Isostatic Structures (5 cr)

Objective

On completion of the course, the student is able to solve the deflection of isostatic beams and frames by using an applicable method, such as the differential equation of a beam, Mohr’s analogy, energy methods or with computer software.

He or she is able to calculate quickly the deflection of frames by using the work integral where using tables for integration. The student applies Maxwell’s reciprocal theorem to structures and is capable to explain its meaning. He or she recognises a statically indeterminate beam or frame and understands its meaning. The student is able to quickly sketch M-, V- and N-diagrams and deflection curves without calculations for beams and frames. In addition to this he or she is able to solve the influence lines of beams and solve M-, V- and N- diagrams for an arch.

Content

1. Using integration to solve the deflection curve of a beam from a differential equation
2. Calculating the deflection of a beam by using Mohr’s analogy
3. Determining displacement with the principles of work and energy
4. Determining displacement for an isostatic beam, frame and truss by using work integral
5. Maxwell’s rule
6. The degree of statical indeterminacy and its meaning
7. Determining of the dimensioning moments of a continuous beam by using tables
8. Quick, routine-like methods for drawing force surfaces and assessing displacements
9. Arches
10. Influence lines
11. Checking deflections and M-, V- and N-diagrams by applicable computer software

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

On completion of the course the student can
- repeat the integration of a differential equation of a deflection curve
- calculate the deflection of a beam by using Mohr’s analogy without difficulty in a simple problem
- recognise the displacement of a beam structure by using work integral
- understand Maxwell’s reciprocal theorem
- recognise the degree of statical indeterminacy
- recognise a continuous beam
- recognise force surfaces, deflection beams and assess the impact of beam span as well as rigidity on deflection, sketch deflection curves and M- and V-diagrams without calculations
- explain the influence line of an isostatic beam
- explain the structural behaviour of an isostatic arch structure
- check deflections and M-, V- and N-diagrams by computer software.

Assessment criteria, good (3)

In addition to the requirements listed above, the student can
- derive the differential equation of a deflection curve
- calculate the deflection of a beam by using Mohr’s analogy without difficulty in all problems
- determine the displacement of a beam structure with work as an integral without difficulty
- use Maxwell’s reciprocal theorem
- determine the degree of static indeterminacy
- solve the force surface of a continuous beam using tables
- draw force surfaces and deflection curves quickly and without difficulty
- solve the force surfaces of an isostatic arch structure
- draw influence lines for isostatic beams.

Assessment criteria, excellent (5)

In addition to the requirements listed above, the student can
- derive and generalise the differential equation of a deflection curve in complicated problems with boundary conditions
- calculate and justify the deflection of a beam by using Mohr’s analogy
- determine and check the displacement of a beam structure with work as an integral by using tables and integration
- describe and apply Maxwell’s reciprocal theorem and understand its significance in creating an elasticity matrix
- determine and explain the influence of the degree of static indeterminacy
- solve the force surface of a continuous beam using tables
- draw force surfaces and deflection curves for beams and frames without difficulty.

Assessment criteria, approved/failed

On completion of the course the student can
- repeat the integration of a differential equation of a deflection curve
- calculate the deflection of a beam by using Mohr’s analogy without difficulty in a simple problem
- recognise the displacement of a beam structure by using work integral
- understand Maxwell’s reciprocal theorem
- recognise the degree of statical indeterminacy
- recognise a continuous beam
- recognise force surfaces, deflection beams and assess the impact of beam span as well as rigidity on deflection, sketch deflection curves and M- and V-diagrams without calculations
- explain the influence line of an isostatic beam
- explain the structural behaviour of an isostatic arch structure
- check deflections and M-, V- and N-diagrams by computer software.

Qualifications

Statics, Basics of the Built Environment, Math and Science Basics 1, 2, and 3