The spring assembly shown below is subjected to applied nodal forces and nodal fixed displacements (DO NOT RE-NUMBER THE
Posted: Tue Jul 12, 2022 8:49 am
The spring assembly shown below is subjected to applied nodalforces and nodal fixeddisplacements (DO NOT RE-NUMBER THE NODES OR SPRING ELEMENTS).
a) Complete the element-node-deformation table below:
Note, express the element deformations in the above table in termsof nodaldisplacements u1, u2, u3, u4, and u5.
b) Draw Free Body Diagrams for the nodes where displacements areunknown (in termsof ks, ka, Fapp, u1,u2, etc.).
c) Generate the nodal force equilibrium equation at the nodeswhere the displacementsare unknown. Present the equation in a standard form.
d) Given the following spring element system data: F = 2000N, E= 20GPa, Aall=25mm2,x1=0mm, x2=20mm, x3=30mm, x4=80mm, x5=60mm. Develop the stiffnessmatrix [K]and the force vector, {f}. Solve the matrix equation for {u}.
e) Develop the deformation vector, {delta}, the strain vector,{epsilon}, and the x-normal stressvector, {sigma}. Determine the strain and stress in spring element3.
k₂ F 3 Fes- 2 k6 ks k4 www k₁ x = x1 x = x₂ x = x3 2F x = X5 k3 X = X4
- The Spring Assembly Shown Below Is Subjected To Applied Nodal Forces And Nodal Fixed Displacements Do Not Re Number The 1 (45.77 KiB) Viewed 29 times
Note, express the element deformations in the above table in termsof nodaldisplacements u1, u2, u3, u4, and u5.
b) Draw Free Body Diagrams for the nodes where displacements areunknown (in termsof ks, ka, Fapp, u1,u2, etc.).
c) Generate the nodal force equilibrium equation at the nodeswhere the displacementsare unknown. Present the equation in a standard form.
d) Given the following spring element system data: F = 2000N, E= 20GPa, Aall=25mm2,x1=0mm, x2=20mm, x3=30mm, x4=80mm, x5=60mm. Develop the stiffnessmatrix [K]and the force vector, {f}. Solve the matrix equation for {u}.
e) Develop the deformation vector, {delta}, the strain vector,{epsilon}, and the x-normal stressvector, {sigma}. Determine the strain and stress in spring element3.
k₂ F 3 Fes- 2 k6 ks k4 www k₁ x = x1 x = x₂ x = x3 2F x = X5 k3 X = X4