Strength I LO im. Tadeusza Kościuszki w Wieluniu Michał Adamski Jan Folleher Szymon Pawlak Karolina Stolarczyk Paulina Szwed Realized under the supervision.

StrengthI LO im. Tadeusza Kościuszki w Wieluniu

Michał AdamskiJan FolleherSzymon PawlakKarolina StolarczykPaulina Szwed

Realized under the supervision of Zenona Stojecka MA

The presentation contains:

Experiments with sausages

The concept of strength, Hooke's law

Science about cracks

The strength of paper

The propagation of cracks

The strength of constructions, crates

Constructions of Leonardo da Vinci

Durable materials

The experiment with a sausage

The experiment with a sausage

The experiment with a sausage

The experiment with a sausage

The concept of strength

Strength - ability of the structure to counter the negative effects (deformations, destroying by cracking) under the action of external forces.

_______________________________Adam Bodnar: Wytrzymałość Materiałów. Podstawowe pojęcia, definicje i założenia

Why something cracks? Hooke’s law:

the tension of the material is directly proportional to the

deformation.

At high stress of he material Hooke's law

is not more applicable.

Why something cracks? The catastrophe is

breaking up the continuity of the material

(crack), short after reaching the maximal

tension.

The value of the maximal tension depends on the structure of the material, and more specifically by

the atomic forces or particles, which the material is made of.

Cracking of materials

Cracks are two surfaces between which the molecular connections or structures are broken.

To achieve the result of cracking, some force is required . The amount of force determines the value of the maximal stress.

The maximal stress required to rapture

the material

= √(EU/8a)

E – Young's module

a –the interatomic distance

U – Energy required to create a raptured surface

Why did the sausage always cracked along?

The force acting along the sausage is from pascal's law: pressure multiplies surface of the cross-section:

To calculate the surface we use the surface area of a circle:

We calculate the cracking surface by multiplying thickness of the skin by the circuit of the sausage:

The stress is a force divided by the circuit surface of the skin.

But which force extends the skin crosswise?To determine this, we cut the sausage crosswise. Again we calculate the cross force:

The surface is now easier to calculate:

The complete force is working on the cross surface of the sausage's skin.

______________________Christoph DrosnerFizyka, daj się uwieść

Science about cracksThe first step to create a modern science about cracks and strength of materials was made by an English engineer and mechanic C. E. Inglis, who in 1913 published his work about stress concentration around the slot in the elastic material.

The stress at the end of the „tip”(1+2√(L/R)) .

For the crack R is really small and that's why the

effective stress is very big.

Science about cracks

All geometric constructions include irregularities – holes, edges. It sholud be taken into account at the design stage because every of them leads to concentration of stress,which can overcross the maximum.

Science about cracks Every force reacts

on a surface of the material, so it is proportional to the amount of lines crossing it. On the surface marked red the force will be bigger than the force pressing on the surface marked blue.

Strength of paper

Paper under microscope

own photos

Paper under microscope

own photos

The fiber direction The transverse

direction - fibers are side by side.

The longitudinal direction – the fibers are one after the other

Paper is stronger in the longitudinal direction as in the transverse one.

Strength by extension

Tension strength is a maximal length, in which the paper can stratch before the final rend.

Tension strength is determined by the direction of the fiber and it is stronger lengthwise than crosswise.

Paper has got a bigger strength for stretching, but worse for rending .

Strength by extension

Strength of paper by extension it is a typical force required for riping the edge of an paper block.

Its dependet of the direction of the fiber iand its bigger crosswise than lengthwise.

A line 2,2m long includes:1. 6 roles of 100m2. 128 pieces of 4,5m = 576m

The first torsion of paper...

16 lines, each consisting of 2 pieces of 4,5m long - they create one of 4 main modules of the line.

It takes between 3 and 4 hours to make the torsion of four modules.

The lines are twisted in two pieces, up to the time the line is ready.

The strength of one module

One module (¼ of the complete line) standed the weight of a 35 kg heavy boy.

The movement of cracks

When we add energy, the crack is moving in the material, leading to its destruction.

Ramification of cracks – the Griffith`s theory:

If a slot should move, there must be a free surface. We assume that the slot is proportional to the length L.

Ramification of cracks – the Griffith`s theory:

To create a slot we need energy.

Ramification of cracks – the Griffith`s theory:

The slot moves from the place, using a part of the energy preserved in the stretched material.

Ramification of cracks – the Griffith`s theory:

The slots that are shorter than Lg are stable. Bigger ones start to grow.

____________________________________

Łukasz A. Turski – Dlaczego coś pęka?, Wiedza i Życie 7/1999

Strength of constructions

Crates Crates are a complex

system of rods, which are connected pivotally. They have an unchanging geometric form.

They are used in almost every construction because they're light and easy to build.

Rigidity condition for crates To get the crate

geometric unchanged, the following condition must be fulfilled:

p = 2w – 3

p – number of rods

w – number of        connections

Various kinds of crates:

Strength of pasta

Strength of pasta

29 kg!!!!

Bridges

Leonardo da Vinci Italian renaissance painter, architect, philosopher,

musician, writer, explorer, mathematician, mechanic, anatomist, inventor, geologist. He created drawings of many structures and machines. One of them is a bridge, which is designed so that its construction allows to omit the fastening elements. The bridge holds together by itself.

Source: malarstwo.awardspace.info

Source: leonardo.org.pl

Source: gnosis.art.pl

Leonardo's bridge

When we apply pressure from the top, it will be transmitted on the next elements of the bridge by friction or appropriate grooves. In this way, all the pressure is transmitted to the ground. That is why the total construction is in balance.

Źródło: http://www.grandadscience.com

Imagination has no limits

The bridge was constructed for the military needs, to cross rivers and other barriers. We can use it for decoration or inspiration to create other things.

Źródło: http://www.dfab.arch.ethz.ch

Source: www.rinusroelofs.nl

Reinforced concrete

Structural element formed by the combination of concrete and steel inserts.

Metal rods are resistant to stretching, but susceptible to compression and bending. Concrete is resistant to compression and breaks sooner than it bends.

Steel in reinforced concrete elements moves mainly to tensile stress, although it is more often used for compression reinforcement . The combination of steel and concrete structures allows you to build various things.

Kevlar

Kevlar is not corroding, it does not burn, the weight per unit is five or six times greater for tensile strength than steel, and it is stronger than glass and carbon fibers.

Graphene Graphene – a plane structure

composed of carbon atoms connected in hexagons. This material is shaped like a honeycomb, and because it has a monatomic thickness it is considered of a two-dimensional structure.

Source: tech.wp.pl

For graphene research Andriej Gejm and Konstantin Nowosiołow from University of Manchester won a Nobel Prize in physics in 2010.

Paper with honeycomb technology

This paper is a lightweight raw material filler of hexagonal structure. Its main characteristic is that it is extremely rigid. It is an internal resource, which can perfectly be used with multilayer structures. Paper can be purchased in rolls. It may be grooved or not, processed by hand or machine.

Sources:

http://www.instron.pl/wa/glossary/Compressive-Strength.aspx

Jerzy Leyko - Mechanika ogólna, Wydawnictwo PWN

Łukasz A. Turski – Dlaczego coś pęka?, Wiedza i Życie 7/1999

http:www.e-sciany.pl

http://www.scopak.com.pl\

Stefan Krause, University of Hamburg / Science

http: www.grandadscience.com

http: www.rinusroelofs.nl