UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
FEA3701
Assessment 01 — 2026
⋄
Module Code: FEA3701
Module Name: Finite Element Analysis
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for FEA3701
at the University of South Africa.
, UNISA | FEA3701 Assessment 01 – 2026
Question 1 [45 Marks]: Direct Stiffness Method – Spring Assemblage
Question: Consider that a 40 kN external force is exerted at node 2 along element 3 in the
positive x-direction. Additionally, consider a 60 kN external force applied at node 4 in the neg-
ative x-direction along element 2. Using the direct stiffness method for the spring assemblage
given in Figure 1, determine the following:
a) The nodal displacements [22 Marks]
b) The forces in each element [15 Marks]
c) The reactions [8 Marks]
The spring assemblage in Figure 1 consists of five spring elements connecting three nodes,
with nodes 1 and 3 fixed (wall supports). The spring stiffnesses (in kN/mm) are:
k (1) = 200, k (2) = 400, k (3) = 600, k (4) = 800, k (5) = 1000
1(a): Nodal Displacements [22 Marks]
Step 1: Individual Element Stiffness Matrices
For a spring element connecting nodes i and j with stiffness k, the element stiffness matrix is:
k −k
[k (e) ] =
−k k
Implying that for each element:
200 −200
[k (1) ] = kN/mm
−200 200
400 −400
[k (2) ] = kN/mm
−400 400
600 −600
[k (3) ] = kN/mm
−600 600
Page 1 of 12
College of Science, Engineering and Technology
⋄
FEA3701
Assessment 01 — 2026
⋄
Module Code: FEA3701
Module Name: Finite Element Analysis
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for FEA3701
at the University of South Africa.
, UNISA | FEA3701 Assessment 01 – 2026
Question 1 [45 Marks]: Direct Stiffness Method – Spring Assemblage
Question: Consider that a 40 kN external force is exerted at node 2 along element 3 in the
positive x-direction. Additionally, consider a 60 kN external force applied at node 4 in the neg-
ative x-direction along element 2. Using the direct stiffness method for the spring assemblage
given in Figure 1, determine the following:
a) The nodal displacements [22 Marks]
b) The forces in each element [15 Marks]
c) The reactions [8 Marks]
The spring assemblage in Figure 1 consists of five spring elements connecting three nodes,
with nodes 1 and 3 fixed (wall supports). The spring stiffnesses (in kN/mm) are:
k (1) = 200, k (2) = 400, k (3) = 600, k (4) = 800, k (5) = 1000
1(a): Nodal Displacements [22 Marks]
Step 1: Individual Element Stiffness Matrices
For a spring element connecting nodes i and j with stiffness k, the element stiffness matrix is:
k −k
[k (e) ] =
−k k
Implying that for each element:
200 −200
[k (1) ] = kN/mm
−200 200
400 −400
[k (2) ] = kN/mm
−400 400
600 −600
[k (3) ] = kN/mm
−600 600
Page 1 of 12
