Isostatic StructuresLaajuus (5 cr)

Course unit code: TX00FL37

General information

Credits: 5 cr

Teaching language: English

Institution: Metropolia

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

Content

• Using integration to solve the deflection curve of a beam from a differential equation
• Calculating the deflection of a beam by using Mohr’s analogy
• Determining displacement with the principles of work and energy
• Determining displacement for an isostatic beam, frame and truss by using work integral
• Maxwell’s rule
• Degree of statical indeterminacy and its meaning
• Determining of the dimensioning moments of a continuous beam by using tables
• Quick, routine-like methods for drawing force surfaces and assessing displacements
• Arches
• Influence lines
• Solving deflections and M, V and N diagrams by applicable computer software

Qualifications

Statics, Basics of Structural Mechanics, Fundamentals of Physics, Mathematics 1 and Mathematics 2

Assessment criteria, satisfactory (1)

The student is able to
• repeat the integration of a differential equation of a deflection line
• calculate the deflection of a beam using Mohr’s analogy in a simple case
• identify the displacement of the rod structure using work integrals
• describe Maxwell’s law
• recognise the degree of statical indeterminacy
• recognise a continuous beam
• recognise force magnitude surfaces, deflection lines of beams and assess the impact of the span length as well as the rigidity of a beam on its deflection
• explain the structural behaviour of an isostatic arch structure
• explain how to derive the influence line of an isostatic beam
• solve displacements, force magnitudes and support reactions of 2D plane structures by suitable computer software.

Assessment criteria, good (3)

In addition to the requirements listed above, the student is able to
• derive the differential equation of a deflection curve
• calculate the deflection of a beam by using Mohr’s analogy in all cases
• determine the displacement of a rod structure using work integrals
• use Maxwell’s law
• determine the degree of static indeterminacy
• solve the force moment diagram of a continuous beam using tables
• draw bending moment and shear diagrams as well as deflection curves
• solve the force magnitude 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 is able to
• derive and generalise the differential equation of a deflection curve for complicated boundary conditions
• calculate and justify the deflection of a beam by using Mohr’s analogy
• determine and check the displacement of a rod structure with work integrals, by using tables and by integration
• describe and apply Maxwell’s law and understand its significance in creating elastic matrices
• determine and explain the influence of the degree of static indeterminacy
• solve the bending moment and shear diagrams of a continuous beam using tables
• draw force magnitude surfaces and deflection curves for beams and frames without difficulty.