Required: Solve for the axial displacements using the Elemental Stiffness method discussed in class and the FEM Frame Code. Determine the Maximum Stress and its location. If the Yield Stress if 440 MPa, does the material Yield?

Required: Solve for the axial displacements using the Elemental Stiffness method discussed in class and the FEM Frame Code. Determine the Maximum Stress and its location. If the Yield Stress if 440 MPa, does the material Yield?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.12.19P: A tension member constructed of an L inch angle section (see Table F-4(a) in Appendix F) is...

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Question

Displacement with elemental stiffness method, the rest the same.

Given: Following Uniaxial Bar.
Required: Solve for the axial displacements using the Elemental Stiffness method discussed in
class and the FEM Frame Code. Determine the Maximum Stress and its location. If the Yield
Stress if 440 MPa, does the material Yield?
E2, A2, L2
O
OD = 14 in.
WT = 0.185 in.
P₁=400 kN
P₂ = 800kN
E3, A3, L3
E₂ = E3 = 190 GPa
L₂ = 1.5 m
L3 = 2.75 m
O
OD = 12 in.
WT = 0.135 in.

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Step 1: Write the given data and what is to find

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Step 2: Assign the nodes and calculate the cross-sectional area of the two rods:

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Step 3: Write the element stiffness matrix for both the bar elements:

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Step 4: Write the global stiffness matrix:

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Step 5: Write the boundary condition and determine the nodal displacements:

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Step 6: Determine the reaction force at node 3:

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Step 7: (a) Determine the maximum stress and its location:

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