## Statics

Statics is the study of the effect of forces on rigid bodies, which are in quilibrium. The main task of static analysis is to determine the equilibrium of the forces applied on a body or a mechanical system.

The equilibrium conditions of statics state that a body at rest remains at rest if the sum of all forces and moments acting on that body is zero. Determining the forces and moments is the basis for the design and dimensioning of structures and components.

Demonstration of force and moment equilibrium in a mechanical force system

##### Learning objectives/experiments

- accumulation and resolution of forces with force parallelogram
- equilibrium of forces
- law of levers, determination of moments and equilibrium of moments
- combined lever systems
- forces in bearings

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Measurement and demonstration of spring deflection, inclined plane and mechanical friction

##### Learning objectives/experiments

- elastic deflection of a helical spring (Hooke’s law)
- dynamic friction as a function of the normal force, contact area and surface properties of the friction body
- determination of the friction coefficient
- rolling friction
- forces on the inclined plane

Construction and mode of operation of three different pulley blocks

##### Learning objectives/experiments

- setup and principle of pulley blocks with 4 pulleys and with 6 pulleys; differential pulley block
- principle of “simple machines”: force transmission, lifting work and potential energy

Mode of operation of single-stage and multistage toothed gear mechanisms

##### Learning objectives/experiments

- transmission ratio of speed and moment on a single-stage gear
- influence of intermediate wheels on the direction of rotation
- transmission ratio on a two-stage gear
- conversion of rotation into linear motion and vice versa

Graphical and experimental determination of forces in a planar central force system

##### Learning objectives/experiments

- graphical breakdown of forces by force parallelogram
- determination of the bar forces on various jib forms
- comparison of: measuring result – calculation – graphical method

Resolution of forces in a simple bar structure

##### Learning objectives/experiments

- measurement of bar forces
- calculation of bar forces by the method of joints
- comparison: measuring result – calculation – graphical method

Investigation of applied forces, generated moments and equilibrium

##### Learning objectives/experiments

- fundamentals of the equilibrium of moments: applied forces, generated moments and equilibrium
- action of forces dependent on the lever arm

Experimental investigation of the important principle of free vectors in statics

##### Learning objectives/experiments

- experimental development of the core principle of “freeing” in statics
- calculation of the support forces for a given position of the clamp weight and for a known angle of inclination
- application of the 1
^{st}and 2^{nd}equilibrium conditions in statics - and full compensation of the support forces by cable forces
- how does the clamp weight position affect the support forces

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Clear demonstration of the equilibrium of moments

##### Learning objectives/experiments

- fundamentals of the equilibrium of moments: acting forces, generated moments and equilibrium
- effect of forces as a function of pulley diameter

Equilibrium of forces and moments and the demonstration of the force reduction on a differential pulley block

##### Learning objectives/experiments

- fundamentals of the equilibrium of moments: acting forces, generated moments and equilibrium
- relation between power savings and cable route

In statics, the internal reactions show the counteraction of forces and moments within a component in response to the action of external forces. Free body diagrams are the main way in which the internal force states are represented in rods, beams and cables.

Application of the method of sections to determine internal reactions of the beam

##### Learning objectives/experiments

- calculation of the reactions arising from the static conditions of equilibrium
- application of the method of sections to calculate the internal forces and moments
- under a point load
- under multiple point loads

- calculation of the shear force diagram

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Application of the method of sections to determine the shear force

##### Learning objectives/experiments

- calculation of the reactions arising from the static conditions of equilibrium
- application of the method of sections to calculate the internal forces
- under a point load
- under multiple point loads

- calculation of the shear force diagram

….

Application of the method of sections to determine the bending moment

##### Learning objectives/experiments

- calculation of the reactions arising from the static conditions of equilibrium
- application of the method of sections to calculate the internal moments
- under a point load
- under multiple point loads

- calculation of the bending moment curve

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Catenary of a free-hanging cable under dead-weight

##### Learning objectives/experiments

- determination of the catenary of a free-hanging cable
- under dead-weight only
- with additional weights
- with a symmetrical setup (chain wheels at same height)
- with an unsymmetrical setup

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Various methods are presented for determining bar forces in plane trusses. Calculation method such as the method of joints and Ritter’s method of sections as well as a graphic method, the Cremona diagram.

Using strain gauge technology to measure bar forces

##### Learning objectives/experiments

- measurement of the bar forces in various single plane trusses
- dependency of the bar forces on the external force
- magnitude
- direction
- point of application

….

Comparison of forces in statically determinate and statically overdeterminate trusses

##### Learning objectives/experiments

- measurement of the bar forces in a statically determinate and a statically overdeterminate, single plane truss
- distribution of forces in the single plane truss dependent on the use of a surplus bar
- dependency of the bar forces on the external force
- magnitude, direction, point of application

- comparison of measuring results with mathematical methods

….

Investigation of bar forces under different load cases

##### Learning objectives/experiments

- measurement of the bar forces in a single plane truss, Howe type
- dependency of bar forces on theexternal force
- magnitude, direction, point ofapplication

- comparison of measuring results with mathematical and graphicalmethods
- method of joints

….

- method of joints

Bars with strain gauge full bridges to measure bar stress

##### Learning objectives/experiments

- calculation of tensile and compressive forces in bars in different load cases: straight and inclined forces
- comparison of measuring results with mathematical methods
- method of joints
- Ritter’s method of sections
- Cremona diagram

Experimental equipment for investigating a suspension bridge, a Gerber beam and various arches.

Supporting cable force and demonstration of bending moments between the roadway support and supporting cables

##### Learning objectives/experiments

- familiarisation with a suspension bridge
- under dead-weight
- under additional weight
- under evenly distributed load
- under unevenly distributed point loads

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Using methods of section and conditions of equilibrium of statics to determine support forces

##### Learning objectives/experiments

- familiarisation with a Gerber beam
- application of the method of sections and the conditions of equilibrium to calculate the support forces for
- point load
- distributed load
- moving load

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Symmetric and asymmetric arch subjected to point, distributed or moving loads

##### Learning objectives/experiments

- familiarisation with three-hinged arches (unsymmetrical and symmetrical)
- application of the method of sections and the conditions of equilibrium to calculate the support forces for
- point load, distributed load, moving load

- investigation of the influence of the load on the horizontal thrust in the supports
- determination of the lines of influence for the supports under a moving load

….

Differences between statically determinate and statically overdeterminate arches under load

##### Learning objectives/experiments

- mechanical principles of the parabolic arch
- differences between statically determinate and statically indeterminate arches
- measurement of the deformations of the arch under load
- measurement of the support reactions on the statically indeterminate arch under load
- calculation of the support reactions

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Friction occurs in all solid bodies that are in mutual contact and that are moved against each other. The cause of the occurring forces is, among other things, the surface roughness which causes the surfaces to interlock.

Force gauge with adjustable air damper to determine friction forces; slip/stick effect

##### Learning objectives/experiments

- difference between static and dynamic friction
- friction forces as a function of
- normal force
- sliding velocity (relative velocities of the friction partners)
- material pairing

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Stationary friction body, uniformly moving support friction surface

##### Learning objectives/experiments

- difference between static and dynamic friction
- friction forces as a function of
- normal force, material pairing, size of contact area
- sliding velocity (relative velocities of the friction partners)
- surface properties of the friction partners

….

Experiments to understand the fundamentals of mechanical friction on an inclined plane

##### Learning objectives/experiments

- determination of the friction coefficients of various material pairings
- transition from static to dynamic
- static equilibrium of forces on the inclined plane
- determination of the angle of inclination as from which sliding occurs (calculation and verification by experiment)

Investigating the influence of the angle of contact, coefficient of friction and belt force on belt drives and belt friction

##### Learning objectives/experiments

- effect of wrap angle, coefficient of friction and cable force (Eytelwein’s belt friction formula)
- comparison of flat belts and V-belts
- consequences of an unadapted V-belt groove