Differential equations in construction engineering (3 cr)

Evaluation scale

0-5

Content scheduling

A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
- Revision of statics and some mechanics of materials
- Revision of derivative and integral
- Integration of piecewise defined functions
- Shear stress and bending moment in beams as functions of position
- Euler-Bernoulli differential equation and it's solution with different initial conditions
- Buckling of columns

Objective

Purpose
After the course you will understand how differential equations are used in civil engineering to calculate deflections in beams.

Competencies
Knowledge and understanding of the differential equations at a level necessary to achieve the other programme outcomes.

Learning outcome
You know what differential equations are. You can solve a differential equation of first order using appropriate tools. You understand the role of initial and boundary conditions. You can solve problems related to construction technology.

Content

Using local extremas in calculating deflections in beams. Concept of differential equations and verifying the results and initial and boundary conditions. Solving a differential equation by integrating. Defining the equation for a load and defining the initial and boundary conditions according to the underpinning. Calculating the shear force, the bending moment, the deflection angle and the deflection and determining and analyzing their graphs.

Location and time

The course will be held at the Rajakatu campus from 25 August to 16 November 2025.

Materials

Learning material written by course teacher.

Some good books about the topic that are available at JAMK library in English:
- Beer, F. P. k., Johnston, E. R., DeWolf, J. T. & Mazurek, D. F. 2015. Mechanics of materials. Seventh edition in SI units. New York: McGraw-Hill Education.
- Bedford, A. & Liechti, K. M. 2020. Mechanics of materials. Second Edition. Cham: Springer International Publishing.

Teaching methods

Face-to-face learning. Lesson attendance is mandatory.

It is necessary to actively calculate course exercises to achieve learning goals.

Employer connections

-

Exam schedules

Final exam during the week starting 10 November
First retake during the week starting 24 November
Second retake during the week starting 15 December

International connections

-

Completion alternatives

No alternative implementations.

Student workload

3op * 27 h/op = 81 h, of which approximately 35 h are reserved for face-to-face learning and the final exam.

Assessment criteria, satisfactory (1)

1: You know the concept of differential equation. You understand how to use differential equations in calculating the deflections in a beam. You can verify the result and the initial and boundary conditions. You can solve the deflection of a beam by a model.

2: You have achieved the desired goals (see the criteria in grade 1). You can solve the deflection of a beam without a model, but your reasoning is sometimes deficient or you make mistakes in calculations.

Assessment criteria, good (3)

3: You have achieved the desired goals (see the criteria in grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly.

4: You have achieved the desired goals (see the criteria in grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Assessment criteria, excellent (5)

5: You have achieved the desired goals (see the criteria in grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Qualifications

You understand concept of derivation and you can use derivatives in optimization. You understand concept of integrals. You can take the derivatives and integrals of functions by appropriate tools.

Further information

Course assessment is based on final exam and exercises.

If a student enrolled in the course does not show activity within three weeks of the start of the course, the enrollment will be rejected.