SEAA3243 Theory of Structures Case Study Semester 2, 2026 | UTM

SEAA3243 Case Study (Complex Problem)

Failure of a 5-Story Car Park

1. Prologue

The structure under consideration is a five-story reinforced concrete car park designed using long-span post-tensioned beams to achieve large, open parking spaces without intermediate supports (See Figure 1). The structural system consisted of an unbraced concrete frame, meaning that the beams and columns alone were responsible for resisting both gravity loads and lateral effects, without the aid of additional bracing elements such as shear walls or braced frames.

The vertical load-bearing system comprises square reinforced concrete columns with crosssectional dimensions of 600 mm × 600 mm, arranged to support the floor system at each level. The floor-to-floor height is 2.7 m. The primary horizontal elements are post-tensioned concrete beams spanning 15.6 m long, and notably, these spans were cast monolithically in a single concrete pour. This construction approach creates strong continuity between spans but also introduces significant restraint forces due to shrinkage, creep, and thermal effects.

Each beam has a substantial cross-section of 2000 mm width and 575 mm depth, designed to accommodate both structural demands and integration with the floor system. To support the flooring, rebates (indentations) were provided along the top corners of the beams. These rebates were specifically shaped to house 150 mm deep precast hollow-core slabs, which spanned transversely between adjacent beams spaced at 7.2 m centers. This system enabled efficient load transfer from the slabs to the beams and then to the columns. The full post-tensioning force was applied at just 3 days after casting (See Figure 2). The entire construction of the car park was completed within a relatively short period of 8 months, indicating a fast-track construction schedule. Such tight timelines often necessitate early loading and rapid sequencing of construction activities, which can influence structural behavior, especially in post-tensioned systems where time-dependent effects (e.g., creep and shrinkage) are critical.

A few days after stressing, specifically 5 to 6 days after the application of post-tensioning force to the first set of beams, significant cracking began to appear throughout the structure (See Figure 3). The cracks were not localized, but rather widespread, affecting both the beams and the supporting columns. In several locations, the crack widths exceeded 0.7 mm, which is considerably larger than typical acceptable limits for reinforced concrete structures and indicative of serious structural distress. The cracking patterns varied in form and orientation, suggesting multiple contributing mechanisms, such as excessive tensile stresses, restraint effects, or unintended load paths.

Figure 1 Layout of the building and structural elements

Figure 2 A typical post-tensioned beam under construction.

Figure 3 Observed cracks on beams and columns

2. Investigation Instruction

Assume that you have been appointed as a structural consulting firm to investigate the distress and potential failure of the multi-story car park building. The objective of this investigation is to identify the root causes of the observed cracking and to propose appropriate remedial and preventive measures. The investigation can be resolved through in-depth engineering knowledge using a fundamental-based approach (WP1). Below is the scope of work that you are expected to fulfil. The scope of work is defined as follows:

a) Material and Structural Assessment

Identify and justify the material characterization tests and structural evaluation methods required to support the investigation. These may include, but are not limited to:

• In-situ and laboratory testing of concrete properties (e.g., compressive strength, modulus of elasticity, shrinkage, and creep)
• Assessment of reinforcement and post-tensioning systems (e.g., tendon force verification, anchorage condition, corrosion inspection)
• Non-destructive testing (NDT) techniques such as ultrasonic pulse velocity, rebound hammer, and ground-penetrating radar
• Monitoring or measurement of existing crack widths, patterns, and propagation

The selected tests should be sufficient to evaluate both the material performance and the structural integrity of the system.

b) Structural Analysis of a Representative Frame

Consider a representative single-bay frame extracted from the structure, consisting of rigid beam-to-column connections and fixed supports at the base, as illustrated in Figure 4. Perform structural analysis for the following loading conditions. This can be achieved through systematic and theory-based formulation fundamentals in the analysis process of the civil engineering discipline (WK3).

Case I: Gravity Load Only

Analyze the frame subjected solely to gravity loading acting on the beam. The gravity load should be idealized as a uniformly distributed load (UDL), calculated based on reasonable engineering assumptions, including:

• Self-weight of structural elements (beam and slab)
• Superimposed dead loads (e.g., finishes, services)
• Imposed loads appropriate for car park usage

Determine and present the following internal force diagrams:

• Bending Moment Diagram (BMD)
• Shear Force Diagram (SFD)
• Axial Force Diagram (AFD)

Case II: Gravity Load + Post-Tensioning Force

Extend the analysis by considering the combined effect of gravity loading (as in Case I) and post-tensioning force applied to the beam. The post-tensioning force may be reasonably estimated based on:

• Beam span and cross-sectional dimensions
• Typical levels of prestressing force used in similar structural systems

The post-tensioning effect should be modeled appropriately (e.g., equivalent load method or tendon profile effects). Again, determine and present the BMD, SFD, and AFD for this case.

c) Comparative Assessment and Interpretation

Compare the internal force distributions obtained from Case I and Case II, and critically evaluate the structural response. Based on this comparison, address the following. There is no obvious solution for this task, so you are required to formulate suitable hypotheses using your knowledge and abstract thinking with some originality in analysis (WP3).

• To what extent can the magnitude and application of post-tensioning force contribute to the observed cracking and structural distress? Consider induced compressive forces, secondary moments, and restraint effects.
• To what extent can the timing of post-tensioning (i.e., early-age stressing at 3 days) influence the development of cracks? Discuss the role of insufficient concrete strength, early-age stiffness, and time-dependent effects such as creep and shrinkage.
• What design, construction, or procedural modifications could be implemented to prevent similar cracking and damage in future projects? Consider aspects such as sequencing, stressing protocols, structural detailing, and load management.
• Based on your findings, propose suitable strengthening and remedial measures for the existing car park structure. These may include structural retrofitting techniques, crack repair strategies, or stress redistribution methods.

Figure 4 Selected frame for analysis

3. Full Report Instruction

This is a group project. The group members of maximum five (5) people will be assigned by the lecturer in the beginning of the semester. 10% of the total marks from the report and presentation will be carried into the final mark for the course.

Report 

In this case study project, you are required to write a group report. The maximum length of the report must not exceed 15 pages of A4 paper, 1.5 line spacing, and 11 font size including figures, pictures and references. The components of the report should include the scope of works given by the client while at the same time professional report writing need to be followed.

Presentation

Prepare the slides for a maximum 10 minutes presentation about the case that your group is reporting. Submit the file to your class lecturer in week 14 (depends on lecturer decision). Class presentation will be in week 15 or to be decided by your lecturer. Every one of the group members must prepare and practice for the presentation.

Learning Outcome

After finishing this group project, the students are expected to be able to:

1. Appreciate the role of engineers in solving complex engineering problems through case study.
2. Learn and practice good presentation skill
3. Write professional technical report
4. Work in a team

SEAA3243 Case Study Marks

The marks for the case study project will be based on the following components: