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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