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Finite Element Analysis of a Truss Structure

A two-bar structural assemblage and a plane truss structure need to be analyzed using the finite element method and hand calculation to determine displacements, reaction forces, and normal stresses.

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Added on  2023-06-08

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This document provides a detailed analysis of a truss structure using the Finite Element Method. It includes calculations for normal stress in each element, local stiffness matrix for each element, and nodal displacement for stress element 2. The study material, solved assignments, essays, and dissertations related to Finite Element Analysis are available on Desklib.

Finite Element Analysis of a Truss Structure

A two-bar structural assemblage and a plane truss structure need to be analyzed using the finite element method and hand calculation to determine displacements, reaction forces, and normal stresses.

   Added on 2023-06-08

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Finite Element Analysis of a Truss Structure_1
Question no.-1:
Let R1 & R4 are reaction force at node 1 & 4
F2= 100KN = 0.1 MN
F3= 100KN = 0.1 MN
A1= 2000mm2 A2= 2000mm2 A3= 2000mm2
l1= 200mm l1= 200mm l3= 200mm
E1= 100GPa E2= 200GPa E3= 100GPa
K1= A1E1/l1 = (2000 X 100 X103)/200 = 1MNmm-1
K1= A1E1/l1 = (1000 X 200 X103)/200 = 1MNmm-1
K1= A1E1/l1 = (2000 X 100 X103)/200 = 1MNmm-1
K=
1 2 3 4
F2 F3
x
1 2 3
F3F2
K1 K2 K3
K1 -K1 0 0
-K1 K1+ k2 K1 K1
-K3K2+K3-K2
0
0 0 -K3 K3
Finite Element Analysis of a Truss Structure_2
K=
Let displacement for node be u1, u2, u3, u4 respectably
From the figure; u1=0, u4=0
Also {F} = [F] {u}
=
R1= -u2
0.1= 2 u2-u3
0.1= -u2 + 2u3
R4 = -u3
Solving equation 2 & 3 we get
U2 = 0.1mm
U3 = 0.1mm
From equation 1 and 4 we get
R1 = -100KN
1 -1 0 0
-1 2 -1 0
-12-10
0 0 -1 1
1 -1 0 0
-1 2 -1 0
-12-1
0 0 -1 1
R1
0.1
0.1
R4
0
0
U2
U3
0
1
2
3
4
Finite Element Analysis of a Truss Structure_3

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