## Strength of materials

Demonstration of Maxwell-Betti theorem

##### Learning objectives / experiments

- elastic line under varying load
- elastic line under various bearing conditions
- demonstration of Maxwell–Betti’s theorem
- elastic line and support forces in statically indeterminate systems

Elastic lines of statically determinate and overdeterminate beams under various clamping conditions

##### Learning objectives / experiments

- investigation of the deflection for statically determinate and statically indeterminate straight beams
- cantilever beam
- single-span beam, dual- or triple-span beam
- formulation of the differential equation for the elastic line

- deflection on a cantilever beam

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Determination of elastic lines of a beam under load using the principle of virtual work and Mohr's Analogy

##### Learning objectives / experiments

- elastic lines for statically determinate or indeterminate beams under load
- determination of the elastic line of a beam by
- the principle of virtual work (calculation)
- Mohr’s Analogy (area moment method devised by Mohr; graphical representation)

- application of the principle of superposition

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Investigation of elastic torsion of bars with open and closed cross-section

##### Learning objectives / experiments

- torsion of a bar
- shear modulus of elasticity and second polar moment of area
- angle of twist dependent on clamping length
- angle of twist dependent on torque
- influence of rigidity on torsion

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Influence of material, cross-section and clamping length on deformation

##### Learning objectives / experiments

- Bending tests
- determination of the modulus of elasticity
- statically determinate systems
- beam mounted on 2 supports; cantilever beam

- statically indeterminate systems

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Elastic deformation of a statically determinate or overdeterminate frame under point load

##### Learning objectives / experiments

- relationship between load application and deformation on the frame
- differences between statically determinate and statically indeterminate frames
- familiarisation with the first-order elasticity theory

for statically determinate and indeterminate systems - application of the principle of superposition

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Principle of virtual forces for calculating deformation

##### Learning objectives / experiments

- bending behaviour of a curved-axis beam
- circular beam
- semi-circular beam
- quadrant beam

- application of the principle of virtual forces (the force method) to calculate deformation

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Application of Castigliano’s first theorem

##### Learning objectives / experiments

- elastic deformation of truss under point load
- calculation of support reaction and bar forces
- principle of work and strain energy
- application of Castigliano’s first theorem to calculate the deformation at a defined point
- verification of the calculated deformation possible by the principle of virtual work

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Demonstration of the resulting characteristics of the contact area as a function of the contact force

##### Learning objectives / experiments

- resulting shape of the contact area under point contact with different radii of curvature
- shape of the contact area as a function of the contact force
- influence of an additional transverse component of the contact force

Elastic behaviour of tension springs under load

##### Learning objectives / experiments

- investigation of the proportionality of the active force and the spring deflection
- determination of the spring constant
- series configuration of two tension springs
- investigation of the influence of the spring constant on the frequency of a spring-mass system

Determination of the buckling load under different conditions SE 112 Mounting Frame required

##### Learning objectives / experiments

- determination of the buckling force for the case of an:
- elastic joint
- elastic fixed end support

- investigation of the buckling behaviour under the influence of:
- of additional shear forces

….

- of additional shear forces

Determination of the buckling load: influence of material, support, and shear force

##### Learning objectives / experiments

- investigation of buckling behaviour under the influence of
- different bearings, clamps
- different cross-sections
- different materials
- additional shear forces

….

Correlation between buckling length, buckling load and various methods of support

##### Learning objectives / experiments

- demonstration of various buckling problems
- Euler case 1 – fixed-free bar
- Euler case 2 – pinned-pinned bar
- Euler case 3 – fixed-pinned bar
- Euler case 4 – fixed-fixed bar

….

Verification of the Euler theory of buckling and buckling behaviour under the influence of material, cross-section, length, and support

##### Learning objectives / experiments

- investigation of buckling behaviour under the influence of
- different bearings and clamps
- different rod lengths and cross-sections
- different materials
- additional lateral load

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Investigation of symmetrical and unsymmetrical bending on a beam. Combined bending and torsion loading using an eccentric force.

##### Learning objectives / experiments

- product moment of inertia (I
_{yz}) and axial second moment of area (I_{y}, I_{z}) - Bernoulli hypothesis
- symmetrical bending on a beam (uniaxial)
- with I-profile
- with L-profile

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Multiaxial loading of samples by bending and torsion

##### Learning objectives / experiments

- generation of multi-axial loads on test samples made of ductile metals:
- steel, copper, brass, aluminium

- generation of various load moments
- pure bending moment
- pure torsional moment

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Complete equipment for practising manual handling of strain gauge technology

##### Learning objectives / experiments

- fundamentals of electrical resistance strain gauges
- preparation of the measuring point
- selection of a suitable strain gauge
- attaching, wiring up and configuring strain gauges on mechanically stressed components
- protection of the strain gauge measuring point against external influences

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Basic introduction to measurement with strain gauges for tension, bending and torsion

##### Learning objectives / experiments

- fundamentals of measuring with strain gauges
- strain gauge types and application techniques
- calculation of the mechanical deformations under tension, bending and torsion
- correlation between mechanical strain and electrical resistance in a strain gauge
- with FL 100.01, FL 100.02, FL 100.03: determination of the modulus of elasticity for various materials from the measurement data of a tensile test

Investigation of deflection and strain to determine the gauge factor of strain gauges

##### Learning objectives / experiments

- fundamentals of measurement using strain gauges
- measurement of deflection using a dial gauge
- determination of the gauge factor of strain gauges

Processing of analogue measuring signals for FL 120 - FL 140 and for GUNT trusses

##### Learning objectives / experiments

- amplification and display of signals from strain gauge measuring points
- processing of measured values on computer
- evaluation of stress and strain analysis experiments, in conjunction with: FL 120, FL 130, FL 140
- evaluation of experiments relating to forces in trusses, in conjunction with: SE 130, SE 110.21, SE 110.22

Investigation of deflection and strain of a membrane under internal pressure; membrane with strain gauge application

##### Learning objectives / experiments

- measure radial and tangential strain using strain gauges
- measure deflection using a dial gauge
- calculate the stresses from the measured strains: radial stress, tangential stress
- determine direction of principal stress
- application of Mohr’s strain circle to determine the principal strains

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Investigation of axial and circumferential stress in a thin-walled cylinder under internal pressure

##### Learning objectives / experiments

- measure strains with strain gauges
- application of Mohr’s stress circle to determine the principal strain
- determine the principal stresses: axial and circumferential stresses by magnitude and direction
- in an open vessel (pipe)
- in a closed vessel(boiler)

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Triaxial stress state in the cylinder wall; cylinder with strain gauge application on surface and in wall

##### Learning objectives / experiments

- measurement of elongations by strain gauges
- application of Mohr’s Circle for the triaxial stress state
- determination of the distribution of direct stress in
- radial, tangential and axial direction

- investigation of correlations between elongation, pressure and stress in the triaxial stress state

Visualisation of mechanical stresses in models subject to varying loads

##### Learning objectives / experiments

- together with the accessories or your own models:
- generate plane stress states in various models under load: bending, tensile load and compressive load
- investigate stress distributions with linear or circular polarised light
- interpret photoelastic fringe patterns: stress concentrations, zero points, neutral strands, areas of constant stress and stress gradients
- graphically and computationally determine the stresses

Representation of distribution of stress and stress concentrations in component models. Can be used in conjunction with an overhead projector.

##### Learning objectives / experiments

- generate plane stress states in various models under load
- compressive load
- tensile load

- investigate stress distributions with linear and circular polarised light
- interpret photoelastic fringe patterns

….