Differential Equations in Construction Engineering (3cr)

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 derivative and integral and the concept of a differential equation
- Integration of piecewise defined functions
- Revision of statics and some mechanics of materials
- Shear stress and bending moment in beams as functions of place
- Euler-Bernoulli differential equation and it's solution with different initial conditions

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

During this course you will study the following topics:

- Defining the equation for a load
- Defining the initial and boundary conditions according to the support
- Concept of differential equations and verifying the results and boundary conditions
- Solving a differential equation by integration
- Calculation the shear force, bending moment, deflection angle and deflection of a loaded beam and determining and analysis of their graphs
- Using local extremas in calculating deflections in beams

Location and time

The course takes place 29.8. - 13.11. at the main campus (Rajakatu)

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

Employer connections

-

Exam schedules

Final exam: 10.11.2022
1. resit: week of 12.12.2022
2. resit: week of 16.1.2023

International connections

-

Completion alternatives

No alternative implementations.

Student workload

3op * 27 h/op = 81 h, of which approximately 30 h are reserved for face-to-face learning and the final exam.

Assessment criteria, satisfactory (1)

Sufficient 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.

Satisfactory 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)

Good 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.

Very good 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)

Excellent 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 the derivative and you can use derivatives in optimization. You understand the concept of the integral. You can take the derivatives and integrals of functions using appropriate tools when necessary.

Further information

Final exam, exercises