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Wiki

The problems which we faced

1. When we started the project we found that having the

material must be with it’s references, but we found that

there is a lot of material without a references so couldn’t

put it in the wiki. And we solved this problem by adding

some videos and presentations instead of this unlicensed

data.

2. The tools which wikispaces provide to us are too limited

but somehow it was effective.

3. We couldn’t make a better design because of this limited

tools and it needs $ to open this tools on wikispaces.

4. Other team members weren’t able to deal with the site

and we sloved this problems by a several meetings.

5. Our logo

1st problem and how we solved it

2nd problem and how we solved it

3rd problem and how we solved it

Objectives The main objective of the project about

this course is to provide future aeronautical

engineers with the means of analyzing and

designing various load bearing structures.

This can be done by learning them How to analyze a system of

forces and obtain the reactions at the supports of structures and

How to analyse the forces in plain trusses. Later, they will study the

nature of stress and strain, and the properties of cross sections,

finally, they will be introduced to the forces and stresses in

members subject to axial, torsion, and bending loading.

Analysis of Trusses

The method of joints: This method uses the free-body-diagram of

joints in the structure to determine the forces in each member.

The method of sections: This method uses free-body-diagrams of

sections of the truss to obtain unknown forces.

Normal Stress and Shearing Stress Definition : - Stress is a measure of the

average force per unit area of a surface

within a deformable body on which

internal forces act. It is a measure of the intensity of the internal

forces acting between particles of a deformable body across

imaginary internal surfaces

Normal Strain Under Axial Loading Normal Strain: It is the deformation in the material due to the effect of

normal force on it's cross section area.

It Denoted by: ε= the deformation / normal length..

It's unit: it has no unit as it is a ratio between to similar quantities.

Axial Loading: It is the normal stress due to the effect of normal force

affect on area.

It Denoted by: σ = normal force / area

It's unit: N/m2

True Stress and True Strain There are two kinds of stress; Engineering stress and True stress.

Engineering stress: it is the force divided by the initial cross section area

True stress: it is obtained by dividing the force by the instantaneous cross

sectional area.

Engineering strain: it can be obtained by the dividing of the total

deformation occurred on the specimen by the initial length

True strain: it can be obtained by recording the length of the specimen and

determine the deformation in each record then divide this deformation on

the corresponding length of the specimen and with the summation of all

stains in all records (or by integration) we can get the true strain εt =

ln(L/L0)

Deformations of Members under Axial Loading

Consider a homogeneous (constant E) rod of

length L and of cross section area A subjected

to a normal force P to make in it a deformation

∆L and strain ε and stress σ , then from Hook's

law σ = Eε , ε = P/AE and since ε = ∆L/L , ∆L = ε L , then ∆L = PL/AE

If the rod is consists of more than one martial and of different cross

section area then the total deformation on the rod is the summation of

the deformation in each portion ∆L = ∑I (Pi . Li / Ai . Ei)

Statically Indeterminate Problems

Statically Indeterminate Problems

They are problems in which the internal forces cannot be determined

from statics alone. In fact, in most of these problems the reactions

themselves-which are external forces-cannot be determined by simply

drawing a free-body diagram of the member and writing the

corresponding equilibrium equations. The equilibrium equations must

be complemented by relations involving deformations obtained by

considering the geometry of the problem. Because statics is not

sufficient to determine either the reactions or the internal forces,

problems of this type are said to be statically indeterminate.

Problems Involving Temperature Changes

Let us first consider a homogeneous rod AB of uniform cross section,

which rests freely on a smooth horizontal surface. If the temperature of

the rod is raised by ∆T, we observe that the rod elongates by an amount

∆L which is proportional to both the temperature change ∆T and the

length L of the rod, then ∆L = α ∆T L (Note if the rod is fixed between

two fixed walls then its area will increase and then it's volume also, the

stain = 0 but there is stress) Where α is a constant characteristic of the

material, called the coefficient of thermal expansion and it has a unit of

a quantity per degree C.

Poisson's Ratio Meaning of Poisson's ratio:

Poisson's ratio is the ratio of transverse contraction strain to longitudinal

extension strain in the direction of stretching force. Tensile deformation

is considered positive and compressive deformation is considered

negative. The definition of Poisson's ratio contains a minus sign so that

normal materials have a positive ratio. Poisson's ratio, also called Poisson

ratio or the Poisson coefficient, is usually represented as a lower case

Greek nu, ν .

· Poisson ratio = - lateral strain / axial strain .

Multiaxial Loading; Generalized Hooke’s Law

The generalized Hooke's Law can be used to predict the deformations

caused in a given material by an arbitrary combination of stresses.

Torsion

Difference between Bars and Shafts:

Bars are members that are subjected to an axial loading along it's axis

but Shafts are members that are subjected to twist or torque

Torsion in circular Shafts

Torsion in thin structures

Torsion in thin walled members

Questions

Thanks for all