Statics & Mechanics of Materials - Calculative


introduction

clip 01: introduction into statics
In the first clip of statics & mechanics of materials it´s all about the definition of important quantities, such as a force or torque / moment.
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finding support reactions / forces

clip 02: beam, loaded with a force
This clip is about the different kinds of supports and how to calculate support reactions. Also the three equations of mechanical equilibrium are discussed.
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clip 03: the free body diagram
In this clip it´s all about seperating a system from ist Support to find the free body diagram.
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clip 04: beam, loaded with an inclined force
In this clip it is explained, how to split a force according the trigonometric functions in two components- to be able to calculate forces.
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clip 05: beam, loaded with an inclined force and torque
Again, it´s all about finding the support reactions. But this time, the beam is loaded by an additional torque / moment.
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clip 06: fixed beam three dimensional
This is the first clip in which we are looking at a three dimensional problem. There are two ways to find the support reactions.
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clip 07: ladder
In this clip it´s not all just about finding the support reactions, but also about the rod / pole force. It is important to seperate the system correctly.
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clip 08: lifting device
In this clip it is explained how to realize  a special rod, what proberties the rod force has and how to calculate with such a rod.
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clip 09: beam with uniformly distributed load
Here you are told how to work with a new form of load, the uniformly distributed load. We are looking for the support reactions.
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clip 10: spring system with uniformly distributed load
In this clip a linear spring occurs. It is explained what properties the spring force has and how to work with it.
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clip 11: spring system with torsion spring
At this spring system not just a linear spring occurs but also a torsion spring. Is a torsion spring treated the same as a linear one? In this clip it is solved.
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friction (static / kinematic)

clip 12: cuboid on an inclined plane
A very important topic in mechanics is friction. There is static and kinetic friction. The difference? Just whatch this clip.
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clip 13: finding an agle somewhere else / summary of forces
It is important to find an angle at another place again- in this clip you are told how to do. In Addition to that a summary of all forces and their properties is provided.
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clip 14: ladder
The ladder is a typical problem when talking about friction. It is a system that often occurs in real live- so this calculations are important. In this clip you are shown how to do.
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clip 15: cable drum
In this clip it´s all about friction once more. Since the equations are little complicated, the problem is calculated for you step by step.
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axial force / shear force / bending moment

clip 16: beam with single force
What are axial force,- shear force and bending moment? Where do they occur and why? How to draw the influence line of them? In this clips is is explained easy comprehensible.
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clip 17: beam with uniformly distributed load
In this clip it is explained, how to calculate axial force,- shear force and bending moment if the beam is loaded by a uniformly distributed load. Also we are asked for the location and amount of the maximal bending moment.
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clip 18: fixed beam with triangular uniformly distributed load
When working with a triangular uniformly distributed load you have to pay special attention on the calculations. For details whatch the Clip.
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centroid

clip 19: compound area
In this clip it´s all about finding the centroid of an area. There is an important formula we can use. It is explained here.
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clip 20: u- shaped area
In this clip it´s all about special cases when talking about centroids of areas.
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clip 21: half circle area
When looking for the centroid of an half circle area, one have to use Guldin´s rule. In this clip you will see how it works.
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moment of inertia

clip 22: rectangle
A very important property that often occurs in mechanics is the moment of inertia. In this clip it is explained what a axial,- and polar moment of inertia is, how to calculate it and also how to use Steiner´s Theorem, also known as parallel axis theorem.
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clip 23: rectangle and triangle
In this clip the calculations of a moment of inertia is practised. There is another method to find the moment of inertia via integration.
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clip 24: asymmetric I- beam
On a compound area you get an optimal practise of the calculation of a moment of inertia. But first you need the knowledge of the position of the centroid.
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deflection curve

clip 25: fixed beam with single force
A central topic of mechanics of materials is the deflection curve. It is an differential equation with special properties. This Clip is about the calculation and applicatoin  of the deflection curve.
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clip 26: statically indeterminate beam
In this clip it´s all about deflection curves again. But the system statically indeterminate. Here you will se what it means, and how the calculations change.
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method of Mohr

clip 27: beam- Mohr´s Method
This clip is about the method of Otto Mohr. A special order of the calculations must be kept.
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clip 28: beam- Mohr´s Method
In this Clip we again use Mohr´s method to find the deflection of a beam. But this time, the beam has different bending stiffnesses.
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clip 29: statically indeterminate system - Mohr´s Method
Once more this is a statically indeterminate system. But the solution should be found via Mohr´s method.
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torsion.

clip 30: fixed beam - torsion
This clip is a introduction into the topic of torsion.
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Statics & Mechanics of Materials - Graphical


equilibrium of three forces

clip 01: lifting device
In this clip- series the problems are solved graphically. Here you will learn how to do this, and what the difference between the space- and the force diagram is.
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clip 02: resulting force
In this clip it is explained how to find a resulting force out of two or more forces.
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equilibrium of four forces

clip 03: ladder
This clip is about how to graphically cut free and find a resulting force.  
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clip 04: ladder
Sometimes also springs appear in graphical examples. Get the clue in here!...coming soon 3
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method of cable polygon

clip 05: beam
In this video the method of cable polygon is explained. ...coming soon 3 It can be a useful tool, if some circumstances do not allow to use another method.
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super- position principle

clip 06: beam
In this clip the graphical super-position principle is explained. ...coming soon 3 Important is to exactly follow the single steps. Here we Show you how to do it.
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friction (static / kinematic)

clip 07: hand barrow friction
In this clip we explain how to transform the coefficient of friction...coming soon 3 to the scetch and how to draw the angle and cone of the limiting friction.
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Kinematics & Kinetics


introduction

clip 01: introduction into kinematics
This is the introductional clip into kinematics. Here it´s all about the basic quantities such as the velocity or acceleration. Also the difference between absolute and relative velocity is explained and what a rotational or translational movement is.
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absolute kinematics

clip 02: hand car (rotation / translation)
In this clip the velocity of a point is calculated via two different methods. The use of different frames of references is practised.
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clip 03: truck
In this clip it is explained how to use a geometrical connection in order to find a velocity or acceleration.
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clip 04: double pendulum
In this clip again we are looking for the velocity and acceleration of vertain points.
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clip 05: rotational movement
The acceleration of a rotational movement is equal special as important. In this clip the expressions are explained.
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relative kinematics

clip 06: kinematics of realtive motion, introduction
This clip is an introduction into the topic of kinematics of relative motion. The difference between a rotating and inertail frame of reference is explained as well as where the formulas come from.
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clip 07: crane
This clip is to practise the usage of kinematics of relative motion. What are the things to pay attention on and how to use the formulas in generell? Here are the answers.
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rolling wheel

clip 08: rolling wheel without slipping
In this clip we will have a look at the velocity distribution of a rolling wheel. The important fact: pure rolling, without slipping.
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center of mass theorem

clip 09: center of mass theorem, introduction
The center of mass theorem, as a Newtonian law, is one of the key points in mechanics. This clip is our start into the topic of kinetics.
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clip 10: roller system, center of mass theorem, plane
In this clip you learn how to apply the center of mass theorem and the simplifications of kinetics compared to kinematics are discussed.
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clip 11: spring system, relative kinematics, center of mass theorem
In this clip kinematic- and kinetic calculations are mixed, which is the basis for understanding the center of mass theorem.
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angular momentum / principle of conservation of angular momentum

clip 12: angular momentum / principle of angular momentum, introduction
This is the introduction clip to the topic of the angular momentum / the principle of angular momentum.
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clip 13: wind plant, principle of angular momentum
This clip is about a typical example of the principle of angular momentum. It is very important to consider the coordinate. This has a high Impact on the calculation.
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clip 14: carousel, angular momentum conserved
This clip explains the phenomenon of the increase of the angular velocity, when the mass is moved to the center of curvature. Here the mathematical proof of what we all know from the playground
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clip 15: pendulum, priciple of angular momentum, plane fall
In this clip we solve a plane problem using the principle of angular momentum. NEW iconNEW iconNEW icon Again appearing in this example: Steiner's theorem.
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energy / law of conservation of energy

clip 16: energy / law of conservation of energy, introduction
In this clip we explain everything about physical energy. Which kinds of energy are there, e.g. kinetic energy and potential energy? When am I allowed to use the law of conservation of energy and when not?
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clip 17: pendulum, law of conservation of energy, angular velocity
In this clip we discuss the fastest way to compute the kinetic energy of a NEW iconNEW iconNEW icon system. Alternally we could have also used Steiner's theorem for that.
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clip 18: flap with weights, law of conservation of energy, springs
This clip is about another example for energy, this time including a spring. NEW iconNEW iconNEW icon The main focus is on potential energy.
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clip 19: wind plant, energy in spatial dimensions
This clip explains how energy of a spatial system is calculated. The rotational...coming soon 3 kinetic energy can also be expressed via the angular momentum.
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work / work-energy-principle

clip 20: work / work-energy-principle, introduction
This is the introduction clip for physical work. In this clip the we tell you the basics.
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clip 21: box with friction, work / work-energy-principle
It is very important to understand applying the work-energy-principle, ...coming soon 3 especially the differences to the law of conservation of energy.
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clip 22: box with friction and spring, work / work-energy-principle
This clip is about the work of a conservative force. Special attention ...coming soon 3 should be taken on the work of the spring.
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power / power-energy-principle

clip 23: power / power-energy-principle, introduction
This clip is an introduction into the topic of power, similar to the one about work but anyhow different.
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clip 24: carriage with driving torque, power / power-energy-principle
In this clip the practical use of the power-energy-principle is explained. ...coming soon 3 The power-energy-principle can also be called "power-energy-principle in differential form.
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oscillations

clip 25: oscillations, introduction
Oscillations appear quite often and therefore they play a key role in physics. Which different kinds of oscillations do exist? What is a harmonic oscillation? What is the meaning of the terms amplitude, frequency and time periode?
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clip 26: roll/springsystem, angular frequency, position of rest
This clip is about the calculation of the socalled undamped angular frequency. ...coming soon 3 The difference between undamped angular frequency and angular freuency is explained.
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clip 27: mass/ springsystem, solution of the oscillation equation
This clip deals with the solution of the oscillation equation. Here the...coming soon 3 maths part comes to the fore. A differential equation is to be solved.
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clip 28: pendulum, linearization of the equation of motion
This clip is about the linearization of the equation of motion. ...coming soon 3 Depending on the linearization diffent approaches have to be done.
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clip 29: spring/ dampersystem, damped oscillation
In this oscillation system a damper appears. A case distiction of ...coming soon 3 the sort of damping has to be done.
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collision

clip 30: collision, introduction
This is the introduction clip for the topic of collision. In here we discuss the different sorts of collision and the most important formulars according to this chapter.
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clip 31: seesaw, elastic collision
In this clip we discuss the elastic collision. In this case the coefficient of...coming soon 3 restitution has a certain value.
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clip 32: seesaw with mass, inelastic collision
This clip is about an example for inelastic collision. ...coming soon 3 The balance of the angular momentum is applied again.
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