LLOOO KSO 5ox(6Nmm A I Soooxloo 200x LON (mm 6000 XSO 75x0 (mm a = € E = 2 20 Nmm 300 lmm 3E2 t5x10x2-4x1o ON/m 80NIMM2