Equipamentos para Laboratório de - WordPress.com...Equipamentos para Laboratório de Resistência...

Equipamentos para Laboratório de

Resistência dos Materiais

Milrian Mendes: +55 81 99786-6527 (Recife)

[email protected]

Eliasibe Luis: +55 51 9 9706-4541 (Porto Alegre)

[email protected]

www.setuplasers.com.br/kit4labs

➢ Caso seja necessário, nos peça a tradução para o Português do conteúdo a seguir.

➢ Esses equipamentos fazem parte do catálogo 1 da GUNT Engineering Mechanics &

Engineering Design. Acesse-o pelo link:

https://www.dropbox.com/sh/vi2u6j20aw68b9p/AACtxjdTEet9BNQVaOSyiV2Va?dl=0

Engineering mechanics – strength of materials gunt2 guntEngineering mechanics – strength of materials

Engineering mechanics and engineering design

077076

Engineering mechanics – strength of materials

Introduction

OverviewStrength of materials 078

Elastic deformations

Basic knowledgeElastic deformations 080

SE 110.14Elastic line of a beam 082

WP 950Deformation of straight beams 084

SE 110.47Methods to determine the elastic line 086

SE 110.29Torsion of bars 088

WP 100Deformation of bars under bending or torsion 090

SE 110.20Deformation of frames 092

FL 170Deformation of curved-axis beams 094

SE 110.44Deformation of trusses 096

TM 262Hertzian pressure 098

TM 400Hooke’s law 100

Accessories

SE 112Mounting frame 101

Buckling and stability

Basic knowledgeStability problem: buckling 102

SE 110.19Investigation of simple stability problems 104

SE 110.57Buckling of bars 106

WP 121Demonstration of Euler buckling 108

WP 120Buckling behaviour of bars 110

OverviewAccessories for WP 120 112

Compound stress

FL 160Unsymmetrical bending 114

WP 130Verification of stress hypotheses 116

Experimental stress and strain analysis

Overview Experimental stress and strain analysis: Strain gauge and photoelasticity 118

FL 101Strain gauge application set 120

FL 100Strain gauge training system 122

FL 102Determining the gauge factor of strain gauges 124

Overview FL 152: PC-based recordingand analysis of strain gauge signals 126

FL 152Multi-channel measuring amplifier 128

FL 120Stress and strain analysis on a membrane 130

FL 130Stress and strain analysis on a thin-walled cylinder 132

FL 140Stress and strain analysis on a thick-walled cylinder 134

FL 200 Photoelastic experimentswith a transmission polariscope 136

FL 210Photoelastic demonstration 138

Overview FL 200 and FL 210: representationof stress distribution in component models 140

Engineering mechanics – strength of materials gunt2 guntEngineering mechanics – strength of materials

Engineering mechanics and engineering design

077076

Engineering mechanics – strength of materials

Introduction

OverviewStrength of materials 078

Basic knowledgeElastic deformations 080

SE 110.14Elastic line of a beam 082

WP 950Deformation of straight beams 084

SE 110.47Methods to determine the elastic line 086

SE 110.29Torsion of bars 088

WP 100Deformation of bars under bending or torsion 090

SE 110.20Deformation of frames 092

FL 170Deformation of curved-axis beams 094

SE 110.44Deformation of trusses 096

TM 262Hertzian pressure 098

TM 400Hooke’s law 100

Accessories

SE 112Mounting frame 101

Buckling and stability

Basic knowledgeStability problem: buckling 102

SE 110.19Investigation of simple stability problems 104

SE 110.57Buckling of bars 106

WP 121Demonstration of Euler buckling 108

WP 120Buckling behaviour of bars 110

OverviewAccessories for WP 120 112

Compound stress

FL 160Unsymmetrical bending 114

WP 130Verification of stress hypotheses 116

Experimental stress and strain analysis

Overview Experimental stress and strain analysis: Strain gauge and photoelasticity 118

FL 101Strain gauge application set 120

FL 100Strain gauge training system 122

FL 102Determining the gauge factor of strain gauges 124

Overview FL 152: PC-based recordingand analysis of strain gauge signals 126

FL 152Multi-channel measuring amplifier 128

FL 120Stress and strain analysis on a membrane 130

FL 130Stress and strain analysis on a thin-walled cylinder 132

FL 140Stress and strain analysis on a thick-walled cylinder 134

FL 200 Photoelastic experimentswith a transmission polariscope 136

FL 210Photoelastic demonstration 138

Overview FL 200 and FL 210: representationof stress distribution in component models 140

Strength of materials

Engineering mechanics – strength of materialsIntroduction gunt2

Strength of materials is based on statics. The idealisation of a real body as a rigid body in statics allows determining the exter-nal and internal forces on structures under equilibrium. Ensur-ing equilibrium is not sufficient for calculating the mechanical behaviour of components, including strength, rigidity, stability, fatigue strength and ductility, in the real world of engineering practice. Knowledge of the deformability of material bodies is required, without consideration of the material.

Strength of materials deals with the effect of forces on deform-able bodies. In addition, material-dependent parameters should be considered as well. An introduction to the strength of mate-rials is, therefore, given by the concept of stress and strain and by Hooke’s law, which is applied to tension, pressure, torsion and bending problems.

Strain gauge

Experimental stress and strain analysis uses the mechanical stress that occurs in components under load to determine the material stress. An experimental method for determining mechanical stress is based on the relation between stress and the deformation it causes. This deformation is known as strain and occurs on the sur-face of the components, which means that it can be measured. The principle of strain measurement is an important branch of experi-mental stress and strain analysis.

Photoelasticity (transmitted light polariscope)

Photoelasticity is an optical experimental method for determining the stress distribution in transparent, generally planar equivalent bodies. Photoelasticity provides a complete picture of the stress field. Areas of high stress concentration and the resulting strain as well as areas under less load can be clearly visualised.

Photoelasticity is a proven method for verifying analytically or numerically performed stress analyses (e.g.: FEM). It is used for both obtaining quantitative measurements and demonstrating complex stress states.

Mechanical stress

When loads, moments, or forces externally act on a compo-nent, it internally creates force flows. The distribution of these loads is called mechanical stress. Mechanical stress is, there-

fore, defined as force per unit area. We distinguish two different cases:

Perpendicular force action on the section, direct stress σ

Parallel force action to the section, shear stress τ

Basic terms of materials strength

Types of stress

Components can be subjected to stress in different ways: tension, pressure, shear stress, bending, torsion, buckling and com - posite stresses.

Elastic deformation, law of elasticity

Machines and components elastically deform under the action of forces. While the load is not large enough, purely elastic defor-mation remains. The law of elasticity describes the elastic defor-

mation of solids when this deformation is proportional to the applied force.

Energy methods

Geometric considerations play a subordinate role in the energy methods. Instead of the previously used equilibrium conditions, we investigate how much work is produced by external forces during deformation of a system and in which energy form and where this work is stored.

In studying the strength of materials, the energy methods are based on the law of conservation of energy and on the principle that all energy transferred to a body or a system from outside is converted to internal energy, e.g. into deformation, change in velocity, or heat.

Different energy methods are used to calculate general systems and to investigate the stability of elastic structures, such as the principle of virtual displacement, the principle of virtual forces, the Maxwell-Betti theorem, or Castigliano’s theorem.

The starting point of all energy methods is the principle of virtual work. It expresses an equilibrium condition and states: If a mechanical system is in equilibrium under the effect of external and internal forces, then the sum of the total virtual work, pro-duced by internal and external forces and any virtual displace-ment are equal to zero.

Experimental stress and strain analysis as proof of stresses

F force, A section, σ stress, τ shear stress

F force, M moment, Mt twisting moment, σ stress, τ shear stress

δW virtual work, δx virtual displacement, δφ virtual twisting angle, M moment, F force

Tension

Bending

Torsion

Pressure

Shearing stress

Bending stresses

Compressive stresses

Tensile force

σ =FA

τ =FA

δW = F · δx = 0; δW = M · δφ = 0

δW = ∑ δW = ∑ F · δx = 0

δW = ∑ δW = ∑ M · δφ = 0

Fσ σσ σ

F force, 1 strain gauge in component not under load, 2 strain gauge in component under load

¡{!(1

¡{!(2

Principle of virtual work

079078

Engineering mechanics – strength of materialsIntroduction gunt2

Strength of materials is based on statics. The idealisation of a real body as a rigid body in statics allows determining the exter-nal and internal forces on structures under equilibrium. Ensur-ing equilibrium is not sufficient for calculating the mechanical behaviour of components, including strength, rigidity, stability, fatigue strength and ductility, in the real world of engineering practice. Knowledge of the deformability of material bodies is required, without consideration of the material.

Strength of materials deals with the effect of forces on deform-able bodies. In addition, material-dependent parameters should be considered as well. An introduction to the strength of mate-rials is, therefore, given by the concept of stress and strain and by Hooke’s law, which is applied to tension, pressure, torsion and bending problems.

Strain gauge

Experimental stress and strain analysis uses the mechanical stress that occurs in components under load to determine the material stress. An experimental method for determining mechanical stress is based on the relation between stress and the deformation it causes. This deformation is known as strain and occurs on the sur-face of the components, which means that it can be measured. The principle of strain measurement is an important branch of experi-mental stress and strain analysis.

Photoelasticity (transmitted light polariscope)

Photoelasticity is an optical experimental method for determining the stress distribution in transparent, generally planar equivalent bodies. Photoelasticity provides a complete picture of the stress field. Areas of high stress concentration and the resulting strain as well as areas under less load can be clearly visualised.

Photoelasticity is a proven method for verifying analytically or numerically performed stress analyses (e.g.: FEM). It is used for both obtaining quantitative measurements and demonstrating complex stress states.

Mechanical stress

When loads, moments, or forces externally act on a compo-nent, it internally creates force flows. The distribution of these loads is called mechanical stress. Mechanical stress is, there-

fore, defined as force per unit area. We distinguish two different cases:

Perpendicular force action on the section, direct stress σ

Parallel force action to the section, shear stress τ

Basic terms of materials strength

Types of stress

Components can be subjected to stress in different ways: tension, pressure, shear stress, bending, torsion, buckling and com - posite stresses.

Elastic deformation, law of elasticity

Machines and components elastically deform under the action of forces. While the load is not large enough, purely elastic defor-mation remains. The law of elasticity describes the elastic defor-

mation of solids when this deformation is proportional to the applied force.

Energy methods

Geometric considerations play a subordinate role in the energy methods. Instead of the previously used equilibrium conditions, we investigate how much work is produced by external forces during deformation of a system and in which energy form and where this work is stored.

In studying the strength of materials, the energy methods are based on the law of conservation of energy and on the principle that all energy transferred to a body or a system from outside is converted to internal energy, e.g. into deformation, change in velocity, or heat.

Different energy methods are used to calculate general systems and to investigate the stability of elastic structures, such as the principle of virtual displacement, the principle of virtual forces, the Maxwell-Betti theorem, or Castigliano’s theorem.

The starting point of all energy methods is the principle of virtual work. It expresses an equilibrium condition and states: If a mechanical system is in equilibrium under the effect of external and internal forces, then the sum of the total virtual work, pro-duced by internal and external forces and any virtual displace-ment are equal to zero.

Experimental stress and strain analysis as proof of stresses

F force, A section, σ stress, τ shear stress

F force, M moment, Mt twisting moment, σ stress, τ shear stress

δW virtual work, δx virtual displacement, δφ virtual twisting angle, M moment, F force

Tension

Bending

Torsion

Pressure

Shearing stress

Bending stresses

Compressive stresses

Tensile force

σ =FA

τ =FA

δW = F · δx = 0; δW = M · δφ = 0

δW = ∑ δW = ∑ F · δx = 0

δW = ∑ δW = ∑ M · δφ = 0

Fσ σσ σ

F force, 1 strain gauge in component not under load, 2 strain gauge in component under load

¡{!(1

¡{!(2

Principle of virtual work

079078

Engineering mechanics – strength of materialsElastic deformations gunt2

Components are differently stressed when subjected to load from external forces. Load causes stresses in the components. The mesh of the material is deformed under force action, e.g. compressed and stretched. This load leads to volume or shape deformation. Unlike plastic deformation, elastic deformation

means that all atoms return to their original position once the force action ends. Different loads lead to typical component deformations.

Deformation of bars due to a twisting moment

When subject to a load due to a twisting moment, bars are twisted about their bar axis. The torsional defor-mation is described by the twisting angle φ. Hooke’s law states that the twisting angle φ is proportional to the externally acting twist-ing moment.

Deformation of beams

Deflection and load-bearing capacity of beams are extremely important in practice, in structural engineering and bridge building as well as in mechanical and automotive engineering.

Deflection depends on the dimensions, material properties and especially on how the beams are mounted at the ends.

Determination elastic behaviour

There is direct proportionality between deformation and applied force. Therefore, it is necessary to know the material properties as well as the stress to determine the strain or elastic deformation. These material properties, known as the modulus of elasticity, describe the relation between stress and strain in the deformation of a solid body with linear elas-tic behaviour. The elastic modulus can be calculated from the measured values of the tensile test or determined graphically

from the stress-strain diagram (also see chapter 6 Materials testing).

In strength of materials, we consider the linear-elastic region, since the deformation of the material is reversible in this region. When designing beams or supporting structures, the linear-elastic region should not be exceeded.

The calculation of deformations under load is described by Hooke’s law of elasticity

Basic knowledge

Extension

ExtensionCompression

Compression

Tensile stress results in the extension of the outer strands, whereas compressive stress results in compression of the outer strands. The neutral strand (green) passes through the centroid and is neither compressed nor extended.

M moment, F force

Torsional stress leads to deformation of the bar.

Mt twisting moment, F force, φ twisting angle, τ shear stress

σ stress, E elastic modulus, ε strain, F force, A area

Elastic modulus for various materials

Material E in N/mm²

steel 2,1 · 105

aluminium 0,7 · 105

concrete 0,3 · 105

wood along the grain 0,7...1,6 · 104

cast iron 1,0 · 105

copper 1,2 · 105

brass 1,0 · 105

φσ = E · ε =

The elastic region is divided into a linear-elastic component a, where the strain is proportional to the stress and is reversible and a nonlinear-elastic component b, where the strain is not proportional to the stress but is still reversible. In the plastic region, the strain is not reversible and the deformation remains even after the force has been removed.

Elastic region of the stressstrain diagram Stressstrain diagram

E =ΔσΔε

Rm1 2 3

σ stress, ε strain, E elastic modulus, Rp proportional limit, Re yield strength, Rm tensile strength, 1 elastic region, 2 plastic region, 3 constriction to fracture, a linear-elastic component, b nonlinear-elastic component, c Hooke’s straight line

081080

Engineering mechanics – strength of materialsElastic deformations gunt2

Components are differently stressed when subjected to load from external forces. Load causes stresses in the components. The mesh of the material is deformed under force action, e.g. compressed and stretched. This load leads to volume or shape deformation. Unlike plastic deformation, elastic deformation

means that all atoms return to their original position once the force action ends. Different loads lead to typical component deformations.

Deformation of bars due to a twisting moment

When subject to a load due to a twisting moment, bars are twisted about their bar axis. The torsional defor-mation is described by the twisting angle φ. Hooke’s law states that the twisting angle φ is proportional to the externally acting twist-ing moment.

Deformation of beams

Deflection and load-bearing capacity of beams are extremely important in practice, in structural engineering and bridge building as well as in mechanical and automotive engineering.

Deflection depends on the dimensions, material properties and especially on how the beams are mounted at the ends.

Determination elastic behaviour

There is direct proportionality between deformation and applied force. Therefore, it is necessary to know the material properties as well as the stress to determine the strain or elastic deformation. These material properties, known as the modulus of elasticity, describe the relation between stress and strain in the deformation of a solid body with linear elas-tic behaviour. The elastic modulus can be calculated from the measured values of the tensile test or determined graphically

from the stress-strain diagram (also see chapter 6 Materials testing).

In strength of materials, we consider the linear-elastic region, since the deformation of the material is reversible in this region. When designing beams or supporting structures, the linear-elastic region should not be exceeded.

The calculation of deformations under load is described by Hooke’s law of elasticity

Basic knowledge

Extension

ExtensionCompression

Compression

Tensile stress results in the extension of the outer strands, whereas compressive stress results in compression of the outer strands. The neutral strand (green) passes through the centroid and is neither compressed nor extended.

M moment, F force

Torsional stress leads to deformation of the bar.

Mt twisting moment, F force, φ twisting angle, τ shear stress

σ stress, E elastic modulus, ε strain, F force, A area

Elastic modulus for various materials

Material E in N/mm²

steel 2,1 · 105

aluminium 0,7 · 105

concrete 0,3 · 105

wood along the grain 0,7...1,6 · 104

cast iron 1,0 · 105

copper 1,2 · 105

brass 1,0 · 105

φσ = E · ε =

The elastic region is divided into a linear-elastic component a, where the strain is proportional to the stress and is reversible and a nonlinear-elastic component b, where the strain is not proportional to the stress but is still reversible. In the plastic region, the strain is not reversible and the deformation remains even after the force has been removed.

Elastic region of the stressstrain diagram Stressstrain diagram

E =ΔσΔε

Rm1 2 3

σ stress, ε strain, E elastic modulus, Rp proportional limit, Re yield strength, Rm tensile strength, 1 elastic region, 2 plastic region, 3 constriction to fracture, a linear-elastic component, b nonlinear-elastic component, c Hooke’s straight line

081080

Engineering mechanics – strength of materialsElastic deformations gunt2 gunt

SE 110.14Elastic line of a beam

1 pinned support, 2 weight, 3 fixed support with clamp, 4 beam, 5 SE 112 frame, 6 dialgauge

Bending on a cantilever beam: f draw down of the beam’s end, x distance, a unloaded regionwith linear elastic line, b loaded region

Elastic line of a cantilever beam: f draw down, x distance; red: calculated values, blue: meas-ured values

Specification

[1] determine the elastic line[2] beams of different materials: steel, brass and alu-

minium[3] 2 pinned supports[4] 1 fixed support with clamp[5] dial gauges for recording the deformation of the

beam[6] storage system for parts[7] experiment setup in the SE 112 mounting frame

Technical data

Beams• steel, LxWxH: 1000x20x3mm• brass, LxWxH: 1000x20x6mm• aluminium, LxWxH: 1000x20x6mm

Weights• 2x 1N (hanger)• 10x 1N• 6x 5N

Measuring ranges• travel: 0…20mm• graduation: 0,01mm

LxWxH: 1170x480x178mm (storage system)Weight: approx. 42kg (total)

Scope of delivery

3 beams2 pinned supports1 fixed support with clamp2 dial gauges with bracket1 set of weights1 storage system with foam inlay1 set of instructional material

Order number 022.11014

G.U.N.T. Gerätebau GmbH, Hanskampring 15-17, D-22885 Barsbüttel, Telefon (040) 67 08 54-0, Fax (040) 67 08 54-42, Email [email protected], Web www.gunt.de

We reserve the right to modify our products without any notifications. Page 2/3 - 12.2016

guntSE 110.14Elastic line of a beam

The illustration shows SE 110.14 in the SE 112 mounting frame.

Description

• beams of different materials:steel, brass and aluminium

Beams are important design elementsin mechanical engineering and buildingconstruction that can deform underload. Beams are subjected to load trans-versely in the axial direction, which leadsto deflection. In linear–elastic materialbehaviour, the bending line, also knownas elastic line, is used to determine thedeflection of beams. Deflection can bedetermined at any point on the beam us-ing the influence coefficients and Max-well–Betti’s commutative theory.

The SE 110.14 unit is used to determ-ine the deformation of a bending beam.To do this, a beam is studied under vary-ing loads, different support conditionsand static overdetermination. The elast-ic line is determined by calculation andverified by experiment.

The experimental setup includes threebeams made of different materials. Twopinned supports and one fixed supportwith clamp are available. The dial gaugesrecord the resulting deformation of thebeam. The parts of the experiment areclearly laid out and securely housed in astorage system.

The entire experimental setup is con-structed in the SE 112 mounting frame.

Learning objectives/experiments

• elastic line under varying load• elastic line under various support con-

ditions• demonstration of Maxwell–Betti’s the-

orem• elastic line and support forces in static-

ally indeterminate systems

SE 110.14Elastic line of a beam

1 pinned support, 2 weight, 3 fixed support with clamp, 4 beam, 5 SE 112 frame, 6 dialgauge

Bending on a cantilever beam: f draw down of the beam’s end, x distance, a unloaded regionwith linear elastic line, b loaded region

Elastic line of a cantilever beam: f draw down, x distance; red: calculated values, blue: meas-ured values

Specification

[1] determine the elastic line[2] beams of different materials: steel, brass and alu-

minium[3] 2 pinned supports[4] 1 fixed support with clamp[5] dial gauges for recording the deformation of the

beam[6] storage system for parts[7] experiment setup in the SE 112 mounting frame

Technical data

Beams• steel, LxWxH: 1000x20x3mm• brass, LxWxH: 1000x20x6mm• aluminium, LxWxH: 1000x20x6mm

Measuring ranges• travel: 0…20mm• graduation: 0,01mm

Scope of delivery

3 beams2 pinned supports1 fixed support with clamp2 dial gauges with bracket1 set of weights1 storage system with foam inlay1 set of instructional material

guntSE 110.14Elastic line of a beam

Description

• beams of different materials:steel, brass and aluminium

Beams are important design elementsin mechanical engineering and buildingconstruction that can deform underload. Beams are subjected to load trans-versely in the axial direction, which leadsto deflection. In linear–elastic materialbehaviour, the bending line, also knownas elastic line, is used to determine thedeflection of beams. Deflection can bedetermined at any point on the beam us-ing the influence coefficients and Max-well–Betti’s commutative theory.

The SE 110.14 unit is used to determ-ine the deformation of a bending beam.To do this, a beam is studied under vary-ing loads, different support conditionsand static overdetermination. The elast-ic line is determined by calculation andverified by experiment.

The experimental setup includes threebeams made of different materials. Twopinned supports and one fixed supportwith clamp are available. The dial gaugesrecord the resulting deformation of thebeam. The parts of the experiment areclearly laid out and securely housed in astorage system.

The entire experimental setup is con-structed in the SE 112 mounting frame.

• elastic line under varying load• elastic line under various support con-

ditions• demonstration of Maxwell–Betti’s the-

orem• elastic line and support forces in static-

ally indeterminate systems

WP 950Deformation of straight beams

1 beam, 2 weight, 3 support with clamp fixing, 4 support with force gauge, 5 dial gauge,6 adjustable hook

Elastic lines for statically determinate (left) and indeterminate (right) cases: 1 single-spanbeam with fixed and movable support, 2 cantilever, 3 beam with 2 fixed supports,4 propped cantilever

Superposition principle: the total elastic line of the statically indeterminate beam (left) is thesum of the deformations of the external force at the support (right)

Specification

[1] elastic lines of statically determinate and indeterm-inate beams under various clamping conditions

[2] 3 steel beams with different cross-sections[3] 1 brass and 1 aluminium beam[4] 3 articulated, height-adjustable supports with force

gauge[5] 1 support with clamp fixing[6] force gauges can be zeroed[7] 3 dial gauges to record deformations[8] weights with adjustable hooks[9] anodised aluminium section frame housing the ex-

periment[10] storage system to house the components

Technical data

Beam• length: 1000mm• cross-sections: 3x20mm (steel), 4x20mm (steel),

6x20mm (steel, brass, aluminium)

Frame opening: 1320x480mm

Measuring ranges• force: ±50N, graduation: 1N• travel: 0…20mm, graduation: 0,01mm

Weights• 4x 2,5N (hanger)• 4x 2,5N• 16x 5N

LxWxH: 1400x400x630mm (frame)Weight: approx. 37kgLxWxH: 1170x480x178mm (storage system)Weight: approx. 12kg (storage system)

Scope of delivery

1 frame5 beams4 supports1 set of weights3 dial gauges1 storage system with foam inlay1 set of instructional material

guntWP 950Deformation of straight beams

Description

• deformation of a beam on two ormore supports under point loads(e.g. single-span beam)

• deformation of a cantilever beamunder point loads

• statically determinate or inde-terminate systems

Beams are key structural elements inmechanical engineering and in construc-tion. A beam is a bar-shaped componentin which the dimensions of the cross-section are much smaller than thelength and which is subjected to loadalong and perpendicular to its longitudin-al axis. The load perpendicular to the lon-gitudinal axis causes a deformation ofthe beam – that is, bending. Based onits size, the beam is viewed as a one-di-mensional model.

The science of the strength of materialsdeals with stress and strain resultingfrom the application of load to a com-ponent. Many fundamental principles ofthe strength of materials can be illus-trated well by a straight beam.

The beam under investigation inWP 950 can be supported in differentways. This produces statically determin-ate and indeterminate systems whichare placed under load by differentweights. The load application points aremovable. Three dial gauges record theresulting deformation. Three articulatedsupports with integral force gauges in-dicate the support reactions directly.The articulated supports are height-ad-justable, so as to compensate for the in-fluence of the dead- weight of the beamunder investigation. A fourth supportclamps the beam in place.

Five beams of different thicknesses andmade of different materials demon-strate the influence of the geometry andof the modulus of elasticity on the de-formation of the beam under load.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged in theframe.

• investigation of the deflection for stat-ically determinate and statically inde-terminate straight beams· cantilever beam· single-span beam, dual- or triple-span

beam· formulation of the differential equa-

tion for the elastic line• deflection on a cantilever beam· measurement of deflection at the

force application point• deflection of a dual-span beam on

three supports· measurement of the support reac-

tions· measurement of the deformations

• influence of the material (modulus ofelasticity) and the beam cross-section(geometry) on the elastic line

• Maxwell-Betti coefficients and law• application of the principle of virtual

work on statically determinate and in-determinate beams

• determination of lines of influence· arithmetically· qualitatively by way of force method

(Müller-Breslau)

1 beam, 2 weight, 3 support with clamp fixing, 4 support with force gauge, 5 dial gauge,6 adjustable hook

Elastic lines for statically determinate (left) and indeterminate (right) cases: 1 single-spanbeam with fixed and movable support, 2 cantilever, 3 beam with 2 fixed supports,4 propped cantilever

Superposition principle: the total elastic line of the statically indeterminate beam (left) is thesum of the deformations of the external force at the support (right)

Specification

[1] elastic lines of statically determinate and indeterm-inate beams under various clamping conditions

[2] 3 steel beams with different cross-sections[3] 1 brass and 1 aluminium beam[4] 3 articulated, height-adjustable supports with force

gauge[5] 1 support with clamp fixing[6] force gauges can be zeroed[7] 3 dial gauges to record deformations[8] weights with adjustable hooks[9] anodised aluminium section frame housing the ex-

periment[10] storage system to house the components

Technical data

Beam• length: 1000mm• cross-sections: 3x20mm (steel), 4x20mm (steel),

6x20mm (steel, brass, aluminium)

Frame opening: 1320x480mm

Measuring ranges• force: ±50N, graduation: 1N• travel: 0…20mm, graduation: 0,01mm

LxWxH: 1400x400x630mm (frame)Weight: approx. 37kgLxWxH: 1170x480x178mm (storage system)Weight: approx. 12kg (storage system)

Scope of delivery

1 frame5 beams4 supports1 set of weights3 dial gauges1 storage system with foam inlay1 set of instructional material

guntWP 950Deformation of straight beams

Description

• deformation of a beam on two ormore supports under point loads(e.g. single-span beam)

• deformation of a cantilever beamunder point loads

• statically determinate or inde-terminate systems

Beams are key structural elements inmechanical engineering and in construc-tion. A beam is a bar-shaped componentin which the dimensions of the cross-section are much smaller than thelength and which is subjected to loadalong and perpendicular to its longitudin-al axis. The load perpendicular to the lon-gitudinal axis causes a deformation ofthe beam – that is, bending. Based onits size, the beam is viewed as a one-di-mensional model.

The science of the strength of materialsdeals with stress and strain resultingfrom the application of load to a com-ponent. Many fundamental principles ofthe strength of materials can be illus-trated well by a straight beam.

The beam under investigation inWP 950 can be supported in differentways. This produces statically determin-ate and indeterminate systems whichare placed under load by differentweights. The load application points aremovable. Three dial gauges record theresulting deformation. Three articulatedsupports with integral force gauges in-dicate the support reactions directly.The articulated supports are height-ad-justable, so as to compensate for the in-fluence of the dead- weight of the beamunder investigation. A fourth supportclamps the beam in place.

Five beams of different thicknesses andmade of different materials demon-strate the influence of the geometry andof the modulus of elasticity on the de-formation of the beam under load.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged in theframe.

• investigation of the deflection for stat-ically determinate and statically inde-terminate straight beams· cantilever beam· single-span beam, dual- or triple-span

beam· formulation of the differential equa-

tion for the elastic line• deflection on a cantilever beam· measurement of deflection at the

force application point• deflection of a dual-span beam on

three supports· measurement of the support reac-

tions· measurement of the deformations

• influence of the material (modulus ofelasticity) and the beam cross-section(geometry) on the elastic line

• Maxwell-Betti coefficients and law• application of the principle of virtual

work on statically determinate and in-determinate beams

• determination of lines of influence· arithmetically· qualitatively by way of force method

(Müller-Breslau)

SE 110.47Methods to determine the elastic line

1 deflection roller with fixture, 2 weight, 3 dial gauge, 4 support with clamp fixing and dialgauge, 5 support with force gauge, 6 beam, 7 device to generate the bending moment,8 frame SE 112

Bending moment characteristic (green/yellow) and elastic line (red) for statically determin-ate beams: 1 single-span beam with mid point load, 2 cantilever beam with point load,3 single-span beam with bending moment as load;MA bending moment on support A, MF bending moment resulting from force F, M bendingmoment, α, β angle of inclination

Bending moment characteristic (green/yellow) and elastic line (red) for statically indeterm-inate beams with centralised point load

Specification

[1] comparison of different methods to determine theelastic line

[2] statically determinate or indeterminate beam[3] 2 supports with clamp fixing, optionally as articu-

lated support with measurement of angle of inclina-tion or clamp fixing

[4] 1 articulated support with force gauge[5] device to generate a bending moment[6] dial gauge with generation of moment to measure

the angle of inclination[7] dial gauge to record the deformations of the beam[8] weights to subject the beam to point loads or mo-

ment[9] weights to determine the clamping moments on

the supports with clamp fixings[10] storage system to house the components[11] experimental setup in frame SE 112

Technical data

Beam• length: 1000mm• cross-section: 20x4mm• material: steel

Measuring ranges• force: ±50N, graduation: 1N• travel: 0…0,20mm, graduation: 0,01mm

Scope of delivery

3 beams2 supports with clamp fixings1 support with force gauge1 device to generate the bending moment1 set of weights3 deflection rollers with fixture3 cables2 dial gauges with bracket1 storage system with foam inlay1 set of instructional material

guntSE 110.47Methods to determine the elastic line

The picture shows SE 110.47 in a frame similar to SE 112.

Description

• comparison of different methodsto determine the elastic line: vir-tual work, Mohr’s analogy

• statically determinate and inde-terminate systems

• various load cases: point load orbending moment

Beams are key structural elements inmechanical engineering and in construc-tion which are subject to deformationunder load. In the case of a simple beamthis deformation can be predicted byvarious methods, such as the principleof virtual work.

The beam under investigation inSE 110.47 can be supported by differ-ent bearing methods. Two supports withclamp fixings and an articulated sup-ports with a force gauge are provided torealise statically determinate or inde-terminate systems. The two supportswith clamp fixings are provided with dialgauges and can also be used as articu-lated supports. These dial gauges en-able the angle of inclination of the beamto be determined at the support. A thirddial gauge records the deflection of thebeam at a random point.

A device is additionally provided to gen-erate a bending moment at a randompoint on the beam. A fourth dial gaugerecords the angle of inclination of thedevice.

The beam is placed under load byweights (point load and coupled forcesto generate the bending moment). Theclamping moment on the supports canbe determined by means of weights.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged in theframe SE 112.

• elastic lines for statically determinateor indeterminate beams under load

• determination of the elastic line of abeam by· the principle of virtual work (calcula-

tion)· Mohr’s analogy (area moment meth-

od devised by Mohr; graphical rep-resentation)

• application of the principle of superpos-ition

• determination of the· maximum deflection of the beam· angle of inclination of the beam

• comparison between calculated andmeasured values for angle of inclina-tion and deflection

SE 110.47Methods to determine the elastic line

1 deflection roller with fixture, 2 weight, 3 dial gauge, 4 support with clamp fixing and dialgauge, 5 support with force gauge, 6 beam, 7 device to generate the bending moment,8 frame SE 112

Bending moment characteristic (green/yellow) and elastic line (red) for statically determin-ate beams: 1 single-span beam with mid point load, 2 cantilever beam with point load,3 single-span beam with bending moment as load;MA bending moment on support A, MF bending moment resulting from force F, M bendingmoment, α, β angle of inclination

Bending moment characteristic (green/yellow) and elastic line (red) for statically indeterm-inate beams with centralised point load

Specification

[1] comparison of different methods to determine theelastic line

[2] statically determinate or indeterminate beam[3] 2 supports with clamp fixing, optionally as articu-

lated support with measurement of angle of inclina-tion or clamp fixing

[4] 1 articulated support with force gauge[5] device to generate a bending moment[6] dial gauge with generation of moment to measure

the angle of inclination[7] dial gauge to record the deformations of the beam[8] weights to subject the beam to point loads or mo-

ment[9] weights to determine the clamping moments on

the supports with clamp fixings[10] storage system to house the components[11] experimental setup in frame SE 112

Technical data

Beam• length: 1000mm• cross-section: 20x4mm• material: steel

Measuring ranges• force: ±50N, graduation: 1N• travel: 0…0,20mm, graduation: 0,01mm

Scope of delivery

3 beams2 supports with clamp fixings1 support with force gauge1 device to generate the bending moment1 set of weights3 deflection rollers with fixture3 cables2 dial gauges with bracket1 storage system with foam inlay1 set of instructional material

guntSE 110.47Methods to determine the elastic line

Description

• comparison of different methodsto determine the elastic line: vir-tual work, Mohr’s analogy

• statically determinate and inde-terminate systems

• various load cases: point load orbending moment

Beams are key structural elements inmechanical engineering and in construc-tion which are subject to deformationunder load. In the case of a simple beamthis deformation can be predicted byvarious methods, such as the principleof virtual work.

The beam under investigation inSE 110.47 can be supported by differ-ent bearing methods. Two supports withclamp fixings and an articulated sup-ports with a force gauge are provided torealise statically determinate or inde-terminate systems. The two supportswith clamp fixings are provided with dialgauges and can also be used as articu-lated supports. These dial gauges en-able the angle of inclination of the beamto be determined at the support. A thirddial gauge records the deflection of thebeam at a random point.

A device is additionally provided to gen-erate a bending moment at a randompoint on the beam. A fourth dial gaugerecords the angle of inclination of thedevice.

The beam is placed under load byweights (point load and coupled forcesto generate the bending moment). Theclamping moment on the supports canbe determined by means of weights.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged in theframe SE 112.

• elastic lines for statically determinateor indeterminate beams under load

• determination of the elastic line of abeam by· the principle of virtual work (calcula-

tion)· Mohr’s analogy (area moment meth-

od devised by Mohr; graphical rep-resentation)

• determination of the· maximum deflection of the beam· angle of inclination of the beam

• comparison between calculated andmeasured values for angle of inclina-tion and deflection

SE 110.29Torsion of bars

1 bar, 2 support block with clamping chuck, 3 angle indicator, 4 disk to apply moment,5 weight, 6 deflection roller with fixture, 7 frame SE 112, A: clamping chuck

Torsion of a bar and measurement of the angles α1 and α2, right: shear stresses on the cir-cular section

Deformation of a rectangular surface element (white): 1 round bar, not deformed, 2 roundbar, twisted, 3 square tube, not deformed, 4 square tube, twisted

Specification

[1] elastic torsion of bars[2] 2 movable support blocks with clamping chuck for

mounting of bars, 1 fixed and 1 movable support[3] 2 movable angle indicators clampable to the bar[4] 4 bars: round bar with full cross-section, tube, lon-

gitudinally slotted tube, square tube[5] application of load to the bar by a mass disk, a de-

flection roller and weights[6] storage system to house the components[7] experimental setup in frame SE 112

Technical data

4 brass bars, L=695mm• round bar, d=6mm• tube, slotted tube d=6mm, wall thickness: 1mm, slot

width: 0,3mm• square tube WxH: 6mm, wall thickness: 1mm

Disk to apply the load• effective radius: 110mm

Angle indicator• measuring range: ±90°• graduation: 1°

Scope of delivery

2 support blocks with clamping chuck2 angle indicators4 bars1 deflection roller with fixture1 cable1 set of weights2 hexagon socket wrenches1 storage system with foam inlay1 set of instructional material

guntSE 110.29Torsion of bars

Description

• elastic torsion of a bar under atorque

• round bar, tube, longitudinallyslotted tube and square tube astest bars

• indication of the angle of twist attwo random points on the bar

Torsion occurs primarily on axles anddrive shafts in motor vehicles and ma-chines. The torsion occurring in theshaft cause cross-sections of the shaftto be pushed together around the longit-udinal axis. When a torque is applied toa shaft the cross-section remains flatand no warpage occurs.

In the event of minor torsion the lengthand radius remain unchanged. Thestraight lines on the outer circumfer-ence of the shaft running parallel to theaxis become helixes. Non-circular cross-sections mostly result in warpage.

SE 110.29 investigates the torsion of abar under a torque. The bar is clampedinto two movable support blocks by achuck. The torque is generated by a cir-cular disk, a deflection roller and aweight. The clamping length and torquecan be varied. The resultant torsion isread-off at two random points on the barby means of angle indicators.

The fundamentals of elastic torsion areillustrated by the round bar. Three otherbars are provided in order to investigatespecial cases: two thin-walled enclosedsections (a tube and a square tube) anda longitudinally slotted tube (thin-walledopen section).

All the component elements of the ex-periment are clearly laid-out and housedsecurely in a storage system. The com-plete experimental setup is arranged inthe frame SE 112.

• 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· round bar with full cross-section· tube· tube, longitudinally slotted· square tube

• calculation of angle of twist• comparison of calculated and meas-

ured angle of twist

SE 110.29Torsion of bars

1 bar, 2 support block with clamping chuck, 3 angle indicator, 4 disk to apply moment,5 weight, 6 deflection roller with fixture, 7 frame SE 112, A: clamping chuck

Torsion of a bar and measurement of the angles α1 and α2, right: shear stresses on the cir-cular section

Deformation of a rectangular surface element (white): 1 round bar, not deformed, 2 roundbar, twisted, 3 square tube, not deformed, 4 square tube, twisted

Specification

[1] elastic torsion of bars[2] 2 movable support blocks with clamping chuck for

mounting of bars, 1 fixed and 1 movable support[3] 2 movable angle indicators clampable to the bar[4] 4 bars: round bar with full cross-section, tube, lon-

gitudinally slotted tube, square tube[5] application of load to the bar by a mass disk, a de-

flection roller and weights[6] storage system to house the components[7] experimental setup in frame SE 112

Technical data

4 brass bars, L=695mm• round bar, d=6mm• tube, slotted tube d=6mm, wall thickness: 1mm, slot

width: 0,3mm• square tube WxH: 6mm, wall thickness: 1mm

Disk to apply the load• effective radius: 110mm

Angle indicator• measuring range: ±90°• graduation: 1°

Scope of delivery

2 support blocks with clamping chuck2 angle indicators4 bars1 deflection roller with fixture1 cable1 set of weights2 hexagon socket wrenches1 storage system with foam inlay1 set of instructional material

guntSE 110.29Torsion of bars

Description

• elastic torsion of a bar under atorque

• round bar, tube, longitudinallyslotted tube and square tube astest bars

• indication of the angle of twist attwo random points on the bar

Torsion occurs primarily on axles anddrive shafts in motor vehicles and ma-chines. The torsion occurring in theshaft cause cross-sections of the shaftto be pushed together around the longit-udinal axis. When a torque is applied toa shaft the cross-section remains flatand no warpage occurs.

In the event of minor torsion the lengthand radius remain unchanged. Thestraight lines on the outer circumfer-ence of the shaft running parallel to theaxis become helixes. Non-circular cross-sections mostly result in warpage.

SE 110.29 investigates the torsion of abar under a torque. The bar is clampedinto two movable support blocks by achuck. The torque is generated by a cir-cular disk, a deflection roller and aweight. The clamping length and torquecan be varied. The resultant torsion isread-off at two random points on the barby means of angle indicators.

The fundamentals of elastic torsion areillustrated by the round bar. Three otherbars are provided in order to investigatespecial cases: two thin-walled enclosedsections (a tube and a square tube) anda longitudinally slotted tube (thin-walledopen section).

• 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· round bar with full cross-section· tube· tube, longitudinally slotted· square tube

• calculation of angle of twist• comparison of calculated and meas-

ured angle of twist

WP 100Deformation of bars under bending or torsion

1 beam, 2 clamp fixing for bending test, 3 support block, 4 weight, 5 device to generate thetwisting moment in the torsion test, 6 support for bending test, 7 clamping chuck for tor-sion test, 8 dial gauge

Beam deflection of a statically determinate (left) and indeterminate (right) system:1 cantilever beam, 2 simply supported beam, 3 propped cantilever, 4 built in beam

Torsion on round bar: F applied force, a lever arm, r radius, γ shear angle, φ angle of twist

Specification

[1] elastic deformation of bars under bending or tor-sion

[2] bending tests with statically determinate and inde-terminate systems

[3] torsion tests with a statically determinate system[4] supports in the bending test may be clamped or

free[5] 2 adjustable blocks with clamping chuck for torsion

tests and supports for bending tests[6] weights to generate the bending or twisting mo-

ment[7] dial gauge with bracket[8] storage system to house the components

Technical data

17 bars for bending tests• material: aluminium, steel, brass, copper• height with LxW 510x20mm: h=3…10mm• width with LxH 510x5mm: w=10…30mm• length with WxH 20x4mm: l=210…510mm• LxWxH: 20x4x510mm (Al, St, brass, Cu)• LxWxH: 10x10x510mm (aluminium)

22 torsion bars• material: aluminium, steel, brass, copper• length with d=10mm: 50…640mm (aluminium)• dxL: 10x50mm/10x340mm (aluminium, steel, cop-

per, brass)• diameter with L=50/340mm: d=5…12mm (steel)

Dial gauge• 0…10mm, graduation: 0,01mm

Tape measure• graduation: 0,01m

Weights• 1x 1N (hanger)• 1x 1N, 1x 4N, 1x 5N, 1x 9N

LxWxH: 1000x250x200mmWeight: approx. 18kgLxWxH: 1170x480x207mm (storage system)Weight: approx. 12kg (storage system)

Scope of delivery

1 frame2 support blocks1 device to generate the twisting moment17 bars for bending test22 torsion bars1 dial gauge with bracket, 1 tape measure1 set of weights including hanger2 hexagon socket wrenches1 storage system with foam inlay1 set of instructional material

guntWP 100Deformation of bars under bending or torsion

Description

• elastic deformation of staticallydeterminate or indeterminatebeams under bending load

• elastic torsion of round bars un-der twisting moment

• influence of material, cross-sec-tion and clamping length on de-formation

Bending and torsion are typical loads towhich components are subjected. Theresultant stresses and deformationscan lead to failure of the component. Anumber of different factors play a role inthis, including the material, the cross-section of the bar, the clamping lengthand the method of bearing support.

WP 100 investigates the influence ofthese factors on the deformation of abar under bending load or twisting mo-ment. A set of test bars has been as-sembled so as to permit direct compar-ison of measuring results. The bar underinvestigation is fixed to two movable sup-port blocks and loaded down by aweight.

A dial gauge records the resulting de-formation. The support blocks includeclamping chucks to hold the torsion barsand supports for the bars in the bendtest. The supports offer a range ofclamping options, enabling statically de-terminate or indeterminate bearing sup-ports to be investigated.

The twisting moment is applied by adevice mounted on a support block. Thepoint of load application to generate thebending moment is adjustable.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged on theframe.

• bending tests· determination of the modulus of

elasticity· statically determinate systems

(beam mounted on two supports;cantilever beam)

· statically indeterminate systems(dual-span beam)

· deformation of a beam dependenton material, geometry (sectionwidth, height and length), type of sup-port and length of span

· formulation of proportional relation-ships for the deformation

• torsion tests· determination of the shear modulus

of various materials· angle of twist dependent on clamp-

ing length, bar diameter· formulation of proportional relation-

ships for the angle of twist

WP 100Deformation of bars under bending or torsion

1 beam, 2 clamp fixing for bending test, 3 support block, 4 weight, 5 device to generate thetwisting moment in the torsion test, 6 support for bending test, 7 clamping chuck for tor-sion test, 8 dial gauge

Beam deflection of a statically determinate (left) and indeterminate (right) system:1 cantilever beam, 2 simply supported beam, 3 propped cantilever, 4 built in beam

Torsion on round bar: F applied force, a lever arm, r radius, γ shear angle, φ angle of twist

Specification

[1] elastic deformation of bars under bending or tor-sion

[2] bending tests with statically determinate and inde-terminate systems

[3] torsion tests with a statically determinate system[4] supports in the bending test may be clamped or

free[5] 2 adjustable blocks with clamping chuck for torsion

tests and supports for bending tests[6] weights to generate the bending or twisting mo-

ment[7] dial gauge with bracket[8] storage system to house the components

Technical data

17 bars for bending tests• material: aluminium, steel, brass, copper• height with LxW 510x20mm: h=3…10mm• width with LxH 510x5mm: w=10…30mm• length with WxH 20x4mm: l=210…510mm• LxWxH: 20x4x510mm (Al, St, brass, Cu)• LxWxH: 10x10x510mm (aluminium)

22 torsion bars• material: aluminium, steel, brass, copper• length with d=10mm: 50…640mm (aluminium)• dxL: 10x50mm/10x340mm (aluminium, steel, cop-

per, brass)• diameter with L=50/340mm: d=5…12mm (steel)

Dial gauge• 0…10mm, graduation: 0,01mm

Tape measure• graduation: 0,01m

Weights• 1x 1N (hanger)• 1x 1N, 1x 4N, 1x 5N, 1x 9N

Scope of delivery

1 frame2 support blocks1 device to generate the twisting moment17 bars for bending test22 torsion bars1 dial gauge with bracket, 1 tape measure1 set of weights including hanger2 hexagon socket wrenches1 storage system with foam inlay1 set of instructional material

guntWP 100Deformation of bars under bending or torsion

Description

• elastic deformation of staticallydeterminate or indeterminatebeams under bending load

• elastic torsion of round bars un-der twisting moment

• influence of material, cross-sec-tion and clamping length on de-formation

Bending and torsion are typical loads towhich components are subjected. Theresultant stresses and deformationscan lead to failure of the component. Anumber of different factors play a role inthis, including the material, the cross-section of the bar, the clamping lengthand the method of bearing support.

WP 100 investigates the influence ofthese factors on the deformation of abar under bending load or twisting mo-ment. A set of test bars has been as-sembled so as to permit direct compar-ison of measuring results. The bar underinvestigation is fixed to two movable sup-port blocks and loaded down by aweight.

A dial gauge records the resulting de-formation. The support blocks includeclamping chucks to hold the torsion barsand supports for the bars in the bendtest. The supports offer a range ofclamping options, enabling statically de-terminate or indeterminate bearing sup-ports to be investigated.

The twisting moment is applied by adevice mounted on a support block. Thepoint of load application to generate thebending moment is adjustable.

The various elements of the experimentare clearly laid-out and housed securelyin a storage system. The complete ex-perimental setup is arranged on theframe.

• bending tests· determination of the modulus of

elasticity· statically determinate systems

(beam mounted on two supports;cantilever beam)

· statically indeterminate systems(dual-span beam)

· deformation of a beam dependenton material, geometry (sectionwidth, height and length), type of sup-port and length of span

· formulation of proportional relation-ships for the deformation

• torsion tests· determination of the shear modulus

of various materials· angle of twist dependent on clamp-

ing length, bar diameter· formulation of proportional relation-

ships for the angle of twist

SE 110.20Deformation of frames

1 U-shaped frame, 2 weight, 3 short clamping pillar, 4 roller bearing, 5 deflection roller withfixture, 6 movable hook, 7 dial gauge, 8 frame SE 112

1 S-shaped frame, 2 long clamping pillar

Example deformations of the statically indeterminate frame under load:red: deformed frame; black: frame under no load

Specification

[1] investigation of the deformation of steel frames un-der load

[2] 1 U-shaped and 1 S-shaped frame[3] statically determinate or statically indeterminate

bearing support possible[4] 1 long and 1 short clamping pillar[5] roller bearing for statically indeterminate support[6] weights with a movable hook to adjust to any load

application point[7] dial gauges record the deformation of the investig-

ated frame under load[8] storage system to house the components[9] experimental setup in frame SE 112

Technical data

Frame made of steel• edge length: 600mm• cross-section: 20x10mm• U-shaped: 600x600mm• S-shaped: 600x600mm

Dial gauges• measuring range: 0…20mm• graduation: 0,01mm

Scope of delivery

2 frames (1x U-shaped, 1x S-shaped)2 clamping pillars (1x long, 1x short)1 support1 set of weights with movable hooks1 deflection roller with fixture1 cable2 dial gauges with bracket1 storage system with foam inlay1 set of instructional material

guntSE 110.20Deformation of frames

Description

• elastic deformation of a staticallydeterminate or indeterminateframe under point load

• U-shaped and S-shaped frame• principle of virtual work to calcu-

late the deformation and supportreaction in a statically indeterm-inate system

A frame is a bent beam with rigidcorners which creates a so-called struc-ture gauge. This means that it spans agap while at the same time creatingheight.

SE 110.20 includes a typical U-shapedframe, such as is used in the construc-tion of halls for example. One end isclamped into place, while the other canbe loosely mounted. When the non-clamped end remains free, the staticallydeterminate frame is investigated. Aroller bearing on the non-clamped endcreates a statically indeterminate frame.The frame is placed under load byweights. The load application points aremovable. Two dial gauges record the de-formations of the frame under load.

By applying various methods (first-orderelasticity theory; the principle of super-position; and the principle of virtualwork), the bending moment character-istics are ascertained for a statically de-terminate and indeterminate frame.From these characteristic curves and achart for integrals (coupling table) thedifferential equation of the bend line isformulated. From the bend line and itsderivations, displacements and the sup-port force on the movable support canbe calculated.

A second, S-shaped frame can be usedto show that the various methods areapplicable to any kind of frame. All thecomponent elements of the experimentare clearly laid-out and housed securelyin a storage system.

The complete experimental setup is ar-ranged in the frame SE 112.

• relationship between load applicationand deformation on the frame

• differences between statically determ-inate and statically indeterminateframes

• familiarisation with the first-orderelasticity theory for statically determin-ate and indeterminate systems

• application of the principle of virtualwork on statically determinate andstatically indeterminate frames· determination of a deformation by

the principle of virtual forces· determination of a load by the prin-

ciple of virtual displacement• comparison of calculated and meas-

ured deformations