FEA3701 Assessment 01 Due 2026

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄


FEA3701: Finite Element Analysis

Assessment 01 — Semester 1, 2026

⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄




FEA3701
Module Code:
Finite Element Analysis
Module Name:
Assessment 01
Assessment:
2026
Due Date:
75
Total Marks:




Submitted in partial fulfilment of the requirements for FEA3701 — UNISA 2026

, UNISA | FEA3701 Assessment 01 – 2026



Question 1: Spring Assemblage – Direct Stiffness Method [45 Marks]


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
negative x-direction. Using the direct stiffness method for the spring assemblage given in
Figure 1, determine:

a) The nodal displacements [22 Marks]
b) The forces in each element [15 Marks]
c) The reactions [8 Marks]

Given spring stiffnesses from Figure 1:


k (1) = 200 N/mm, k (2) = 400 N/mm, k (3) = 600 N/mm, k (4) = 800 N/mm, k (5) = 1000 N/mm



Nodal connectivity (from the figure):

• Element 1: nodes 1–2
• Element 2: nodes 2–3 (upper branch, 400 N/mm)
• Element 3: nodes 2–3 (middle branch, 600 N/mm)
• Element 4: nodes 2–3 (lower branch, 800 N/mm)
• Element 5: nodes 3–4 (1000 N/mm)


1a) Nodal Displacements [22 Marks]


Step 1: Element Stiffness Matrices


Each spring element has the standard 2 × 2 stiffness matrix:
 
1 −1
[k (e) ] = k (e)  
−1 1


Implying that:

 
200 −200
[k (1) ] =   (nodes 1, 2)
−200 200



Page 2 of 11